'v un- n-qnw- ~Yv1-wur Jig, _ 3‘ km. a . 3 :3” .r n .4 , . p. » gm". L»... a... . ”haw; 11125:; Mistamun 2 "9M _/ .. ‘3‘";th .-.. “our: U This is to certify that the dissertation entitled THEORETICAL, NUMERICAL AND EXPERIMENTAL STUDY ON VENTURI VALVES FOR STEAM TURBINE INFLOW CONTROL presented by Donghui Zhang has been accepted towards fulfillment of the requirements for the Ph.D. degree in Mechanical Engineering ‘ Aetxv 4 Maidr Fri ssor’s Signature ’3 [fibril-ml Date MSU is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State Unlverslty PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE ' DATE DUE DATE DUE 6/01 c:/CIRC/DateDue.p65-p. 15 THEORETK VENTURI V THEORETICAL, NUMERICAL AND EXPERIMENTAL STUDY ON VENTURI VALVES FOR STEAM TURBINE IN FLOW CONTROL By Donghui Zhang A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 2003 l THEORETll VENTURI Because of the i have been widcl )7 for about half 3 cc remitted. lmprmc complicated natur from being fully \ mormelhods. wl The literature i of fluid mechanil instability. unstc: mathematic mod 3-D and 3-[ urge amplitud ,i: ABSTRACT THEORETICAL, NUMERICAL AND EXPERIMENTAL STUDY ON VENTURI VALVES FOR STEAM TURBINE INFLOW CONTROL by Donghui Zhang Because of the converging diverging configuration of the valve passage, ventun' valves have been widely used in large turbines to regulate inlet flow as turbine governing valves for about half a century. From the 1960’s, a number of valve failure incidents have been reported. Improvement to current designs was strongly demanded, but due to the complicated nature of the fluid structure interaction mechanisms, valve failure is still far from being fully understood. There are several improved designs obtained by trial and error methods, while the rules, or even a clear direction for improvement is non-existent. The literature in this field is reviewed. Based on former research and basic knowledge of fluid mechanics and structure dynamics, the theoretical investigation of the flow instability, unsteady forces, and fluid-structure interaction mechanisms are performed and mathematic models are derived. A 2-D and 3-D numerical investigation was performed here. The study confirmed that large amplitudes of hydraulic forces, moment and torque are caused by unexpected asymmetric flow patterns. All these excitations can result in severe valve vibration and can finally break the valve. Improved designs were simulated by using CFD tools and shown to result in symmetric flow patterns and a reduction in the intensity of excitation at the plug balanced position. An experimental system was designed and built. The experimental data on a '/2 scale valve were obtained. The study confirmed that asymmetric unstable flows are the root cause of valve problems, such as noise, vibration, and failure. ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor, Dr. Abraham Engeda for his guidance, support and encouragement throughout my graduate study. I would also like to thank Dr. Norbert Miiller, Dr. Craig W. Somerton, Dr. Charles R. MacCluer and James Hardin for serving on my guidance committee and giving me valuable suggestions to my research. Particular thank goes to Ronald Aungier at Elliott Company for initiating this work and for fruitful discussions. Of course, I wish to express my gratitude to Elliott Turbomachinery Co. for supporting this project. My deepest thanks go to my wife, Yuqing Chen for her endless love, understanding and continuous support that makes my life enjoyable. I am also very thankful to Christopher Zielesch and Roy Bailiff for their help in building the experiment rig. Special thank goes to Dr. Yunbae Kim and Petter Menegay at Dresser-Rand Company for help in CF D and fiiendship. Michael J. Cave at Solar Turbines Company and James M. Sorokes at Dresser-Rand Company are specially acknowledged for giving me the chances for internship and for their encouragement. I also appreciate the assistance and friendship from the students in the turbomachinery lab during my Ph.D. program at Michigan State Univeristy: Yinghui Dai, Muhammad M. Raheel, Faisal Mahroogi, J aewook Song, Zeyad Alsuhaibani, Dr. Fahua Gu (former graduate now working at Concepts ETI), and the students in Dr. Muller’s group. iv TABLE OF CONTENTS LIST OF FIGURES - - - - - -- - ............... - - -vii LIST OF TABLES - - -- - -- - - - -- x NOMENCLATURE - xi CHAPTER 1 - -- -- -- -- 1 INTRODUCTION - -- - - - -- - -- - - - -- - - - - ..... l 1.1VALVES ....................................................................................................................... 1 1.1.1 Steam turbine valves ........................................................................................... 2 1.1.2 Turbine inlet control valve ........................................................... ' ...................... 2 1.2 DEMANDS ON THE STUDY OF TURBINE STEAM CONTROL VALVES ............................ 5 1.3 OBJECTIVE AND STRUCTURE OF THE PRESENT STUDY ............................................... 6 CHAPTER 2 - FUNDAMENTALS AND THEORY ANALYSIS 2.1 FLOW THERMODYNAMICS .......................................................................................... 7 2.1.1 Basic governing equations ................................................................................. 8 2.1.2 Ideal process for I-Dfluid passing the valve ..................................................... 9 2.1.3 Flow through actual valves and valve performance ........................................ 14 2.2 HYDRAULIC FORCES ................................................................................................ 18 2.2.1 Drag and lift extended by fluid ......................................................................... 18 2.2.2 One-dimensional analysis on unsteady hydraulic forces acting on plug......... 30 2.3 ANALYSIS ON FLUID STRUCTURE INTERACTION ....................................................... 36 2.3.1 F low-induced vibration .................................................................................... 3 7 2.3.2 Random model for random vibration ............................................................... 4 7 CHAPTER 3 - - - - 52 LITERATURE REVIEW - - _ _ 52 3.1 FLOW ASYMMETRY AND INSTABILITY ..................................................................... 52 3.2 FLUID FORCES .......................................................................................................... 57 3.3 FLOW-INDUCED VIBRATION ..................................................................................... 59 3.3.1 Low velocity incompressible flow-induced vibration ....................................... 59 3.3.2 Flow induced vibration for steam turbine inlet control valve .......................... 60 3.3.3 Self-Excited Vibration ...................................................................................... 73 3.3.4 Acoustic eflects ................................................................................................. 79 3.3.5 F low impingement ............................................................................................ 83 3.3.6 Valve improvement design ............................................................................... 85 3.3.7 The recent research .......................................................................................... 86 CHAPTER 4 - - - - _- - - - -91 2-D NUMERICAL INVESTIGATION--- - 91 4.1 NUMERICAL MODELING ........................................................................................... 91 4.2 RESULTS AND DISCUSSION ....................................................................................... 94 4.2.1 .tsi‘m' 4.3.3 .i/dfil‘ 4.3.3 Press 5 4.3.4 Fora : 4.3.5 Fluid 4.3 AXALYSlS 4.3.1 P0551! 4.3.3 Other {TJDBUD CEMETER S JD C FD ANAL 5.l Nl‘MERK" .-\ 52 HOW PAT 5.3 FORCE. Tc 5.4 3-D SlMl'l CHAPTER 6 EXPERIMEN' til EQL‘IPW-f dbllhcr 6.1.2 Pr'pi 6.1.3 l'ali 6.1.4 Earp (>2 EXPERl} 6.2.2 Fir 4.2.1 Asymmetric flow pattern ................................................................................... 94 4.2.2 Mass flow rate and total pressure ratio ........................................................... 98 4.2.3 Pressure along the valve surface ................................................................... 102 4.2.4 F Orces and moment caused by fluid ............................................................... 104 4.2.5 Fluid structure interaction mechanism .......................................................... 108 4.3 ANALYSIS ON IMPROVING DESIGN .......................................................................... 1 12 4.3.1 Possible improved designs ............................................................................. 113 4.3.2 Other tested designs ....................................................................................... 117 4.3.3 Discuss on an improved design ...................................................................... 119 CHAPTER 5 - 123 3-D CFD ANALYSIS _- 123 5.1 NUMERICAL MODELING ......................................................................................... 123 5.2 FLOW PATTERNS .................................................................................................... 124 5.3 FORCE, TORQUE AND MOMENT .............................................................................. 126 5.4 3—D SIMULATION RESULTS FOR IMPROVED DESIGNS ............................................. 133 CHAPTER 6 141 EXPERIMENTAL INVESTIGATION 141 6.1 EQUIPMENT SETUP ................................................................................................. 141 6.1.1 Vacuum pump ................................................................................................. 143 6.1.2 Piping system .................................................................................................. 144 6.1.3 Valve and chests ............................................................................................. 144 6.1.4 Experiment measurement system design ........................................................ 148 6.2 EXPERIMENT RESULT AND DISCUSSION ................................................................. 150 6.2.1 Mass flow rate ................................................................................................ 150 6.2.2 Flow regions and patterns ............................................................................. 152 6.2.3 F low asymmetry ............................................................................................. 158 6.2.4 Flow instability ............................................................................................... 162 6.2.5 Superposition of pressure oscillation and difl'erence ..................................... 1 71 CHAPTER 7 - _ 172 CONCLUSION -- 172 BIBLIOGRAPHY - 174 vi Fig. 1.1 Turbim‘ . Fig. 1.2. Cross 5‘. Fig. 1.3 the Veil Fig. 2.1 ldealirat I Fig. 2.2 The elio Fig 2.3 Ideal ant Fig. 2.4 \i'alx e cf Fig. 2.5 Valve an Fig. 2.6 Drag esti Fig. 2.7 Hydraulit Fig. 2.8 L'nstead} Fig. 2.9 Pressure I Fig. 2.10 Pressure Fig. 2.11 Pressurt Fig. 2.12 Asmm Fig 2.13 Flow 1H1 Fig. 2.14 3-D \‘ie' Fig. 2.15 Plug \iF Fig 2.16 Pressuri LIST OF FIGURES Images in this dissertation are presented in color. Fig. 1.] Turbine and steam inlet control valve .................................................................... 3 Fig. 1.2. Cross section of multiple venturi valves (after J. Hardin) .................................... 4 Fig. 1.3 The Venturi valve and its failure (after J. Hardin) ................................................. 5 Fig. 2.1 Idealization of valve ............................................................................................... 9 Fig. 2.2 The effects of plug travel on the flow through a valve ........................................ 10 Fig. 2.3 Ideal and actual flow in a valve between same inlet state and exit pressure ....... 11 Fig. 2.4 Valve efficiency and mass flow rate .................................................................... 17 Fig. 2.5 Valve and flow pattern ......................................................................................... 18 Fig. 2.6 Drag estimation .................................................................................................... 22 Fig. 2.7 Hydraulic drag number ........................................................................................ 27 Fig. 2.8 Unsteady hydraulic forces .................................................................................... 31 Fig. 2.9 Pressure distribution and resulting forces at one instant ...................................... 32 Fig. 2.10 Pressure and forces at one instant with shock or separation .............................. 33 Fig. 2.11 Pressure-friction drag/lift relation and fi'iction forces due to separation ........... 33 Fig. 2.12 Asymmetric jet flow after valve throat .............................................................. 35 Fig. 2.13 Flow induced vibration mechanism ................................................................... 38 Fig. 2.14 3-D View of unbalanced forces .......................................................................... 38 Fig. 2.15 Plug vibrations due to unbalanced forces .......................................................... 39 Fig. 2.16 Pressure distribution and forced in response of Vibration .................................. 42 Fig. 2.17 Interaction of lateral and Spinning flow ............................................................. 45 Fig. 2.18 Random phenomena ........... 48 Fig. 2.19 Simplified excitation-response model for plug vibrations ................................. 51 Fig. 3.1 Stall in diffuser ..................................................................................................... 53 Fig. 3.2 Possible flow patterns due to stall in valve .......................................................... 53 Fig. 3.3 2-D flow changing from subsonic to supersonic (after A. Shapiro) .................... 55 Fig. 3.4 Visualized transonic flow for airfoil (after Becker) ............................................. 55 Fig. 3.5 Drag-plug travel characteristic (afier Schuder) .................................................... 58 Fig. 3.6 Fluid excitation mechanisms (after Naudascher) ................................................. 59 Fig. 3.7 Lateral and axial vibration models (after Araki) .................................................. 61 Fig. 3.8 Two-dimensional model test equipment (after Araki) ......................................... 63 Fig. 3.9 Flow patterns with different valve opening and pressure ratio (after Araki) ....... 64 Fig. 3.10 Visualized flow pattern at a different pressure ratios (after Araki) ................... 64 Fig. 3.11 Improved valve design and flow patterns (after Araki) ..................................... 65 Fig. 3.12 3-D test valve and pressure sensor positions (after Araki) ................................ 66 Fig. 3.13 Flow patterns for 3-D valve test (after Araki) ................................................... 67 Fig. 3.14 Pressure oscillation and plug acceleration at different patterns (after Araki).... 68 Fig. 3.15 Surface pressure oscillation of old valve model (after Araki) ........................... 69 Fig. 3.16 Surface pressure oscillation of improved valve model (after Araki) ................. 69 Fig. 3.17 Plug acceleration (after Araki) ........................................................................... 70 Fig. 3.18 Power spectra of surface pressure oscillation and acceleration (after Araki) 71 Fig. 3.19 Correlation between square root of PSD and RMS (after Araki) ...................... 72 vii Fig. 3.20 Twit. 111.321 1111c Fig. 3.22 Schem I Fig. 3.23 Fluul 1 111.324 Fluid 1 Fig. 3.25 Stabili' 11E. 3.26 Test 11 i111.3.27Rcsu11 111.328 Flow p 11;. 3.29 51111111, Fig. 3.30 lmpingt Fig. 3.31 Valx‘e c Fig 3.32 Two 1111 Fig. 3.33 An imp Fig. 3.34 Pressur Fig 3.35 Time II Fig. 3.36 Zoomir Fig. 3.37 Pressur ooooooooooooooooooo Fig 4.1 Samplel Fig. 4.2 Flow pa? Fig 4.3 Variatio Fig. 4.4 \‘an'atio Fig. 4.5 Mass 111‘ Fig 4.6 Mass 111‘ ig. 4.7 Total pr: ig. 4.8 Pressure Fig. 3.20 Typical valve lift characteristic curve and pressure oscillation (afier Araki) 73 Fig. 3.21 Valve configuration (afier Eguchi) .................................................................... 73 Fig. 3.22 Schematic of the system (after Eguchi) ............................................................. 74 Fig. 3.23 Fluid force coefficients test model (after Eguchi) ............................................. 76 Fig. 3.24 Fluid force coefficient, Zxx, determined by test result (after Eguchi) ................ 76 Fig. 3.25 Stability analysis of vibration modes (after Eguchi) .......................................... 78 Fig. 3.26 Test valve for noise (after Heymann) ................................................................ 79 Fig. 3.27 Result of noise tests for different valve configurations (after Heymann) .......... 80 Fig. 3.28 Flow patterns and regions (after Heymann) ....................................................... 81 Fig. 3.29 Solving of acoustic resonance for an operating turbine valve (after Widell) 82 Fig. 3.30 Impingement mechanism (after Ziada) .............................................................. 84 Fig. 3.31 Valve configuration for impingement analysis (after Ziada) ............................. 84 Fig. 3.32 Two directions for optimize valve plug shape ................................................... 85 Fig. 3.33 An improved valve design (after Zarjankin and Simonov) ............................... 86 Fig. 3.34 Pressure pulsations before high vibration of No.2 valve (after .1. Hardin) ........ 87 Fig. 3.35 Time trace of pressure pulsations (after J. Hardin) ............................................ 88 Fig. 3.36 Zooming in View of the pressure pulsations (afier J. Hardin) ........................... 88 Fig. 3.37 Pressure pulsation frequency spectrum during valve vibration (after J. Hardin) ................................................................................................................................... 89 Fig. 3.38 Streaklines and reverse flow region of new valves (after J. Hardin) ................. 90 Fig. 4.1 Sample computational grid .................................................................................. 92 Fig. 4.2 Flow patterns and pressure field .......................................................................... 93 Fig. 4.3 Variation of asymmetry ratio ............................................................................... 95 Fig. 4.4 Variation of average velocity ratio at center plane .............................................. 97 Fig. 4.5 Mass flow rate ...................................................................................................... 98 Fig. 4.6 Mass flow rate ratio between left side and overall .............................................. 99 Fig. 4.7 Total pressure ratio .............................................................................................. 99 Fig. 4.8 Pressure and Mach number distribution ............................................................ 101 Fig. 4.9 Vertical force on plug ........................................................................................ 103 Fig. 4.10 Variation lateral force ...................................................................................... 105 Fig. 4.11 Moment caused by vertical force ..................................................................... 105 Fig. 4.12 Ratio of viscous to total forces and moment .................................................... 106 Fig. 4.13 Variation of parameters at different ratio at fixed opening of 10.6% .............. 107 Fig. 4.14 Forces and moment changing due to lateral displacement on plug ................. 109 Fig. 4.15 Excitation under lateral vibration ..................................................................... 110 Fig. 4.16 Self-excitation mechanism in vertical direction .............................................. l 10 Fig. 4.17 Sketch of valve safe operation area ................................................................. 1 12 Fig. 4.18 Flat cut design .................................................................................................. 113 Fig. 4.19 Variation of lateral force under different cut angle at 10.6% opening ............ 114 Fig. 4.20 Three other improved designs .......................................................................... 115 Fig. 4.21 Comparison of lateral force at Opr=10.6% for different designs .................... 115 Fig. 4.22 Comparison between improved designs at 10.6% opening ............................. 117 Fig. 4.23 Several other designs ....................................................................................... 118 Fig. 4.24 Comparison with original design at 10.6% opening ........................................ 118 Fig. 4.25 Flow patterns for improved valve design ......................................................... 119 Fig. 4.26 Comparison of lift and moment between old and improved design ................ 120 viii 1:12.427 ThC it r16. 4.28 The 1. Fig. 5.1 Compu‘ Iii. 5.2 3-1) 116. I13. 5.3 3D 1161 1125.4 3-D 1161 I165] Absolutt 11;. 5.8 summit Fig. 5.9 Viscous Fig. 5.10 Total p Fig. 5.11 Pattern Fig. 5.12 Pattern Fig. 5.13 Pattern Fig. 5.14 Flow p, Fig. 5.15 Flow p; Fig. 5.16 Lateral Fig. 5.17 Compa F 18- 6.1 Venturi ' 58- 63 Pictures “8- 6.3 Picture ( F38 6.4 Chests a Fig 6.5 Va]... 5, Fig, 6.6 ValVe p. Fig 0.7 Valye 3‘ Fig. 6.8 Static p. ig. 69 Pressun Fig 6‘10 PICIUrr Fe 6.11 Choke Fig. 4.27 The forces and moment changing due to lateral displacement ........................ 122 Fig. 4.28 The forces and moment changing at 10.6% opening ....................................... 122 Fig. 5.1 Computational grid ............................................................................................ 124 Fig. 5.2 3-D flow pattern (e) at pressure ratio of 0.9 and 23.1% opening ....................... 125 Fig. 5.3 3-D flow pattern (c) at pressure ratio of 0.9 and 10.6% opening ....................... 125 Fig. 5.4 3-D flow pattern (e) at pressure ratio of 0.5 and 10.6% opening ....................... 126 Fig. 5.5 Drag variation with pressure ratio ...................................................................... 127 Fig. 5.6 Drag variation with valve opening changing Pr=0.9 ......................................... 128 Fig. 5.7 Absolute values of lift, moment and torque ....................................................... 130 Fig. 5.8 Maximum excitations at difi‘erent opening when Pr=0.9 .................................. 131 Fig. 5.9 Viscous effect at 14.7% opening ....................................................................... 132 Fig. 5.10 Total pressure ratio and mass flow rate variation at 14.7% opening ............... 132 Fig. 5.11 Pattern (a) at Pr=0.9 and Opr=10.6% for dish bottom design ......................... 133 Fig. 5.12 Pattern (e) at Pr=0.5 and Opr=10.6% for dish bottom design ......................... 134 Fig. 5.13 Pattern (d) at Pr=0.5 and h/D=10.6% for dish bottom design ......................... 134 Fig. 5.14 Flow patterns for flat out design at Opr=10.6% ............................................... 135 Fig. 5.15 Flow pattern (c’) at Pr=0.5 and Opr=6.5% for flat out .................................... 135 Fig. 5.16 Lateral force, moment and torque for improved designs ................................. 136 Fig. 5.17 Comparison between original and improved designs ...................................... 139 Fig. 6.1 Venturi valve test System .................................................................................. 141 Fig. 6.2 Pictures of the experiment system ..................................................................... 142 Fig. 6.3 Picture Of vacuum pump .................................................................................... 143 Fig. 6.4 Chests and valve ................................................................................................ 145 Fig. 6.5 Valve stern and plug ........................................................................................... 146 Fig. 6.6 Valve plug and pressure sensor positions .......................................................... 146 Fig. 6.7 Valve seat and pressure sensor positions ............. ' .............................................. 147 Fig. 6.8 Static pressure sensor positins at different valve opening ................................. 147 Fig. 6.9 Pressure measurement system ............................................................................ 148 Fig. 6.10 Pictures for static pressure measurement system ............................................. 149 Fig. 6.11 Choked mass flow rate variation with valve opening ...................................... 151 Fig. 6.12 Dimensionless mass flow rates at different openings ...................................... 151 Fig. 6.13 Flow regions ..................................................................................................... 153 Fig. 6.14 Pattern A and corresponding pressure distribution .......................................... 153 Fig. 6.15 Pattern C and corresponding pressure distribution .......................................... 156 Fig. 6.16 Pattern D and corresponding pressure distribution .......................................... 157 Fig. 6.17 Pattern E and corresponding pressure distribution .......................................... 158 Fig. 6.18 Pressure difference variation with pressure ratio at different openings .......... 161 Fig. 6.19 Maximum pressure difference and corresponding pressure ratio .................... 162 Fig. 6.20 Pressure oscillation at different pressure ratios and 0.085 h/D opening .......... 166 Fig. 6.21 Pressure oscillation at pr=0.7 under 0.375 h/D opening .................................. 167 Fig. 6.22 Peak-to-peak value of pressure oscillation ...................................................... 169 Fig- 6.23 Peak-to-peak value of pressure oscillation at plug center ................................ 169 Fig- 6.24 Peak value of pressure oscillation with opening changing .............................. 170 Fig- 6.25 Superposition of pressure oscillation and difference ....................................... 171 ix 1311631 On'gi‘ 1311166.] Pumg‘ LIST OF TABLES Table 3.1 Original valve natural frequency ...................................................... 92 Table 6.1 Pump performance table .............................................................. 148 A.B.C.D.E A A,B,C,D,E Opr Pr NOMENCLATURE Area Flow regions and patterns Damping factor Vertical force, Diameter of plug Young’s modulus or energy Force Shear modulus Traveling of valve plug, cutting hi ght or enthalpy Moment of inertia or node number Stiffness or node number Lateral force Length or vertical displacement Mass, Mach number Moment around holding position Mass flow rate Opening ratio=h/D Pressure Pressure ratio Radius or gas constant Radius Temperature or torque Time xi 01-8 01,1 PI E1 Sh Vi: Se V V “SBQWSm’O Subscript 0,1,..8 01,1 1/2 8V8 Tangential velocity Velocity Volume Angle Density Damping ratio Pressure ratio or 3.14 Efficiency Shear stress Viscosity Seat throat and plug area ratio Plug stem and plug area ratio Natural frequency Plug natural position or maximum cross section Pressure sensor number or flow pattern number Inlet total Inlet/outlet chest Average quantity Equivalent Gauge Isentropic Lateral xii 111111 5631 .\1. N1 Ori \"ui Rat ‘ Slat: \le Total Vertil max Maximum value Node number or natural Original design Valve plug side Ratio Static Valve seat side Total Vertical xiii l.l\'alves Valves are \\ vessels. Flow r‘c can be perfo mic automatically. Valves can be flow control valx Special purpose \ F 10‘11’420111r01 \ tin-off sen'ice. thI globe valve. pisto diaphragn Val \ie 2 Valves CHAPTER 1 INTRODUCTION 1.1Va1ves Valves are widely used fluid control elements in piping systems or on fluid contained vessels. Flow regulation and pressure control are two major functions of valves, which can be performed by adjusting closure member position either by manually or automatically. Valves can be roughly divided into four main categories according to their functions: flow control valves, reverse flow prevent valves, pressure-control valves and other special purpose valves. - Flow-control valves are most commonly used valves to serve three major functions: on-off service, throttling and diverting. There are various types in this category, such as globe valve, piston valve, gate valve, plug valve, ball valve, butterfly valve, pinch valve, diaphragm valve and so on. They are either manual valves or control valves. Manual valves are manually operated or power-operated but manually controlled valves; Control valves are operated automatically on the Signal obtained by timing or sensing fluid properties by a control unit. Generally all manual valves can be changed to control valves. Reverse flow prevent valves are more commonly called check valves, which are automatic on-off valves that open with forward flow only to prevent reverse flow. Closure is designed to automatically be operated by its weight, by back-pressure, by Special designed mechanism, such as spring or by a combination of forgoing. ‘7. k P; V Pressure-cor are most comn‘ protect system There are 5111 specific applica 50 011. 1.1.1 Steam tur As a large flu 53611111 turbine \ L1 there are large 11' lnlercept ValVQ ! and by P353 \‘alv emergency servi ‘25 Show in I boiler 11110 The tu control Valve mt Pressure-control valves are more commonly Specified as pressure relief valves, which are most commonly used valves in this category. Pressure relief valves are designed to protect system against excessive pressure. There are still a lot of valves called special purpose valves, which are designed for specific applications, such as flush bottom valves, sampling valves, solenoid valves and so on. 1.1.1 Steam turbine valves As a large fluid system, steam turbine has various types of valves. The major duty of steam turbine valves is to regulate the steam flow to or from or through the turbine, so there are large number of flow control valves, such as inlet control valve, reheat turbine intercept valve, steam seal regulator make-up valve, astem valve, and all kinds of throttle and by pass valves. There are also check valves like reheat-stop valve, safety valves for emergency service and special purpose valves. 1.1.2 Turbine inlet control valve AS shown in Fig. 1.1, turbine inlet control valve is used to regulate steam flow from boiler into the turbine. In response of desired frequency and load, the valve controls steam flow rate through the turbine, which produces the right amount of power output. A control valve must be able to operate at high temperature and pressure with possible large temperature and pressure drop, be free from instability or chatter of the control system from the close to wide open state. Flow pressure drop when passing through a valve is inevitable and can cause poor thermal efficiency. A higher thermal efficiency is very important to turbine, so it is important for valve to be able to control flow with minimum pressure drop- 621113134“): cons. WW 1‘. V’mturi valve regulate the flou turbine. The val\ The closure hear 30m the fully 61. 563118 essentially is mounted 011 UN like “1'0 Convert." pres-Wye 1088, As turbines beg,- Finu‘rne fl pressure drop. In general, structure, control and thermodynamic concerns must be carefully considered when design a turbine control valve. www.mtcac.jpicadets_ethassanetst—turbine.html Fig. 1.1 Turbine and steam inlet control valve Venturi valves are widely used in modern turbines as turbine governor valves to regulate the flow entering the turbine. Fig.1.] shows a typical single venturi valve in a turbine. The valve has a moving component, closure, a stationary seat, and valve chest. The closure head, called the plug, is operated by a controller through the closure stem from the fully closed to the fully open position in response to desired turbine output. The seat is essentially a converging-diverging nozzle with a very short converging section and is mounted on the bottom of the valve chest. The cross-section of the valve passage looks like two converging-diverging nozzles formed by one side of the plug and of the seat, pointing to the valve center. This design is believed to be able to minimize the total pressure loss. As turbines became larger, the larger venturi valve should be used to handle greater volume flow rate. It is very difficult to overcome the critical hydraulic force for control and maintain t at partial load . instead of one All valves are 1 turbine is not rt clearance D > ( opened first. ;\'1 previous valve 1 -— . .A‘ w r_/ and maintain the performance. For modern large turbines, to improve turbine efficiency at partial load and reduce the lifting force required, multiple smaller valves are used instead of one large valve. These valves are operated in sequence, as shown in Fig. 1.2. All valves are in the closed position with the initial clearances (A through D) when the turbine is not running. The valve opening is controlled by the liftbar. Because the clearance D > C > B > A, when the lifibar is lified by the lifirod, the No. 1 valve is opened first, No.2 second, No. 3 third, and No. 4 last. Each valve starts to open as the previous valve is almost fiilly open. Thus there is overlap. 1‘” m l p/LIFTROD l l I """"" 3 i 3““‘1 ' sTEAM CHEST COVER fl‘i‘fl _________________ ' _____ 4 l ! l l l 4 F l l l 1 Valve No. 4 i | | i Valve No. 3 , Valve No. 2 JLLJJl Valve No. 1 l -- l l . l . D C . l A 1 l “or [151:4 :1 l _ -_ IT I LL T2 LL - é , T O . Q Q _ 'O' @ O O O O @ l@'_ - O I LIFTBAR I l/ L z \I --_._-_J.J— l l l ....... _ STEAM CHEST : I ' . VALVE |I l l ' PLUG VALVE i ‘ l SEAT -l . ..~-——~. ,,.——-—~. .24— l l t 1 l i l 1 l 1 1 1' 1 STEAM TO FIRST STAGE NOZZLE BANKS Fig. 1.2. Cross section of multiple venturi valves (after J. Hardin) 1-2 Demands 0. Nomany, 111. fully open valve Situation, The hig forces (lire to the Silrface cause gm. in a very shon tir malarial fatigue. 1 STEM _ T— l 1‘ CRACK INITIATION LOCATION Fig. 1.3 The Venturi valve and its failure (after J. Hardin) 1.2 Demands on The Study of Turbine Steam Control Valves Normally, the inlet valves are operated under very severe conditions. For example, in thermal power plants, the steam inlet temperature, pressure, and pressure drop through a fully open valve can reach as high as 1000°F, 4,000Psi and 200Psi respectively. In such a situation, the high speed flow can be very asymmetric and unstable. Thus, hydraulic forces due to the strong asymmetric and unstable pressure distribution along the plug surface cause severe problems, such as vibration and noise. The valve plug can be broken in a very short time due to the large amplitude of forces, or in long-term operation due to material fatigue. It is very costly to stop the turbine to replace a valve. Since the 1960’s, more and more valve failure incidents were reported due to increasing turbine size and upstream steam pressure. Because of the complicated nature of the flow through a valve, until the early 70’s, there was still no big progress in this research area. There were several papers investigating the valve noise and failure problems. First, increasing the rigidity of the structure was proved insufficient. Then the sclf-excllcd \: Fears of ex PCr Vibration “as does 110‘ do m f reason for \‘31‘ A recent \‘Lll Steam turbine l: det'eloped in th‘ fully open and T‘ seat into the SIC" ShOlm in Fig. 1.- which means the 1.3 Objective at As multiple-V way. the stud 3' Cl is to clarify the f can cause valve 1 work has been at 1- Theory an; ‘) . LIIErature : self-excited vibration was denied as the reason, according to Araki’s research and 10 years of experience of a plant in the former Soviet Union. This means that the valve plug vibration was not a result of feedback from the flow vibration, and so adding damping does not do any good. Finally, the flow-induced vibration was believed to be the main reason for valve failure. A recent valve failure was reported in 1998. The valve started operation in a multistage steam turbine in 1998. After 3 months of running, the No. 2 valve failed after the crack developed in the location shown in Fig. 1.3. It happened as the No.1 valve was almost fully open and No. 2 valve was at an opening of O. 147(h/D). The falling plug drove the seat into the steam chest wall approximately 0.7in. The failed valve stem surface is shown in Fig. 1.3. Before the failure, there was higher noise coming out of the machine, which means that chattering may have existed. 1.3 Objective and Structure of The Present Study As multiple-valves are essentially several single venturi valves mounted in a parallel way, the study concentrates on the single venturi valve. The objective of the present study is to clarify the fluid and failure mechanism of venturi valves to obtain regions, which can cause valve failure and to design new valves to improve their reliability. The research work has been accomplished systematically to achieve the goals with following steps: 1. Theory analysis of fluid valve interaction and valve vibration 2. Literature review of former research 3. Numerical simulations for current valves and improved valve designs 4. Experimental investigation of current venturi valves The cross 59 between plug 3 seat facing the lifted to control push all the W3) liti position. M; aposition after ‘ fully open posit: reaches maximt There were a CHAPTER 2 FUNDAMENTALS AND THEORY ANALYSIS The cross section of a valve passage is shown in Fig. 2.1. Flow passes the space between plug and seat. The plug is normally made as semi-sphere shape. The upper side seat facing the plug is arc shape. In response of feedback signals of turbine output, plug is lifted to control the inlet flow rate. Fully closed position was defined as when the plug is push all the way on the seat and no flow can pass by the valve, which is also called zero lift position. Mass flow rate will increase as the plug is lifted from fully closed position to a position after which the mass flow rate remains constant. This position is defined as fully open position. After fully open position, the valve plug can still be lifted until reaches maximum lift position. There were a lot of reports on valve plug vibration and break, which were believed as the result of flow-structure interaction. It is still unclear that how they interact with each other. So it is necessary to have a study on both the fluid side and valve plug side to clarify the interaction mechanism between them. 2.1 Flow Thermodynamics The flow in valve is highly complex, three-dimensional, turbulent, viscous, and unsteady. But important information can be obtained by the basic governing equations and one-dimensional analysis. 2.l.l Basic 3" ln m051 015 L in changing pll accumulation 1' comanll.V equd The \'al\'C is 1 betreated as 3‘“ thus reduces to In the absener the stagnation er steady state proe Eguation of statt As the steam t is ideal gas. \\'i‘ he 2 ,as satisfies 1 2.1.1 Basic governing equations Continuity In most cases, turbine operates with constant output, which means flow is steady. Even in changing plug lift process, as the valve is little compare with big mass flow rate, mass accumulation in valve can also be ignored. Define valve inlet as 1 and exit as 2, the continuity equation becomes m1: P1V1A1= m2 = P2V2A2 (2.1) Energy balance The valve is little, so fluid potential energy changing is ignored and also the valve can be treated as adiabatic wall. The energy balance relation for flow passing through a valve thus reduces to V2 V2 hor :hoz = hl +j—=h2 +12; (2.2) In the absence of any heat and work interactions and any changes in potential energy, the stagnation enthalpy of a fluid remains constant when passing through a valve during steady state process. Equation of state As the steam temperature is very high when passing through the valve, it can be treated as ideal gas. With constant gas constant, R, specific heats, Cv and Cp, and their ratio, k, the gas satisfies following state equation: P = pRT (2.3) \cuton secor‘ Motion equ Momentum Second law oi“ \ ThemIOd}'na reVersible com! F10\\,“ \ \ SQat Newton second law Motion equations are used to deduce vibration-governing equations 2 F = ma (2.4) 2F}? = J5 (2.5) Momentum equation is used to analysis hydraulic forces acting on valve plug _ a _. _ _ _. 2F=§Jdev+ ijV-dA (2.6) Second law of themodmmics Thermodynamics second law is used to deduce the basic thermodynamic relations for reversible compressible flow process and to define valve efficiency. 2.1.2 Ideal process for 1-D fluid passing the valve As shown in Fig. 2.1, flow passing through a venturi valve can be idealized as one- dimensional compressible ideal gas passing through a converging-diverging _/_>2 _\ Throat Venturi valve Converging-diverging nozzle Fig. 2.1 Idealization of valve Driven by I valve with a l\ boiler supplies position to full converging-til \. ditlerent \‘alye Driven by the pressure difference between valve inlet (1) and outlet (2), flow enters the valve with a low velocity at stagnation pressure P01, which can be treated as constant as boiler supplies constant pressure steam to turbine. As plug traveling from wide-open position to fully closed position, valve exit pressure P2 falls down. According to converging-diverging nozzle theory, the flow will experience different process with different valve lift, as shown in Fig. 2.2. P2 P 01 A/r B I” s ' C onic Shock/‘1 1 D M g D Sonic Shock! 1 i A B KL Inlet Throat Exit Fig. 2.2 The effects of plug travel on the flow through a valve At wide-open position, the flow remains subsonic throughout the valve. The fluid is accelerated before throat while pressure keeps decreasing, until reaches the highest velocity and lowest pressure at throat, then slow down with pressure increasing at the diffuser section of the valve. The maximum Mach number is less than unit at the valve throat and flow is not chocked. The valve acts as a diffuser. As the plug travels to closed position, P2 keeps dr0pping. At one critical position (curve B), the throat Mach number reaches unit. The valve still acts as a diffuser. The 10 velocity and 1" becomes sonit bemreen critic closed posltlot \lhen rah c accelerating to decreases. Thi between throat increase in pres valve. In real Vachs lmPOSSlble {0 3C much P2 dTOppet Pronenv Relatio Flg' 2‘3 Ideal - velocity and pressure change as same way as large open situation except at throat flow becomes sonic. This position is called critical position. It is called almost wide open between critical position and wide-open position. Between critical position and fully closed position, it is called almost close. When valve is almost close, as shown in curve C, the sonic fluid at throat continues accelerating to supersonic velocities in the diverging section of valve as pressure decreases. This acceleration comes to a sudden stop as a shock develops at the section between throat and exit causing a sudden drop in velocity to subsonic levels and sudden increase in pressure. Then the fluid continues to decelerate further in remaining part of valve. In real valves, because the exit section is normally designed over diffused, it is impossible to accelerate fluid to supersonic, as shown curve D, at valve exit even how ' much P2 dropped; Propm Relation_s for isentropic flow of ideal gas passing through a valve l P0 P02 h 01 Pozsh Actual ds=0 Shock x y \ p2 / 28h 2ish 2s a: Fig. 2.3 Ideal and actual flow in a valve between same inlet state and exit pressure 11 Flow is ass process. all st. relations for s ty—ilish) shoe Flow is assumed isentropic except for the shock region (x—>y in Fig. 2.3). As isentropic process, all stagnation properties, T0 , P0 and p0 remain constant. The basic property relations for subsonic and sonic (01 —>2s), and for supersonic flow before (01 —>x) or alter (y—>2ish) shock are shown as following: T ( 2 l“ (2.7) p0 k—l 2 I: P [ ( 2 )M] (2.8) Po 1"] 2 k“ _=1+ __ p l i 2 lwl (2’9) k+t A 1 2 k—.1 2 2(k—1) , =— — 1+ —— M A* M[[k+ll[ [ 2 J J] (2'10) Above equations show that the relation between stagnation properties and static properties can be express as a function of Mach number. The Mach number is essentially the function of cross-area. In the equation, k is specific ratio and is constant for ideal gas. Mass flow rate Under steady flow conditions, the mass flow rate can be expressed as function of Mach number, valve throat area. R is gas constant. k+l a k k—l 2(l—k) m=A MP 1+——M2 o RTol 2 :| (2.11) 12 After critic can be simpli As both inlc proportional [t Shock ware Changes in flui. Occur in a Very flow PYOCess tf as being isentrt shown as follo. After critical position, flow is choked as Mach number turns to unit. Above equation can be simplified as following: k+l . . k k+1 zo—k) m=A PollRTl 2 ] (2.12) 0 As both inlet conditions and specific heat ratio remain constant, the mass flow rate is proportional to throat area, which changes with plug lift. Shock Waves Shock wave occurs when flow in valve is supersonic, as shown in Fig. 2.2. Abrupt changes in fluid properties, such as pressure, temperature, Mach number and density, occur in a very thin section, creating a shock wave. As shown in Fig. 2.3 the curve x—>y, flow process through the shock wave is highly irreversible and cannot be approximated as being isentropic. The basic property relations before (x) and after (y) shock wave are shown as following. _ (k-1)Mf+2 V 2kM2—(k—1) (2°13) T, _ 2+(k—1)Mf —- 2 (2.14) T, 2+(k—1)My P, _1+ka P —1+kM2 (2°15) x y 13 _ + 2 (2.16) _ y x p —PT (2.17) x x y P 2 L ()y _1+kMx k—‘l 2 k—l 7-——1+kM2[ +7 My (2.18) x y According to above equations, after shock, the stagnation pressure and velocity decrease while the static pressure, temperature, density, and entropy increase. 2.1.3 Flow through actual valves and valve performance Actual flow process is not ideal as above discussion. Besides shock, two major factors, friction and flow separation also cause irreversibility, making the real process looks like 01—92 without shock or 01 —>2$h with shock instead of 01 —>23 and 01—-)2ish respectively in Fig. 2.3. The fi'iction effects are mostly confined to the boundary layer, while separation occurs when flow area increases faster than fluid expansion, or simply, over diffusion. Xalve efficiency To evaluate a valve, the valve efficiency can be defined by comparing actual kinetic energy at valve exit to kinetic energy at valve exit for isentropic flow from the same inlet state to the same exit pressure as shown in equation (2.1%). It can also be defined in terms of total pressure loss or total pressure ratio as shown in equation (2.1%). 14 For subsoni hOI " hz or2.sh 77,. = (2.1%) km —h25 AP P 7: =1— 0 =4” (21%) ° P... P... For subsonic flow, they can be related as k—l _ 10m," —1 v 1'0 _1 (2.208) 72-0 77, = (2.2%) 7:01 Fig. 2.4a shows the typical relation variation of efficiency and pressure ratio for subsonic situation. The total pressure loss is due to fiiction. In supersonic flow, shock waves can produce much greater total pressure loss as shown in Fig. 2.13. Thus another parameter, total pressure recovery 77, , is defined as total pressure ratio over total pressure ratio portion due to fiiction. In theory the total pressure loss due to shock waves can be predicted by equation 2.16. In real situation, at high Mach number (bigger than 1.5), the result from equation 2.16 is higher than experiment data. Thus an equation from Military Specification 5008B can be used here as n, =1 Msi (2.2001) 77, =1—0.075(M -1)"35 10.31, this term will be negative. This is true for most case, as we do not want fluid passing the valve with such a big pressure drop. Based on above analysis, the drag number changing with above three dimensionless variables is shown in Fig. 2.7. When uniform flow passing through a semi-sphere body, the drag always has same direction as flow. But to valve, it is not true. The drag number can be negative, which means the flow pushes the plug outside, or positive, which mans the flow sucks the plug to seat. The drag number is zero when any of these specific values/1'5, 1* and 6* , is satisfied. This is the most favorite operating situation for valve, easy to be operated and vibration being great reduced. These should be considered when design a valve. For continence, the drag is assumed as positive in this thesis, except when specified. There are no experiment data to show the accuracy of our model. In 1976, Zaher M. Moussa gave some data about the relation between the drag number and pressure ratio by running Davis’ computer program as shown in Fig. 2.7b. The basic idea of the program is to use computer solve the equation (2.22) to obtain pressure drag. Moussa did not explain the data. Compared the 10% and 20% lift lines with our theoretical relation between drag number and pressure ratio, they match very well. The drag and pressure ratio are linearly related when flow is choked (pressure ratio less then the dotted line). 26 b- RCluti +Dh 0 ............................ I I I : l I g : : Dir-no ‘Dh l l 3 0 6’ 2." It; 1 a. Relation between dimensionless groups D], 20 40 60 80 L%2100 200 0 IZ'O 1 b. Relation between drag number and pressure ratio from computation result Dh Wide open position ,/ 0% 100% Travel “ft 200% c. Plug drag-travel characteristic Fig. 2.7 Hydraulic drag number 27 As plug t: independent . think the rea thus the (10“ force remain higher the prt outside of the ratio between Saint This pr( ratio scale dur W Nm Ollly xvi llfi as shown i NONI)" lift 1 valtes. If [he \ POSitiom the d ACCOFdin Q t I An second and lift As plug travels to fully open position, at the low pressure-ratio, the drag becomes independent on pressure ratio, as the horizontal lines on the left side of dashed line. We think the reason is that the shock waves happen outside the valve or the control volume, thus the downstream pressure has no influence on the fluid inside the valve, so that the force remain constant. This is not a big concern, because the bigger the plug lift is, the higher the pressure ratio. In real turbine, it is unlikely that the shock waves happen outside of the valve. At higher plug lift, the drag still has linear relation with the pressure ratio between the dashed and dotted lines. The slopes at different plug lift are almost same. This proved our equation (2.41). One thing needs to be mentioned that the pressure ratio scale during which curve show linearity is decreasing as the plug travels to its maximum lift position. At two times of wide-open lift, there is no such relation anymore. Drag-plug travel characteristic Not only with pressure ratio and geometry difference, the drag changes also with plug lift as shown in Fig. 2.7c. The solid lines are characteristic cures with fixed pressure ratio. Normally lift position changing affects the total pressure ratio, even it is one out of eight valves. If the valve affects pressure ratio from 0.9 (closed position) to maximum lift position, the drag-plug travel characteristic will look like the dashed line. According to equation (2.37), if valve inlet and outlet total pressures are fixed, only second and fifth terms determine the drag. In valve opening process, we know from one- dimensional analysis the average pressure increases, so does the absolute value of second term. When the valve starts open, the mass flow rate and average z-direction velocity component increase quickly, then the mass flow rate slows down when plug lift reaches 28 F the eovemir So the fifth | its flat incre each other. s maximum lif hill] term in c position. the ' 1545: With 2. Dinar:P} Ul Where "'th be. and drag UUm) the governing point as shown in Fig. 2.4 and becomes constant after wide-open position. So the fifth term starts as a sharp increasing, then after about wide-open position, enters its flat increasing region. Because the force caused by the two terms are opposite with each other, so the combination effect results in the drag-travel characteristic as shown in Fig. 2.70, the drag increase before the wide-open position then drops quickly. To understand the characteristic, drags at wide-open position (maximum drag) and at maximum lift position (minimum drag) should be obtained. To get maximum drag, the fifth term in equation (2.38) can be simplified by using flow properties at throat. At that position, the valve throat area equals the seat throat area. Also we assume the jet direction is 45 ° with z-direction. Therefore, the equation (2.38) and (2.39) can be changed to - 2 7! 2m D =P7IR2—r2 ——P +P +P Rz—Rz -PzzR2+——fl 233 max 01( ) 6(01 m 02)( o) 02 o 2750”,]?5 (- a) D D max Where mm is maximum mass flow rate at wide-open position, can be obtained by equation (2.11) for subsonic or (2.12) for supersonic. For maximum lift position, we assume the plug is too far away from seat, so this becomes a static fluid problem. Define a control volume as shown in Fig. 2.6b. The drag and drag number are simply D . =—szzr2 (2.38c) mm D = —/1 (2.39c) h min 29 We ‘10 m showing thL Where Ll almost C10Sec From Wide between the” Brain to e“ " 22.2 One-d“ As diSCUSS' are SymmCUl' dimensionS- 1 2.8. lift oscill Some reports value of lift C severe vibratf mechanisms lr stability of We do not have enough data to develop an empirical equation, but there are some data showing there is approximately linear relation between drag and plug lift, so before wide open position, the relation can be expressed as Li — Li alt (Dhmax _ D halo) (2.40) D =1) +—— h alc l-Lialc Where Li is the ratio of plug lift with wide-open position lift. The subscript, alc, means almost closed position. The equation can be only used from fully closed position to wide- open position. From wide-open position to maximum lift position drag, there seems no good linearity between them. For guessing, we still can use the linear interpolation between Dhmx and Dhmin to get the drag. 2.2.2 One-dimensional analysis on unsteady hydraulic forces acting on plug As discussed before, the lift acting on plug is zero if the geometry and flow patterns are symmetric. The drag is a function of pressure ratio, plug lift and geometry dimensions. In real cases, both drag and lift are also functions of timeas shown in Fi g. 2.8, lift oscillates around 0 while drag around a number we can get by analysis of 2.2.1. Some reports show that the peak-to-peak value of drag can reaches to 1,000 lbs, while the value of lift can reaches to 3,200 lbs. This oscillation is very dangerous, it can results in severe vibration of plug and potential failure of valve. Here we will discuss the major mechanisms that cause oscillation of hydraulic forces Instability of highly turbulence flow 30 Aceordin as pressure to time and Where, P According to fluid turbulence theory, all the instantaneous continuum properties, such as pressure and velocity, fluctuate rapidly and randomly about a mean value with respect to time and spatial direction. Thus the pressure can be express as P(x,t) = F (x) + P(x,t)' (2.45) — 1 t +At Where, P (x) = “A; It: P(x, tldt , is time average pressure at a fixed point x. Drag D W Lift 0 W Fig. 2.8 Unsteady hydraulic forces The pressure along upstream, downstream, and valve surface at one instant fluctuates as shown in Fig. 2.9a. If integrating the pressure on both left and right sides, the pressure drag and lift may become asymmetric in both magnitude and acting points as shown in Fig. 2% and moment can be generated at this instant. This will start the plug vibration, which inverse makes more pressure fluctuations. Influence of Separation and shock instability on drag and lift Separation occurs when flow met an adverse pressure gradient, while shock occurs when flow is supersonic and the back pressure is different with some special value, P" as shown. They are different fluid phenomena’s. But for this case, two characteristics are in 31 fluid press“ Pot K Ideally. Ih‘ central line 0 vibration. thC‘ earlier in Fig} remain almOS the average 1: left side is le' side is higher Of course. in common, first they both occur in valve diffusion region or after valve throat; second, fluid pressure jump suddenly after shock or separation points as shown in Fig. 2.10a. P 01 - - . P01 Up stream ' ._ Down stream : ‘ ' P02 . Valve surface l ' P02 a. Pressure distribution b. Forces Fig. 2.9 Pressure distribution and resulting forces at one instant Ideally, the separation point and shock wave point should be symmetric with the central line of valve. Due to instability of high velocity compressible flow or structure vibration, the points become asymmetric, let’s say, both separation and shock happen earlier in right side than in left side. If we assume that the pressure after separation remain almost constant, we can get same conclusion both for shock and separation that the average pressure on left side is less than right side. That means the pressure drag on left side is less and the pressure lift is more than right side. The force acting point on left side is higher and further from central line than right side. These also cause momentum. Of course, in next instant, the shock and separation may happen earlier in left side than right side, or separation earlier in one side while shock later, or in subsonic flow only separation happens. To actual three-dimensional flow, the changing also occurs in annular direction. The pressure force magnitude and acting position changes in response of shock or separation instability. The hydraulic forces can repeat the changing randomly or with a frequency depend on flow conditions. The plug will be harmonically excited, if 32 fl ‘ this frequer valVe. This * Purl P. l- D/L .l‘x) qo Sepffiatio W - e discus“. di‘a SJ a: ea ratio 3% tn; q‘East‘s as this frequency is close to plug natural frequency. Severe vibration will be experienced by valve. This situation should be avoid. P01 \\\ I P2 \ \ E —————— I \ \ I ”—-’— ' \ \ . A I \ \\ I 3'7 . I \\\ l I Separation g \g g ' I Pal: .. ............. . -.x ............................. . Sonic; \\ . 5 \ Shoc g - I ‘ . i \‘xa i a ! ‘~~- i ! “~ P** - ................ left —-—ideal —right a. Pressure distribution b. Pressure Forces Fig. 2.10 Pressure and forces at one instant with shock or separation D/L Total ------. -- ----- I I _ . Pressure u l Friction g I I I O S 0 S l Aseparan'on 1 Atom! a. Drag/lift changing with area ratio 1). Friction forces Fig. 2.11 Pressure-friction drag/lift relation and friction forces due to separation Separation has influence not only on pressure drag/lift, but also, on friction drag/lift. We discussed that total drag/lift is summation of pressure drag/lift and skin friction drag/lift. The drag/lift can be expressed as function of separation area to total semi-sphere area ratio as shown in Fig. 2.11a. The pressure drag/lift decreases while friction drag/lift increases as the area ratio increases. This is because the friction mainly occurs in 33 boundary ll pressure dr. To discus happens ear drag/lift nil. inetion drag According ratio less that has same tren more than 51 . The region bC dmgtlift rama results in the L Will results in Separathn has I R .. . ‘ubmnlc or SM mos: 93563 nor e . Omfib Stable Wession of o boundary layer attached area, the more area in separation, the less friction. While for pressure drag, the more separation, the more the drag is. To discuss the separation influence on friction drag, we also assume that separation happens earlier in right side than in left side. Due to the reverse trend, the friction drag/lift will have exactly opposite way with the pressure drag/lift. The forces due to friction drag/lift difference will have opposite trend as shown in Fig. 2.11 b. According to total D/L curve, three domains can be defined. The domain with area ratio less than so is called friction dominant region, in which the total drag/lift changing has same trend with friction drag/lift changing with area ratio. The domain with area ratio more than $1 is called pressure dominant region, in which pressure drag/lift dominates. The region between dashed lines is called separation insensitive region, in which total drag/lift remains almost constant. So in pressure dominant region, separation instability results in the unbalanced force pattern like Fig. 2.10b, and in friction dominant domain, it will results in the force pattern like Fig. 2.11b. In separation insensitive region, the separation has no effect on valve. Unsteady jets and vortex After separating from both seat and plug, the flow can be idealized as free jet, either subsonic or supersonic. The shock we discuss before is normal shock wave. We think in most cases normal shock waves happen if the flow is supersonic and after that flow becomes stable free subsonic jet. There is still possibility that the jet is supersonic with a succession of oblique expansions and shocks or possible conical waves, which combined together results in the basic characteristic of supersonic jet, instability. The instability also causes pressure fluctuation resulting in unbalanced forces as shown in Fig. 2.8b. 34 Actual f. shown in F ' asjntmetrit~ generated d side to side the plug nat EXpansi Actual flow is constrained by seat wall and encountering with the jet from other side as shown in Fig. 2.12. Also it is three —dimensional. The annular jet flow may become asymmetric, thus the flow leave valve with x and y-direction velocity component. Lift is generated during this process. This asymmetry can change in annular way or simply from side to side and can be random or with a frequency. If the frequency equals or is close to the plug natural frequency, resonance will happen, great vibration altitude will occur. Oblique Normal shock h k Expansro Vertex A S 0C Main flow/a direction a. Supersonic jet b. Subsonic jet Fig. 2.12 Asymmetric jet flow after valve throat We believe that the jet instability is the result of instability of separations on both plug side and seat side. The separation we discussed before just focus on the plug side separation. We assume the valve geometry is symmetric, so does velocity distribution, and mass flow rate is same. According to continuity, if the flow separation on left side of plug is later than right side, the flow separation on the left side of seat will be earlier. As shown in Fig. 2.10b, the main flow velocity has momentum normal to z—direction which causes lift. Vortex occurs in the separation region as shown in Fig. 2.12, because jet flow causes big velocity gradient. The 3-D flow is too complex to have regular vortex arrangement 35 like vortex Sll'UClUIE. Other mech There are such as ups secondary f these have ‘ act as key r 13 Analys NOt‘mall 0‘ Slmplyt llldtlceh] Vt Structure 3 internal fic flow Putter Sh“mun“: \ of “0mm. mdUCed \"i Slim-Werner about Self like vortex wake. The irregular arrangement of vortex still has random impulses on structure. Other mechanisms There are also other possible flow mechanisms counting for the unbalanced forces, such as upstream flow instability, upstream vortex direct impingement on plug, and secondary flow in jet region. We believe that compared with above three mechanisms, these have much less influence on plug. They may behave like vibration trigger, but not act as key roles to maintain or strengthen the plug vibration. 2.3 Analysis on Fluid Structure Interaction Normally, fluid structure interaction means flow instability caused structure vibration, or simply flow-induced vibration. For a pure flow-induced problem, like the wind- induced vibration of bridges, the interaction is one way, from flow to structure while the structure almost has no influence on flow. For this valve problem, because it is an internal flow passing an immersed body, the structure vibration has strong influence on flow pattern and instability. The structure vibration caused by flow instability due to structure vibration is called self—excited vibration. So the plug vibration is a combination of flow-induced vibration and self-induced vibration. We think in this problem, flow- induced vibration plays major role, while self-induced vibration is auxiliary to either strengthen or weaken the vibration. In this part, we will analysis how the plug vibrates due to the flow instability mechanisms discussed in 2.2, meanwhile, do some analysis about self-induced excitations. 36 2.3.1 Flo“ Flow-in induced vi We dist result in h; the valve [ and down associated resonance For lOC; forces can interactioi llldUCed \' 0" the fig. research V “Jere gen: 2.3.1 Flow-induced vibration Flow-induced vibration can generally be divided into two categories: local flow induced vibration and piping system-induced vibration. We discussed the mechanisms that cause unsteady hydraulic forces on plug and finally result in hydraulic induced vibrations. All these forces are extended by the flow around the valve plug. This kind of vibration is called local flow induced vibration. The valve and down stream pipe form a piping system. The vibration in response of mechanism associated with the system is called system-induced vibration. Most known is acoustic resonance in valve piping system. For local flow induced vibration, the mechanism is like direct feedback. The unsteady forces cause plug vibration and vice verse. The research focuses on valve and local flow interaction. The vibration is normally random. While mechanism of acoustic resonance induced vibration is like a feedback loop as shown in Fig. 2.11. The research is focused on the flow valve piping system. The plug will vibrate with one dominant frequency. Our research will focus on local flow induced vibration, because we think this mechanism is more general and basic. Based on one dimensional hydraulic force analysis, three dimensional forces and moment acting on plug at t instant are shown in Fig. 2.13. Thus vibrations in three directions, axial, lateral and spinning, are generated. For convenience, another coordinate system, zi-a-B, is defined from the plug stem beginning position. The relation between two coordinates at t instant is: Z, = 2 +1 (I) , where l(t) is the stem length at t instant, the plug length without stress is 10. 37 L( t) Flow in SFSIEm in with 1h e \9' Valve Dlu whole 3m gscmatior BecauSe t‘ Plu Plug vibration —> Fluctuations 0f . g . flow through Vibration T valve U d React force Acoustic pressure nstea y l fluctuation on 4— oscillation in forces - plug 121126 a. Local flow b. Acoustic induced vibration resonance Fig. 2.13 Flow induced vibration mechanism Assumptions a. 3-D view b. Up view 0. Side view c. Front view Fig. 2.14 3-D view of unbalanced forces Flow induced vibration can be modeled as a second-order mass-spring-damping system in response to hydraulic force excitation as shown in Fig. 2.14. We do not deal with the vibration due to lift changing or control induced vibration. From Fig. 1.2, the valve plug is mounted on a beam to be operated. The whole multiple-valve vibrates as a whole structure. The beam vibrates due to vibration from all the valves and pressure oscillation around it as a continuous system serving as a base excitement for single valve. Because the beam is much stronger than plug stem, from practice, in most cases, the 38 beam ex pt" remains st; In reality. vibration go the vibration know in real the “Severe“ .um. That the hydlaUHC {Or it beam experiences much less vibrations. Due to above reasons, we assume that the beam remains stationary, which means zi-a-B coordinate remains stationary. *dashed line is balanced position ' a. Axial vibration b. Lateral vibration c. Spinning vibration Fig. 2.15 Plug vibrations due to unbalanced forces In reality, the three direction vibrations occur simultaneously. This make the three vibration governing equations coupled by nonlinear terms. So another assumption is that the vibrations are not influenced with each other, they can be treated separately. We know in real situation, the vibrations in three directions are not very big. In some report, the “severe” vibration, which causes valve failure, can only reach amplitude of 100-400 pm. That means we can get a decent result with such an assumption. Compared with the hydraulic forces, body force is too small. Thus plug and stem body force is ignored. Axial vibration 39 The plui.‘ vibration is in zdirectt The firs the mass 0 The sec Structural Damrii n g damping 1 energy 10: vibrati0n. The plug can be treated as a point mass attached at the end of mass less shaft. The axial vibration is due to the unsteady drag. By using Newton second law, the motion equation in z—direction is derived as: 2 me d l(t)+cdl(t) q dt2 dt +kz(l(t)_10)_D(t):O (2.45) The first term is inertia force. The plug equivalent mass can be obtained by integrating the mass of plug and stem. The second term is damping force mainly from stem internal friction, which is called structural damping, and friction from fluid, which can be treated as viscous damping. Damping factor c thus is summation of structural damping factor, cs, and viscous AEcyc AEcyc X27110, ' X 2 damping factor, cv. For harmonic vibration, cs = is the ratio of energy loss per cycle to the square of displacement amplitude. It is a property of material, which can be obtained from experiment. (1)5 is plug vibration frequency; For random vibration, it is very difficult to get exact value of structural damping factor. In this case, viscous damping is also impossible to get from theory. The structure damping is believed to be the major damping in this case. Ems. The third term is spring force. kz : ( )2 is equivalent spring constant or stiffness plt for stem. The stem density p is treated as constant. E is Young’s modulus. The stiffness in stem stretching process is less than in depressing process. This term is nonlinear. 40 D0) is t plug vibra. drag increal excitation t weaken the In later; Point mas POSition, ( amplitude 10 elimlna D(t) is the drag on plug at t instant. Drag is unpredictable due to flow instability. The plug vibration also has influence on drag. When the plug is stretched from the balanced position to positive deviation as shown in Fig. 2.15a, the valve throat area decreases, which means pressure loss increases and downstream total pressure decreases. Thus the drag increases during this process. Combined with decreasing of stiffness, this self- excitation tends to strengthen the axial vibration when plug has positive deviation and weaken the axial vibration when the plug deviation is negative. The natural frequency is Lateral vibration In lateral direction, the vibration can be idealized as a mass less cantilever with end point mass. The vibration is due to the moment of forces around the fixed stern holding position, 0. When we analysis moment, the geometry of plug is considered. For small amplitude oscillation, which is true in practice, we approximate sina by a, and cosa by l to eliminate nonlinear terms. By using equation (1.2) in vibration direction, the motion equation can be dza da aeqlz dzz +CalE+kaCd2 :M(t) (2.46) First term is inertia moment of plug with equivalent mass; Second term is the moment from mainly structural internal and flow friction damping with damping factor, ca. Third 351, I3 term comes from spring force of stem. Spring stiffness, kg = , can be treated as 41 constant. \ The natural M (i) i defines the important ' unstable. S model. The thrr 2.163, “he left throat Different f based on O constant, while 13 is the polar moment of inertia] of the cross-sectional area of the shaft. k Th t 1f ' (00.. = a C na ura requency IS Meq M (t) = D(t)x (RD (t))+ f.(t)x ((f + RL(t)) . ‘2’): (2.47) ‘ M (t) is the momentum due to hydraulic drag and lift. Its direction, u: with x-axis, defines the vibration direction and its amplitude, M(t), affects the vibration. So it is very important to determine this term. It is very difficult because all the terms in equation are unstable. Some qualitatively analysis must to be done to simplify the lateral vibration model. The throat area of valve shown in Fig 2le becomes asymmetric as shown in Fig. 2.16a, when plug starts vibration. For example, at t moment, it is moving to left side, the left throat area is less than right side. Thus the pressure distribution becomes asymmetric Different flow situation causes different pressure distribution along the valve surface, based on one-dimensional analysis. ------------- M51 ——M>l ----------’---left ----ideal —right a. Vibration and forces b. Asymmetric pressure distribution Fig. 2.16 Pressure distribution and forced in response of vibration 42 0‘! possibility big pressu left side is acting pos moving it moment t moment 1 Norman) less than before, 1} mOmem In CliSt For sonic or subsonic flow, the integration of fluid pressure (doted line) along left side of valve is less than right side (solid line) when flow is subsonic. There is also another possibility that left side is supersonic while left side is sonic or subsonic, which causes big pressure difference as shown in Fi g. 2.16b. Under both situations, the lift and drag in left side is less than right side. Thus the overall lift points to left and the overall drag acting position moving to left shown in dotted arrow in Fig. 2.16a. As plug continues moving to left, both lift and drag acting point deviation becomes bigger. Thus the moment of lift pushes the plug further left side to strengthen the vibration while the moment of hydraulic force pushes the plug to its balanced position to stabilize the plug. Normally, the drag is much bigger than lift. So even its acting distance around 0 is much less than lift, we still think it can play a big role in valve stability. As we discussed before, the drag goes down to zero or a value not strong enough to overcome the lift moment at some open position. The plug will experience severe vibration. In case of supersonic flow, shock waves in right side occur earlier than left side due to more diffusion in left side. Thus left side average pressure is higher than right side. The total drag and lift will behave in opposite way to subsonic flow situation as shown in solid arrows in Fig. 2.16a. The moment of drag is minimized as two trend encounter with each other, the plug move to left while the drag acting point moving to right. This is lift moment dominant region. As the lift moment tries to stabilize the plug, we think the plug will experience a high frequency low amplitude vibration compared with sonic flow. Of course, the plug vibration also has strong influence on other instability mechanism, like turbulence, separation, and jets. But the way is quite unpredictable or not as regular as above discussion. For turbulence, this is always a random excitement mechanism to 43 plug vibra boundary gradient at- separates ' side the ilc flow has it Based C situation. Q 10 drag an F0? SUI plug vibration. For separation, adverse pressure gradient and flow kinetic energy in boundary layer determine the separation area. In diverging region, both the pressure gradient and kinetic energy of flow are larger than right side. So we just assume the flow separates at almost same place in both sides with oscillation. For jets, because even in left side the flow velocity is bigger and the mass flow rate is less. Thus we assume that the flow has moment oscillating around a same value in both sides. Based on above analysis, the moment term can be simplified according to flow situation. For sonic flow, the moment direction is combination direction of moment due to drag and lift, the amplitude is: M (t) = (aD(t) + L(r))l (2.49) For supersonic flow, the lift defined the vibration direction, the moment of lift is: M (t) = L(t)l (2.50) Spinning vibration In [3 direction, the valve also experiences vibration, like a disk attached at the end of a mass less shaft, as shown in Fig. 2.13c, in response of torque caused by lift as shown in Fig. 2.15c. The motion equation can be derived as 2 Jd'B da eq dtz +cflE+kflflzTL(t) (2.51) The first term is inertia term. Jeq is equivalent moment of inertia of the stern and plug around the center point of semi-sphere. Second term is damping moment due to internal and skin friction. C3 is equivalent damping factor. The third term is moment of spring 44 force. k term is tor l l- The spin (0&2 less due to axial vibrut Plane as Sht “llh same ( direction. 5 direction is angle v to ) a. ROt "le Rel‘I GI, l force. ’93 = is equivalent torsion stiffness, while G is the shear modulus. The last term is torque of lift, TL (1) = LUXRL (I) X Z) . The natural frequency is The spinning vibration is believed as the weakest vibration because the torque is much less due to little acting distance of lift. But it is still believed to be more dangerous than axial vibration, because it cause the lateral vibration keeping changing directions in x-y plane as shown in Fig. 2.17a. Assume, at t instant, the lift acts on plug as dashed arrow with same direction as +x. If drag moment is ignored, the plug lateral vibration is in x- direction. Some moment later, due to the spinning vibration in [3 direction, the lift force direction is rotated \l! anti-clock wise. Thus the lateral vibration changes direction with an angle w to x-axis. Also, the rotation can cause rotation of asymmetric jet. Seat . v,§ Plug x i . 4“.— B .;.- E \. ‘_E___ ‘J ‘.\ l yV/ ‘V ' """""""" r """"""""""" a. Rotation changes lateral b. Lateral vibration influence vibration direction on spinning vibration Fig. 2.17 Interaction of lateral and spinning flow Relation between flow-induced excitation and self-excitation 45 Assho direction causes tan applying ) By assu into the v: by using r Now if HOW inst: finally Ca. instab” it 3' If We a: with Iinie J ‘3) Car As shown in Fig. 1.2, the steam flow normally enter the chest mounted valves with the direction normal to valve plug. Assume the velocity, Vs as shown in Fi g. 2.5b. Thus causes tangential velocity, VB. Flow enters the valve with z—direction velocity, V. By applying Momentum equation in B-direction, we can get torque acting on plug Tu = ,0 JWfidA — IVVfldA (2.523) At A2 By assuming all the flow enter the control volume (dashed rectangle) at right side goes into the valve and no flow exit and enter at left side, we can get the force acting on plug by using momentum equation in x-direction F : mVs (2.533) S Now if we assume, the plug is at this balanced position, eccentric with seat. Due to flow instability, the velocity in three directions and oscillating mass flow rate, which finally cause unbalanced force and torque. This mechanism is called upstream flow instability. It is a kind of flow-induced excitation, but as we mentioned in 2.2, this mechanism is not a key role in flow-induced vibration. If we assume the plug is vibrating, and the velocity of three directions are constant with time changing; VB is symmetrically distributed; The V is uniform in this cross section. At t moment when the plug moves to -y-direction with angle a, the equation (2.52a) can be reduced to Tu = pVVfl(A, — A2) (2.52b) 46 Also d effect on . This is '. have effect mechanisrr Based 0 strong vib of drug 3C 0Pllmizim frchEmI} lale‘ral 3TH asymmeu the ValVe . 0n Vibratit ) ~32 Rant The Wu. .3 . . can be Obta Also due to eccentric, the force in equation (2.53a) excites a moment, which can have effect on spinning vibration and direction changing of lateral vibration. M . = F.R. = "'IVJ (25%) This is a typical self-excitation mechanism. The actual situation is both mechanisms have effect on plug vibration. The above example is just to show how these two mechanisms interact with each other and contribute to plug vibration. Valve optimum design Based on above analysis, the valve should be designed following some rules to avoid strong vibration. We believe that the severe axial vibration occurs when large amplitude of drag acts on valve. When designing a valve, it is recommended to use equation (2.40) optimizing valve geometry to minimize the drag at that point to about zero at the valve frequently opening postion. This can great reduces the axial vibration amplitude. For lateral and spinning vibration, the basic rule is to reduce the flow instability or asymmetry, which is defined by the plug and seat shapes. So it is important to optimize the valve shape to guide the flow in a symmetric way. We are not concentrate on material properties of plug. But according to above analysis on vibrations of three directions, materials with higher shear modulus, Young’s modulus, and structural internal friction are preferred when design a valve plug. 2.3.2 Random model for random vibration The equations of motion in three directions are obtained. So if the right side terms of equations or excitation terms, D(t), M(t), and TL(t) can be determined, the valve motions can be obtained. As we discussed before, because so many factors, like instability of 47 turbulenc be predict This kind excitation By using BéCaUse [h Can be 1 fm input lei‘m While m C. fldmpjng rat “Us We C turbulence, separation or shock waves, affect the lift and drag, the excitation terms cannot be predicted or cannot be expressed as explicit time description as shown if Fig. 2.18. This kind of excitation is called random excitation. The response of a system to random excitation is called random vibration. lorororB DorMorTL Fig. 2.18 Random phenomena By using Fourier transform, the three motion equations can be transformed to 0(a)) = H (60)] ((0) (2.54) Because they have similar form, so we write three equations as one. 6(a)) is output term, can be 1 for axial vibration, or for lateral vibration and B for spinning vibration; i(w) is input term, can be any of the three excitation, D, M and TL. 1 min): —w2 + 2242020,) (2'55) 19(0)): C. I Where mi can be me , me 12, or J6 , de ndin on direction of vibration. 4’ = is q q ‘1 p6 g 2 k m V i i damping ratio. Thus we can get the relation between input and output as 0(2) 2 [:10 - w)h(zU)dzU (2.56) 48 | Where‘ Relation t First. \\ The me AUIOCQ f, at two I: “TE mt aSSOClalet lime d0m tr (e k Where h(a7) is system response to a unit impulse. Relation of mean value of input and response First, we need introduce some basic conceptions in random vibration theory. The mean value means time average value. For function f, the mean value is . 1 t f = E( f) = 1153; I0 f(t)dt (2.57) Autocorrelation is the mean value of products of the instantaneous values of function, f, at two times t=t and t=t+r. R. (r) = Elf(t)f(t + 2)] (2.58) The mean squared value is a random variable provides a measure of the energy associated with the function. f2 :EUzlzRfGI)=lim-:-J:f2(t)dt (2.59) —)00 Power spectral density (PSD) is variable concerning properties of a random variable in time domain. It shows the spectral distribution of average energy. S f (w) = ER! (r)e“"”’dr (2.60) If we know the PSD, the autocorrelation can be obtained as 1w) = [:5, (WW (2.61) Two important relations between excitation and response variable are 49 From b value for l direction PSD rt Signal. A unknow- tacitam the exp, We 1. effec1 C equittic At di 5 = E(0(t)) = H(O)E(I(t)) :kL (2.62) S. (w) = S, (w)|fi(w)|2 (2.63) From basic physical knowledge about the valve vibration we can get that the mean value for Drag is D, while both moment and torque are zero. Thus the mean value in axial D direction vibration is k— and is zero in both a and [3 direction vibrations. Z PSD relation is still unknown because we do not know either the excitation or response A 2 signal. Also the value of IH (w)l cannot be obtained by theory, as damping factor is unknown. So experiment data is needed. As it is difficult to measure all information of excitation and response of three directions, a more simplified model is needed to direct the experiment. Simplify excitation a_s dynapric pressure oscillation We know the basic excitation is drag and lift for plug vibration. Ignoring the viscous effect on valve, we assume the total drag and lift equal pressure drag and lift. Discretizing equation with equal area in semi-sphere, we can get _. N _. D=P012.Aup_ZPkZ.AA (2.64) k=l At direction ii , the lift is N -. L = Z P“? 0 sin 6k (2.65) 50 The pres considered random vi am iQTqui shown in in abm fevi‘lECt “F .mSlt-"tbllitl Stat Side. Points [0 [his mod _I_)Ql_~ .299 Valve-fluid system .__T__, Excitation Response Fig. 2.19 Simplified excitation-response model for plug vibrations The pressure is not been considered as a function of space domain. They were considered as N independent variables that influence the drag and lift resulting in plug random vibration. Thus we can get a simple model. Rather than consider force, moment and torque as input, we consider the pressure oscillation as plug system excitation, as shown in Fig. 2.16. In above model, we consider pressure as basic excitation for the system. Pm and P02 reflect up and down stream turbulence instability, P1 to PN represent the turbulence instability of flow when passing through a valve. Some pressure points also are taken in seat side, we can get information of jet and vortex instability. Thus we use finite pressure points to represent integration of pressure along plug surface. This is the basic purpose of this model and basic theory of experiment. 51 3.l Flow .-‘ For dill-u. separates in which is car boundary l; dimension; Patterns it MES. W range of l; develgpfi when on let flow ( flow is , Stall ha; preSSure ‘ like 3' CHAPTER 3 LITERATURE REVIEW 3.1 Flow Asymmetry and Instability Stall in diffusion process For diffusing flow in a divergent passage, stall or backflow happens as boundary layer separates from the wall. The boundary layer separation is due to the adverse pressure gradient, which is caused by pressure rise due to diffusion. Kline et a1 reviewed the topic of stall and boundary layer theory in 1956. In their study on diffusion process in straight-walled two- dimensional diffusers for incompressible flow, stall regimes were identified. Four typical flow patterns were found as shown in Fig. 3.1. For a fixed diffuser length and inlet width ratio, UW=5, when flow is low turbulence, at small diffuser angle, no stall happens (Pattern a); In the range of larger angles, from 16° to 20°, large transitory stall zone was found (Pattern b); Fully developed steady stall (Pattern c) occurs in the range of 20° to 80°. This pattern is nearly steady; When diffuser angle is wider than 80°, flow separates from both sides and become nearly steady jet flow (Pattern d). The inlet flow condition has some effect on the flow patterns. But before the flow is choked in the inlet, the stall happens in a similar way. It was also pointed out that stall happens in a position where the wall curvature changes sharply or under a high adverse pressure gradient due to shock wave. This can be used to explain flow phenomena in venturi valve and to improve valve design. All above analysis is about symmetric straight 2-D diffuser. Kline et al did not discuss the stall problem in a general asymmetric curved wall diffusion passage. Referring to boundary layer theory, we make an assumption here that the flow behaves like in a symmetric diffuser, but stall is easier to occur in the sharper curvature side due to larger adverse pressure gradient. 52 The val ‘2 analysis. tl‘ valve. Thu) other \sith nozzles. \vit The valve can be treated as an annular of 3-D converging diverging nozzles. To simplify analysis, the valve is further idealized as 2-D infinite wall with same cross-section area as real valve. Thus the valve becomes a combination of two converging diverging nozzles facing each other with an angle. Here the major concern goes to the interaction of two converging diverging nozzles. 4 ____/> ____> —’ ’ Q \5 3. Flow b. Large c.Fully developed without stall Transitorv stall steady stall ‘1' Jet flow Fig. 3.1 Stall in diffuser l l i / whiff .5. 'l, ' H 't .( Pattern (b') Pattern (c) Pattern ((3) Fig. 3.2 Possible flow patterns due to stall in valve Based on ID stall analysis, 6 basic flow patterns may possibly occur according to the paper of D. Zhang and A. Engeda. Pattern (a’) occurs when there is no stall in both sides. When fully developed steady stall happens in plug side, pattern (21) occurs. When stall happens in plug side at 53 right and unsteady. in one side also possilc High veloc The vet formed b) symmetrit the conve and decre flow is di llovv~ flov happen fc (COTTVCrgi IIItttSOnjc A- Sha C0nsidcn. a FCgiOn ( “10¢in i pressure 1 h Tick-Side Shack We right and seat side at left, pattern (c) happens. Due to transitory stall, pattern (b) and (b’) are unsteady, which may be symmetric or asymmetric (not shown in Fig. 3) with one stall near plug in one side and another stall near seat in the other side. Pattern (e) is caused by jet flow. There are also possible intermediate flow patterns not shown here either. High velocity compressible flow theory The venturi valve can be considered as an annular of converging diverging nozzles formed by plug surface and seat surface. In Chapter 2, one-dimensional theory for symmetric nozzle is summarized. The compressible flow is considered as isentropic. In the converging part of valve, the flow will be accelerated with increasing Mach number and decreasing static pressure. In diverging part, for subsonic flow, after valve throat, flow is diffused with decreasing velocity and increasing static pressure. For supersonic flow, flow will be continuing accelerated with decreasing static pressure. Shock may happen for supersonic flow. The transition flow changing from pure subsonic (converging and diverging) to pure subsonic-supersonic (converging-diverging) is called transonic flow. In one-dimensional theory, the transition is a process with continuities. A. Shapiro explained the study done by Emmons about the transition process while considering two-dimensional effects. For pure subsonic flow, as the back pressure drops, a region of supersonic flow develops near the throat wall as shown in Fig. 3.3a. The flow velocity is sonic at the boundary of this region and main flow is subsonic. As the back pressure is reduced further, the supersonic region grows with shock wave happening at backside region as shown in Fig. 3.3b. Then two growing regions join together with shock waves happening in the plane of after the throat as shown in Fig. 3.3c. The 54 supersonic and finall} supersonic region keep growing with the shock plane moving toward the exit of nozzle, and finally becomes pure subsonic-supersonic flow inside the nozzle. lM- Fig. 3.26 Test valve for noise (after Heymann) I b0”0* Heymann investigate the relation between noise level and Mach number for different shapes of valves at different plug lift. The basic test valve configuration is shown in Fig. 3.26, air goes through from a high pressure inlet chest to a low pressure outlet chest. 79 a Acoustic efficiency is defined as 77“ = . W8 is sound power and w, = émv 2. As Wf shown in Fig. 3.27, the test result shows that the normally the acoustic efficiency increase with the increasing Mach number. It reaches maximum value at some point. Then it starts decreasing. The turning point is different due to different valve shape and lift ratio. 10‘2 - 10-2 2 .. 103- “3 10+ LOGmM Fig. 3.27 Result of noise tests for different valve configurations (after Heymann) We know the Mach number is a function of pressure ratio. For a valve with fixed opening, the smaller pressure ratio is, the higher the Mach number. The recessed shape valve looks like the improvement valve in the paper of Araki at el. According to our observation, the curve at the lift ratio of 0.15 for recessed shape valve in Fig. 3.27 is actually the combinations of the curves for lateral and longitudinal vibrations at lift ratio 80 of 0.175 in Fig. 3.17b, if we look the acceleration and acoustic efficiency as same physical meaning terms. There are two peak points in Fig. 3.27, first one is at low Mach number, which means high pressure ratio. We think this peak is due to lateral acceleration peak in Fig. 3.17b; The second peak is at high Mach number or small pressure ratio. We think this one is due to severe longitudinal vibration peak in Fig. 3.17b. Our conclusion is that even the downstream piping systems are different for two experiment, the results match in a qualitative way. Heymann also observed the flow pattern changing phenomena as shown in Fig. 3.28. The annular flow and core flow pattern are actually called type A and type C pattern respectively in Araki’s paper. The flow pattern regions also match with the Fig. 3.13a and with a little difference with Fig. 3.13b. The opposite region boundary in two figures is because here pressure drop ratio is used while in Fig. 3.13, the pressure ratio is used. CORE FLOW REGION ' (HIGH NOISE) _O 00 r ’0 g m g 0'7 ' HYSTERESIS' o g 0.6- . a.“ 05- (LOWNOISE) 0 4 _ ANNULARFLOW ' REGION ‘ 0.3 I I x 2 COREFLOW 0 0.02 0.04 0.06 0.03 01 Valve Lift f Dia. Ratio Fig. 3.28 Flow patterns and regions (after Heymann) Acoustic resonance 81 As we mentioned in Chapter 2, for the acoustic resonance the research subject should be the valve piping system. Even same valve design, due to different down stream piping system, the valve may experiences different vibrations. So the research in this field is case by case. a.“ I, VALVEBEAM 4780mm '- VIBRATION MODE — —-I ..........._...._...........'T: C ”Hill” I VALVE No.2 I I ‘ : _, ACOUSTIC lNLET S'I'EAM SPEED OF SOUND , _ OSCILLATION FLOW C ONDI'IIONS: 1N PIPE: 47 OfMS MODE IN P=68 bars 175mm STEAM PIPE t=284 degree C ; massflow=640 kg’s . ' DYN. PRESSURE TYPICAL SPECTRUM OF MEASUREO ACCELERATION ON SERVO SPINDLE ACC. AWLITU'DE ‘ 1D 0 50 100 150Hz LENGTH OF PIPE ACOUSTY WAVELENGTH AT MECH. RESONANCE FREQUENCY Fig. 3.29 Solving of acoustic resonance for an operating turbine valve (after Widell) 82 Widell studied the failures of servo spindle and couplings for an operating turbine inlet valve as shown in Fig. 3.29. The bar lift type multiple-valve is composed of 9 separated mushroom-like valves. The valves are lift one by one by two hinged beams, which is controlled by servomotor. Two inlet emergency stop valves supply steam to valve casting. After the casting, the steam is led by valve downstream pipes with different lengths to two steam chests, one on each side of the first stage of the turbine. Severe vibration of casting and servo spindle with frequency 63 Hz and amplitude about 100-400 um occurs in the No. 5 operating range. The power output is between 270 and 320 MW. By both using theory analysis and experiment of testing the beam vibration mode, an S-shaped mode with a frequency close to 64 Hz is confirmed. Then acoustic impedances of No. 5 downstream pipe and terminal impedance at turbine end are calculated and proved by test. From all above information, No. 5 valve is judged unstable while all others are stable. Acoustic resonance occurs between the beam and No. 5 valve- piping system. The logical method is suggested to lengthen the downstream pipe after No. 5 valve. But considering the real situation, it is more convenient to removal the No.5 valve with less influence on turbine performance. The valve is removed, then after 7 years of operating, the vibration never happened again 3.3.5 Flow impingement Powell (1953) recognized the impingement mechanism of shear flows as shown in Fig. 3.30. The vortex caused by velocity gradient is strengthened as traveling down stream producing regular pressure and velocity fluctuations. These fluctuations are drastically 83 self-enhanced at some frequencies when meet an edge. It causes severe structure vibration or noise problems. Separation Vortex Formation Impingement Fig. 3.30 Impingement mechanism (after Ziada) \E-E-s 4 3. 2 §=§V \— § \§ 1 5V l.Stem / 4.Shroud 2.Chest I 5.Inlet 3Rings T 6.Exit Fig. 3.31 Valve configuration for impingement analysis (after Ziada) By using above theory, Ziada et a], studied the excitation mechanism of a kind of turbine control valve as shown in Fig. 3.31. When passing through the valve throat, flow separation occur possibly form the valve stem or seat. Then due to the flow impingement on the downstream corner of plug shroud, the flow instability is enhanced. Repeating separation and reattachment of the jet to downstream comer would generate great 84 pressure fluctuations. If the pressure fluctuations were coupled to the acoustic resonance of the valve chest, severe vibration and noise would occur. It was found that this kind of excitation likely occurs when high-speed jet separates after valve throat and the valve dimension is much small than the jet movement in unit time. An effective counter- measure is suggested to eliminate the impingement boundary, when impingement excitation occurs. 3.3.6 Valve improvement design Two directions to improve valve design by either cutting the nose semi-sphere shape of venturi plug or extending it as shown in Fig. 3.32. As we mentioned before, Araki designed an improved valve by cutting the semi-sphere nose. The better performance was observed by experiments and practical operation in turbines. Zarjankin and Simonov designed a valve by extending the nose as shown in Fig. 3.33. The new valves were installed in all kinds of turbines like R-50-130, PT-80-130, K-300-240, T-100-130, and T-250-240. In more than 15 years observation in some turbines, the new design was proved to have high reliability. L J Cutting Extending Fig. 3.32 Two directions for optimize valve plug shape In our view, because the flow is better guided passing through a valve with extending nose, the thermal efficiency of extending nose valve is higher than the valve with cutting 11086. 85 v \i\V axle/A V! as \\\\\ .3 'il . - a” Qi’jv rigs! 1y; i 7175 _ M\\ I, .\\\\\\\ .— 7!” \) ! .‘I \'. \ II My; .J: /. ‘il I I ',‘:-"\ 51' I Fig. 3.33 An improved valve design (after Zarjankin and Simonov) 3.3.7 The recent research In 2003, two papers were published about the failure cases of steam turbine venturi valves. D. Zhang and A. Engeda reviewed the literature in this field and investigated the flow phenomena by using CFD tools for the valve. Improved designs were also reported. The detail CFD results will be shown in Chapter 4. Recently, J. Hardin, F. Krushner and S. Koester published another paper describing two turbine venturi valve failures and designed a new valve that showed good flow stability. A recent valve failure was reported in 1998 at Elliott Turbomachinery Co. The valve (shown in Fig. 1.2 and 1.3) is a real valve, which started operation in a multistage steam turbine in 1998. After 3 months of running, the No. 2 valve failed after the crack developed in the location shown in Fig. 1.3. It happened as the No.1 valve was almost fully open and No. 2 valve was at an opening of 0.147(h/D). The falling plug drove the seat into the steam chest wall approximately 0.7 in. The failed valve stem surface is 86 shown in Fig. 1.3. Before the failure, there was higher noise coming out of the machine, which means that chattering may have existed. Just before the valve has the severe vibration, the frequency spectrum for the pressure port transducer at downstream of No.2 valve was tested. Fig. 3.34 shows the high amplitude, 66.6 psi, of valve vibration occurs at frequency of about 350Hz. This is due to the “organ pipe” resonance since the transducer was not flush-mounted. The long time trace period of four seconds of pressure pulsations is shown in Fig. 3.35. Zooming in the Fig. 3.35 for a quarter-second time trace of pressure pulsations, Fig. 3.36 shows clearly that the sharp drops in pressure are at an average of 35Hz. The pressure pulsation during high valve vibration is also tested as shown in Fig. 3.37. The frequency is 32 Hz. So the pressure pulsation at frequency between 30 and 40 Hz is caused by unstable flow. OX2354 Hz Yz66.59175 PSI POR'rz . 100 I I g I I i . PSI ”"‘I"”;"‘ “ "I““"“"‘ I- f “I” ‘1 Peak r” If‘ “ l I ‘tr'rv ”"— “‘* ‘ ' 3 ____.‘_.. ___...__.__. ___ _ -m. _ - I _- I I . “I“ H.” i i iOHz ' Frequency "Sq—810‘Hz Fig. 3.34 Pressure pulsations before high vibration of No.2 valve (after J. Hardin) 87 PORT 2 1500 PSI l ' 1000 . 7 _ .. “ 0 Time -Seconds 4.0 Fig. 3.35 Time trace of pressure pulsations (after J. Hardin) Sharp Drops In Pressure - At Average Frequency Of 35 Hz_ 350 Hz Pulsations Due To Port 'Organ Pipe'I Frequency . PORT 2 2| kPS /di 0 Time - Seconds 0.25 Fig. 3.36 Zooming in view of the pressure pulsations (after J. Hardin) 88 0X32 Hz Yz77.49376 PSI DX264 Hz Y:55.94395 PSI >< X1296 Hz Y:24.82405 PSI +Xz352 Hz Y:85.897l7 PSI PORT2 100 PSI Peak Fig. 3.37 Pressure pulsation frequency spectrum during valve vibration (after J. Hardin) The valve natural frequency was tested as shown in table 3.1. Both bending mode frequency and torsion mode frequency decreases with decreasing pressure load of the valve. This is due to the changing of stem length and mass as the valve moves to change the pressure load. Table 3.1 Original Valve Natural frequency (after J. Hardin) Pressure Load (Lbs.) Bendig Mode Freq.(Hz) Torsion Mode Freq. (Hz) 325 208/238 850/930 675 268/282 1050/ l 160 1325 290/310 1200/1240 The steady state CFD analysis was performed in the paper. By changing the curvature of plug, three new valves, cutoff, concave and hybrid, were designed. Three new valves at both large and small openings are simulated and the streaklines of results are shown in Fig. 3.38. The flow is annular flow for each case. The annular flow pattern is preferred and proved more stable by Araki et al. In terms of this, the new designs are better than old one. According to test data, the hybrid valve is more stable and is with less vibration. 89 Low Lift High Lift (same flow area) (same flow area) Cutoff Plug Concave Plug Hybfid Plug Fig. 3.38 Streaklines and reverse flow region of new valves (after J. Hardin) 90 CHAPTER 4 2-D NUMERICAL INVESTIGATION Because it is very difficult to express the drag and bending moment as function of time due to complicity of flow structure interaction, it is very difficult to get analysis solution for equations in Chapter 2. Experiment is very important to help us to understand fluid nature, but due to some reality issues, we have no way to obtain a lot of detail important information from experiment alone. 2-D model was calculated by using commercial CFD package, TASCFLOW. The steady state flow field, forces and moment at plug balanced position and fluid structure interaction mechanisms by arbitrarily adding displacement on valve plug were investigated. 4.1 Numerical Modeling TASCGRID was used to generate the grids. The whole grid composes four blocks, left and right side chest (i=50,j=30,k=4 for each), throat (i=50,j=150,k=4), and downstream seat (i=50, j=50,k=4), totally 46,000 nodes. A cross section of the mesh is shown in Fig. 4.1. The grid density around the plug (the darker area) is much greater because this is the most concerned area. The flow is treated as steady state, compressible, turbulent ideal gas with high speed. For inlet boundary condition, constant total pressure and total temperature is imposed. The wall is treated adiabatic. Constant static pressure is used at valve exit. Because this is a 2-D problem, symmetric boundary condition is used at k=l and 4 surface. All cases were convergence to maximum residence in the order of 10“. The y+ value of the valve plug surround region is allowed to vary from 40 to 400. Except the plug geometry, same grid is used for improved valve design simulations. 9] \\\\\\\\\\\\ III! §\~‘\\\\\\\\\\\ mini \\\\‘\\\\“\ “I §\§§\\\\\\m\\\‘l‘u § : %\\\V\l\\\\\\1‘\l r s is: § ‘§ §\\\\\\\\\\\\\ “Rx Redeem“ “\§ e;% N» §§$e~$v ii fitsem :~s$§s§. , H mun v MI I I‘ll“ ’ / ilhlllmll I'll”! “I II "I"! I II”! I” "III/II I M II" III, WW \\ “R“ W mes II Wm”? ["0 $“W Ill/q I n “\\\\\\\\ “mm“ um“ \\\ w u\\\“ x w» VA \\\\\\\M\ a“! Pattern (b) l lllllllllll [III/Ml? 92 .9. . ~ ~ .“I. 0.0. I~::.~. \\‘\\‘sMOOQ ‘~“"" I ’li Pattern (c) Pattern (c) Fig. 4.2 Flow patterns and pressure field 93 4.2 Results and Discussion 4.2.1 Asymmetric flow pattern Five basic flow patterns are found at different pressure ratio, defined as downstream static pressure over upstream total pressure, and valve opening ratio, defined as plug opening over plug diameter, as shown in Fig. 5.2. The plots at right show the velocity field while plots at left show the corresponding static pressure field. Even the boundary conditions and geometry are perfect symmetric, three patterns are asymmetric, especially pattern (c) showing strongly asymmetric. Pattern (a) is most wanted flow pattern for the valve. The flow accelerates before the valve throat, then slows down at valve diverging part and attached to the seat on both side. Pressure distribution is symmetric, which means less force occurs. This pattern happens in large opening and large pressure ratio situation. The difference between pattern (b) and (a) is that flow starts separation from seat in both sides. It is also relatively symmetric as a transition pattern between pattern (a) and (c). Pattern (c) is most unwanted flow pattern. Passing through valve throat, flow decelerates with one side attaching the seat and another side attaching the plug. Pressure is asymmetric essentially causing huge hydraulic forces and moment. This is dominant flow pattern as valve large (not as large as pattern (a)) opening. One thing interested is that the right side flow always attaches the plug at this pattern (In coarse grid with 1/4 density as this one, we do have some results that flow attaches left side plug. For that grid at 10.6% opening and pressure ratio 0.9, from same initial guess, one result show the flow attaching left while another attaching right looking like flip imagine. We did not try in fine grid, because converging is time consuming). Pattern (d) is transition pattern between pattern (c) and (e). At down steam of the seat, the pressure is asymmetric, while 94 relatively symmetric surrounding the valve. According to former visualized result done by Araki et al, this is a transient region. Pattern (d) is symmetric pattern, normally occurs in small pressure ratio situations. Above flow patterns agree well with our predicted flow patterns in Fig. 3.2. When opening ratio is less than 20%, flow pattern changes from (c) to (d) as the pressure ratio drops from 0.98 to 0.2. No pattern (a) and (b) found. For example, when the opening ratio is 10.6%, pressure ratio between 0.98 and 0.51 is the pattern (c) region; between 0.51 and 0.28 is pattern ((1) region and then becomes pattern (e) region. Similar experiment has been done by Araki et al, their visualized flow pattern shows the two critical pressure ratio are about 0.46 and 0.25 instead of our result of 0.51 and 0.28, we can say that somehow our CFD results are confirmed. The region of pattern (c) decreases as pressure opening increasing. O. 55 T I I T I l f Asymmetry Ratio 0 O 8 e 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pdpm) —-- h/D=6.5°/o + WD=10.6°/o + WD=14.7°/o + h/D=19.0% —9— ND=23.0°/o + ND=27.2°/o Fig. 4.3 Variation of asymmetry ratio When opening ratio is more than 20%, which is the region not shown in the former research, the flow pattern changes in the sequence of pattern (a), (b), (c), (d) and (e). Not 95 as dominant as in small opening, the pattem (c) occurs at the pressure ratio of about 0.8. Before pattern (0), it is the region of Pattern (b), which is very narrow. Large pressure ratio is the region of pattern (a). Pattern (d) is dominant pattern. It is not enough to just understand the visualized flow pattern, because even in the same pattern, the intensity is different. Thus two dimensionless parameters are defined to describe the asymmetry of flow pattern in a quantitative manner. Asymmetry ratio is defined as the arc length between center of downstream separation area and left end along the valve surface over the plug arc length. The center position is defined as the lowest average Mach number plane normal to plug surface. This means how far the attaching flow reaches. When the ratio is 0, it means the right side flow attaches all the way along plug surface while 0.5 means perfect symmetric flow pattern. As shown in Fig. 4.3, the asymmetry ratio changes with the pressure ratio in a similar manner at different valve openings. At fixed opening, as pressure ratio decreasing, the center meet point moves further and further to left until it reaches some point, then it starts to retreat and flow becomes more and more symmetric. At same pressure-ratio, the flow is more symmetric at larger valve opening. The peak point occurs at higher and higher pressure ratio as valve opening larger and larger. At small opening and small pressure ratio situation, the asymmetry ratio has large oscillation. This is because at down stream there are big vortexes, which affect the accuracy of the asymmetry ratio. To show the flow pattern in another way, the average velocity ratio between tangential component and overall velocity is defined to capture the speed angle at the center plane normal to plug surface. The more the tangential velocity ratio is, somehow means the more asymmetric the flow pattern is. It means that flow fully attaching the center point 96 of plug without any departure velocity component when the ratio is l, and 0 means no attachment at the center point. The asymmetry trend in Fi g. 4.4 confirms the trend in Fig 4.3. 1.1 . . O.9+---~ ---——'- ..... : ....... 7’ 07 0.5“ ----- *1-—~r——__ 0.3 -- —————————————— ----- 2 --------- .» 44 ' : - -0.1 . t t r t 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratlo(P;/Po1) -— h/D=6.5°/o + h/D=10.6% + h/D=14.7% —)(- h/D=19.0% —a— h/D=23.0% —o— h/D=27.2% Velocity Ratio Fig. 4.4 Variation of average velocity ratio at center plane To understand why the flow pattern phenomena happen, the passage of valve at each side is considered as a converging diverging nozzle. As the curvature of seat side is sharper and over diffuses the flow, the adverse pressure gradient is larger than plug side, which turns slowly. Thus separation is easier to happen in the seat side. At large pressure ratio, when the flow does not have enough momentum to form free jet, the separation in the seat side pushes it attaching to the plug surface. Because in the opposite side, flow has the same trend to attach to the plug, They fight each other for attaching to the plug. As the result, one side, for some reason has more momentum, pushes the other side flow attaching to the seat to reach a relative stable state. As a result, flow pattern (c) happens. At same opening, as pressure ratio keeps decreasing, both sides of flow have more momentum to become more straight instead of bending attachment, pattern ((1) happens. 97 Finally both of them become symmetric free jets meeting at the center point, which form the pattern (e). This is how flow pattern changes at small openings. At large opening, the converging part of flow passage becomes shorter. Guided by upper side of plug surface, the flow has more vertical velocity component. The flow has more momentum to overcome the separation in seat side while the adverse pressure in plug side is larger. So flow of both sides attaches to the seat forming pattern (a). As pressure ratio decreases, flow departures from the seat side to form pattern (b). As pattern (b) developing further, two jets meet at down stream of seat. Commonly two meeting flow are not stable. Even the flow become more and more straight, they still do not have enough momentum to become free jets. So a more stable pattern (c) happens. After that, as pressure ratio decreases more, same story happens as small opening situation. The flow patterns change from (c) to (d) and (e). 4.2.2 Mass flow rate and total pressure ratio 1.1 . . . T . e 1.0 2 ' ' . : : : E 0.9 -~-—-—h/D=6.5% r ----- : ----- 1 ----- g 08 —- +WD=10.6°/o i- ————— i ————— 4' ----- 4 s E 07 __+h/D=14.7%!_ _____ i ______ I _______ _, in ' i i 1 i 8 06 __ +ND=19.0°/o :L _____ i _____ _,: _____ 1: _______ J E +WD=23.0°/o I j i : 0'5 I _._ h/D=27.2°/o F ””” E ””” i:- """"" ' 0.4 I i l I i : : 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pg/P01) Fig. 4.5 Mass flow rate 98 0-51 f v f f I T 0.50 ' . 3 0.49 —~ ------ ————— : - a —-—h/D=6.5°/o E : . . a; 0-48 ‘i+h/o=1o.6%i"’”§ “““ " “““ u—‘z 0-47i"+h/D=14.7%;‘ “““ j ““““ ' """ 3 0.46 i“-—x—h/D=19.0°A>i ---- E ''''' i- ----- E g 0-45~~+ivo=23.0°/o;*“-"i"-"i""i ----- 5 ----- 0.44 -I + h/D=27.2%‘ ----- 1 ----- f ----- g ----- g ------ 0.43 I i i 'r i i i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pa/Pm) Fig. 4.6 Mass flow rate ratio between left side and overall 1.0 I I j 0.9 8 0.8 — 1 ‘ -' «in; 0.7 — . ’2 +h/D=1o.6% 5 g 3': J +wo=14.7% , g 9:0:4 + —x—h/D=19.0°/o‘ 5 O 3 __________ l _____ +h/D=23.0°/o ‘ '2 0.2 . 4 l .+ VD=2.7'2% 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio(P2/Po1) Fig. 4.7 Total pressure ratio 99 .3-” ..... T-_.--u--_.-+ 11....HILI rrrrr h \....\i..\...rir”irri _ u u ._ u u u “ T+ .1 m..- H _ u _ e m .n _ _ _ _ anus .9 _ ii.-- 11...-.l h .n hi _ _ _ m s_ m u . e” s 1.-- P M P Mr ...+ + _ L- -- -._ T+-..--T+ . . D M u u n u _ a I 5 ”til. I _ 09.876.54.3210. 10000000000 395:2 nos—z new 5%.. 35 40 45 50 15 20 25 30 0 1 5 Passage(%) a. Pressure & Mach distribution for Pattern (a) h/D=10.6% P2/P01=0.2 H i . _ llllllllll .rlllLIlllril l..l .---R .......... .1 T fl mg ||||||| b m .0 fl _ g _ .B h .n h r _ C _ c i S a S a P M P M . . . x L L . 0. 5 0. 5. 5. 0. 3 2 2 1 O O hon—E32 nous. 0:5 Satan 25 30 35 40 45 50 5 10 15 20 Passage(%) 0 b. Pressure & Mach distribution for Pattern (e) h/D=23.0% P2/P01=0.9 100 PsIP01 Z """"""""""""""" . 5 ...................... a _left 9 . i 5 0-1 “t —~—Mach_left —o—Mach_right 0.0 ; . + ; ; . ; 1 '. o 5 10 15 20 25 so 35 4o 45 50 Passage(%) c. Pressure & Mach distribution for Pattern (b) Subsonic h/D=10.6%, P2/P01=0.9 —.— Ps_left + thhJeft r i — Ps_right —~— Mach_right a..- -——¢- Ps/P01 and Mach Number 0 5101520253035404550 Passage(%) d. Pressure & Mach distribution for Pattern (c) Supersonic h/D=10.6%, P2/Pm=0.6 Fig. 4.8 Pressure and Mach number distribution Fig. 4.5 shows how mass flow rate changes with the pressure ratio at different valve opening. Because the valve exit area is much larger than valve throat area, the flow can 101 be choked at large pressure ratio. Mass flow rate passing the left side valve passage over overall mass flow rate is defined as mass flow ratio. As shown in Fig. 4.6, at large Opening, they are symmetric. While at less opening and large pressure ratio, the mass flow rate at right side, which flow attaches to the plug, is more than the side, which flow attaches to the seat. This is either the reason or the result of asymmetric flow pattern. Less mass means less momentum in this side. So the flow retreats to attach to the seat in the battling with the other side, which attaches to the plug. This also can explain why the flow at large valve opening is choked at larger pressure ratio than small openings in Fig. 4.5, because for symmetric inlet mass flow rate, two passages choke at same time, while for asymmetric situation, one chokes after another. Total pressure ratio changing with the pressure ratio and opening is shown in Fig. 4.7. It drops as pressure ratio decreasing. Normally, at same pressure, at larger opening, total pressure ratio is larger, which means total pressure loss is less. There is no big difference at large pressure ratio. 4.2.3 Pressure along the valve surface Corresponding to flow pattern, there are symmetric or asymmetric pressure patterns as shown in Fig. 4.2. The pressure ratio and Mach number along the plug surface are shown in Fig. 4.8 for pattern (a), (c) and (d). l of x—axis means value in left or right end (i=1), while, 50 means data gotten from the center of plug (i=75). The Mach number is obtained at j=25 (i=1 is plug surface, j=50 is seat curve and interface between center block and seat block) to capture the main flow situation. Except d. in Fig. 10, which shows the Pattern bin supersonic flow situation, all other plots are identical cases with corresponding plots in Fig. 4.2. 102 For symmetric pattern (a) and (e), the pressure and Mach number distribution are symmetric also as shown in a. and b. in Fig. 4.8. Pressure drops and Mach number increases. The sudden flat pressure line in converging part is due to separation. For Mach number, because it is not following the flow direction after throat, it does not capture the shock wave accurately in supersonic flow situation. But it captures the vortex phenomena. The minimum Mach number captures the center of vortexes in both sides. The pressure and Mach number is asymmetric when flow pattern is asymmetric. For pattern (c) at large pressure ratio, flow is subsonic. As the mass flow rate of flow attaching side is larger than the other side, the Mach number is larger and pressure is less. Because the separation happens much earlier in left side and no separation happens in attaching side, there is a pressure jump in left side. For supersonic flow, before throat, every thing is symmetric. After throat, pressure is recovering in both sides. Because separation happens earlier, the pressure jumps earlier in left side. 0.7 . . . . , . 0 6 —-—h/D=6.5% +h/D=10.6% -- ----- ° +h/D=14.7% +h/D=19.0% ; . 0-5 - +h/D=23.0% —o—h/D.-.27.2% '. ‘ 0.4— ————— ----- 5- a ----- I» ............ m I I l l E. 0.3- ------ ----- ' ..... ; ----_T _____ a I ' ‘ : : : 0.2 F """"""""" r ‘ i . ----- r-——--" ————— T _____ 0.1» ..... 5 ...... 3 _____ 0.0 """E’ """"" ‘1' ~~~~ i—~----E ----- i‘ ..... -001 | l i 1 T: I l l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pa/P01) Fig. 4.9 Vertical force on plug 103 4.2.4 Forces and moment caused by fluid In highly turbulence flow, there are many mechanisms that can cause unsteady forces and moment, such as pressure oscillation and instability of separation or even plug asymmetry with seat by manufacturing error. All of these make it almost impossible to predict forces acting on valve. But it is very important to understand the steady forces and moment acting on plug, which can help to understand fluid structure interaction mechanism. The dimensionless drag is shown in Fig. 4.9. Drag increases as pressure ratio increases. The curves are almost linear at small valve opening or after choke at large valve opening. This trend agrees with the theory analysis in Chapter 2. At different opening under same pressure ratio, the drag is less at large opening after flow is choked. The equation cannot predict this changing, but according to some data from industry, this is true. Dimensionless lateral force and moment caused by drag are shown in Fig. 4.10 and Fig. 4.11 respectively. They are defined as same way as dimensionless vertical force, for lift, substituting drag with lift and for moment, with moment over plug radius in numerator. Essentially, they are caused by the asymmetric pressure distribution along plug surface. They have same trend and almost similar amplitude, which can be proved analytically by integrating along the plug surface. The positive value means that for moment the direction is clockwise, while the lateral force points to right. At fixed valve opening, as pressure decreasing, the lift and force increases until reaching a peak value then decreases. At same pressure ratio, as valve moving toward the seat from wide opening, the moment and force increases until reaching peach point at about 11% of 104 opening ratio, then started decreasing. Even they are not simulated, for maximum opening and fully closed situation, this becomes fluid static problem, both moment and force become 0. 3.5 . . I A 3.0 'I --------------- I ---------- E: 2.5 - ----- ' --------- f g 2.0 ~ -------------- I u_ 1.5 -. ————— ' ----- i E 1.0 - -------------------- f; 0.5 —- ------------ 0.0 -0.5 . . r r r . . . 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (P2/Po1) -—— h/D=6.5°/o + h/D=10.6%+ h/D=14.7% —x— h/D=19.0°/o —a— h/D=23.0%—o— h/D=27.2% Fig. 4.10 Variation lateral force 3.5 . l I | l _—-b-— l | | l .1-— l l l I I 1—-——r l l I l l l l l l l J— _P_ l l _1__1__ Moment(%) 9.0.4.4101“? 0010010010 [11111 ‘0.5 I I I I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio(P2lPo1) —— h/D=6.5% + h/D=10.6% + h/D=14.7% -X- h/D=19.0% —B— h/D=23.0°/o -0— h/D=27.2% Fig. 4.11 Moment caused by vertical force 105 + VIs_Dr(10.6%) + \fis__Lr(10.6°/o) _ + \fis_Mor(10.6%) —a— VIs_Dr(27.2°/o) I I I I .__|._H-_.1,_A_, I I I I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Presure Ratio (Pg/P01) Fig. 4.12 Ratio of viscous to total forces and moment With the fact the amplitude of dimensionless lift and moment are about the same, the equation (3) can be simplified to Mo 2 L 0(1, — 1) with the counterclockwise direction. lr is the ratio between stem length and plug radius. Normally lr is much bigger than 1, which means the lift defined the amplitude of total moment and the direction. The forces and moment mentioned above are total forces and moment including both friction and pressure difference. Fig. 4.12 shows that the viscous force and moment is only a little fraction. At small pressure ratio, the viscous lift accounts a little bit more. For example, at 10.6% opening, the viscous lift ratio is about quarter of total lift. This is because the total force is very small at small pressure ratio. 106 Understandingfluid mechanism at steady state All parameters we mentioned above are shown in Fig. 4.12 for 10.6% opening situation. The dimensionless lift and moment are 1/3 of their original value to show other curves clearly. Average Mach number is obtained at the same plane of the average tangential velocity component ratio obtained. + D + L/3(%) + Mo/3(%) —x— M —— Ur —9— Mass l —o— Ptr +Asyrn —)K— Vis_Dr -—I-—Vis_Lr 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 _Vis_Mo, Pressure Ratio (Pale) + Mach I l I I __I p '1 n ( |_. _.-‘_ I I I I A_ _I_- -L- Fig. 4.13 Variation of parameters at different ratio at fixed opening of 10.6% As shown in Fig.4.2 and 4.8, there is huge pressure distribution between two sides in Pattern (c) comparing with others. Pattern (b) and (d) are less asymmetric, while pattern (a) and (e) are very symmetric. By comparing the lift and moment amplitude in Fig. 4.13, it is very clear that it is the flow asymmetry that makes the pressure distribution along the vale surface asymmetric and finally causes big amplitude lift and moment. This is confirmed by Fig. 4.13 in a more qualitative way. Two key parameters determine the lift and moment amplitude, flow asymmetry and pressure difference. The Mach number represents the pressure difference, because according to thermodynamics compressible 107 flow theory and Fig. 4.8, at same inlet pressure, pressure decreases as Mach number increasing. That means with Mach number increasing, the average pressure in the plug attachment side decreases, and more pressure difference occurs between two sides. Also another important factor, asymmetry ratio, means how much difference of acting area of two sides of the flow. The more the ratio is, the bigger the area difference is. The force is pressure times area, so some how, the trend of lift and moment changing is defined by Mach number timing asymmetry ratio as shown in Fig 4.13. In high pressure ratio, the asymmetry ratio decreases a little bit, while Mach number increase quickly. This causes the steep slope of lift and moment as pressure ratio is higher than 0.9. Then asymmetric ratio starts to decrease, while Mach number increase slowly, the lift increasing speed slows down until reaches the peak value in between the pressure ratio of highest Mach number and Lowest asymmetry ratio. Then it drOps quickly as Mach number drops and flow becomes more symmetric. 4.2.5 Fluid structure interaction mechanism It is far from enough to only understand the steady state flow mechanism. In reality, plug vibrates driven by the forces and moment, which affect the fluid forces also. To understand the interaction mechanism, displacement is added in both vertical and lateral directions on valve plug. Interestingly for subsonic flow, symmetric geometry causes asymmetric flow while asymmetric geometry causes symmetric flow. When the plug moves from its balanced position, the flow pattern changes from (c) to (a) immediately and keeps the pattern. This means that in large pressure ratio, the asymmetric flow pattern does not have strong stability, it always has tendency to become symmetric. For sonic or supersonic flow, the 108 flow pattern (c) is very stable. There is no result showing that it changes pattern due to geometry asymmetry. .- ———.-——‘ p--_—-—-<-—— ._..._ _..__._._. _-_ ....... Forces and Moment(%) L r'o o N A a) + L Pr=0. + Mo(Pr=0, :_ _ _ _' _ + L Pr=0.9 + Mo Pr=0.9 I r +d (Pr=0.7) —e—dD( r=0.9) : : -6 I I I I I I I I If -2.5 -2.0 -1.5 -1.0 -O.5 0.0 0.5 1.0 1.5 2.0 2.5 Lateral displacement (%) Fig. 4.14 Forces and moment changing due to lateral displacement on plug By looking at the forces and moment change due to plug displacement, it is clear that the plug lateral vibration is due to hydraulic forces and it also affects the vertical force, which can cause or strengthen the vertical vibration. The data in Fig. 4.14 are obtained when opening ratio is 10.6%. Driven by lift, the plug moves to positive direction, then the excitation amplitude drops. It reaches some maximum displacement position, forced by the combination of stem bending force and dropping hydraulic force. Then it moves back. It reaches some point in other side, and come back again. This is a typical self-excited vibration mechanism. For subsonic flow, the excitation looks like a part of sin wave, while for supersonic flow is linear by simple assuming that pIUg vibrates within in —O.5% to +05%. The vibration center point is defined as x=0 pOint. Then the excitation for supersonic flow can be expressed as y=kx, while subsonic 109 =ksinx. By assuming, the vibration is perfect harmonically, x=sint, then the two excitation basically can be expressed in time, as part of sin wave as shown in Fig. 4.15. By using Fourier series, the periodic excitation can be expressed as infinite series of sin or cos wave. If there is a frequency matches the plug natural frequency, resonance happens, which can cause huge amplitude lateral vibration. .9. I: o I c: .2 =3 ‘5 m 3:: 3 .2 LL] I: o (I) .o :r U) t Fig. 4.15 Excitation under lateral vibration Opr=0.59 j 4 Fig. 4.16 Self-excitation mechanism in vertical direction Plug lateral movement not only has effect on lateral excitation, but also has strong effect on vertical excitation when flow is subsonic as shown in Fig. 4.16 in the same way and at about same amplitude. That means the excitation can be expressed as same equation as lateral subsonic excitation. Also, resonance may occur. When flow is 110 supersonic, the lateral force has very little influence on drag. So in this way, the worst situation for the valve probably happens in large pressure ratio, when both lateral and vertical vibration resonate simultaneously. The vertical vibration can be analyzed by using the same way as lateral vibration. Fig.5.7 shows clearly how the vertical displacement affects the drag. At pressure ratio about 0.8, there is little difference between the drag in different opening. As the pressure ratio departure to less, the difference becomes larger and larger due to different curve slopes. The smaller the opening is, the steeper the curve is. To explain it clearly, enlarged sketch is shown in Fi g. 4.16. For example, if at balanced position opening ratio is 0.6, when the plug moves toward larger openings, such as 0.59, instead of reduce the value, the vertical force becomes bigger, pushes the plug further until stern spring force push it back. When the plug moves to small opening, as drag drops, same thing happens. In reality it is even worse because the pressure ratio changes with opening. 80 instead of oscillation in the cycle of 1-0—2, the drag oscillates within bigger cycle of 2-0—4. This is typical self-excitation mechanism. For pressure ratio larger than 0.8, reverse process happens which means it is impossible to form the self—excitation mechanism. In reality, the valve is operated either at large pressure ratio with large opening or small pressure ratio with small opening. So, based on above analysis, the self-excited vibration can only happens in small opening situation, which is confirmed by former Soviet Union researchers. The vertical force has strong influence on plug lateral vibration in the blank area b6tween two nearest lines in Fig 4.16. For example, if the plug vibrates between the Opening ratio 6.5% and 10.6%. At pressure ratio of 0.4, the lift changes from 0 to 2.5. Of 111 course, no plug can vibrates with such large amplitude in reality. This example is just to show how the lift changes. The influence of pressure ratio changing due to vertical vibration make the problem more complicated Opening Ratio(%) 0.4 0.6 0.7 0.9 Opening Ratio Fig. 4.17 Sketch of valve safe operation area Based on all above analysis, all areas may cause problem are superposed in following Fig. 4.17. In the darker area, possibility that the valve has serious problem is less. It is hard to accept such a narrow safe operation area. So the design should be improved to reduce lateral and vertical vibration excitation mechanism. 4.3 Analysis on improving design Reducing the lift and moment acting on valve at balanced position is very important to reduce vibration, because they are the driven excitation of valve vibration. The key to improve design, in terms of reduce lateral force and moment, is making the flow pattern Symmetric. As we analysis before, the asymmetric flow attachment on plug side is one important cause of flow asymmetry. Also, we know that the longer the flow attach the 112 plug side, more possible that it cause unbalanced force. 80 the main idea to improve the valve design is to make the flow attach the seat side and separates earlier in plug side 4.3.1 Possible improved designs rI , / a. , e f/ f I, ‘x / .\ ,. ‘\ \lre/ ///_, '\ Fig. 4.18 Flat cut design As we know that stall happens in a position where the wall curvature changes sharply, a simple improved design came out by cutting center part of plug at the angle 0 shown in Fig. 4.18. To show the influence of cut angle on lateral force clearly, the value in Fi g. 4.1% is the absolute ratio of lateral force for cutting edge valve and maximum lateral force for original valve (Low). Similar with original design, lift changes with pressure ratio. But the range of pressure ratio with large amplitude of lateral force decreases as 0 increases. This is due to the decreasing of asymmetric flow pattern region and interaction area between plug and fluid. For original valve, asymmetric flow pattern occurs when pressure ratio is higher than 0.5. For 44.9° cutting design, only symmetric flow patterns can occur. In Fig. 4.1%, the absolute ratio of maximum lift and original valve maximum lift is plotted with different cut angle. From 0=0° to about 30°, the maximum lateral force (me) decreases slowly. From 0=30° to about 40°, lateral force decreased dramatically. After 40°, there is little force remaining, under such situation and only symmetric flow 113 patterns happen, pattern (a) at large pressure ratio and pattern (c) at small pressure ratio. This design is called flat cut. 1.0 e 3'; —e— 0 0° 2 o 3 —— +27.5° 5° +33.6° v 0 6 T" +37 5° § +38 2° I2 04 ““ +38 8° E 2 0.2 1 (U _l 0.0 '— 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pa/P01) a. Variation of lateral force with pressure ratio at different cut angle .0 .0 P r" h 0) (D O I 1 I L- __.L..__-_ 9 N I I I I I l I I l I | Maximum Lift (Lmax/Lomax) .O o __4__-_-I—-———|_.__-_ I r 20 Cut angle (0) O —-L O 00 O A O 50 b. Variation of maximum lateral force with cut angle Fig. 4.19 Variation of lateral force under different cut angle at 10.6% opening 114 I I ._-- L ——' . ‘ I I I I , l Y /--{M‘\--. b—J -. ’ e Het .. —— ”X :4: 6 —-- ——BW\ “It," ”i/ F“— _.l ‘\ ,. #— .‘l l \ I. I R0 , '. If I I ' R1 I I Ret Il I ' I I I I a. Arc cut 0. Dish bottom 0. Guiding Fig. 4.20 Three other improved designs 0.01 I . . . 3.? + Dishbottom 60° ' g 0.008 -.+Dishbottom45° I"“"I'" -'L ---; ...... g + Dishbottom 30° 5 5 5 3 7: 0.006 --—x—Ri/r=1ArcCut ------ 2 —9— Flat Cut I I E i .2 0.004 ----- I- ----- Tun-I" 1.-__;__-_-: ------ Eu : ' : : : : 0 _ I --_'-,__ I - -I --‘Mr _____ I_ - 4 ‘5 0.002 . ' . I I -| ' ' . I i 0 I I I I I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (P2’Po1) Fig. 4.21 Comparison of lateral force at Opr=10.6% for different designs Five other improved designs were simulated. The cut angle 0 is 45°. For are cut, Ri/r=1, for dish bottom, 8=60°, 45° and 30°, h/r--0.15. The lateral force ratio of between improved designs and maximum value of original design (Lomax) is shown in Fig. 4.21 for different designs. Both are cut and dish bottom design are better than flat cut. For are cut, when Ri/r is 1, the lateral force reduced to half of flat out design (Ri/r=oo). In this way, reduce Ri can further reduce lateral force. For dish bottom design, the lateral force decreases as 8 increases. From 5=30° to 45°, the lateral force has a big decrease, after 115 45°, there is no big dr0p in lateral force. For example, when 8=60°, the maximum lateral force reduced to about 1/5 of flat cut design. Plug comer angle y is defined as the angle between tangential direction of plug side profile with cutting edge as shown in Fig. 4.20. In this case, the comer angle is reduced in this way, flat cut, dish bottom 30°, are cut (which is 45°) or dish bottom 45° and 60°. This is just the way that lateral force reduces. So in our view, making the comer angle sharper is an efficient way to reduce lateral force at constant cut angle. The dish bottom design is better than are cut design if the comer angle is same. Compared with above improved designs, the guiding design as shown in Fig. 4.200 is more “active”. The curvature of plug not only can cause separation happen in plug side by the sharp corner, but also can guide flow attaching the seat side. Thus lateral force and moment can be reduced. It basically is welding an extended part on the flat cut plug. Four parameters defined the plug curvature, cutting angle 0, extending height ratio Het/r, extending radius ratio Ret/r and the extending radius Rc. Because of so many parameters, two of them are fixed, the cutting angle 0=45°, and the extending radius Rc equals the seat side cure radius. Under opening ratio of 10.6%, two different combinations, Ilet/r=0.65+Ret/r=0.68 and Ilet/r=0.75+Rct/r=0.59, are tested and result is shown in Fig. 4.22. To show all the curves clearly, the value of second combination is 1/6 of actual value. Compared with original design, both designs can reduce the lateral dramatically. The peak lateral force, such as under pressure ratio of 0.7 is caused by asymmetric separation after the flat cut part. Separation is sensitive to extension curvature. For example, the peak value of second combination is 15% of original design but is about 13 times of first combination. A well guided design, such as the first combination, can 116 reduce the force to the same level of flat cut design or maybe even better. More simulations need to be done to optimize guide valve design due to so many parameters defining the curvature. According to above discussion about improved designs, the flat cut and dish bottom designs are preferred because they can reduce excitations dramatically and also easier to be manufactured than the guiding design. 0.025 I I a + Dishbottom 60° :55 0.02 —~ +Flat Cut 0 +0.65*0.68 i 0.015 I» +0.75*0.59(L/6) § .2 0.01 — ——————————————— - ----- — To 3 3 0.005 - 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio Fig. 4.22 Comparison between improved designs at 10.6% opening 4.3.2 Other tested designs As shown in Fig. 4.23, four other designs were also simulated. The plug radius was increased two times to be design (a), one half time and being cut to be design (c). A semisphere was welded on the flat out is design (b). Design ((1) is a simple guiding design. The CFD results under 10.6% opening are shown in Fig. 4.23. All designs are better than original valve in terms of lateral force, especially at large pressure ratio. But 117 still dish bottom (60°) design is better than them at large pressure ratio as shown in Fig. 4.24. i B I . I . I 2.5 I r —o—-a ; ; I —l—b I 2 ~ J, ------------- +0 I —x—d I‘ 1-5 ‘” —o—original “““““““ fl ___--.J.. .4 I .0 01 l Absolute Lateral Force(%) -___L...__.._ 0.2 0.4 0.6 0.8 1 Pressure Ratio (P2/Po1) Fig. 4.24 Comparison with original design at 10.6% opening 118 4.3.3 Discuss on an improved design a. Pattern (a) for improved design b. Pattern (c) for improved design Fig. 4.25 Flow patterns for improved valve design Based on above analysis, the dish bottom 60° is a simple and good design. So the detail CFD results are discussed here. Only Pattern (a) and (d) happens for the new design as shown in Fig. 4.25. Under same opening, flow pattern changes from (a) to (d) at almost same pressure ratio as old design changing from pattern (c) to (d). Due to this reason, the lifi and moment are reduced dramatically as shown in Fig. 4.26a. The drag of new design is almost same as old one as shown in Fig. 4.26b. To compare the difference 119 of them, the drag value at opening ratio of 14.7% is doubled for both old and new design. Even though there is no big difference found. Viscous effect is only a very small portion as same way as for the old design. ,_..__.,. _~_.___ Lift and Moment(%) : -O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pg/P01) —o— L(New_10.6°/o) —a— Mo(New_10.6%) + L(New_14.7%) —x— Mo(New_14.7°/o) + L(O|d_10.6%) + Mo(OId_10.6°/o) + L(Old_14.7%) —— Mo(Old__1 4. 7%) a. Lift and moment 1.3 I f f + New_10.6°/o) —o— Old_10.6% 0-9 ‘” + 2*New_14.7% " ‘ ‘5 “““ 1.1 4- ).___.-___.- _.——__ _..___.—_ ———_——_4 q——-4—-—4———« g: 0.7 + +2*O|d_14.7% ------------------------ D 0.5 4 ................. 0.3~ ------------------------------------------- 0.1 _ ----- . -: ------ ----------- : ————— -01 . . i i i I. . i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pg/P01) b. Drag Fig. 4.26 Comparison of lift and moment between old and improved design 120 Because at the plug balanced position, the lift and moment is very small, the bending moment, which pushes the plug to one side, is eliminated. To understand the fluid structure mechanism, plug lateral displacement is added as same way of the old design under same opening and pressure ratio, Opr=10.6%, Pr=0.9. As shown in Fig. 4.27, the lateral displacement has no influence on vertical force. This eliminates the vertical vibration excitation due to lateral vibration for old design. For lateral force and moment due to vertical force, symmetric result around 0 obtained as the valve moves from one side to the other side. The moment has linear relation with lateral displacement similar to the supersonic result of the old design. Amplitude of lift changing is much less than the old design and only occurs at near center point region. At same 0.46% displacement, lateral force and moment caused by drag changes very little, while drag changes linearly. So that means the excitation due to pressure oscillation (vertical vibration) is limited. When for some reason, such as pressure disturbance of upstream, the plug starts move to positive displacement position. The lift becomes positive and increasing. The moment becomes clock wise and increases in amplitude. Both combines together to push the valve moving further. This is a typical self-excitation mechanism, which is not found for the old design at same situation. For two reasons, it is still believed a much better design than the old one, first, the self-excitation is not strong as the amplitude of lift is very small; second, at the valve balanced position, there is no steady bending moment to cause the valve displacement. Because the drag changing with openings remains same, the self-excitation mechanism still exits for new designs at small pressure ratio. But as shown in Fig 4.28, the difference of the lift and moment at different opening is much less than old design at 121 any region. So it eliminates the lateral excitation due to vertical vibration. Based on above analysis, the new design is better than current design in terms of forces, moment and fluid structure interaction. 2.5 a E 1.5 ~- ————————— ‘5'. E 0.5 w‘ I ‘3- o I 2 . u 415 -'--'~ ---------- —————————————— c I . a . . E -1.5 ~ ————————————— f ------------- l ------------- _| . I -2.5 l L -1.5 -0.5 0.5 1.5 Lateral Displacement(%) Fig. 4.27 The forces and moment changing due to lateral displacement 0.6 0.4 1 0.2 — 0.0 J -0.2 4 -O.4 * . -0.6 ~ -- -0.8 i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pg/P01) Forces and Moment — -_ _._ —1.-—— .... ...__ —-4 ..-... Fig. 4.28 The forces and moment changing at 10.6% opening 122 CHAPTER 5 3-D CFD ANALYSIS 5.1 Numerical Modeling CFD is used to get the steady state flow field, forces and moment at balanced position of the plug for 3-D flow following the similar process as 2-D CFD analysis. Calculations were performed using TASCFLOW. CFX-BUILD was used to generate the grids. For convenience to build grid, the coordinate is moved from position shown in Fig. 2.5 in the -z direction to a position where x-y and seat throat are in same plane. According to 2-D analysis, up stream air chest has little effect on simulation results, as long as symmetric boundary conditions are used. To save time and be more general, chest is not simulated. Totally 290,124 nodes, whole grid composes four blocks as shown in Fig. 5.1, z>0, outside ring-shape block (i=41,j=81,k=31), center box-shape block (i=21,j=3l,k=21); at z<0, seat ring-shape block (i=81,j=81,k=21), center box shape block (i=21,j=81,k=21). Because simulations were done for different valve openings, the throat grid (z>0) size changes to make grid density about the same. Grid density around the plug is much greater because this is the most concerned area. The flow is treated as steady state, compressible, turbulent ideal gas with high speed. For inlet boundary condition, constant total pressure and total temperature are imposed. The wall (Fig.5.l b) is treated adiabatic smooth surface. Constant static pressure is used at valve exit. All cases were converged to maximum residence in the order of 103. The y+ value of the valve plug surround region is about 400. Similar grid is used for improved valve design simulations. 123 a. Grid blocks 1). Valve inna' surface 0. Cross secli on grid Fig. 5.1 Computational grid 5.2 Flow Patterns According the simulation result, three flow patterns happen. At large opening (h/D>20%), due to large volume flow rate, the valve is full of flow. A little region of separation happens at plug center. Separation may happen in down stream seat side near exit, which has very little effect on the plug. This pattern can be considered as large mass flow rate pattern (a) or (e). For convenience, it is called pattern (e) as shown in Fig. 5.2. When opening ratio is less than 20%, at large pressure ratio, flow passes through the valve asymmetrically as shown in Fig. 5.3. As shown in x=0 and y=0 cross-section velocity field, stall happens earlier in left side (+x and +y direction) of plug and right side (-x and —y direction) of seat. At z/r:0 plane, secondary flow happens. Two vortexes are symmetric about +45° line counting form +x with displacement from seat center line. Velocity field at z/m-l plane clearly shows that flow attaches the quarter phase of +x to +y seat and separates from other part. This is a typical 3-D pattern (0) flow. Pressure field is plotted in both fringe and contour forms. After the valve throat, the average pressure on 124 +x+y phase of plug is bigger than on opposite part. This finally can cause force, moment and torque acting on plug. if?" 17.x " i" ““4 ,7" \b‘ "‘ 1" a” " v. 1 :3; " ,‘,‘..‘"’ , )4' tr ' xtffi. ~~- ’ - 2 z *5, .3 l " 3' L f i II 5‘ : xéo plane y=0 plane Fig. 5.2 3-D flow pattern (e) at pressure ratio of 0.9 and 23.1% opening l if, 11 .‘\ "V- - i‘~ .. .4 7 t»... 4 w . .. -, L ""1 p,.__.,. . . / " 1 1‘ { , l‘ l l l x=0 plane y=0 plane z/'r=>(>)7plane z/r=~l plane a. Velocity Field ,, 1 t... 3.. ; f ‘ ‘ I 7i l l ‘ L I ‘ \,| l l ‘=. f l l g l l ; I .l \ l l f [I \I. i ‘l l l‘ I i i y=0 plane ....i Z/F0.25 plane z/r=0 plane b. Pressure field Fig. 5.3 3—D flow pattern (c) at pressure ratio of 0.9 and 10.6% opening As pressure ratio decreasing, the flow pattern changes form (c) to (e). As shown in Fig 5.4, free jet flow pattern (6) is almost symmetric around axis 2. Secondary flow happens 125 in the center of z/r=0 plane. Main flow is at the center and separates from seat as shown in z/r=-1 plane. The pressure distribution around plug is also quite z-axis symmetric. The trend that flow changes form pattern (a) to (e) agrees with 2-D result under small opening situation. Pattern (a) is not found in 3-D simulation results. i ' ‘; l ‘ 1 ‘ I i i ‘ )F—‘O plane ‘ z/rIO plane z/ri-lg plane 3. Velocity Field z/r=0.25 plane z/r=0 plane A b. Pressure field Fig. 5.4 3-D flow pattern (e) at pressure ratio of 0.5 and 10.6% opening 5-3 Force, Torque and Moment . . D The percentage of d1mensronless drag, D = ' Dirt) 2 , is shown in Fig. 5.5. Dt is the absolute drag; P01 is the inlet total pressure; r0 is the radius of the plug. Because the grids do not include upstream plug surface, the drag here means vertical force acted by the 126 passing fluid. Drag increases as pressure ratio increases, which agrees with 2-D result. The drag difference between different opening ratios is larger at smaller pressure ratio. At about pressure ratio about 0.9, drag at different opening has the least difference. It is observed that the peak unbalanced lateral force, moment and torque occur under such pressure ratio. In 2-D simulation result, drag has least difference at pressure ratio of about 0.8. Under such situation, peak lateral force and moment also occur, especially for big opening situation. This may because the flow is about to be sonic under such pressure ratio. This is confirmed by the calculation results of mass flow rate variation with pressure ratio both in 2-D and 3-D situation. 90 -—-———q ————-1 .._——_l___—.—_—1 LI, I l I I l | 7|? I l I I l I I I + h/D=6.5% + h/D=10.6°/o + h/D=14.7°/o I I I .l I I l I I I r ...,I__‘____l__‘ _ I l I l I l .—4)—-.——— 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pg/P01) Fig. 5.5 Drag variation with pressure ratio Under pressure ratio of 0.9, plug opening affects drag value as shown in Fig. 5.6. From almost closed situation, drag decreases until opening reaches about 10%, then starts increasing. This trend agrees with the experiment result of Schuder and Moussa’s unpublished computation data. According to some failure report, this is also the opening 127 when valve failure frequently occurs. In Schuder’s paper, large drag oscillation at this turning point was found. We suspect that some properties in this turning point cause large drag oscillation, which finally may cause large amplitude vertical vibration. 90 .' . T 88 - :r ~ g ------- g ------------------- e 86- ——————————— 2— ———————— ;. ————————— i ———————— . —————————— g? I I I i 5 84 ‘ """""" g """""" { ““““““ g “““““ g """"""" 32 - —————————— . ----------- jr --------- ' ---------- g ---------- 80 i I i 'f 0 5 1O 15 20 25 Opening Ratio (th°/o) Fig. 5.6 Drag variation with valve opening changing Pr=0.9 L Dimensionless lateral force, L: ‘ 2 , and moment, M 0 =-fl3—, are defined orro ‘ 7‘? 01"0 similar with dimensionless drag. Lt is the absolute lateral force and Mot is the absolute moment caused by drag. Torque is caused by lateral force around plug center, non- Tu 3 . Oer dimensionlized as TL = Tu means total torque acting on plug. Absolute values of dimensionless lift, moment and torque at three openings and different pressure ratios are plotted in Fig. 5.7. Lateral force and moment have similar variation trend with pressure ratio changing at one fixed opening. At small opening situation, only one peak occurs at pressure ratio of about 0.9. As opening becomes larger, another peak starts to occur at small pressure ratio region. This peak has less amplitude and moves toward the 0.9 128 pressure ratio peak, which has maximum values, as opening increases. In 2-D large opening situation, the maximum values occur at pressure ration about 0.8. Torque is caused by friction. It is much less than lateral force and moment at large pressure ratio. 0.4 T I . +L(%) : 0-3 “"+Mo(%)*----f ------ . +TL(°/o) E 0.2 4 --------- : ——————— .i ....... ....... 0.1 7 ' 0 I: L ' ' 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pale) 3. Valve opening ratio h/D=6.S% 0.4 l P-—— - 4... _-—- 0.3 “‘+M0(°/o)H—__---L ______ . I l l l l I I l l l i I l I l I i I I I I —«.._-__ _1____—— 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pg/P01) b. Valve opening ratio h/D=10.6% 129 —-¢-—-|-—-1- -— --4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio(P2/Po1) c. Valve opening ratio h/D=14.7% I l +—-< I I I I c'» o 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pa/P01) d. Direction of lateral force Fig. 5.7 Absolute values of lift, moment and torque According to CFD result, lateral force and moment are always in one direction. The lateral force direction at different valve opening and pressure ratio is shown in Fig. 5.7d. It randomly point to an angle in the range of —60° to 80° counting from +x direction. Torque normally changes from clockwise to anticlockwise at pressure ratio between 0.5 and 0.7. 130 More results at pressure ratio of 0.9 and different openings are shown in Fig. 5.8. Force, moment and torque have similar trend. They increase dramatically from very small opening to 5% opening. Then it declines slowly. After 15% opening, it decrease quickly. At opening ratio between 5% and 15%, they remain high value, which may cause large amplitude vibration. In reality, due to big loss, it is uncommon to have a large pressure ratio of about 0.9 at small valve opening. This is the reason it is believed that the most dangerous opening is between 10% and 15%. Some valve failures under such openings were reported. From here we know that to avoid valve operating at the position and pressure ratio, which can cause peak value force and moments, is an important way to reduce the possibility of valve failure. 0.4 0.3 ~ 0.2 - 0.1 — Opening Ratio (hID%) Fig. 5.8 Maximum excitations at different opening when Pr=0.9 The forces and moment mentioned above are total force, moment and torque caused by both friction and pressure difference. Fig. 5.9 shows the ratio of viscous effect with total absolute values at 14.7% opening. Compared with pressure difference, viscous 131 effect is very small, maximum 2%. Due to the smaller absolute value, at small pressure ratio, the viscous effects account a little bit more than at high pressure ratio. These agree with 2-D simulation results. Torque ratio is not shown here because it is 100% caused by friction. 0.020 7 j g , g g + Vis_Lr 0,015 - ................. :L ..... 5---.+Vis_Mor_. E E + Vis_TLr 0.010— ...... - ..... ._ ————————————————————————— 0.005 -— -' ______________________ 0.000 t I i i r I i 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pg/P01) Fig. 5.9 Viscous effect at 14.7% opening 1.1 --w 1.0% 0.9 ‘ 0.8 : 0.7 — ------- . ------ E I _-'--I- ------ + Totalpressureratio — 0.6 - ------ ------ ’ “““ —-— Massflowrate(IWMmax) ‘ 0.5 ‘ : : : 1 : 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (P2’Po1) Fig. 5.10 Total pressure ratio and mass flow rate variation at 14.7% opening 132 Fig. 5.10 shows how mass flow rate and total pressure ratio change with the pressure ratio at 14.7% valve opening. Because the valve exit area is much larger than valve throat area, the flow can be choked at large pressure ratio of 0.9. Total pressure ratio drops as pressure ratio decreases. 5.4 3-D Simulation Results For Improved Designs Similar with 2-D analysis, three symmetric flow patterns are captured for dish bottom improved design (0:45°, 5=60° and l1/r=0.15). As shown in Fig. 5.1], pattern (a) happens in about same region of pressure ratio and opening for original design pattern (c). Accoring to velocity field in different view, after valve throat, stall happens in the plug side afier the sharp conner. In seat side, no stall happens and flow attaches to the circumferential seat wall. Both velocity field and pressure field are pretty z-axis symmetric. No secondary flow is captured at down stream. z/r:0 plane z/rI-l plane z’rZO plane b. Pressure field Fig. 5.1 1 Pattern (a) at Pr=0.9 and Opr=10.6% for dish bottom design At small pressure ratio, flow becomes free jet flow as shown in Fig. 5.12. Due to the curvature of plug, flow joins further downstream than pattern (0) in original valve design. The cross section pressure and velocity field is more symmetric than 2-D result For original desrgn flow pattern (e), secondary flow happens in z/r=0 plane while here no secondary flow is captured. 5.11 .» at. _. x20 plane y—0 plane z/r=0 plane z/r=-l plane a. Velocity field / A. ., / \ «7 . \ ~. 1 f I I. ll x20 plane flrIO plane b. Pressure field Fig. 5.12 Pattern (e) at Pr=0.5 and Opr=lO.6% for dish bottom design x=0 plane 9:0 plane z/r=0 plane a. Velocity field \ 1% fir? $2.._JI___7¥ I I I x=0 plane z/r=0 plane z/rI-I plane L/r’ b. Pressure field Fig. 5.13 Pattern (d) at Pr=0.5 and h/D=10.6% for dish bottom design There IS an intermediate flow pattern (d) occurs between pattern (c) and (e) as shown in Fig 5.13. It is also z-axis symmetric. In 2-D dish bottom and 3-D original design 134 simulations, this pattern is not captured. In this pattern, at down stream, the free jet shape is like a ring, not like the joined circular free jet in pattern (e). The velocity fields are plotted in Fig. 5.14 for flat cut design. Similar flow patterns occur in similar region as dish bottom design in most cases. But at small opening and pressure ratio, an asymmetric flow pattern (0’) happens as shown in Fig. 5.15. Strong secondary flow happens in z/r=0 plane. In dish bottom design under same situation, the flow is in pattern (e). For this reason, dish bottom is thought a better design than flat cut. f]; i ~. ‘1,“ _‘ €_ - A = : mom... L(10.6%) e i j TL(6. 5%) 5 1 5 5 Mo(6. 5%) W L(6.5%) L 1 _ : , ‘ 3 g : ' O 0.2 0.4 0.6 0.8 1 TL(10.6°/o) } I Dish bottom I Flat cut Mo(10.6°/o) ' El nial L(1 0.6%) TL(6.5°/o) M0(6.5°/o) L(6.5°/o) b. Lateral force, moment and torque at pressure ratio of 0.9 137 100 Pressure Ratio (Pg/P01) 0. Vertical Force 1. 1. o. o. o. o. o. o. censuses: 9:32“. .58 Pressure Ratio (Pg/P01). (1. Total pressure ratio at h/D=10.6% 138 1.1 L I ' . T . . g ‘ l '5 1.0 ~--- I ..... E ; ' E 0.9 “ ‘‘‘‘‘ f ----------------- .L ----- J. ......... E 0.3- —————— + ----------------- :~ ----- e ----- ; -- G i I i I h 0.7 "‘ “ """" f """""""""" l" """ 1 ------ I “““““ g +ongnal “5 °'6“--flat """ """ s """ é 0-5 ‘ ‘ +dish """ E“ “““ i """ J. """ : """ 0.4 t % i i i t 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pressure Ratio (Pg/P01) e. Mass flow rate at 0pm10.6% Fig. 5.17 Comparison between original and improved designs To compare the performance of original and improved designs, the absolute values of excitations, total pressure ratio and mass flow rate ratio are plotted in Fig. 5.17. It shows that the maximum excitation values at different pressure ratios for improved designs are much less than original design, except for flat out design maximum moment at 6.5%. Only at small pressure ratio, big amplitude of moment of flat out designs occurs, which is due to flow pattern (c’). The values at pressure ratio of 0.9 are plotted in Fig. 5.17b. It shows that at large pressure ratio, the improved designs are much better than original design in terms of reducing fluid induced excitations. The trends of drag changing with pressure ratio are similar as shown in Fig. 5.17c. Two improved designs have almost same amplitude of drag under same condition. At pressure ratio larger than 0.8, drag of original design is smaller. At pressure ration smaller than 0.8, it is a little bit larger than improved designs. 139 The total pressure ratio of original valve is larger than improved designs, especially at small pressure ratio. The ratio of mass flow rate and maximum mass flow rate of original design is shown in Fig. 5.17e. At large pressure ratio, the original valve can by pass more mass flow than flat out design, which can by pass more than dish bottom design. 140 CHAPTER 6 EXPERIMENTAL INVESTIGATION 6.1 Equipment Setup A5 Atm inlet 7 8 l _ ® {9).— 4 3 I I JG Atm inlet 1 a. Schematic experiment system Air Inlet Dischorg r il Air Inlet . _. 1. __. 1. inlet silencer 2. support structure 3. orifice 4. inlet chest 5. test valve 6. outlet chest 7. bypass valve 8. throttle valve 9. vacuum pump b. Autocad drawing of test system Fig. 6.1 Venturi valve test System The test system was constituted as shown in Fig. 6.1. A wind tunnel was built to test the flow patterns and instability when passing through the valve. A vacuum pump is used to build low pressure in test valve downstream to suck air through the test valve (5). The 141 ambient air enters the inlet pipe (1) through the orifice (3) then enters inlet chest (4). To avoid upstream and down stream influence and non-uniform inflow effect, the diameters of chests and inlet pipe are much larger than valve diameter. As a result, the pressure variation is very small and flow velocity is much reduced at inlet and outlet chests. The inlet chest and outlet chest can be considered as big tanks with constant pressure. The pressure of outlet chest is controlled by a throttle valve (8) and a bypass valve (7). The pump can be throttled to reach higher vacuum level. The by pass valve opens to increase out let chest pressure. The different combination can make full potential of the vacuum pump to reach desired pressure ratio. Some pictures of the system are shown in Fig. 6.2. a. View from inlet pipe side b. View from vacuum pump side Fig. 6.2 Pictures of the experiment system 142 5.1.1 Vacuum pump Fig. 6.3 Picture of vacuum pump The ROOTS RAMTM Whispair 616 DVJ Dry Vacuum Pump is selected as shown in Fig. 6.2. It is a heavy—duty unit with an exclusive discharge jet plenum design that allows cool atmospheric air flow into the casing. This unique design permits continuous operation at vacuum levels to blank-off with a single stage unit without water injection. Standard dry vacuum pumps are limited to approximately 16" Hg vacuum because operation at higher vacuum levels can cause extreme discharge temperatures resulting in casing and impeller distortion. The Roots Whispair vacuum pump's cooling design eliminates the problems caused by high temperatures at vacuum levels beyond 16" Hg. Whispair vacuum pumps reduce noise and power loss by utilizing an exclusive wrap- around plenum and proprietary Whispair jet to control pressure equalization, feeding backflow in the direction of impeller movement, aiding rotation. The general statistics of the vacuum pump are shown in the table below. 143 Table 6.1 Pump performance table Frame Speed Maximum 12” Hg 16” Hg 20” Hg 24” Hg 27”Hg Size RPM Free Air Vac. Vac. Vac. CFM Vac. CFM Vac. CFM CFM at CFM at at BHP at BHP CFM at BHP BHP BHP 616] 1750 2367 1015 36 901 47 748 59 448 71 * 80 2124 1310 44 1196 58 1043 72 743 86 * 97 2437 1556 51 1443 67 1290 83 990 99 244 1 11 3000 2001 63 1887 83 1734 102 1434 122 688 137 The pump is driven by a 100 HP motor at speed of 2500 RPM. It sucks the air to build vacuum in outlet chest and discharge air directly to room. At pressure ratio of 3, the vacuum pump can produce a maximum flow of about 1300 acfm and 54 acfm at a pressure ratio of about 10. Even no water needed for cooling, it can take inlet air temperature as high as 175 °F. 6.1.2 Piping system All the pipes are in the upstream of vacuum pump. The pipes, flanges, Tees, and chests are made of PVC pipes, which are easier handle than metal and strong enough for the vacuum. 6.1.3 Valve and chests As shown in Fig. 6.4, the chests are built here to maintain constant up stream and down stream pressure of the test valve. Their diameters are much larger than inside diameter of seat to reduce the flow velocity. The inlet chests is a Tee shape with inlet flow coming 144 from inlet pipe with much larger diameter than inside of pipe to reduce the influence of upstream inflow. The 1/2 scale test valve seat is mounted in the center of plate separating the inlet and outlet chests. Hold in the center of inlet chest, the threaded test valve stem can be rotated to adjust valve opening. The white cables are for measurement of pressure on plug surface. They go through inside of stem pipe to data acquisition equipment. The static pressure was measured in 9 positions one the plug surface. The labels of positions are shown in Fig. 6.6. The center sensor (position 0) is designed to take both static and dynamic pressure. There are 12 static pressure positions on the seat inner surface. The white pipes go through wall of inlet chest to data acquisition equipment for static pressure measurement. 7 dynamic pressure ports are also designed at the positions of screws in Fig. 6.7. Because the valve was tested under different openings, Fig. 6.8 shows the pressure locations at different openings. Inlet chest valve stem valve plug . . a- i. ,l m :1. ~.= @- '. “‘ - m u. u valve seat outlet chest Fig. 6.4 Chests and valve 145 Plug Fig. 6.6 Valve plug and pressure sensor positions 146 Seat Fig. 6.7 Valve seat and pressure sensor positions iii. fl. a l h/D=o,o22 _ . h/D=0.189 . i 7 i l . . . . l . l . . . i I I ”0:01“; ' h/D=0 357 Fig. 6.8 Static pressure sensor positins at different valve opening 147 6.1.4 Experiment measurement system design The major concern of this experiment is about pressure. Two kinds of pressure sensors were designed to be used, static pressure and dynamic pressure. The measurement system for pressure is shown in Fig. 6.9. I ____________ H _____ 1 I Inline Amplifier ' Valve Seat | Tape Record I HA“ an "H Transducer St t' Pr T b SignalConditioner I are essure u e oooooooo SignalAnalyser o o o oo o o o :l | | l I | Digital SensorArray I>I+1Ii Floppy Disc x Computer Ethernet Fig. 6.9 Pressure measurement system Besides the 21 locations‘in plug and seat surface, the pressure was also measured in inlet/outlet chests to get the pressure ratio (PFPouucl/ijet) and inlet pipe orifice to get mass flow rate. Through the white pressure tubes, the pressure signals were transferred to digital data acquisition array, then to the computer for recording and analyzing. 2 sets of Scannivalve 3017 digital sensor arrays with 32 Channels were used. The rate of data acquisition is 200 samples/channel/sec. 148 Fig. 6.10 Pictures for static pressure measurement system 7 dynamic pressure transducer installation ports were designed for PCB Model 105B02 in plug head, seat. 1 accelerometer installation surface is designed for PCB 352 A10. The system of two 4-chanell signal conditioner, one tape recorder, one signal analyzer and computer with signal processing software was made and ready to get data. The signal from the PCB pressure transducer was conducted to an inline amplifier through a coaxial cable. The inline amplifier conditions the transducer output signal. The signal was then passed on to the signal conditioner through a 50—feet low-noise coaxial cable. Even though one inline amplifier was used for each transducer, one signal conditioner was used for all four signals. The signal conditioner powered both the inline amplifier and the PCB transducer and could also amplify the signal with fixed gain of l, 10, 100. The amplified signals from the signal conditioner were transferred to a 4-channel digital tape recorder and stored on to a tape. The stored data on to a tape were transferred to a PC for further processing and analysis through the signal analyzer and the signal processing software. The output connectors can develop the input signals or the tape 149 reproduction signals. The real time signals are monitored through two-channel HP signal analyzer. The HP signal analyzer also provided the capability for on-line signal analysis through the various features available with it. It was possible to obtain the power spectrum, phase and cross-correlation between two signals for on-line monitoring of the valve. Even the dynamic pressure gauges and data acquisition system was designed, in this first stage of our test, dynamic pressure gauges were not installed. So following discussion will be focused on static pressure data analysis. 6.2 Experiment Result and Discussion 6.2.1 Mass flow rate The non-dimensionalized mass flow rate, maximum (choked) mass flow rate at different openings over mass flow rate at wide opening (h/D=0.734), is shown in Fig. 6.11. The opening ratio is defined as the valve lift from the closed position (h) over the valve plug diameter (D). Maximum mass flow rate increases quickly before 30% opening, then slowly to about 50% opening, and remains constant at greater openings. Thus 50% opening can be defined as the fully open position for this valve. The mass flow rate variation with changing pressure is shown in Fig. 6.12. To compare mass flows at different openings, the mass flow rate is non-dimensionalized as mass flow rate over maximum (choked) mass flow rate at the same valve opening. At small valve openings, for example h/D=0.022, the flow is choked at about Pr=0.6. At larger openings, the choke pressure ratio is larger. At wide opening, h/D=0.734, flow is choked at Pr=0.8. From this figure, the transonic region can be roughly judged, for example, at h/D=0.147 and pressure ratio between 0.65 to about 0.8, the flow is transonic and likely unstable. 150 0.7 62 33 2 32... 8:08:52". 8:25 Opening Ratio (h/D) Fig. 6.11 Choked mass flow rate variation with valve opening . n . . _ . . _ 584 _ 863 n 0.1.7. 1..OOO% " T: _ . u 477 .645 _O.1.3 " 000 .................. ._-.+._v+i . . _ "361 .423 "0.1.2 "000 ........... ._-.+:., . . . u n n 269 . . _ 208 _ _ _ 0.1.1. . u u .000 u u m t: a 4 w J 2 0. 8 6 A 2. 0. 1 1 0. 0. 0 0 0 36E 83225323. 26E 8a: 1.0 0.8 0.6 Pressure Ratio (Pa/P01) 0.4 0.2 Fig. 6.12 Dimensionless mass flow rates at different openings 151 6.2.2 Flow regions and patterns By considering pressure distributions, pressure oscillation frequency, and amplitude, four major flow regions, A, C, D, and E, are identified in terms of valve Opening and pressure ratio, as shown in Fig. 6.13. In regions A, D, and B, one kind of pressure distribution occurs. Pressure oscillates with high frequency and small amplitude. This is due to strong turbulence. In region C, several types of pressure distribution keep changing to each other. Large amplitude of pressure oscillation occurs due to the flow pattern changing. All transition regions between C and other regions are included in region C. Thus region C is the most unstable region. Since the flow is three-dimensional, it cannot be made visible. The flow pattern is analytically determined using the measurement results of the static pressure distribution and pressure oscillation. As mentioned before, the static pressure on the surface with which the flow is in contact is lower than that on the surface with which the flow is not in contact. Also, the pressure on the surface over which the flow is steadily in contact varies randomly, with larger amounts of variation than in the regions where flow is separated. These trends were proved to be true by the experimental results of Araki. The flow patterns and corresponding pressure distribution are roughly drawn in Fig. 6.14. The pressure in Fig. 6.14 is gauge pressure (psi). The two cross sections where sensors are located are perpendicular to each other for each pattern in the figure. Even the “visualized” flow patterns are not very accurate due to the complicated flow and difficulty of judgment from limited numbers of sensors, but they can still help to understand the flow phenomena. 152 Pressure Ratio (lePl) 0 0.1 0.2 0,3 0.4 0.5 0.6 0.7 Opening RatloflIlD) 0.8 Pe (psi) Fig. 6.13 Flow regions i i l §Véflé§ il l li7§ . ii Pattern A Pattern A(hID=0.085, Pr=0.95) + Pout 1 2 3 4 5 6 Sensor Fig. 6.14 Pattern A and corresponding pressure distribution 153 Pattern A happens in region A, where there is a small opening and a large pressure ratio. Pattern A is almost symmetric but not axisymmetric. Flow attaches to the seat in one cross section, while it expands to the center in the other cross section. % W W 8s 8% as s l :s Pattern C Pattern C' \ \ / Z/ \ L41 \ / \ i i \ I; 1 ill l Hi i l i ll 1 Pattern Co Pattern C1 Pattern Co (hID=0.022, Pr=0.7) '35 l . I I -4.0 ~ ------------- l ----------- -------- l- ----- -------- --------- : : ' : ‘ > ’7; 4.5 - —————— t ——————— ' —————— 'r ———————————————— : --------- e . ' : : 0 ...... i ....... ________ l ........ 0' 5'0 : ' : ; +Seat -55 __---_---.i .............. L----_.__;-- +Pin - -6.0 l i i l l 1 2 3 4 5 6 7 Sensor 154 Pattern C1 (hID=0.085, Pr=0.8) .1 —+— Seat —9— Pin + Pout =0.8) Pr 085 =0. Pattern C (W + Seat 43— PIn + Pout -_________.-—¢ Il||llllrl "|' In'l I'llll'IIII-llll' lllllllllllllll 'I'l] -------r-——-----+-———-—l -2.0 -2.5 Sensor 155 Pattern C' (hID=0.147, Pr=0.8) _——__‘ ———.-——— I l l l I I l v PG (psi) .____— —-— -—— _——————— —-—— -__---— -—---——--—— + Pout Sensor Fig. 6.15 Pattern C and corresponding pressure distribution Region D is located in the lower left part of the chart. Pattern D as shown in Fig. 6.13 happens. It is almost axisymmetric free jet due to supersonic result from small opening and pressure ratio. After valve throat, flow expands and joins together. The direction is not straight down, thus touch the seat in some place down stream. Flow in region B is axisymmetric. Due to large mass flow rate at large opening, flow is full of or almost (with some separation at downstream seat side) full of the valve. Separation occurs in the center of plug. Flow in region C is most unstable. A lot of reported failures occur in this region. For pattern C, flow attaches to one side of the seat and separates from the other and joins together near the plug center in one cross section. In the other cross section, flow attaches to the seat sides and the two streams join farther from the plug center. Part of the flow also attaches to the plug center. The ‘hollow’ region actually is full of flow shown in the other cross section and a vortex. This is a very unstable flow pattern. It can change to three other patterns: C0, C1, and C’. At a small opening (h/D<0.064), the flow pattern 156 keeps changing between C0, C1, and sometimes C. At somewhat larger opening, it keeps changing between C and C1. At opening ratios larger than about 0.106 NB, the flow pattern oscillates between patterns C and C’. As the transient regions between different regions are also included in region C, at the boundary of the region, some intermediate flow patterns happen. By comparing Fig. 6.11 and Fig. 6.12, it was found that flow in upper part of region C is transonic. \ 9%,; 9%,? H) l iii Pattern D Pattern D (hID=0.022 Pr=0.35) -8.0 . . '85 __ +Seat _____ l _______ J _______ ________ -9.o —- +P‘” -9.5 *- -10.0 - -10.5 — -11.0 -11.5 Pe(psD Fig. 6.16 Pattern D and corresponding pressure distribution 157 \ / \'/ ll @lll it ill Pattern E —.———--a-—— Pattern E (hID=0.357, Pr=0.55) PG(psD Sensor Fig. 6.17 Pattern E and corresponding pressure distribution 6.2.3 Flow asymmetry An asymmetric pressure distribution can cause forces resulting in plug vibration. Thus time—averaged pressure differences between opposite pressure sensors are calculated. In Fig. 10, Aveseat AP means time-averaged (IPl-P3|+|P2-P4|)Sea/2. Here P1, P3, P2, and P4 are measured static pressures from the sensors 1, 2, 3, and 4 in the seat as shown in Fi g. 6.7. Avein AP means time-averaged (lPl-P3|+|P2-P4|) gl2; Aveout AP means time— piu averaged (IPS-P7|+|P6-P8|) /2. P1, P3, P2, P4, P5, P6, P7, and P8 are measured static plug pressures from the sensors 1, 2, 3, 4, 5, 6, 7, and 8 in the plug as shown in Fig. 6.6. 158 Aveplug AP means (Aveout AP+Avein AP)/2. The pressure difference is nondimensionalized by the inlet chest pressure P]. Pressure difference variations with pressure ratio at different valve openings are shown in Fig. 10. At small openings, the plug side pressure difference has similar trends and similar amplitudes to the seat side. The peak value occurs at some place near the pressure ratio of 0.5 located in region C at most cases (at very small opening, such as h/D=0.022, the peak pressure happens in region D). At a middle opening (hID=0.l68), the seat side pressure difference is higher than that on the plug side. At large openings, which are located in region B, the plug side pressure difference is very small at large pressure ratio, similar to all other openings. Then, as pressure ratio is decreased, the plug side pressure difference increases and reaches a constant value at a pressure ratio of about 0.7. At this opening, flow diffuses in the seat passage after the throat. At pressure ratios between 0.65 and 0.85, asymmetric flow happens in the passage after the throat, making the seat side pressure difference much larger. APIP1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pa/P1) 159 +aveseat 0-04 ‘ """""""""" +avein l" 0.03 ‘r _____ +aveout __ : —l:+—aveplug 0.02 -r ---------- | ------- ' ----------- 0.01 - ------------ X X ------ O I l l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 09 1.0 Pressure Ratio(P-JP1) a. Changing from region A to C to D with decreasing pressure ratio AP/P1 0.09 0.08 _ +aveseat 0.07 * +avein 0.06 _ +aveout 0.05 l +aveplug 0.04 0.03 - 0.02 - 0.01 _ —--—-—d —.——_._ __.___ _-—-_ _--__-_.__-_a ____— _———— ——— - —-———-----_ ———-- --——— ———-— --———--—-—— 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio(leP1) b. Changing from region C to E with decreasing pressure ratio 160 0.06 + aveseat 0.05 ~~ .- 0.04 - $ 0.03 J < 0.02 _ 0.01 - 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pressure Ratio (Pg/P1) c.RegionE Fig. 6.18 Pressure difference variation with pressure ratio at different openings The maximum average pressure difference across the plug surface (aver_plug), its corresponding pressure ratio (Pr_plug), and maximum average pressure difference across th e seat surface (aver_seat) are shown in Fig. 6.19 for different valve openings. As the valve plug travels to the fully open position, the maximum pressure difference in the plug side decreases. The seat side pressure difference increases and reaches its peak value at about 0.23 h/D opening, then drops down. Because the pressure difference in the plug side causes hydraulic forces on the plug, for venturi valve, smaller openings mean more possibility of valve failure when upstream pressure is constant. Compared with Fig. 8, the pressure curve shows that the maximum pressure difference happens in the lower part of region C in most cases except the very small opening situation such as h/D=0.02. Under very small Opening situation, the maximum pressure difference happens in region D. 161 0.8 - 0.7 I 0.6 ~ 0.5 - 0.4 10.3 ~ 0.2 . 0.1 0.14 r 4 . . . . , +aveDP—P'UQ: : : : : : : : 0.121—0—aver_seatl—--'r- .'- 4- -4- +Pr_o|ug : : : ' ' : : :. E 0'1“ .”'T‘” " ‘1' ‘1 a : : : : : : ' : :1 4 0-08‘“ 1*“ '1‘ E I l l I I I l I I I .. 3906"?“- - - ~ .‘ éo-m—HW l l I I ' ' | I 0-021~-t-- : 0 A r J r r r r r r r r 0.02 0.04 0.06 0.08 0.11 0.13 0.15 0.17 0.19 0.23 0.36 Opening Ratio (th) Pal P1 Fig. 6.19 Maximum pressure difference and corresponding pressure ratio 6.2.4 Flow instability 162 in Fig. 6.21. Pressure oscillation is due to turbulence with small amplitude. Pressure oscillation on the plug surface at 0.085 h/D opening is shown in Fig. 6.20. The numbers from 0 to 8 are the sensor numbers on the plug surface as shown in Fig. 6.6. For example, the curve 0 shows the absolute gauge pressure (psi) oscillation at the plug center. The x-axis is time. At large pressure ratio, Pr=0.95, pressure oscillation is random around some average mean value with small amplitude. This is in region A. Flow is typically turbulent. At pressure ratio of 0.9, it is clearly shown that the flow pattern jumps from A to Co then quickly to C]. At pressure ratio of 0.8, flow pattern A disappears, while patterns C0, C1, and C keep changing to each other with large amplitude and low frequency. Decreasing pressure ratio further, the pattern changing frequency becomes higher until the pressure ratio reaches 0.4, below which the flow becomes pattern D, supersonic free jet flow. The trend is the same for any other valve opening except the very large opening (h/D>0. 168). At very large openings, only pattern E occurs, as shown th=0.08 5, Pr=0.95 c-UB-K - «tr 3.. Ilallltltrrwww ulnlwlnllnmllm :3 ° -1. . f6 tiffllI Wu were: _5 ~. .‘ , W. . 1 . —5 4.4 “8 t -100 , 1104.085, Pr=0.9 Plug . Sensor# I . , _D ,.‘ q -- - -l ---' ---- .' ..- _1 “WW I13. ’3'.“ i .4 ”HM-‘1’ h‘lll. '.""ll'-- 2 "*5 .. r M " ' _ 3-2.0- MW... l1» 1,, WWW M- _: A 1W“ «Wu WWUWW __5 -25- -- - - ' ------------- _5 —7 —8 -3.0 t r t 163 Plug Sensor# th=0.08 5, Pr=0.8 Plug Sensor# l‘lll)=0.08 5, Pr=0.7 j 164 P (M -4.0 -50." 43.0 J -7.0 -. -8.0 hD=0.08 5, Pr=0.6 Plpsn 110811.085, Pr=0.5 165 7 0 hID-no.08 5, Pr'0.4 Plug Sensor# W —0 an 4_ —; 2.; I _. CL ——4 -90 . . ——5 t v \ a ‘ ‘1 A I . I, l ‘ .lfl 1*“: I\ 1". 11" . I It 911 _ I J; —6 1- . Ill . w W' l l“ “J- WW3 l,‘ " i ll} “11" ”:11 —7 ——a -1U.0 . a r . . l hD=0.08 5, M43 Plug E O. —5 -10 wL" ”1‘5," 509.6%”! :k; 6‘3”””' __5 —7 '11 I l f I —8 t Fig. 6.20 Pressure oscillation at different pressure ratios and 0.085 h/D opening 166 hD=0.35 7, Pl=0.7 -1.0 Plus Sens or# — U -1 .5 - ------------------------------------------------------------ _1 A L . 1 2 '2 -2 0 WM“ *M“-’e‘«”* '9‘" J! fimfi%%%‘i — 3 I \‘Vv’1WJW’HI‘Wfl"\./\IWW'\WJAV‘JW‘N’w‘l‘flurW‘v‘M/W\.A~“'W _ 4 raev’M-I wtl‘w w' "" “‘r'mms—5 -2 5 4r ---------------------------------------------------------- _ 5 — 7 -3 .0 . . . . , _ 8 t Fig. 6.21 Pressure oscillation at p1=0.7 under 0.375 h/D opening To compare the pressure oscillation amplitude, the maximum peak-to-peak value of oscillation AP is calculated. It is also nondimensionalized by the inlet chest pressure P1. Pressure oscillation maximum peak-to-peak values at different positions on the plug surfaces at three openings are shown in Fig. 6.22. The numbers from 0 to 8 are the sensor numbers on the plug surface, as shown in Fig. 6.6. At small or large openings, a large amplitude pressure oscillation happens in the region near the plug center, while at middle openings, it occurs on the whole surface. The center pressure oscillation mainly causes vertical force oscillation, and the pressure oscillation of the upstream side surface of the plug mainly causes lateral force oscillation. So, for a real valve, large amplitude of vertical vibration will happen at small openings, whereas large amplitude of both lateral and vertical vibration will happen at middle openings. This may be a reason that the recent reported valve failure happened at the opening ratio of 0.147 h/D. 167 APIP1 _——-d Pressure Ratio (Pg/P1) a. At small valve opening APIP1 0.12 0.10 0.08 0.06 0.04 0.02 0.00 h/D=0.106 l / 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Pressure Ratio (P21P1) b. At middle valve opening 168 Pressure Ratio (P-JP1) _ Plug 0.05 ”0'0"” Sensor# +0 0.04 / 1 .. 03 +2 E +3 <1 .02 +4 +5 0.01 6 o ——7 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 _8 Pressure Ratio (Pg/P1) c. At large valve opening Fig. 6.22 Peak-to-peak value of pressure oscillation 0.14 T I I I I I I ND 012- ————— l —————— 1 ..... +0022 ' 5 E E 3 l 5 E +0043 0'10‘ ”””” T””i """"" I “““ ‘1”"1 ” +0064 i 0'08“ """ 1 ‘‘‘‘ 1 “““ ' ----- :- +0085 0‘: 006 ‘b’ 'L "' ‘— -:- 4— 4' ___l +0.106 . l : E +0126 004%“ " . T"ma—0.147 0'02 ‘ l ' —-—0.168 0.00 ‘ l i : L E i 1' +0189 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 +0-231 —o.357 K Fig. 6.23 Peak-to—peak value of pressure oscillation at plug center Fig. 6.23 shows the pressure oscillation, AP/ P1, of the plug center at different openings. At small openings, there are two peaks. As the opening increases, the two peaks move toward each other. They join together, becoming one flat peak for 0.085 h/D opening. Then the curve becomes more flat with increasing valve opening. 169 The peak pressure oscillation (oscillation_center curve) at plug center for each opening is shown in Fig. 6.24. The corresponding pressure ratio for the peak pressure oscillation is also shown as the curve with triangle labels (Pr_peakP). maximum average pressure difference across the plug surface (aver_plug) is the dashed curve with square labels. It is the same curve as in Fig. 6.19. The peak value for pressure oscillation occurs at the opening of th=0.064, then it decreases with increasing valve opening. The absolute value of the pressure oscillation at the plug center is higher than the average pressure difference for the plug, which means that the pressure oscillation may be more dangerous than the asymmetric pressure distribution. The pressure ratio at which the maximum pressure oscillation occurs is about 0.7. At this pressure ratio, flow is mostly transonic, which agrees with the theory mentioned above. The pressure ratio line is located in the middle part of region C. 0.14 0.12 ~ a.- 0-1 "‘ I l \ : : .....- aver_plug % 0-03 1 """"" f ‘ ‘ ' . """""" —o—-oscillation_center d: E q. ' ' r 0.4 } E 0.%___L___ i_ : ___+Pr_peakP l '5 : : \ i i I I I T 4" 0.3 2 0.04-_,:,-, 1 fi-..‘ —1 I i i : : : : ~~¢----9~~...' : 0°?- 0.02:1 A- 1' : -l— . "1? .”~'i"'01 o I I I I I I I l I I I 0 0.02 0.04 0.06 0.08 0.11 0.13 0.15 0.17 0.19 0.23 0.36 Opening Ratio (hID) Fi g. 6.24 Peak value of pressure oscillation with opening changing 170 6.2.5 Superposition of pressure oscillation and difference Based on the above analysis, the pressure oscillation and difference amplitude are superposed in Fig. 6.25. Region C is a dangerous region for valve operation in terms of flow asymmetry and instability. In the upper part of region C (around Pr=0.7), flow is quite unstable due to the flow pattern changing. This is because in such a situation, the flow is transonic, which is fluctuating, and fighting for the plug attachment as mentioned above in the discussion of theory. At the lower part of region C (around Pr=0.5), the flow is more asymmetric. This is the result of asymmetric flow expansion. The lower left part (red) of Region C is highly dangerous. P ressure Ratio (Pg/Pd 0.05 0.1 0.15 0.2 D Opening Ratio(h/D] [j APfPr=0412 APr’P1=0.09 APfPl=006 APIP,=0.04 Fig. 6.25 Superposition of pressure oscillation and difference 171 CHAPTER 7 CONCLUSION This study confirmed that asymmetric unstable flow is the root cause of valve problems resulting in large amplitude of unsteady forces, moments and torque. The valve plug can be broken in a very short time by the large amplitude of the excitations, or in long-term operation by small amplitude of the excitations. An analytical and numerical study on turbine governor valve was performed to clarify the fluid/plug interaction mechanism. Large adverse pressure gradient due to diffusion or shock waves cause stalls when flow is diffused through valve as internal flow. Stalls in both valve plug and seat side are not axilly symmetric. This causes asymmetric flow patterns for current design. The asymmetric flow pattern for current design causes asymmetric pressure distribution along plug, which finally generates huge unbalanced force and moment at valve natural position. The interaction between fluid and plug is the excitation mechanism that causes plug vibration. Vertical and lateral vibration affect each other and make the valve operation situation even worse. The key point to improving the design is to make the flow pattern symmetric for any situation. Changing the valve plug curvature is proved to be a simple way to improve the valve design by both theory and numerical method. Making the plug curvature sharper than seat side is one way to make flow separate in plug side earlier than in seat side to push the flow attach seat side and reduce its influence on valve plug. Several improved designs were studied. They are better than current design in terms of reduced excitations 172 of valve vibration, especially in large pressure ratio situation. The dish bottom design is recommended because it can make flow more symmetric and reduce the excitations significantly at any pressure ratio according to the validation by CFD data. It is also easy to be manufactured. Flow asymmetry and instability of a l/2-scale venturi valve for a steam turbine was determined from tests at different valve openings and pressure ratios. The results showed that asymmetric and unstable flow occurs in the valve, which can result in plug vibration causing valve failure. Regions with large amplitude of pressure oscillation and difference were identified for the current valve design. 173 BIBLIOGRAPHY Araki, T; Okamoto, Y; Ootomo, F, “Fluid Induced Vibration of Steam Control Valves”,Toshiba Review, Vol. 36, issue 7, ISSN 0372-0462, Tokyo Shibaura Electric Co., Kawasaki, Japan, pp.648-656, 1981 Becker, J. V., “Characteristics of Wing Sections at Transonic Speeds”, NACA-University Conference on Aerodynamics, 1948 Eguchi, Tsuyoshi; Hirota, Kazuo; Honjo, Masanobu; Magoshi, Ryotaro, “Study of Self- Excited Vibration of Governing Valves for Large Steam Turbines”, Mitsubishi Heavy Industries, Ltd, 1982 Emmons, H. W., “The Theoretical Flow of a Frictionless, Adiabatic, Perfect Gas Inside of a Two-Dimensional Hyperbolic Nozzle”, NACA Tech. Note, No. 1003, 1946 Mattingly, J .D., “Elements of Gas Turbine Propulsion”, McGraw-Hill, 1996 Hanin, R.A., O Tipah Kolebanii Reguliruyushih Klapanov Parovih Turbin, Teploenergetika, 9., p.19, 1978 Hardin, J ., Krushner, F., Koester, S., “Elimination of Flow-Induced Instability From Steam Turbine Control Valves,” Proceedings of the Thirty-Second Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 99-108, Sept. 2003 Heymann, F. J., “Some Experiments Concerning Control Valve Noise”, Engineering Report, Westinghouse Electric Corp, Lester, Pennsylvania Heymann, F. J. and Staiano, M. A., “Steam Control Valve Noise”, Engineering Report, Westinghouse Electric Corp, Lester, Pennsylvania Kline, S. J., Abbott, D. E., and Fox, R. W., “optimum Design of Straight walled diffusers”, ASME Journal of Basic Engineering, 1959 Kline, S. J ., “On the Nature of Stall”, ASME Journal of Basic Engineering, vol. 81, series D, no. 3, September 1959 Kuo, Y. H., “On the Stability of Two-Dimensional Smooth Transonic Flows in Local Supersonic Velocities”, NACA Tech. Memo, No. 1215, 195 Liepmann, H. W., Ashkenas, H., and Cole, J. D., “Experiments in Transonic Flow”, US. Air Force Technical Report, No. 5667, 1948 Moussa, Z. M., “Current Status of the RDC Steam Turbine Valve Study”, Internal report of Elliott Company, 1976 174 Schuder, Charles B., “Understanding Fluid Forces in Control Valves”, Intrumentaional Technology, Journal of the Instrument Society of America, May 1971 Shapiro, A. H., ”The Dynamics and Thermodynamics of Compressible Fluid Flow”, Vol. 2, The Ronald Pres Company, 1954 Weaver, D.S., “Flow Induced Vibrations in Valves Operating at Small Opening”, IAHR Symposium Proceedings, B13, Karlsruhe, Germany, 1979 Widell, Karl-Erik, “Governing Valve Vibrations in A Large Steam Turbine”, IAHR Symposium Proceedings, B14, Karlsruhe, Germany, 1979 White, F.M., “Fluid Mechanics”, McGraw-Hill Inc., Third Edition, 1994 Zarjankin, A.; Simonov, B., “New Control Valves, Their Parameters and Service Experience in the Turbines”, J oint- Stock Company for the Development of New Technologies in Energetics, ENTEK, Co. Ltd., Russia Zhang, D.; Engeda, A., "Venturi valves for a steam turbine and improved design considerations", Journal of Power and Energy, Vol. 217 Part A, 2003 Zhang, D., Engeda, A.; Hardin, J .; Aungier, R. " Experimental Study of Steam Turbine Control Valves ", Submitted to Journal of Power and Energy (#C07903) Ziada,S., Buehlmann,E.T.; Bolleter,U., “Flow impingement as an excitation source in control valves”. Journal of Fluids and Structures 3, 529-549, 1989 175 IIIIIIIIIIIIIIIII