". «Ti-m ac: u ‘2." V 10‘9"; ‘ ‘ 1". .3134 {"N" s; “Egg “, .33ka - "k r5 .. ’1: \ 4" ~ 5 ‘ 1‘: ‘33 u,.- l . ’3: '- ‘ wr “-1.; I: 3173‘79‘fi‘g V .n};.-e~r and“; \ ,- »,« vamp:- ‘Lnfcdw’. ~ .436 -' " ‘n‘ "a“ ‘ ~- :4} 2t“ ‘wt‘ ‘ - 1 . . ,- Wu; “fluv- \ - m4.- 531%??? . “"—’~}'u‘4 , .. ‘q ‘4 ;._...\~ ”09A ,— ' é" a. _’ 3’ ,q; 9;, 9.!) -;};?;--7 g‘s-‘V‘ La" .45 (5.741 3::9 ‘. v v '3‘»! -:‘ \ ‘§ "'4... f, . .5... a!) no 19,1". I l" . .71.}; 913‘ f‘," 57"“ .1: ‘1‘ ' fl» ff “-3 w :an‘ < , n.-.‘ Hymns: u'v-HH" ‘ ' 13bebov l! LIBRARY Michigan State University IT lllllllllmlllllllll J W ll 1 ‘ 31293005115485 _ : li This is to certify that the thesis entitled THE EFFECTS OF FORCING ON A SINGLE STREAM SHEAR LAYER AND ITS PARENT BOUNDARY LAYER presented by Richard Courtney Haw Jr. has been accepted towards fulfillment of the requirements for M. S. degree in Mechanical Engineering ‘ ’ Major pays”: Date 9”” «(Ma-(r I 3.93 0-7639 MS U is an Aflirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE] l #filg T—‘filfi MSU Is An Affirmative Action/Equal Opportunity Institution ____g-___ __ _ , THE EFFECTS OF FORCING ON A SINGLE STREAM SHEAR LAYER AND ITS PARENT BOUNDARY LAYER BY Richard Courtney Haw Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering 1989 ABSTRACT THE EFFECTS OF FORCING ON A SINGLE STREAM SHEAR LAYER AND ITS PARENT BOUNDARY LAYER By Richard Courtney Haw Jr. The detailed response of a large R0(O) single stream shear layer to a sinusoidal forcing at x - O has been documented. The increased width and measures of the phase dependent response in the shear layer are characterized by velocity magnitude measurements. These observa- tions are consistent with and complement those of Fiedler and Mensingl. Fiedler, H.E. and Mensing, P. [1985] "The Plane Turbulent Shear Layer with Periodic Excitation", Journal of Fluid Mechanics, vol 15, pp281-309. I dedicate this thesis to my wife, Valerie iii ACKNOWLEDGMENTS The support of the NASA-Lewis Research Center, Grant NAG-3-67l for this work is gratefully acknowledged. iv TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES . NOMENCLATURE CHAPTER 1 INTRODUCTION 1.1 Overview 1.2 Similar prior work 1.3 The current experiment CHAPTER 2 2. H .4 EXPERIMENTAL EQUIPMENT AND PROCEDURES Experimental Facility .1 Tunnel .2 Traverse system .3 Forcing System Measuring Equipment .1 Pressure measurements .2 Anemometry Data Acquisition System .1 Computer system .2 Primary A/D .3 Phase pickup Data Processing .1 Single Wire Page . viii xiv 11 ll 12 12 13 13 CHAPTER CHAPTER 4 .4.2 Compact Vorticity Probe .4.2.1 Calibration .4.2.2 Processing .4.2.2.1 Determination of the u,v components .4.2.2.2 Accuracy .4.3 Phase Averaging CHARACTERIZATION OF THE EXPERIMENTAL CONDITIONS .1 Boundary Layer .1.1 Bleed setting procedure .1.2 Turbulent Characteristics .1.2.1 At separation .1.2.2 Prior to separation .2 Forcing system .2.1 Forcing frequency .2.2 Effect of the forcing on the flow .2.2.1 U - 0 Data 0 .2.2.2 Perturbations of the separating boundary layer .3 Entrainment .4 Probe Positioning RESULTS AND DISCUSSION .1 Response of the upstream boundary layer to the forcing input .2 The Velocity Field in the Neighborhood of the Separation Lip vi l4 . l4 . 16 16 17 17 . l9 . 19 19 . 20 . 20 . 22 . 23 . 23 . 24 . 24 . 2S . 27 . 27 . 29 . 29 3O 4.2.1 Mean velocity profiles for the unforced condition 4.2.2 Mean velocity profiles for forced condition 4.2.3 Kinematic Reynolds stress in the separating shear layer 4.3 Evolution of the unforced and forced shear layers 4.3.1 Mean velocity profiles 4.3.2 Phase averaged data 4.4 Response of the entrainment field to the forcing input CHAPTER 5 CONCLUSIONS APPENDIX A EFFECT OF WALL CONTACT ON HOT-WIRE CHARACTERISTICS APPENDIX B DROP TEST CALIBRATION TECHNIQUE APPENDIX C ZERO MEAN FLOW PRESSURE MEASUREMENTS APPENDIX D NUMERICAL DATA LIST OF REFERENCES vii 3O 3O 32 32 32 34 39 . 42 129 132 135 136 182 LIST OF TABLES Table 1 - Forcing Amplitude Measures A.l - Wall Contact Calibration Results D.1 - No Flow Hot-wire Mean Velocities D.2 - No Flow Hot-wire Rms Velocities D.3 - No Flow Microphone Mean Voltages D.4 - No Flow Microphone Rms Voltages D.5 - Compact Probe G (x/00-1.0) D.6 — Compact Probe E (x/00-1.0) D.7 - Compact Probe G (x/00-1.O) D.8 - Compact Probe G (x/00-1.O) D.9 - Compact Probe 5737 (x/00-1.0) D.1O Compact Probe E (x/00-3.0) D.11 - Compact Probe u (x/00-3.0) D.12 - Compact Probe G (x/00-3.0) D.13 - Compact Probe G (x/00-3.O) D.14 - Compact Probe 5737 (x/00-3.O) D.15 - Mean velocity straight wire results D.16 - RMS velocity straight wire results 0.17 - Entrainment Field 5 (9--60°) D.18 - Entrainment Field 6 (0--60°) D.19 - Entrainment Field 3 (0--60°) viii Page . 25 131 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 161 171 172 173 .20 .21 .22 .23 .24 .25 .26 .27 .28 .29 .30 .31 Entrainment Field 3 (0--60°) Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Entrainment Field Field Field Field Field Field Field Field Field Field Field u'v' (0--60°) E (o-—45°) (9--45°) Cl 3 (9--45°) G (o--45°) 3737 (a--45°) E (o--90°) (0--90°) Cl 3 (o--90°) G (o--90°) u'v' (0--90°) ix 174 175 176 176 177 177 178 179 179 180 180 181 LIST OF FIGURES Figure 1 Separation lip geometry for Fiedler and Mensing [1986] 2 Plan view of experimental facility 3 Test section 4 Schematic Representation of the Traverse System 10 ll 12 13 14 15 16 17 18 19 20 21 Boundary Layer Development Section Entrainment Throttling Chamber Detail Entrainment Flow Conditioning Schematic Representation of the Traversing Mechanism Forcing Piston Detail Forcing Piston Side View Forcing Piston Isometric View Typical hot-wire Modified wire mounting for boundary layer surveys Schematic presentation of Compact Vorticity Probe Data Taking System Optical phase pickup and conditioning circuit Raw calibration versus fitted 1-f(n) curve. Clauser Plot of unforced BL at x/0O - 0.0 Clauser Plot of forced BL at x/0o - 0.0 Boundary layer mean profile at x/000-0.0 Boundary layer momentum thickness Page . 44 . 45 . 46 . 47 . 48 . 49 . 50 . 51 . 52 . 53 . 54 . 55 . 56 . 57 . 58 . 59 . 6O . 61 . 62 . 63 . 64 22 23 24 25 26 27 28 29 3O 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 Boundary layer friction velocity Power spectrum of Power spectrum of Power spectrum of Hot-wire Hot-wire Hot-wire Hot-wire Response Response Response Response piston acceleration (2-0.0) piston acceleration (z--h/2) piston acceleration (z-+h/2) to Forcing with no Flow ¢ - O to Forcing with no Flow ¢ - 90 to Forcing with no Flow ¢ - 180 to Forcing with no Flow ¢ - 270 Entrainment Setting Procedure Boundary layer mean profile at x/00--5.0 Comparison of phase averaged min/max U+ Y+ at x/fi0 - -5.0 Comparison of phase averaged min/max U+ Y+ at x/0O - -20.0 Streamwise data sampling locations Phase Phase Phase Phase Phase Phase Phase Phase Phase Phase Phase Phase averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged averaged V/Uo at ¢-0.0 $7110 at ¢-9o.o G/Uo at ¢-1so.o 3/110 at ¢-27o.o 6u 6v 6u 6v 6u 6v 6u 6v at at at at at at at at y/0O y/oo y/00 y/00 Y/90 y/00 y/00 y/oo - 0.0 - 0.0 - -l.02 - -l.02 - —3.06 - -3.06 - -9.36 - -9.36 xi . 65 . 66 . 67 . 68 . 69 . 70 . 71 . 72 . 73 . 74 . 76 . 77 . 79 . 80 . 81 . 82 . 83 . 84 . 85 . 86 . 87 . 88 . 89 . 90 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 7O 71 72 Forced velocity component intensity relationships u'v' in the separating boundary layer Unforced Shear Layer Isotachs Forced Shear Layer Isotachs Forced Shear Layer Isotachs (Fiedler and Mensing [1985]) Mean Mean Mean Mean Mean Mean Mean Mean Mean Mean Mean Mean Mean Unforced condition velocity histogram at x/flO - 60 6u versus phase velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity profiles at x/0o - 1 profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles profiles at at at at at at at at at at at x/00 x/0O x/0o x/00 x/0o x/00 x/0o x/0o x/fi0 x/00 x/0o profiles at x/oO 8u Su 6u 6u 6u versus phase versus phase versus phase versus phase versus phase contours contours contours contours contours contours at x/o at x/0 at x/0 at x/0 at x/0 at x/0 xii O 0 0 0 0 0 3 5 10 15 25 4O 6O 77 115 153 192 230 - l -3 - 5 - 10 - 15 - 25 . 91 . 92 . 93 . 94 . 95 . 96 . 97 . 98 . 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 73 74 75 76 77 78 79 80 81 82 83 84 Su 6u 6u 6u 6u 6u 6u Determination of disturbance phase Convection speed in the developing versus versus versus versus versus versus versus phase phase phase phase phase phase phase contours contours contours contours contours contours contours at at at at at at at x/oo x/0o x/0 x/Oo x/0o x/00 x/oo 40 6O 77 115 153 192 230 location shear layer Width measures in the developing shear layer Entrainment field velocity vectors Schematic representation of entrainment mass flux xiii 116 117 118 119 120 121 122 123 124 125 126 127 Nomenclature coefficients for Collis and Williams equation piston amplitude polynomial coefficients local skin friction coefficient frequency hot wire voltage velocity at hot-wire velocity on wire 3 velocity on wire 4 Reynolds number based on 0 Strouhal number streamwise velocity fluctuation u' at phase angle ¢ streamwise velocity in wall units friction velocity free Stream velocity lateral velocity fluctuation v' at phase angle d entrainment velocity piston width streamwise coordinate virtual shear layer origin xiv lateral coordinate lateral coordinate in wall units transverse coordinate GREEK SYMBOLS w A angular acceleration angle in the XY plane between velocity vector and axis or X array probe velocity fluctuation see (13) boundary layer displacement thickness hot-wire voltage ratio offset hot-wire voltage ratio momentum deficit thickness or angular position momentum deficit thickness at separation kinematic viscosity locally scaled perturbation level, see (14) phase angle angular acceleration width measure of the forced shear layer, see (17) SPECIAL SYMBOLS <") <”) (< >) <>f time average of the quantity ( ) rms of the fluctuating quantity () phase average of the quantity ( ) the quantity ( ) for the forced condition xv INTRODUCTION 1.1 Overview Forcing and its effect on fluid flows has become an accepted tool in the study and control of flow systems. It has been used both as a diagnostic tool, to explore the development and interaction of coherent structures, and as a method of controlling the behavior of the flow. A number of forcing methods have been used in order to pro- vide a perturbation to the flow; among these are the use of an oscil- lating trailing edge, acoustically driven slots, external acoustic forcing, and mechanical piston methods. There have been numerous studies into the effects of forcing on free shear layers. Substantial information can be found in the review articles (e.g. Fiedler [1988] and Hussain [1986]) and in the original publications which they cite. The investigation presented here documents the effect of a planar mechanical piston forcing on a single stream shear layer; it can be noted that this is one of the lesser studied free shear layers. The single stream shear layer can be characterized by its primary flow velocity scale U and the thickness of the separating boundary layer 0 60. The velocity scale U0 is constant over the length of the flow field; 0(x) can be used as a width scale to characterize the unforced shear layer. In the case of the forced shear layer the velocity field is a function of phase time and definition of a width measure becomes somewhat problematic. 1.2 Similar prior work The effects of sinusoidal forcing of the separating boundary layer in a single stream shear layer have been studied by Fiedler and Mensing [1985] and Disimile [1986]. An acoustic forcing mechanism was used in the Fiedler and Mensing study; the acoustic wave was applied to the separating boundary layer through a wave guide channel. Two separate trailing edge geometries were used in their study, see Figure 1. The separating boundary layer for their study had an R9 value of 830. Experimental observations of the resulting large scale motions included both hot-wire measurements and smoke visualizations. Hot-wire measurements in the shear layer indicated maximum 3 levels at St-(x-xo)f/Uo a 1. This result, combined with the flow visualization data, suggests that the large scale coherent motion has its maximum organization at this location. A comprehensive evaluation of the effect of forcing frequency and amplitude effects on the shear layer is provided by the Fiedler and Mensing study. The Disimile investigation, which was executed on the same ap- paratus as the current study, used a mechanically driven piston to provide a low amplitude forcing of the separating boundary layer. Ex- pressing the forcing piston amplitude as A(t) - A0 cos wt, the Dis- imile investigation was performed using A0 - 0.76 mm, or A0/0O a 0.12. The Disimile study revealed the formation of a large scale coherent motion and documented its translation properties in phase time. A negligible influence by the forcing input on the separating boundary layer was indicated. 1.3 The current experiment The study documented here, which was designed to build upon the previous investigations, was to examine the effect of large amplitude forcing at separation on the separating boundary layer. The effects of forcing on the developing shear layer constituted the second phase of the present study. A third phase of the work was to examine the behavior of the entrainment field for the shear layer, and its response to the strongly forced shear layer. The experimental approach taken was to provide a large amplitude forcing to a large separating boundary layer. In particular, a forc- ing amplitude of A0/00 - 0.58 was used with a separating boundary layer characterized by R0(0) = 5500. and 00 = 6.5 mm. Phase averaged measurements, using a single hot-wire anemometer, were performed throughout the development region of the shear layer and the upstream boundary layer. Planar velocity vector measurements in the entrain- ment region were provided through the use of a 4 wire probe. As a result of the large physical dimension of the separating boundary layer (00 - 6.5 mm) a 4 wire probe was able to be used to examine the planar velocity field just downstream of the separation lip. EXPERIMENTAL EQUIPMENT AND PROCEDURES 2.1 Experimental Facility 2.1.1 Tunnel The tunnel used for the present study was a single stream shear layer suction tunnel, a plan view of which is presented in Figure 2. The test section for the tunnel was subatmospheric, with the open volume of the laboratory between the fan exit and the inlet to the tunnel serving as a settling chamber for the return flow. The test section for the tunnel is shown in Figure 3, with a 0.5m x 0.8m core flow exiting into a 1.7 m x 0.8 m x 3.0 m test section. (The height for the entire area shown in Figure 3 was a constant 0.8 m.) The tun- nel was equipped with a glass wall over the entire length of the test section which enabled optical positioning methods to be used to locate the probe. The test section, downstream of the separation step (at x - 0.0) was equipped with a movable floor traversing mechanism, as shown schematically in Figure 4. The prime mover for the tunnel was a Chicago 30.5 SQA airfoil fan powered by a 15 Hp variable speed DC motor. The motor was equipped with a tachometer feedback control system which maintained the motor speed to within i 0.5% of the set value. Flow conditioning upstream of the test section was provided by three two-dimensional contractions with an overall contraction ratio of 22.6 to 1. Additional conditioning was provided by turbulence manipulators downstream of the first two contractions. These -manipu- lators consisted of a 3.175 mm diameter honeycomb with an l/d ratio of 8, and a set of 30 mesh screens spaced 12.7 mm apart. A final asym- metric contraction, to the boundary layer development section,was placed downstream of the manipulators. The boundary layer development section, as shown in Figure 5, conditions the boundary layer upstream of the separation lip. This conditioning takes the form of removing the upstream boundary layer formed during the last contraction through use of a separate bleed fan. This low momentum fluid was extracted using a splitter plate as shown in Figure 5. The plenum downstream of the splitter plate ex- hausted into the receiver through a Buffalo Forge 37v fan. This fan was driven by a 3 Hp A/C constant speed motor through an adjustable speed belt drive allowing the adjustment of the bleed flow. A distributed roughness trip mechanism, consisting of 609. mm of 16 grit sandpaper, was employed. This trip method was based on the work by Klebanoff and Diehl [1951]. The distributed roughness was followed by 1290. mm of smooth wall. The final 655. mm of wall con- sisted of white formica covered particle board providing a surface with the following desirable characteristics; a) A low surface roughness; which minimized wall roughness effects on the developing boundary layer. b) A non—conducting surface; which provided desirable heat transfer properties. When operated near a conducting surface the heat loss from a hot-wire anemometer will give rise to signifi- cant errors in measurement. Usage of a non-conducting surface such as formica covered particle board minimizes this effect. c) A white smooth surface; which enabled an optical wire-shadow positioning method to be used to accurately determine the position of the hot-wire when near the wall. In contrast with many single stream shear layer facilities, the facility used in this study had the attribute of being able to both condition and to have control over the fluid stream entrained by the shear layer. The entrained fluid was taken from the open laboratory volume through filter media and into a settling chamber. One wall of the settling chamber consisted of a series of throttle modules, which allowed for the control of the flow rate through the use of a sliding throttle plate as shown in Figure 6. The flow passed through the throttle modules, then through a coarse screen, a contraction to the 0.8 m test section height, and into a honeycomb and fine screen tur- bulence manipulators; see Figure 7. 2.1.2 Traverse system The probes were positioned by means of a 3 axis traversing sys- tem, shown schematically in Figure 8. This traverse consisted of a rack and pinion drive in the X direction, a screw feed drive in the Y direction, and a worm gear drive in the 0 direction. Each axis was driven through stepper motors under computer control. The resolution in the X, Y, and 9 directions were .8 mm, .01 mm, and .02 degrees respectively. 2.1.3 Forcing System Forcing of the separating shear layer was provided by a motor driven piston forcing mechanism. The basic mechanical system was em- ployed in previous research of lower amplitude forcing effects; see Disimile [1984] and Figure 9. The piston was belt driven using a con- stant speed (1760 RPM) 1 Hp AC motor and variable pitch pulleys. The piston motion was obtained using an eccentric as shown in Figure 10. The time dependant position of the piston can be written as: A - A0 x cos(¢) (1) Where d is the angular position of the rotating shaft. This study was performed using an amplitude AO - 3.84 mm and a frequency of 16.1 Hz. Phase information was obtained through use of an optical pickup on the forcing piston drive shaft as shown in Figure 11. 2.2 Measuring Equipment 2.2.1 Pressure measurements Pressure measurements were made using an MKS baratron model 310 1 Torr pressure transducer and 170M 6—C amplifier. The overall uncer- tainty for all pressure measurements is i.08% of indicated plus i.00001 Torr. 2.2.2 Anemometry All hot-wire measurements in this study used locally fabricated hot-wires and probes. A typical straight wire is shown in Figure 12. The wire itself is 5 micron tungsten with an overall length of 3 mm and an active length of 1 mm. The inactive portions of the wire are copper plated to a nominal diameter of 50 microns. The wires were mounted on the tips of jewelers broachs, the plating as well as the small diameter prongs lead to minimal interference effects. The meas- urements were all performed with the wires operated in the constant temperature mode at a nominal overheat of 0.7. Two types of probes were used in this study, single wire probes and a compact vorticity probe. The single wire probes consisted of a 10 single wire as described above, operated with the wire parallel to the Z axis. A modified wire mounting was used for the wires involved in the boundary layer measurements. Specifically, the wire was mounted on the side of the tip of the broachs, rather than the end of the broachs; see Figure 13. This allowed the active portion of the wire to be brought closer to the wall. The compact vorticity probe is a 4 wire probe allowing for the resolution of velocity components and gradients in a single- plane. The probe is shown schematically in Figure 14 and consists of a single X array, with the addition of two straight wires. The individual wires are as described above. As can be seen from Figure 14, the overall size of the measure- ment area is 1 mm2 normal to the mean flow. Although no large scale model studies have been performed on this probe to determine possible prong interference effects, results up to the time of this writing in- dicate that such effects are minimal. Measurements at various orien- tations in the calibration stream return the correct values given the probe orientation. In addition measurements of the thermal interfer- ence between wires, obtained by running all possible on and off com- binations of wires while the probe is in the calibration stream, show no thermal interference between wires. Two types of anemometers were used in this work; these were the DISA model 55M01 and the T81 model 1755. In both instances the 11 nominal output was approximately 4.5 volts at the free stream speed of 13 mps. Electrical noise levels for both types of anemometers were approximately 1 millivolt rms. Frequency response for the anemometry was approximately 20 KHz at 13 mps. 2.3 Data Acquisition System 2.3.1 Computer system The computer system used for both the data taking and all data processing was a DEC 11/73 microcomputer; this system is shown diagrammatically with the associated data acquisition and laboratory interface hardware in Figure 15. This computer consisted of the cen- tral processing unit, two RD-53 70 megabyte hard disk drives, a 90 megabyte Tk50 tape drive, an AXVllC A/D, a KWVllC programmable clock, a DRVllJ digital interface, a DRVllW DMA interface, and miscellaneous other serial and networking interconnects. The AXVllC A/D provided limited sampling capability which was used primarily for monitoring the tunnel speed and other experimental parameters prior to the actual data taking. The DRVllJ digital interface and KWVllC programmable clock, in conjunction with a custom built stepper motor translator and driver system provided computer control over the traversing system. r. -—-‘___n '3’ 12 2.3.2 Primary A/D The primary A/D used for the experimental work was a TSI IFA200 12 bit simultaneous sample 10 channel unit. This A/D was configured to provide an input signal range of 0 to +5 volts, giving a least sig- nificant bit level of 1.22 millivolts. The IFA200 is a self contained unit providing it's own internal clock and sampling circuitry. Inter- face to the ll/73 computer was through a DRVllW DMA interface, provid- ing a maximum single channel sample rate of 50 KHz, and-a total throughput of 250 thousand samples per second. The IFA200 used was a true simultaneous sample A/D, consisting of 10 independent A/Ds which were driven by a common sample signal. An analog delay adjust in the sample signal was provided, and for all data in this study the A/D was calibrated to provided a channel to channel sample uncertainty equivalent to a 0.0001 mm convection length at the typical free stream velocity of 13 mps. 2.3.3 Phase pickup The phase trigger used to conditionally sample the forced data in this study was provided by means of a metal tab passing between the sensing elements of an optical pickup, see Figure 11. This arm was mounted at a radius of 100 mm giving a mechanical positional uncer- tainty of approximately 0.2 degrees. An electrical schematic of the pickup and conditioning circuit is shown in Figure 16. The electrical output from the pickup is 13 amplified, fed into a one-shot multivibrator, buffered to standard TTL levels and fed to the IFA200 A/D. The one-shot multivibrator is used to provide a positive output duration of approximately 30% of the forcing period. The overall uncertainty caused by the electrical sys- tem is negligible for the forcing period used. 2.4 Data Processing 2.4.1 Single Wire The hot wires were all calibrated in the low disturbance free stream flow of the tunnel. The physical location x - 150. mm and y - -250. mm was used for the calibrations. The calibration data were obtained as the mean of 2000 samples taken at 200 Hz. A single cali- bration data set consisted of measurements at 7 or more speeds ranging from 1.0 to 13.5 mps. A pitot static tube was used in conjunction with the MKS baratron pressure transducer to provide the reference velocity. The calibration data were used to define the coefficients (A,B,n) in the modified Collis and Williams relation, E2-A+BxQn (2) where E is the measured wire voltage and Q is the tunnel speed.These A, B, and n were values determined by using an ordinary least squares method to determine A and B given n, and minimizing that relation as a 14 function of n. All processing of the anemometry data was executed by first con- verting the measured voltages to velocities using the calibration con- stants on a data point by data point basis, and then performing statistical processing on the resulting velocities. 2.4.2 Compact Vorticity Probe 2.4.2.1 Calibration The calibration of the compact vorticity probe was also executed in the low disturbance free stream flow of the tunnel at X - 150. mm and Y - -250. mm using a pitot static tube and the Baratron pressure transducer as a velocity reference. Sampling details for a single calibration point were the same as those used for a straight wire; however, as a result of the processing algorithm used, the calibration data were required at a number of angles (0) with respect to the flow. These data were taken at angles from -36° to +36° in 6° steps. Since small differences in the velocities measured by the wires can translate into large gradients because of the compact size of the probe, improved calibrations were obtained by using one of the straight wires rather than the pressure transducer as a velocity reference. This was accomplished by first fitting A,B,n values to the two straight wires for all angles, then selecting the wire with the minimum standard deviation (based on velocity) and using the resulting 15 coefficients for that wire along with the calibration data to generate the calibration velocities for the other three wires of the probe. Calibration constants were then determined for all wire and angle com- binations using the new velocities. The variation in the hot wire response with respect to flow angle was modeled by defining a voltage ratio C as follows: § - E(7) / E(0) (3) where E(1) is the hot-wire voltage at the probe angle 1 and E(O) is the hot-wire voltage at the probe angle of 0. This function is non- linear and strongly speed dependant. At any given speed the function can be modeled as a polynomial. Since the function has an inflection. around f-l.0, it is advantageous to redefine the voltage ratio as an offset value: 0 - 3(7) / E(0) - 1-0 (4) which allows 1 to be accurately modeled as a rational polynomial of the form: 5 4 3 2 1 - qu + C4" + C3" + C2” + Clq + Co (5) Where CS’C4’C3'CZ’C1’CO are fitted coefficients. Typical rms values Of this fit are 0.3°. Representative calibration data and fitted l6 curves are shown in Figure 17. Since equation 5 is a strong function of velocity, see Figure 17, a separate set of coefficients were determined at 51 discrete speeds equally spaced over the range from the minimum to the maximum calibra- tion speed. The n value at each speed and angle is computed from cal- culated voltages using the A,B,n values for the wire at that angle and the arbitrary speed. 2.4.2.2 Processing 2.4.2.2.1 Determination of the u,v components The x and y velocity components of the flow (u and v) can be com- puted by knowing the velocity magnitude in the xy plane, and the indi- cated velocity from one of the slant wires. The velocity magnitude was taken as the average of the indicated velocities from the two straight wires, Q3 and Q4. Once this velocity had been determined, the flow angle 1 could be computed from either of the slant wires. In practice the angle was computed using both of the slant wires, and this angle was compared to the calibrated angle range. If the indi- cated angles were both within the calibrated range, (-36° < 1 < +36°), the average is used. If only one computed angle was outside of the calibration range the value which lay within the calibration range was used. If both angles lay outside the calibration range the 1 - f(n) polynomial for the wire most normal to the flow was extrapolated to yield the angle, and the point was marked as suspect. 17 Since the response of the vertical wires does, to a slight de- gree, depend on the flow angle, two calculations were made for each wire at each point in the data set. For the second calculation the angle information from the first calculation was used to determine the calibration constants A(1), B(1), and n(1) to be used in the deter- mination of Q3 and Q4' 2.4.2.2.2 Accuracy The accuracy of the processing algorithm was verified for each set of experimental data by processing time series data taken in the free stream during calibration. In all cases the computed flow angles were within 0.5° of the physical probe angle. The validity of the extrapolations of the n - f(1) relation were verified by taking time series data in the calibration stream at probe angles with respect to the flow direction of i6° beyond the normal calibration range. The extrapolated values, so computed, were ac- curate to within il.0°. 2.4.3 Phase Averaging Phase averaged data acquisition was performed by sampling both the analog input channels of interest and the conditioned phase signal from the forcing mechanism optical pickup at a high data rate.The resulting time series was then divided into intervals based on the pickup signal. Each of these intervals, representing one forcing 18 period, was then divided into 16 equally spaced intervals and the phase average sample extracted from the time series at these points. As an example consider a block of data where the leading edge of the pickup signal occurred at data points 1 and 384. Dividing the forcing period into 16 intervals, only points 1, 25, 49... would be saved; corresponding to phase locations of 0., 22.5, 45.0... degrees. For this study, data were taken at 5000 samples per second, and the mean forcing period was 62 milliseconds. This gives an uncer- tainty of i 0.6 degrees in any specific phase value due to the sam- pling rate.Since the subdivision of the intervals over which the phase averaging was performed was based on one revolution of the arm, uncer- tainties due to long term, (time scales greater than one forcing period) variations in motor speed were eliminated. In addition this method allowed for accurate monitoring of the actual motor speed, since the length of each period sampled is also saved. For all of the data presented in this thesis, the variation in the periods was on the order of the sampling time of 0.2 milliseconds, or 0.3% of the mean period. CHARACTERIZATION OF THE EXPERIMENTAL CONDITIONS 3.1 Boundary Layer 3.1.1 Bleed setting procedure The boundary layer formed during the final contraction was removed through a bleed slot as shown in Figure 5. The initial at- tempt at a setting for the bleed port flow rate was accomplished visually by using tufts at the bleed port; those observations proved difficult to interpret with the desired precision. In an attempt to achieve a better bleed setting, velocity profiles were taken just upstream of the bleed slot using a single hot-wire probe. The bleed flow was then adjusted to yield a locally symmetric velocity profile about the leading edge of the splitter plate. Upon examination of the boundary layer profiles at the separation lip, it was found that this approach yielded too large a bleed flow, and a distorted downstream velocity profile. 19 20 The final approach taken to set the bleed flow was to adjust the bleed flow rate such that the an optimum turbulent boundary layer pro- file was obtained at the separation lip. 3.1.2 Turbulent Characteristics 3.1.2.1 At separation The boundary layer data were plotted in law of the wall coordi- + + nates, U and Y ; + u U - fi_ (6) 1' yU y+ - -;,-’ (7) Cf 1/2 U = U0 -5 (8) The local skin friction coefficient (Cf - rw/0.5pUg) was deter- mined from a Clauser [Clauser 1951] plot. The momentum thickness, 0 was determined from o — E—[13—] dy (9) * and the displacement thickness, 6 was determined from 21 * ii 6 - 1'fi_ dy (10) Clauser plots for the separating boundary layer are presented for the unforced case in Figure 18 and for the forced case in Figure 19. The resulting Cf values were 2.95x10.3 for the unforced case and 3.03x10-3 for the forced case. The unforced boundary layer had a momentum thickness at separation (00) of 6.72 mm, with a displacement thickness 6* of 9.11 mm, yielding a shape factor of 1.36. For the forced condition 90 was equal to 6.02 mm and 8* was equal to 8.21 mm yielding a shape factor of 1.36. Ur at separation was 0.485 for the unforced condition and 0.492 for the forced condition. In addition turbulent intensity measurements in the boundary layer yielded a max- imum value for u'/UT equal to 2.65 in the unforced case. Mean profiles for the separating boundary layer, for both the.un- forced and forced condition, were plotted in law of the wall coordi- nates (u+,y+) [Coles 1962] as shown in Figure 20. As indicated in the figure, the data show very good agreement with the law of the wall, 0* - 5.6 loglo y+ + 4.9 (11) over the log law region. This agreement, along with a shape factor of approximately 1.4 and a u'/UT value of approximately 2.5 indicate an equilibrium turbulent boundary layer [Hussain 1983]. 22 3.1.2.2 Prior to separation The momentum thickness 0 and friction velocity (Ur) for the developing boundary layer are shown in Figure 21 and Figure 22. As indicated in Figure 21 the boundary layer follows the expected pattern of growth up to a streamwise location of x/00 - -l.0. A decrease in the momentum thickness is indicated at the separation lip; this ef- fect is presumably due to acceleration at the separation lip. The boundary layer growth rate, (d0/dx), can be related to the wall friction coefficient for an equilibrium boundary layer as: - 2 g (12) This comparison was made with the experimental data over the range ~30 < x/0o < -l.0 and found to be in poor agreement. Given the limited streamwise span of the data, accurate resolution of do/dx would have required a determination of 0 to a precision not possible with the experimental configuration used. The uncertainty in the determined 0 values is hypothesized to be the cause of the poor agree- ment of the data applied to (12). 23 3.2 Forcing system 3.2.1 Forcing frequency The forcing frequency for this study was chosen based on the prior work of Mensing and Fiedler [1985]. Their studies showed a max- imum intensity of G at a saturation length XS, defined as XS - f/UO, approximately equal to l. The forcing frequency used in this study, 16.2 Hz, was chosen based on this criteria to give a saturatign loca- tion of 0.8 m, or 30% of the test section length. The resulting Strouhal number based on the separating boundary layer thickness, (foo/U0), was 0.0081. The natural frequency of the shear layer, as exhibited by fluctuations in the entrainment field, was 3.5 Hz or fGO/Uo - 0.0018; see Foss et.al. [1987]. The data sampling and processing method provided data on every forcing period taken during this study. The rms fluctuations of the period were below the measurement uncertainty involved in the sampling (0.2 msec). The frequency domain content of the forcing system was examined by placing piezo-electric accelerometers on the forcing piston at a variety of locations. Power spectra of the measurements taken at the piston center, and either extreme end are shown in Figure 23 through Figure 25. As indicated the piston motion has little harmonic content at the center of travel. A small amount of energy is found in 24 harmonics at either end; presumably these are a result of minor deflections of the forcing piston. 3.2.2 Effect of the forcing on the flow An accurate determination of the forcing level, by a given forc- ing apparatus, is one of the major problems in experimental work on forced flows. For the present study, two approaches were taken to ac- curately quantify the effect of the forcing on the separating boundary layer. Measurements were made with no primary flow in order to iso- late the effect of the piston forcing on the air mass in its neighbor- hood, and measurements were made in the separating boundary layer under nominal test conditions. 3.2.2.1 U0 = 0 Data Both velocity and pressure measurements were made in the neighborhood of the separation lip with no mean flow. Velocity meas- urements were made using a single wire hot-wire anemometer; pressure measurements were made utilizing a microphone and pinhole chamber ar- rangement. For the hot-wire measurements, calibrations were performed using a drop-test calibration technique; see appendix Appendix B for more information on this technique. The wire was calibrated in the data taking orientation, (with respect to the gravitational field), in order to minimize the error introduced by the natural convection field 25 of the hot-wire. The results of the hot—wire measurements are presented in Figure 26 through Figure 29; the velocity data presented therein are in units of meters per second, and the coordinates are non-dimensionalized with respect to the piston width (wp). As ex- pected, there is a strong shadow effect of the separation lip. Results for x>0 suggest a strong jet pumping effect which generated a mean entrained velocity in the -y direction. The technique used for the pressure measurements is documented in Appendix C, and tabular results are presented in Appendix D. The data showed no significant change in the amplitude of the rms pressure fluctuations over the measurement domain; the technique used ap- parently registered the acoustic wave generated by the piston. 3.2.2.2 Perturbations of the separating boundary layer The forcing amplitude can be characterized by three non-dimensional velocity measures; the rms velocity of the piston, the magnitude of the imposed velocity in the direction of piston mo- tion, or the velocity change at some point in the separating boundary layer. Specifically, all of these velocities can be non-dimensionalized with respect to the free stream velocity. The forcing levels for the current study were large with respect to the prior work of Disimile [1984], and corresponded to the larger ampli- tudes used by Fiedler and Mensing [1985]. Specific levels are shown in Table 1. 26 Table l - Forcing Amplitude Measures Forcing Measure Amplitude vpiston/U0 0'021 vf/U0 0.015 ~2+ ~2 1/2 (v vf+ uf) /Uo 0.045 As would be expected, there is some attenuation from the piston face velocity to the induced v velocity (vf) in the separating boun- dary layer. The large difference in the maximum velocity change in ~2 1/2 +uf) velocity (GE/no) should be noted. the flow ((3% /U0) relative to the magnitude of the induced v If the physical size of separating boundary layer is relatively small, for example 00 - 1.14 mm in the Fiedler and Mensing [1985] study, hot-wire velocity measurements are limited to those which can be made with a single wire probe. Since a single wire probe resolves a planar velocity magnitude, an important distinction should be made between the total induced velocity change and the induced velocity change in the transverse direction; the former being larger due to steerage of the sharp velocity gradient near the wall. As indicated in Table l, for the present study the ratio of total to transverse in- duced velocity fluctuation was 3 to 1. Due to the small physical size of the separating boundary layer in other studies magnitudes are often expressed using the former measure since only single hot-wire probes can be utilized. This 27 should be clearly delineated from the magnitude of the induced v velo- city, the former being much larger in magnitude due to steering of the sharp velocity gradient near the wall. 3.3 Entrainment The throttle plates were adjusted to give a "natural" shear layer, or dU/dX a 0.0. The value of dU/dX was determined from meas- urements of E in the high speed nonvortical flow at two streamwise lo- cations as indicated in Figure 30. The resulting value of dU/dX represented a velocity defect over the indicated range of less than 1% of the free stream velocity. 3.4 Probe Positioning Determination of the probe position for the data taken in the boundary layer and near the separation point for the shear layer is critical due to the steep velocity gradients in the Y direction. A preliminary attempt to verify the wire location by heat transfer to the wall was attempted. However, due to the minimal thermal effect provided by the wall it proved to be difficult to approach the wall close enough to get an accurate position and still not come in physical contact with the wall. A number of calibration tests showed that coming in contact with the wall, even slightly, al- tered the characteristics of the wire; see Appendix A. The final positioning wires for the boundary layer optical one. A point light an angle of approximately 14 it then cast a shadow which ing device viewing normal to accurately positioned to 0. the wire was placed slightly traverse was driven so as any mechanical play in the traversing system had been taken up. amount of play was nominally 28 method used in the case of the straight and near separation point data was an source was used to illuminate the wire at degrees. When the wire was near the wall could be measured through use of a sight- wire to be the wall. This allowed the 2 mm from the wall surface. In each case closer to the wall than this, then the to move the wire away from the wall until The .2 mm. For positioning of the compact vorticity probe the wall shadow approach could not be used due to the construction of the probe. the runs by placing it directly behind the separation Y - 0. mm. The Y location was For using the compact vorticity probe, the probe was positioned step at X - 5. mm and ascertained by means of a sighting device positioned directly downstream of the separation point. RESULTS AND DI SCUSSION 4.1 Response of the upstream boundary layer to the forcing input Mean velocity distributions, 5(y), were obtained in the boundary layer region for -30 s x/o0 S 0. These data were evaluated using the Clauser chart technique (Clauser [1954]) to determine the wall shear stress; see Figure 22. As shown in Figure 20, the mean velocity pro- file at the separation point for the forced and unforced conditions were only slightly different. However, at x/0o - -5 the mean profiles for the forced and unforced conditions were essentially the same; see Figure 31. The effect of the forcing at x/0O - -5 was, however, still visible as a difference in the phase averaged values; see Figure 32. Farther upstream, at x/00 - -10, the effect of the forcing is minimal; see Figure 33. 29 30 4.2 The Velocity Field in the Neighborhood of the Separation Lip 4.2.1 Mean velocity profiles for the unforced condition Velocity distributions for the forced and unforced conditions, u(y) and v(y), were obtained for the separating flow at x/00 - l and x/fiO - 3; see Figure 34. The mean velocity profile of the transverse velocity component for the unforced condition, V(y), is presented in Figure 35. As indicated in the figure, the transverse velocity has a mean positive value near y - 0, and the magnitude is greater at x/0o - 3 than at x/6o - 1. This behavior is apparently the result of the cavity formed by the piston and bounding plate assembly, which creates a low pressure region on the downstream side of the separation lip. 4.2.2 Mean velocity profiles for forced condition Mean velocity profiles of the transverse velocity component for the forced condition, (y), are presented in Figure 36 through Fig- ure 39. Also shown for reference on these figures is the physical geometry of the forcing piston for the indicated phase condition. As indicated in Figure 36, at d - 0° the piston is fully extended towards the flow, is larger than the unforced case, and the difference is more pronounced at x/0o - 3 than at x/00 - 1. As the piston retracts through ¢ - 90° to ¢ - 180°, Figure 37 and Figure 38, the difference between <$> and G is increased. At ¢ - 270°, Figure 39, the piston is at its maximum velocity in the -y direction and while a 3 at 31 x/o - 1, there is still a significant increase of over 3 at 0 x/9 - 3. 0 In order to better identify the phase behavior of the forcing on the flow, a velocity difference 6u can be defined as: 6n - - (13) where is the average over all phase angles. To clarify the response of the separating shear layer to the forcing input, Su and 6v are plotted as a function of the phase angle ¢; see Figure 40 through Figure 47. At y/00 - 0, Figure 40 and Fig- ure 41, 6h is much larger than 51 as a result of the lateral displace- ment of the fluid with a large velocity gradient. At y/00 - -1 5h has decreased with respect to 6% and the difference between 5h.at x/0O - l and at x/0o - 3 has been reduced. At y/0o - -3 the magnitudes of ii and 5% are approximately equal and show little change from x/0o - l to x/00-3. In the outer edge of the forming shear layer, y/0o - -9.5, 6u is nearly zero while 6v indicates a strong influence of the forc- ing. These data suggest a lateral displacement of the separating boundary layer in the iy direction by the action of the forcing. This hypothesis leads to the definition of the quantity 6, defined as 5 - 43—— <14) 32 which was computed for both the x/oO - l and x/l9O - 3 locations; see Figure 48. For an idealized condition of a lateral displacement of a velocity gradient 5 should be a constant. As indicated in Figure 48, f is approximately constant for l S x/00 S 8. 4.2.3 Kinematic Reynolds stress in the separating shear layer The kinematic Reynolds stress distribution for the separating flow, along with data for an equilibrium turbulent boundary. layer (Klebanoff [1954]), are presented in Figure 49. As indicated in the figure there is little change in the high speed region, both the data at x/o0 - l and x/00 - 3 are in good agreement with an equilibrium boundary layer. In the region -4 S y/0O S -0.5 the relaxation of 5737 as a result of the removal of the wall is indicated; the increase of 5737 in the region -0.5 S y/0o S 1 for the evolving shear layer can also be seen. 4.3 Evolution of the unforced and forced shear layers 4.3.1 Mean velocity profiles Mean and phase averaged velocity data were obtained using single wire measurements for the region 1 S x/0o S 230. Isotachs for the un- forced conditions are presented in Figure 50 and Figure 51, along with similar amplitude results from the Fiedler and Mensing [1985] study. As can be seen from the figures, the strongly forced shear layer exhi- bits a stepped growth rate, with a plateau at 1.0 < (x-xs)f/Uo are significantly larger than U0. The data for the unforced condition (at the same streamwise location as Figure 60), indicate the lack of a similar effect; see Figure 66. The cor- responding minimum values for the forced condition are are also inferred to represent pressure effects. 34 4.3.2 Phase averaged data The evolution of characteristics in the forced flow field can be readily seen from phase averaged isotachs of the single wire data. Plots of 6u (as defined in 13) versus the phase angle d are presented in Figure 67 through Figure 79. The characteristics of these data can be plausibly related to the forcing effects as noted in the following: a) For the region downstream of the separation lip, l S x/0 S 5, Figure 67 to Figure 69, the positive (¢ a 120) 0 and negative (d a 270) locations represent the effects of the piston motion in the +y and -y directions respectively. The primary effect of the forcing at this point is a steer- ing of the large mean velocity gradient; as shown in the figure the influence region is quite limited in the y direc- tion. At x/0O - 5, the appearance of isolated correlation contours in phase space can be noted. For the sake of brevity these will be referred to simply as correlation con- tours in the following discussion. b) For 10 S x/oo S 25, Figure 70 to Figure 72, the positive and negative correlation contours are better defined and the re- gion of influence is wider. At x/0o - 25 the centroid of the correlation contour is located closer to the high speed side of the shear layer than it was at x/oO - 10. 35 c) For 40 S x/O S 77 (Figure 73 to Figure 75), the magnitudes 0 of the correlation contours reach a maximum and the forma- tion of correlation contours of opposite sign on the low speed side of the shear layer is first noted. The correla- tion contours on the high speed side of the shear layer will be referred to as the primary correlation contours, while those on the low speed side will be referred to as the secondary correlation contours. d) For 115 S x/0o S 153 (Figure 76 to Figure 77), the primary correlation contours have migrated farther in the direction of the high speed side; the intensity of the primary cor- relation contours has continued to decrease, while that of the secondary correlation contours has increased. e) For 192 S x/0o 5230, Figure 78 to Figure 79, the intensity of the primary correlation contours has dropped below that of the secondary correlation contours; the secondary cor- relation contours dominate the field. The distinctive feature of the correlation contours allow a con- vection velocity to be defined at a given downstream location. Speci- fically the phase shift between the correlation contour peaks at two x/o locations, see Figure 80, can be related to a time difference us- 0 ing the forcing period as follows: 36 (15) f ¢2'¢1 t2-t1 - 350 + 360 n x r where n is an integer number of forcing periods. If the data loca- tions are sufficiently close together, as is the case in the current study, n is 0. From this time difference and the spatial distance between the data sampling locations, a convection velocity for the disturbance can be defined as: U - 2 1 (16) Using these procedures, the convection speed was determined for the data locations x/oO 2 15; see Figure 81. The increasing UC values as function of x/0o are rational considering the previously noted migration of the primary disturbance towards the high speed side of the shear layer. The width of the disturbance region A(x) can be arbitrarily de- fined using the integral quantities Zn m J J l5ul(y-yc)2 dy «M 2 on A - 0 ' (17) 2a m J J |6u| dy dd 0 co where yc is the centroid of the disturbance field, as defined in (18). 37 2x m J J I6UI(y) dy d¢ 0 00 y - 2 (18) C 1r m J J l5u| d)’ M 0 co The data for A/fiO as a function of x/O0 are presented in Figure 82 along with the growth rates of 0(x) for the forced and unforced conditions. Empirically, the growth of the disturbance field can be described as a power law relationship: A/0O - 0.0063 (x/oo)1-6“ (19) for 0 s x/o0 5 60.0 and as a linear relationship: A/0O - 0.0784 x/flO - 0.319 (20) for 77 s x/oO s 192. The discontinuity of the growth rate at x/00 a 60 is apparently related to the indicated saturation (ie. the peak 6u value) at this x location. The indicated linear growth rate is nominally the same as the growth rate of 0(x) over the same domain. 38 Fiedler and Mensing [1985] also observed a saturation effect; theirs was defined in terms of the maximum of the transverse velocity components. Defining this streamwise location as xs, their result showed that for a forcing level which was comparable to that used in the present study, f(xS-xo) Uo a 0.75 (21) where xo was defined as a virtual origin. This virtual origin-was de- fined from their data of xS - xs(f) at a given amplitude. It was ob- served that (1/f) is a linearly increasing function of xs. An extrapolation of this relationship to (l/f) 4 0 defined the x0 value for the given forcing amplitude. An apparent origin cannot be determined herein since a single frequency was used in the present study. In order to compare the two investigations, it can be assumed that only kinematic effects are represented in the f, xs, and U0 relationships and a comparison of the values (fo/UO) can be made for "equivalent" forcing amplitudes. The present observations permit the maximum value of / U0 - 0.045 (22) 1/2 f. l [ 52 + v: to be determined at x/fio = 1. Similarly, Fiedler and Mensing [1985] present data from a single hot—wire immediately downstream of the 39 slot. Their values of (0.065) and (0.0065) bracket those of the present study. Defining a saturation length for the current study based on the maximum 5u values results in a value of X8 - 0.5 m. Hence, fx 3 U0 - 0.62. (23) Using the Fiedler and Mensing [1985] (l/f) a xS results and in- terpolation for the forcing amplitude parameter, a frequency of 13.2 Hz is estimated for the saturation length of the current study: 0.5 m. The corresponding fo/UO value is 0.60. The striking agreement between these two results, in spite of the significant differences in the forcing geometries and in the Reynolds numbers of the separating boundary layers (5500 of 830), supports the assumption that the forcing process is kinematic in character. 4.4 Response of the entrainment field to the forcing input Velocity vector measurements of the entrained flow were performed in the region 100 S x/0O S 200 for both the unforced and forced condi- tions. The data for the unforced condition and the mean forced condi- tion are presented in the form of a velocity vector plot in Figure 83. As indicated in that figure, there is a noticeable mean steering ef- fect of the entrained fluid beyond the active, (ie. vortical), shear layer. Prior investigations in the same facility, Ali et.al. [1985], 4O verified a uniform velocity at the exit of the entrainment condition- ing section, 10 < x/00 < 420, for the unforced condition. The ob- served mean steering is consistent with other observed data for the facility as discussed in the following. An evident feature of the isotachs for the forced shear layer is their greater width on the low speed side of the shear layer. This clearly suggests that a greater mass flux exists at a given downstream location. Other evidence, however, does not support this interpreta- tion. Specifically, with the fan motor set to a fixed operating speed, it was observed that the free stream velocity of the primary flow (U remained unchanged between the unforced and forced condi- 0) tions. Since the U value is dictated by the pressure difference from 0 the atmosphere to the test section and since the constancy of the: 1) pressure rise from the receiver (ie., the domain that receives the flow from the test section and delivers it to the fan) to the atmos- phere and ii) the fan rpm, dictate a constant operating point on the characteristic curve, it is inferred that the volume flow rate through the fan is a constant. It is therefore concluded that the magnitude of the entrainment flow rate into the test section is not affected by the forcing. These separate observations can only be compatible if there is a significant steering effect of the entrainment streamlines as shown schematically in Figure 84. Specifically, with forcing, the entrainment fluid is added to the active shear layer and the flux of 41 vortical fluid at a given x/0O value is larger than that of the un- forced case. Similarly, the streamline trajectories of the unforced case deliver a significant volume flow rate of non-vortical fluid past a given x/00 plane, shown as fim in Figure 84 As a result of experimental difficulties, identified below, quan- titative measures of the steering could not be obtained to verify the above hypothesis, However, the qualitative trends of the data are ap- parent, and they support the proposed flow model of Figure 84.- Previous flow visualization measurements in the entrainment re- gion, Foss [1987], indicated a mean flow angle for the entrained fluid of approximately 60°. Based on this data, quantitative measurements were made in the entrainment region using a compact vorticity probe oriented at an angle of 60°. Additional surveys were made at probe orientations of 45° and 90°. The resulting data indicated a strong steering effect, causing the measured velocity to tend to be aligned with the probe body. This effect could be caused by aerodynamic in- fluence of the probe body, momentum wake effects of the wire support prongs, thermal wake interference between the wires, or perhaps a com- bination of all three. The exact cause of this effect is not clear at the time of this writing. CONCLUSIONS A relatively small perturbation of the separating boundary layer evolves into a strong perturbation of the developing shear layer. The effect of the forcing on the separating boundary layer for the geometry of the current study is twofold: i) A lateral displace- ment of the mean velocity profile for y/0o > 1 and ii) an unsymmetri- cal widening effect for y/oO < 0. For the region 0 < y/o0 < l a combination of these effects is inferred. For equivalent forcing amplitudes, the qualitative evolution of the shear layer is consistent with the prior work of Fiedler and Mens- ing [1985]; specifically, quite similar values of (fxs/UO) were ob- served in spite of quite different values of the forcing methods and separation lip geometries. 42 43 Phase averaged variations (6u) about the mean values of forced flow (6u) exhibit closed contours in phase space. A convection velo- city of the closed contours can be computed from the phase shift between two axial locations (see Figure 81). A width measure of the disturbance field can be defined as a moment of 6u in phase space (see Figure 82). The apparent motions of the closed contours are con- sistent with the trends observed for the computed convection velocity. The entrainment region outside the active shear layer exhibits a mean steering of.the flow field for the forced condition relative to the unforced condition. This mean steering is consistent with other observed data for the facility. 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I , .\. «\R I I \\.. 1 w 100.0m I ...\.v u I “s\ .l .. \ 1 w R 100.0m 1 ww.nnw-m\w\ I T AESECBEV 0008...” mlm , 0 _ AESEMEEV 08.80 ale 1 »_ b _ p _ 0 pp p b _ b p p —_ .b p _ p r p —-—b b b P p _ 00.0m 77 //////////// ///////////// \\\\\\\\\\\\\\\\\\X\ Figure 34 — Streamwise data sampling locations 78 EI/I/I/I/I/lj/ ’//////////// 0.100 ' . —0.050 Y/6 Figure 35 - Unforced G/UO in the separating boundary layer V(x.y.¢) / U0 79 ‘ E//////////// I//////////// 00100 I I l I I I I I l ' 0.050- . X = 39 / ’\ ' / / j / q - - -""" -— fl: __ / / / \ o‘ooo-:===:—-~—"—" ' X = 19 -00050 1 I I I I U I I I l I I U U I U I I U I I -2.0 -1.5 --1.0 -o.5 0.0 Y/B Figure 36 - Phase averaged G/UO at V(x.y.¢) / U., 80 EI/I/l/I/l/l i 3 go 2 90. §L ------- (p = 0.0 O 0.100 ~ . d .1 cu d a: I q -| all I I I I I I -00050 I I I I I I I I I I I I I I I I 1 -2.0 - 1.5 ' - 1.0 -0.5 0.0 Y/B Figure 37 - Phase averaged G/UO at ¢=90.0 81 go = 180.0 0.0 I I l l l I I ‘8 II 7 El/I/l/////l/lllll/ ///////// 0.100 I I I I I I I l I I I I l d X = 39 ' Do 0.050: :- \ X = 19 . 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OJVN P P um musoucoo wmmca mamum> s 8 0Ame P - PP wuswPP 000.0.vl (lg/A 121 0.000 NmH I 0m\x um muzoucou mmmca mamum> Sm I an muswPP S I 0.0Vm 0.0m: 0.0mP 0.00 P P P P P P 000.0%! 000.00 00 //fi& 122 0.000 P 0.mom P P 0mm I 0P\x um mudoucoo mmmxa m5mum> am I on mudem S . 0.0_¢N 032 OJNP 0.00 0.0 P P P P — P P P P P coo-owl . Y/Bo Y/oo 123 “U.()O()’I“V ‘ v I y - 'fi‘fi—V—Vfi—I‘fi—‘fififi-"" -. q . g -‘ —v-‘v ‘V “0"QPl'W—v—fi'fi—w-PI . l . -4 I 4 40.000- l — . I 2 -I I 1 . l I 20000.. J \~ . a. . ‘> . ”b d I . . / 0.000—I J ‘ l «W ' —2o.ooo-\\\ 4 l ‘ I ‘40.000 T ‘I Y I 1 fi v I vvvvv I VVVVV I I 1 Wfi '—I I 1 1 0.0 60.0 120.0 180.0 240.0 300.0 300.0 G" M1 = 115.4 6 qp‘ = 55. 60.000 . ..., ..... ,. P.-. ..... , ..... , -. . .I ‘ ‘ .. i .I 40.000- l " q I d d 1 . | . 20.000- ~00 " - 1a u/m § +‘d27 -I (P x, = 153.8 a «a, = 249. Figure 80 - Determination of disturbance phase location 124 o.nw.vN 0.0—ON voowm .26.“ olo. .3on :9: film. “whoa umofiw wcwmoao>ov ofiu CH woman Cofiuoo>coo - Hm ouswwm o . . m \ x oJm— 0.0.5 0.0m 06¢ — _ r _ p b — _ p p b — p F — b — P — o.v.o 125 mema uwocm wcfimoao>ov ofiu CH monumwoe Luvws - mm ouswwm o m_\ x 0.0_¢N 0.30m . 0.0%.. 0.0_N_ Qmm .5} o {\Uoouounflg Elm om\voououm «In .. 4 \\ 10..v “ \ u g _I 10.0 n .l 4 1.0.NF [0.3 126 muouoo> kufiooao> vaowm uCoECHmuucm - m0 ouswflm O®\N 0.0mm 0.000 0.03 0.09 0.03 0.000 p _ _ _ t p _ _ _ _ _ _ t r _ _ _ _ . _ p O.OH| - /////- H w / w, H I W W/ A» 0» a» .» I000 . .w I - - y» I l - - .0 ,0 - , , l , ‘ W x I H.0.00 . fl . I _ _ _ _ t + _ _ _ _ . _ _ _ . t F _ _ . 1 _ 0.0: 09/& 127 \X\ \\\\\\\\\\\\\\\\\ [- \\\ \\\\\\\\\\\\\\\\\ Forced Condition Figure 84 - Schematic representation of entrainment mass flux APPENDICES APPENDIX A EFFECT OF WALL CONTACT ON HOT-WIRE CHARACTERISTICS A hot-wire anemometer, being a thermal device, is strongly ef- fected by the proximity of a thermally conducting wall. Even when heat loss effects are minimized through use of a poorly conducting wall there is appreciable heat loss to the wall at small wire—to-wall distances. If one of the prongs, which supports the copper plated 5 p tungsten wire, comes into contact with the wall, the heat loss is strongly intensified. This effect can be used to accurately locate the position of the wire by moving the wire towards the wall until a sharp increase in the anemometer output is noted. This positioning method was evaluated for the current study; it was abandoned after it was discovered that bringing the wire into contact with the wall modi- fied the wires characteristics. To quantify the variation in wire characteristics, a number of consecutive calibrations were performed with the same wire. All calibrations were executed over a period of 3 hours, during which time 129 130 the temperature of the room remained constant to within 1° C. The subject wire had been operated for several days, and it was operated for over two hours in the calibration flow before the first calibra- tion. The wall under consideration was Formica faced, and meticu- lously cleaned using isopropyl alcohol prior to the study. In each case the wire was calibrated: i) one or more times in the calibration stream, ii) positioned using the wall contact method, and iii) moved back into the calibration stream and recalibrated. The above pro- cedure was executed for a number of cases; see Table A.l for the resulting data. The calibrations indicated with a "yes" under the heading contact in Table A.1 came into contact with the wall prior to the calibration. The velocity error in Table A.l was obtained using the following procedure. The calibration constants for the first calibration were used to compute a reference voltage from an arbitrary reference velo- city of 10.0 meters per second. The velocity error for each calibra- tion was then evaluated as the difference between the computed flow speed (using the reference voltage) and the reference velocity of 10.0 meters per second. 131 Table A.1 - Wall Contact Calibration Results Std. Computed Velocity Run Contact A B n Dev. velocity error A 9.041 3.769 0.41 0.007 10.00 0.00 B Yes 8.744 3.520 0.42 0.005 11.98 1.98 C 8.852 3.380 0.43 0.012 12.11 2.11 D 8.707 3.519 0.42 0.008 12.09 2.09 E Yes 8.365 3.621 0.41 0.010 13.00 3.00 F 8.648 3.336 0.43 0.009 13.09 3.09 G Yes 8.142 3.779 0.40 0.011 13.14 3.14 H 8.475 3.467 0.42 0.006 13.23 3.23 I 8.496 3.453 0.42 0.008 13.28 3.28 J 8.589 3.325 0.43 0.012 13.37 3.37 K Yes 8.247 3.621 0.41 0.009 13.36 3.36 L 8.414 3.459 0.42 0.009 13.48 3.48 As indicated in Table A.1, the hot-wire characteristics underwent a large change when the wire was brought into contact with the wall. The mechanism behind the change is unknown. For the current study, it was of sufficient interest to ascertain that this type of positioning method was not usable given the experimental configuration. APPENDIX B DROP TEST CALIBRATION TECHNIQUE A novel low speed calibration method was employed for calibration of the hot-wire used in the zero free stream velocity (UO-O) study. The general details of the calibration technique have been previously detailed, Haw [1987]. The specifics on the method used to obtain the reference velocity for the current study are detailed in the follow- ing. The force balance for an arm in a uniform gravitational field can be written as a _ m381§§92r (8.1) where a is the angular acceleration of an arm of mass m and moment of inertia J. 132 133 Since the mechanical properties of the arm are constant all of the constant terms can be merged into a single constant A. Adding ad- ditional constants to account for aerodynamic drag (B) and for bearing friction (C), the resulting force balance is a - A sin(0) - 802 - Cw (8.2) This equation of motion can be solved numerically to yield the position and velocity at any time given the appropriate initial condi- tions. To improve the numerical accuracy, the equation for the angular velocity of the arm can be expanded in terms of a Taylor series and applied at discrete time steps to yield: II'AE I'.A_t_ 'E 01+1 - {[(wi 4 + 01 ) 3 + mi] 2 + w1}At + 01 (8.3) 'I'éE I'A_t_ I wi+1 - [(0i 3 + 01 ) 2 + wi]At + 01 (8.4) where the subcripts i and 1+1 denote the current and the subsequent time steps and the deriviatives of the velocity are given as: w' - a - Asin(0) - 3.02 - Cw (3.5) w" - (Acos(0))w - Zwa' - Cw' (8.6) 134 w"' — w'[Acos(0) + 28w'] + w[wAsin(9) - 280"] - Cw" (8.7) The constants A, B, and C were obtained by minimizing the mean square error in position between the numerical simulation, (from (8.3) and (8.4)), and a series of experimentally measured data points. Although an analytic solution was not possible, numeric results were readily obtained using a steepest descent solution method to minimize the mean squared positional error. The constants obtained in this manner were used in the numerical simulation for the fall, (8.3) and (8.4), to provide the calibration velocities. APPENDIX C ZERO MEAN FLOW PRESSURE MEASUREMENTS Measurements of the pressure field induced by the piston were made for the condition of zero mean flow (Uo - 0). The forcing fre- quency was sufficiently high, and the pressures sufficiently low to make measurements using a conventional tap and pressure transducer configuration impractical. A microphone, modified with a surrounding cavity and pinhole arrangement, was used as detailed in the following. A Bruel and Kjaer type 4166 wide response condenser microphone was used with a locally fabricated cavity and pinhole. The microphone had a free air response of O to 20 KHz and an open circuit sensitivity of 48.6 mv per Pa. The microphone cavity consisted of a 17 mm diame- ter cylinder 5 mm long with a 1 mm hole at one end and the microphone face (17 mm diameter) forming the other end. The resulting resonant frequency of the chamber (1900 Hz), was well above the measurement range of interest. 135 APPENDIX D NUMERICAL DATA The following tables contain the primary experimental data for the current study. The data in the tables are non-dimensionalized in the following forms: a) The velocity measurements of the active shear layer and boun- dary layer are non-dimensionalized with the free stream velocity (U0); the corresponding data locations are non-dimensionalized with the separating boundary layer momentum thickness (00). b) The measurements of the velocity and pressure for the no-flow data are presented in dimensional form. The velocity measure- ments are given in meters per second; the pressure measurements are given as output voltage from the microphone amplifier. In both cases the corresponding data locations are non-dimensionalized with respect to the forcing piston width (wp). 136 HNHHHHHHl—‘HHH HUIU'INH OOQOOOOOOOOOOOOOOOOOQUILDU'IMLRUIWUIUIU1 137 Table D.1 - No Flow Hot-wire Mean Velocities Unforced Phase averaged data (at angle d) y/wp data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .77 .044 .167 .151 .243 .211 .127 .214 .341 .38 .038 .142 .133 .210 .191 .113 .167 .276 .00 .036 .147 .120 .178 .162 .104 .172 .274 -.38 .037 .155 .113 .146 .139 .101 .169 .269 -.77 .030 .152 .107 .123 .119 .093 .154 .251 -1.54 .040 .138 .098 .098 .095 .080 .122 .201 -3.08 .029 .086 .067 .065 .064 .055 .068 .104 -6.15 .042 .060 .052 .047 .047 .045 .047 .059 -10.00 .025 .053 .049 .047 .045 .045 .049 .056 -23.08 .030 .053 .051 .049 .048 .048 .050 .053 -.38 .027 .024 .024 .030 .032 .028 .026 .028 -.38 .024 .034 .037 .057 .058 .042 .039 .054 -.38 .030 .100 .085 .163 .148 .085 .098 .191 -.38 .034 .140 .098 .134 .132 .087 .135 .244 -.38 .036 .086 .098 .149 .137 .084 .101 .158 -.38 .029 .358 .263 .308 .356 .305 .279 .301 -1.00 .042 .022 .023 .025 .027 .025 .024 .024 -l.00 .039 .036 .040 .059 .062 .046 .041 .053 -1.00 .041 .062 .067 .112 .109 .072 .068 .105 -1.00 .041 .116 .081 .098 .100 .072 .102 .180 -1.00 .033 .087 .082 .115 .107 .073 .096 .147 -1.00 .046 .190 .252 .309 .268 .285 .290 .281 -10.00 .024 .018 .018 .019 .019 .019 .018 .018 -10.00 .029 .022 .023 .024 .025 .025 .023 .022 -10.00 .032 .021 .022 .023 .024 .023 .022 .021 -10.00 .034 .028 .027 .028 .029 .028 .028 .029 -10.00 .025 .036 .034 .032 .032 .032 .034 .038 -10.00 .037 .045 .041 .037 .035 .036 .041 .048 -10.00 .032 .067 .061 .055 .052 .054 .063 .074 -10.00 .021 .110 .103 .095 .091 .097 .111 .126 -10.00 .018 .047 .044 .042 .040 .040 .044 .051 315.0 .319 .261 .261 .261 .245 .204 .115 .066 .057 .054 .027 .050 .189 .244 .141 .297 .023 .052 .102 .183 .135 .243 .018 .022 .021 .028 .039 .049 .074 .123 .051 N \ € '6 HNHHHHHHHHHH 00000COOOOQOOOOOQOOOQU‘UIUIUIUIUIUIUIUlU'I HU‘U‘INH Unforced data w Y/p .77 .38 .00 -.38 -.77 -1.54 -3.08 -6.15 -.38 -.38 -.38 -.38 -.38 -.38 -1.00 -1.00 -l.00 -1.00 -1.00 -l.00 -10.00 -10.00 -10.00 -10.00 -10.00 -10.00 ~10.00 -10.00 -10.00 .002 .001 .002 .004 .002 .006 .001 .005 .002 .002 .002 .003 .005 .005 .005 .003 .005 .003 .002 .004 .003 .004 .004 .005 .005 .005 .003 .004 .006 .002 .004 .014 .016 .017 .012 .011 .009 .013 .013 .011 .018 .003 .002 .004 .013 .011 .070 .004 .002 .003 .015 .012 .032 .004 .005 .008 .006 .007 .009 .017 .022 .024 138 Table D.2 - No Flow Hot-wire Rms Velocities Phase averaged data (at angle ¢) 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .016 .013 .007 .004 .004 .004 .007 .010 .010 .017 .003 .002 .003 .004 .010 .095 .004 .003 .005 .005 .008 .058 .004 .005 .008 .006 .006 .008 .015 .022 .021 .020 .019 .012 .008 .007 .005 .005 .007 .008 .016 .003 .003 .005 .012 .014 .153 .005 .004 .007 .010 .014 .062 .004 .005 .009 .006 .005 .006 .014 .022 .019 .016 .014 .008 .007 .006 .006 .005 .006 .007 .015 .003 .003 .005 .010 .012 .110 .005 .005 .006 .011 .012 .131 .004 .005 .009 .006 .005 .006 .014 .022 .018 .008 .007 .005 .004 .004 .004 .005 .007 .008 .015 .003 .002 .003 .004 .007 .054 .004 .003 .004 .004 .007 .147 .004 .005 .009 .006 .005 .007 .015 .023 .020 .016 .017 .017 .012 .012 .013 .010 .008 .010 .016 .003 .002 .003 .018 .014 .029 .004 .003 .004 .017 .015 .082 .004 .005 .008 .006 .006 .009 .018 .025 .025 .022 .023 .025 .019 .019 .018 .019 .013 .013 .018 .003 .003 .005 .026 .018 .021 .004 .003 .006 .028 .019 .044 .004 .005 .007 .007 .008 .011 .020 .026 .029 315.0 .025 .028 .028 .019 .017 .014 .019 .015 .013 .018 .003 .002 .007 .022 .017 .033 .004 .003 .005 .024 .018 .029 .004 .005 .007 .007 .008 .011 .019 .025 .028 x/w P‘NJF‘P‘P‘F‘P‘P‘P‘P‘P‘F‘ HMUNH OOOOOCOOOOOOOOOOWDOOOOUIUIUUIWUUIU'IUIUI Table D. Unforced y/wp data .77 2.326 .38 2.327 1 .00 2.326 1 -.38 2.327 1 -.77 2.327 1 -1.54 2.326 1 -3.08 2.326 1 -6.15 2.326 1 -10.00 2.327 1 -23.08 2.327 1 -.38 2.326 1 -.38 2.326 1 -.38 2.326 1 -.38 2.325 1 -.38 2.326 1 -.38 2.326 1 -1.00 2.327 1 -1.00 2.327 1 -1.00 2.327 1 -1.00 2.327 1 -1.00 2.328 1 -l.00 2.327 1 -10.00 2.327 1 -10.00 2.328 1 -10.00 2.327 1 -10.00 2.326 1 -10.00 2.326 1 -10.00 2.325 1 -10.00 2.325 1 -10.00 2.327 1 -10.00 2.326 1 0.0 .945 .028 .015 .145 .206 .274 .312 .488 .489 .667 .417 .371 .289 .257 .293 .467 .444 .385 .338 .329 .375 .553 .584 .609 .602 .577 .617 .589 .617 .622 .650 139 No Flow Microphone Mean Voltages Phase averaged 45.0 90.0 1.352 2.188 1.409 2.193 1.442 2.223 1.516 2.246 1.562 2.204 1.664 2.303 1.644 2.188 1.776 2.232 1.810 2.272 2.034 2.529 1.728 2.119 1.648 2.115 1.517 2.092 1.480 2.089 1.487 2.115 1.620 2.104 1.738 2.175 1.618 2.129 1.553 2.080 1.502 2.045 1.488 2.063 1.621 2.189 1.875 2.330 1.838 2.268 1.786 2.266 1.796 2.223 1.741 2.211 1.769 2.196 1.759 2.182 1.760 2.162 1 2 .789 .160 135.0 Nwwwwwwwwwwwwwmwwwwwwwwwwwuwwuw .299 .259 .260 .233 .165 .178 .050 .019 .018 .063 .982 .063 .156 .210 .202 .041 .950 .061 .143 .191 .166 .013 .012 .048 .027 .060 .046 .054 .036 .020 .975 data (at angle d) 225.0 180.0 .354 .288 .295 .208 .179 .102 .110 .972 .997 .913 .101 .154 .264 .291 .240 .064 .098 .160 .218 .243 .233 .028 .999 .976 .985 .994 .988 .993 .986 .976 .934 NNNNNNNMNLA’U’WWUOWUWU’MWwNNNUMMWUUUJ nnmmmnmwmwwwwwwwwwwwwNNNwwwwwww .383 .333 .299 .211 .191 .073 .108 .966 .903 .626 .048 .126 .227 .268 .262 .113 .022 .135 .162 .234 .233 .083 .824 .827 .857 .855 .897 .891 .893 .891 .847 270.0 .524 .477 .452 .427 .427 .349 .452 .401 .357 .044 .493 .462 .506 .498 .439 .489 .423 .426 .471 .502 .485 .482 .306 .326 .371 .407 .412 .420 .425 .435 .443 NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN 315.0 .243 .329 .320 .396 .414 .459 .547 .624 .645 .658 .661 .585 .486 .463 .462 .589 .684 .574 .527 .489 .511 .587 .747 .717 .689 .673 .665 .679 .684 .692 .735 P‘P‘F‘P‘F‘F‘F‘F‘P‘F‘P‘P‘F‘F‘F‘F‘P‘P‘F‘P‘P‘F‘F‘F‘F‘F‘F‘P‘P‘P‘P‘ x/w P‘NJF‘F‘P‘P‘F‘F‘F‘F‘P‘F‘ c>c>¢>c>c>c>c>c>c>c>m>c>t>c>c>c>m>c>t>c>m>uauauauauauruauaoauw l-‘U'ILDNH 140 Table D.4 - No Flow Microphone Rms Voltages Unforced Phase averaged data (at angle d) y/wp data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0 .77 .016 .292 .122 .116 .126 .199 .161 .195 .38 .017 .275 .126 .102 .129 .172 .140 .178 .00 .018 .254 .112 .111 .128 .155 .132 .170 -.38 .016 .235 .112 .102 .102 .158 .126 .160 -.77 .017 .240 .106 .108 .097 .151 .122 .156 -1.54 .016 .222 .097 .106 .094 .140 .114 .152 -3.08 .015 .184 .092 .099 .091 .135 .101 .141 -6.15 .015 .156 .091 .110 .085 .108 .094 .123 -10.00 .016 .136 .081 .105 .084 .093 .086 .105 -23.08 .016 .133 .111 .100 .099 .078 .090 .099 -.38 .015 .169 .095 .103 .089 .115 .102 .132 -.38 .016 .195 .113 .106 .098 .119 .113 .147 -.38 .017 .213 .112 .098 .101 .121 .119 .134 -.38 .016 .236 .106 .101 .104 .134 .169 .169 -.38 .016 .228 .100 .097 .107 .135 .164 .168 -.38 .017 .211 .095 .093 .090 .114 .111 .137 -1.00 .015 .165 .106 .107 .090 .117 .099 .136 -1.00 .017 .218 .101 .100 .091 .121 .135 .150 -1.00 .017 .235 .106 .101 .097 .133 .153 .154 -1.00 .017 .216 .109 .093 .098 .134 .165 .166 -1.00 .016 .232 .097 .091 .098 .127 .137 .167 -1.00 .016 .194 .089 .099 .110 .126 .126 .136 ~10.00 .016 .120 .092 .103 .091 .098 .082 .102 -10.00 .016 .134 .098 .108 .088 .101 .087 .107 -10.00 .016 .135 .090 .092 .086 .096 .080 .108 -10.00 .016 .138 .083 .099 .078 .100 .083 .105 -10.00 .016 .135 .083 .093 .085 .093 .082 .101 -10.00 .017 .134 .073 .094 .075 .091 .080 .098 -10.00 .016 .131 .073 .089 .074 .093 .076 .102 -10.00 .017 .137 .081 .089 .073 .097 .076 .101 -10.00 .016 .138 .089 .095 .076 .097 .083 .096 .171 .174 .140 .132 .126 .122 .102 .089 .089 .084 .087 .109 .131 .152 .137 .122 .095 .109 .128 .134 .133 .126 .084 .085 .084 .082 .083 .084 .075 .078 .082 x/0 P‘F‘F‘P‘F‘P‘F‘h‘h‘F'F‘F‘F‘F‘P‘P‘P‘F‘F‘P‘F‘F‘F‘F‘P‘ 0 OOOOOOOOOCOOOOOOOOOOOCOCO 141 Table D.5 - Compact Probe E (x/00-1.0) Unforced y/0o data .55 .028 .038 .37 .030 .039 .18 .048 .055 -.00 .211 .227 -.15 .475 .488 -.28 .569 .576 -.43 .614 .625 -.66 .650 .655 -.82 .669 .673 -1.02 .685 .693 -1.27 .706 .709 -1.59 .724 .727 -1.98 .746 .752 -2.46 .772 .773 -3.06 .796 .794 -3.81 .830 .827 -4.74 .865 .865 -5.89 .909 .906 -7.05 .948 .945 -8.20 .980 .978 -9.36 .996 .995 -10.51 1.001 1.000 -11.66 .999 .999 -12.81 1.002 1.000 -13.97 1.001 1.000 P‘P‘P‘F‘ Phase averaged data (at angle ¢) 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .038 .039 .054 .238 .508 .595 .640 .672 .686 .706 .724 .739 .763 .782 .802 .837 .869 .912 .951 .980 .998 .002 .000 .001 .000 P‘P‘P‘F‘ .039 .039 .059 .254 .527 .611 .652 .680 .697 .717 .732 .749 .768 .789 .809 .844 .879 .917 .957 .985 .999 .003 .001 .002 .001 h‘h‘h‘h‘h‘ .062 .066 .081 .243 .521 .610 .654 .684 .702 .716 .737 .752 .771 .792 .817 .846 .883 .922 .960 .986 .001 .006 .004 .004 .003 F‘P‘P‘F‘F‘ .062 .069 .090 .223 .491 .590 .638 .669 .690 .700 .725 .744 .764 .788 .813 .843 .880 .920 .959 .990 .004 .008 .007 .007 .005 F‘P‘P‘F‘P‘ .054 .057 .078 .203 .461 .560 .615 .646 .669 .688 .709 .728 .749 .773 .799 .833 .872 .915 .953 .985 .002 .007 .006 .007 .006 F‘F‘P‘P‘ .046 .047 .066 .206 .461 .553 .606 .639 .660 .678 .699 .721 .742 .764 .790 .824 .862 .909 .947 .979 .999 .004 .004 .004 .004 315.0 P‘P‘P‘P‘ .039 .041 .060 .216 .468 .559 .613 .643 .663 .679 .701 .720 .743 .769 .790 .825 .860 .905 .944 .977 .995 .001 .001 .002 .002 N \ Q F‘h‘h‘h‘P‘F‘F‘F‘P‘F‘P‘P‘P‘P‘P‘F‘P‘P‘F‘F‘P‘F‘P‘F‘P‘ c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c><> 0 142 Table D.6 - Compact Probe a (x/00-1.O) Unforced MO I I I I I I I I I I I I ¢>G>\JU1¢‘Uiu3h>hJFJPJP‘I I I I I P‘F‘P‘F‘ UDBDF‘CD .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .81 .97 data .0125 .0125 .0209 .0737 .0933 .0814 .0754 .0738 .0748 .0734 .0712 .0716 .0697 .0676 .0669 .0639 .0609 .0560 .0481 .0351 .0215 .0116 .0080 .0067 .0060 0.0 .0161 .0160 .0228 .0733 .0900 .0803 .0759 .0726 .0724 .0744 .0713 .0697 .0702 .0682 .0664 .0642 .0616 .0563 .0480 .0363 .0226 .0113 .0084 .0064 .0059 Phase averaged data (at angle d) 90.0 135.0 45.0 .0157 .0158 .0239 .0753 .0918 .0802 .0709 .0715 .0733 .0731 .0700 .0706 .0689 .0671 .0648 .0649 .0606 .0545 .0480 .0350 .0211 .0116 .0079 .0063 .0061 .0160 .0167 .0258 .0777 .0901 .0747 .0734 .0723 .0721 .0712 .0697 .0681 .0668 .0669 .0642 .0621 .0600 .0546 .0456 .0329 .0204 .0110 .0078 .0066 .0060 .0246 .0236 .0266 .0708 .0891 .0771 .0726 .0717 .0716 .0716 .0695 .0677 .0650 .0653 .0650 .0620 .0596 .0538 .0456 .0347 .0207 .0111 .0077 .0063 .0059 .0253 .0275 .0285 .0683 .0971 .0816 .0748 .0716 .0724 .0710 .0712 .0685 .0669 .0663 .0651 .0616 .0611 .0547 .0480 .0338 .0209 .0118 .0077 .0064 .0059 .0225 .0235 .0274 .0693 .1002 .0865 .0757 .0745 .0722 .0730 .0723 .0695 .0702 .0676 .0660 .0653 .0595 .0553 .0483 .0351 .0214 .0106 .0081 .0063 .0061 .0197 .0203 .0246 .0745 .0946 .0835 .0787 .0788 .0743 .0726 .0727 .0702 .0707 .0691 .0674 .0666 .0623 .0565 .0484 .0350 .0198 .0122 .0081 .0065 .0058 180.0 225.0 270.0 315.0 .0172 .0173 .0250 .0755 .0948 .0832 .0781 .0722 .0748 .0720 .0727 .0713 .0692 .0683 .0653 .0651 .0601 .0542 .0496 .0361 .0223 .0125 .0082 .0069 .0060 x/0 h‘h‘h‘h‘h‘h‘h‘h‘h‘P‘P‘P‘h‘h‘P‘F‘h‘h‘h‘h‘k‘h‘h‘h‘h‘ c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c> 0 y/60 .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 -10. -11. -12. -13. 51 66 81 97 143 Table D.7 - Compact Probe G (x/00-1.0) Unforced data .001 .000 -.001 .018 .024 .016 .010 .005 .002 .002 .001 -.001 -.002 -.001 -.003 -.003 -.003 -.002 -.001 -.001 -.001 - -.001 - -.001 - -.001 - -.000 - Phase averaged 0.0 45.0 90.0 135.0 .001 .001 .000 .019 .030 .021 .014 .009 .008 .007 .006 .004 .003 .003 .000 .000 .001 .000 .001 .000 .000 .000 .001 .002 .001 .001 -.001 .000 .000 .020 .023 .032 .033 .024 .025 .018 .018 .016 .016 .012 .013 .012 .013 .011 .011 .010 .012 .009 .010 .007 .012 .006 .009 .007 .012 .006 .012 .004 .010 .005 .011 .005 .010 .005 .009 .004 .008 .003 .007 .002 .006 .003 .007 .001 -.000 -.002 -.004 -.003 .020 .025 .018 .013 .010 .009 .008 .009 .008 .007 .008 .008 .010 .010 .009 .010 .011 .009 .009 .008 .007 .008 data (at angle d) 180.0 -.001 -.002 -.006 .014 .022 .014 .007 .002 .003 -.001 -.001 -.002 -.001 .001 .000 -.001 .003 .004 .004 .006 .006 .006 .006 .005 .006 225.0 270.0 -.000 .001 -.002 .000 -.005 .003 .010 .015 .020 .023 .012 .013 .004 .006 -.002 .001 -.003 .001 -.004 .003 -.004 .003 -.007 .004 -.006 .007 -.008 .008 -.008 .008 -.008 .010 -.006 .009 -.004 .007 -.003 .007 -.002 .005 -.000 .004 -.000 .004 .000 .004 -.000 .004 .001 .003 315.0 .001 .001 -.000 .016 .024 .014 .009 .004 .002 .002 -.000 -.002 -.002 -.002 -.004 -.005 -.006 -.005 -.006 -.003 -.004 -.004 -.004 -.004 -.003 x/fi P‘P‘P‘P‘F‘F‘F‘P‘h‘h‘h‘h‘h‘k‘P‘P‘P‘F‘P‘F‘P‘F‘F‘P‘P‘ 0 COOOOOOOOOOOOOOOOOOOOOOOO Unforced mo .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 -3. .74 .89 .05 .20 .36 .51 .66 .81 .97 81 144 Table D.8 - Compact Probe G (x/00-1.0) data .0060 .0061 .0126 .0561 .0615 .0457 .0412 .0391 .0402 .0395 .0396 .0401 .0393 .0398 .0393 .0381 .0373 .0335 .0286 .0221 .0157 .0100 .0063 .0050 .0041 0.0 .0091 .0090 .0156 .0581 .0583 .0443 .0409 .0400 .0383 .0397 .0389 .0401 .0402 .0385 .0395 .0384 .0365 .0326 .0285 .0228 .0154 .0100 .0063 .0050 .0041 Phase averaged data (at angle ¢) 45.0 90.0 135.0 .0096 .0095 .0154 .0613 .0600 .0444 .0408 .0390 .0394 .0399 .0393 .0396 .0390 .0391 .0384 .0386 .0359 .0325 .0274 .0217 .0151 .0093 .0063 .0047 .0040 .0089 .0084 .0156 .0614 .0563 .0430 .0395 .0392 .0385 .0387 .0384 .0383 .0386 .0396 .0388 .0381 .0364 .0330 .0274 .0210 .0160 .0098 .0063 .0048 .0040 .0179 .0162 .0184 .0583 .0576 .0427 .0402 .0405 .0406 .0392 .0387 .0383 .0387 .0393 .0387 .0371 .0364 .0329 .0274 .0205 .0156 .0093 .0062 .0048 .0039 .0209 .0210 .0277 .0585 .0611 .0468 .0402 .0401 .0390 .0400 .0403 .0409 .0385 .0401 .0400 .0371 .0355 .0323 .0278 .0211 .0159 .0097 .0058 .0048 .0039 .0167 .0185 .0242 .0550 .0648 .0480 .0405 .0395 .0406 .0391 .0387 .0397 .0386 .0400 .0402 .0384 .0367 .0326 .0287 .0226 .0156 .0104 .0063 .0052 .0040 .0119 .0126 .0205 .0571 .0619 .0457 .0429 .0412 .0392 .0399 .0401 .0408 .0413 .0401 .0401 .0403 .0368 .0331 .0292 .0225 .0146 .0097 .0071 .0049 .0041 180.0 225.0 270.0 315.0 .0092 .0092 .0173 .0572 .0621 .0459 .0416 .0411 .0392 .0389 .0391 .0377 .0395 .0392 .0393 .0385 .0363 .0327 .0290 .0215 .0156 .0108 .0063 .0050 .0042 145 Table D.9 - Compact Probe u'v' (x/90-1.0) Unforced Phase averaged data (at angle ¢) >< \ as O F‘F‘F‘P‘F‘F‘P‘P‘P‘h‘h‘h‘h‘h‘h‘h‘b‘h‘F‘P‘F‘P‘P‘h‘h‘ OOOOOOOOOOOOOOOOOOOOOOOOO MO I I I I I I I I I I I I €>GD\JU1¢‘UJUDNDF‘P‘P‘P‘I I H U .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 -10. -11. -12. .97 51 66 81 data .0005 .0003 .0007 .0186 .0188 .0139 .0142 .0133 .0148 .0146 .0144 .0144 .0143 .0143 .0140 .0136 .0126 .0108 .0076 .0038 .0014 .0004 .0001 .0001 .0000 0.0 45.0 90.0 135.0 .0006 .0007 .0012 .0175 .0141 .0127 .0140 .0130 .0140 .0147 .0144 .0132 .0143 .0129 .0137 .0143 .0123 .0101 .0075 .0037 .0014 .0004 .0001 .0000 .0000 .0008 .0007 .0013 .0212 .0194 .0134 .0121 .0127 .0136 .0145 .0139 .0130 .0132 .0124 .0130 .0143 .0108 .0094 .0074 .0035 .0013 .0003 .0001 .0001 .0000 .0003 .0003 .0013 .0211 .0174 .0111 .0118 .0129 .0133 .0137 .0123 .0120 .0133 .0131 .0140 .0126 .0118 .0101 .0069 .0033 .0013 .0003 .0001 .0000 .0000 .0011 .0008 .0011 .0192 .0172 .0122 .0137 .0134 .0153 .0148 .0135 .0129 .0124 .0125 .0130 .0116 .0119 .0099 .0072 .0029 .0012 .0002 .0001 .0000 .0000 .0016 .0021 .0026 .0205 .0202 .0167 .0145 .0136 .0143 .0154 .0158 .0147 .0139 .0134 .0146 .0121 .0122 .0099 .0073 .0034 .0015 .0005 .0001 .0001 .0000 .0013 .0012 .0018 .0181 .0235 .0149 .0127 .0132 .0149 .0153 .0150 .0127 .0142 .0153 .0149 .0145 .0123 .0103 .0074 .0036 .0014 .0003 .0001 .0001 .0000 180.0 225.0 270.0 .0009 .0008 .0015 .0208 .0196 .0131 .0163 .0151 .0146 .0136 .0154 .0146 .0160 .0150 .0152 .0152 .0129 .0099 .0077 .0038 .0010 .0003 .0001 .0000 .0000 315.0 .0007 .0006 .0014 .0196 .0197 .0167 .0141 .0119 .0140 .0129 .0135 .0136 .0138 .0146 .0136 .0137 .0128 .0100 .0082 .0034 .0016 .0004 .0000 .0001 .0000 X \ Q: 0 uwuwwwwwwwwwwwwwwwwwwwwwu c:c>c>c>c>c>c>c>c>c>c>c>b>b>E>E>E>c>c>c>c>c>c>c>c> Table D.10 - Compact Probe E (x/00-3.0) Unforced y/6O data .55 .093 .090 .37 .120 .125 .18 .199 .213 -.00 .307 .327 -.15 .418 .442 -.28 .497 .517 -.43 .579 .594 -.66 .638 .642 -.82 .659 .664 -1.02 .680 .677 —1.27 .699 .703 -1.59 .719 .720 -1.98 .742 .739 -2.46 .767 .762 -3.06 .794 .790 -3.81 .826 .825 -4.74 .864 .862 -5.89 .906 .904 -7.05 .946 .942 -8.20 .975 .974 -9.36 .995 .992 -10.51 1.001 .999 -11.66 1.001 1.000 -12.81 1.002 1.001 -13.97 1.002 1.002 HHHH 146 Phase averaged data (at angle ¢) 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .103 .151 .233 .363 .468 .552 .612 .660 .675 .693 .709 .729 .748 .769 .797 .830 .866 .909 .948 .975 .993 .000 .001 .000 .001 .120 .159 .257 .390 .505 .578 .644 .682 .697 .712 .729 .743 .759 .780 .808 .839 .873 .913 .950 .979 .997 l. 1. 1. 1. 001 001 001 002 HHI—‘H .127 .158 .252 .386 .506 .578 .649 .687 .699 .720 .735 .751 .767 .789 .814 .843 .879 .919 .956 .982 .999 .004 .004 .004 .004 P'F‘F’F‘h‘ .118 .144 .213 .324 .441 .525 .597 .660 .687 .705 .726 .742 .764 .784 .814 .847 .883 .925 .962 .989 .004 .008 .008 .007 .007 P‘P‘P‘F‘h‘ .100 .124 .185 .280 .391 .462 .556 .627 .661 .683 .702 .727 .750 .773 .804 .836 .874 .919 .957 .986 .003 .009 .009 .009 .009 P‘F‘F‘F‘ .085 .112 .180 .288 .382 .467 .548 .614 .648 .669 .692 .712 .734 .761 .791 .824 .863 .909 .948 .979 .998 .005 .007 .007 .008 315.0 F‘P‘P‘h‘ .085 .117 .190 .296 .402 .483 .566 .623 .647 .668 .693 .714 .733 .762 .788 .821 .857 .904 .942 .976 .993 .001 .003 .003 .004 x/O wwwuwwwwwwuwwwwwwwwuwwwww 0000000000000000000000000 0 y/0O .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .81 .97 147 Table D.11 - Compact Probe Unforced data .0440 .0630 .0899 .1068 .1150 .1107 .0971 .0804 .0763 .0734 .0724 .0713 .0692 .0674 .0656 .0637 .0603 .0552 .0467 .0354 .0209 .0107 .0071 .0058 .0052 0.0 .0428 .0659 .0975 .1128 .1157 .1076 .0901 .0770 .0742 .0719 .0696 .0697 .0704 .0679 .0642 .0629 .0602 .0552 .0466 .0342 .0217 .0119 .0072 .0060 .0053 E (x/00-3.0) Phase averaged data (at angle d) 90.0 135.0 45.0 .0512 .0773 .0987 .1150 .1146 .1051 .0846 .0764 .0730 .0734 .0712 .0696 .0672 .0676 .0668 .0646 .0604 .0545 .0463 .0348 .0227 .0102 .0071 .0058 .0053 .0546 .0748 .0974 .1057 .1055 .0960 .0827 .0734 .0705 .0703 .0694 .0706 .0673 .0650 .0641 .0626 .0596 .0553 .0460 .0333 .0177 .0097 .0072 .0058 .0051 .0574 .0749 .0981 .1108 .1114 .1029 .0838 .0740 .0709 .0689 .0698 .0686 .0654 .0657 .0629 .0608 .0612 .0553 .0451 .0344 .0189 .0103 .0075 .0059 .0052 .0532 .0737 .0998 .1162 .1270 .1178 .1027 .0804 .0738 .0725 .0684 .0682 .0671 .0657 .0657 .0604 .0593 .0524 .0437 .0319 .0188 .0106 .0076 .0056 .0052 .0488 .0662 .0917 .1129 .1221 .1251 .1121 .0897 .0771 .0746 .0720 .0704 .0676 .0663 .0654 .0646 .0576 .0549 .0451 .0339 .0196 .0103 .0071 .0057 .0054 180.0 225.0 270.0 .0442 .0620 .0905 .1079 .1173 .1181 .1094 .0850 .0770 .0748 .0725 .0717 .0712 .0663 .0659 .0638 .0606 .0552 .0476 .0354 .0208 .0109 .0075 .0063 .0054 315.0 .0396 .0651 .0910 .1114 .1174 .1119 .0984 .0817 .0800 .0731 .0718 .0710 .0680 .0671 .0660 .0644 .0619 .0546 .0479 .0351 .0224 .0104 .0081 .0060 .0054 x/0 wwwwwwwwwwwwwwwwwwwwwwwww 0 0000000000000000000000000 y/0o IIIIIIII o I on omumbWWNI-‘HI—‘H' I I I P‘P‘h‘ Canard .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 -10. .66 .81 .97 51 Table D.12 - Compact Probe G (x/60-3.0) Unforced data .004 .017 .027 .027 .018 .010 .007 .005 .004 .001 .000 -.001 -.003 -.004 -.004 -.004 -.003 -.004 -.004 -.004 -.004 -.004 -.003 148 Phase averaged data (at angle ¢) 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .003 .011 .038 .044 .047 .041 .033 .031 .027 .022 .022 .018 .015 .011 .008 .006 .007 .004 .003 .002 .002 .000 .000 .000 .006 .023 .043 .058 .057 .048 .042 .039 .037 .032 .029 .026 .022 .019 .016 .015 .012 .009 .008 .008 .006 .005 .004 .004 .55 -.002 -.002 -.003 -.002 -.003 .37 -.003 -.003 .010 .025 .039 .036 .029 .018 .015 .013 .013 .010 .008 .006 .003 .001 .000 .001 .002 .002 .004 .004 .004 .005 .004 .000 .017 .043 .051 .047 .041 .034 .030 .030 .026 .025 .021 .019 .016 .014 .012 .012 .011 .010 .009 .008 .007 .006 .006 -.005 -.001 .006 .017 .030 .032 .023 .012 .007 .008 .006 .002 .000 .000 .001 .001 .002 .004 .006 .005 .005 .005 .004 .004 .005 .001 .001 .001 .007 .019 .018 .010 .001 .003 .007 .011 .009 .012 .012 .012 .012 .011 .007 .005 .004 .003 .003 .003 .002 .001 .001 .004 .001 .016 .017 .023 .012 .000 .004 .006 .007 .010 .012 .011 .012 .013 .012 .010 .010 .009 .008 .008 .008 .007 .006 315.0 -.001 -.001 .005 .019 .023 .027 .020 .010 .005 .004 .002 .000 -.003 -.003 -.007 -.007 -.007 -.007 -.008 -.008 -.008 -.007 -.008 -.007 -.006 x/0 wwwwwwwwwwwwwwwwwwwwwwwww 0000000000000000000000000 0 Table 9.13 - Compact Probe G (x/oo-3.0) Unforced y/oo .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .81 .97 data .0390 .0526 .0747 .0864 .0875 .0770 .0614 .0468 .0424 .0411 .0400 .0402 .0404 .0405 .0391 .0386 .0368 .0332 .0279 .0219 .0155 .0098 .0062 .0048 .0039 0.0 .0388 .0577 .0807 .0942 .0888 .0749 .0578 .0453 .0430 .0402 .0395 .0396 .0402 .0388 .0387 .0377 .0364 .0326 .0284 .0221 .0153 .0103 .0060 .0048 .0038 149 Phase averaged data (at angle ¢) 90.0 135.0 180.0 225.0 270.0 45.0 .0461 .0647 .0868 .0973 .0878 .0741 .0539 .0439 .0419 .0393 .0390 .0388 .0393 .0393 .0386 .0386 .0362 .0325 .0272 .0222 .0157 .0096 .0062 .0048 .0038 .0504 .0670 .0854 .0948 .0862 .0697 .0546 .0427 .0409 .0383 .0380 .0391 .0382 .0389 .0385 .0381 .0362 .0324 .0274 .0212 .0134 .0087 .0064 .0047 .0037 .0560 .0651 .0833 .0951 .0821 .0727 .0503 .0442 .0397 .0387 .0385 .0397 .0386 .0398 .0393 .0369 .0367 .0317 .0264 .0212 .0148 .0093 .0061 .0048 .0037 .0524 .0674 .0806 .0907 .0885 .0777 .0644 .0487 .0456 .0416 .0407 .0406 .0397 .0404 .0387 .0383 .0367 .0316 .0272 .0214 .0145 .0085 .0062 .0048 .0038 .0430 .0560 .0736 .0869 .0902 .0809 .0685 .0528 .0457 .0425 .0408 .0407 .0408 .0410 .0392 .0392 .0368 .0315 .0283 .0210 .0149 .0095 .0064 .0050 .0037 .0359 .0485 .0702 .0845 .0855 .0757 .0632 .0490 .0452 .0423 .0409 .0403 .0407 .0392 .0397 .0379 .0364 .0324 .0284 .0228 .0145 .0096 .0062 .0057 .0040 315.0 .0354 .0521 .0749 .0882 .0862 .0763 .0590 .0462 .0434 .0421 .0409 .0399 .0396 .0389 .0392 .0380 .0372 .0343 .0284 .0223 .0157 .0094 .0062 .0048 .0038 x/0 wwwwwwwwwwwwwwwwwwwuwwwww 0000000000000000000000000 0 y/Oo .55 .37 .18 .00 .15 .28 .43 .66 .82 .02 .27 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .81 .97 Table D.14 Unforced data .0080 .0180 .0390 .0547 .0542 .0395 .0250 .0152 .0146 .0144 .0141 .0143 .0139 .0144 .0136 .0132 .0122 .0101 .0068 .0038 .0014 .0003 .0001 .0000 .0000 0.0 .0080 .0194 .0498 .0659 .0543 .0344 .0216 .0144 .0129 .0118 .0128 .0139 .0140 .0136 .0123 .0118 .0121 .0097 .0065 .0037 .0014 .0005 .0001 .0000 .0000 - Compact Probe u'v' (x/00-3.0) 150 Phase averaged data (at angle ¢) 180.0 225.0 270.0 315.0 45.0 .0111 .0306 .0538 .0753 .0565 .0418 .0196 .0130 .0122 .0115 .0117 .0135 .0131 .0132 .0132 .0137 .0109 .0096 .0062 .0040 .0018 .0003 .0000 .0000 .0000 90.0 135.0 .0156 .0318 .0539 .0597 .0490 .0311 .0200 .0096 .0118 .0119 .0118 .0118 .0115 .0116 .0114 .0134 .0120 .0087 .0063 .0033 .0009 .0002 .0001 .0000 .0000 .0189 .0299 .0510 .0606 .0450 .0343 .0141 .0137 .0117 .0095 .0129 .0129 .0108 .0132 .0121 .0118 .0131 .0092 .0068 .0037 .0012 .0002 .0001 .0000 .0000 .0156 .0292 .0485 .0611 .0611 .0397 .0238 .0167 .0154 .0133 .0138 .0134 .0134 .0135 .0127 .0121 .0123 .0084 .0061 .0031 .0011 .0001 .0001 .0000 .0000 .0094 .0185 .0351 .0576 .0582 .0515 .0290 .0202 .0145 .0165 .0137 .0147 .0136 .0145 .0149 .0154 .0122 .0096 .0062 .0036 .0012 .0002 .0000 .0000 .0000 .0081 .0128 .0357 .0518 .0562 .0391 .0258 .0190 .0162 .0155 .0152 .0157 .0146 .0136 .0143 .0125 .0126 .0104 .0075 .0044 .0011 .0003 .0000 .0001 .0000 .0056 .0179 .0395 .0583 .0543 .0406 .0244 .0154 .0165 .0139 .0141 .0128 .0127 .0136 .0140 .0133 .0129 .0107 .0070 .0036 .0015 .0002 .0000 .0000 .0000 x/o ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. 0 000000000000000000000000000000000000000000000 Unforced y/0O data ~.03 .175 ~.09 .377 ~.15 .470 ~.21 .515 ~.28 .552 ~.34 .574 ~.43 .595 ~.53 .617 ~.66 .644 ~.82 .661 ~1.02 .689 ~l.28 .707 ~1.59 .728 ~1.98 .751 ~2.46 .779 ~3.06 .805 ~3.81 .839 ~4.74 .879 ~5.89 .925 ~7.05 .961 ~8.20 .984 ~9.36 .990 ~10.51 .989 ~11.66 .990 ~12.82 .991 ~l3.97 .988 ~15.12 .990 ~.03 .200 ~.09 .324 ~.15 .465 ~.21 .519 ~.28 .542 ~.34 .562 ~.43 .582 ~.53 .604 ~.66 .629 ~.82 .655 ~1.02 .678 ~l.28 .699' ~1.59 .719 ~1.98 .743 ~2.46 .773 ~3.06 .800 ~3.81 .834 ~4.74 .875 151 Table D.15 ~ Mean velocity straight wire results .151 .379 .473 .515 .552 .577 .596 .617 .644 .663 .688 .707 .724 .748 .778 .804 .845 .881 .926 .961 .985 .991 .991 .992 .991 .989 .989 .185 .327 .464 .517 .544 .561 .583 .604 .628 .651 .679 .697 .721 .743 .774 .802 .837 .873 Phase averaged data (at angle ¢) 0.0 45.0 90.0 135.0 180.0 225.0 270.0 .144 .372 .468 .514 .551 .578 .595 .621 .644 .668 .688 .705 .728 .751 .778 .807 .843 .881 .927 .962 .987 .992 .991 .993 .992 .990 .990 .175 .316 .462 .515 .546 .563 .587 .606 .630 .657 .681 .700 .725 .742 .773 .803 .835 .878 .149 .374 .472 .516 .554 .579 .600 .618 .645 .665 .687 .708 .730 .754 .782 .809 .843 .882 .928 .964 .986 .993 .992 .993 .993 .990 .991 .190 .330 .462 .521 .545 .564 .587 .607 .633 .656 .681 .701 .723 .751 .776 .805 .838 .879 .148 .377 .476 .522 .554 .581 .601 .621 .646 .667 .690 .712 .728 .753 .784 .811 .847 .883 .928 .964 .986 .993 .993 .994 .993 .991 .991 .182 .329 .470 .522 .547 .567 .586 .613 .638 .657 .680 .705 .723 .749 .777 .807 .840 .880 .169 .398 .482 .523 .557 .579 .603 .624 .646 .668 .692 .710 .733 .756 .783 .815 .849 .887 .929 .965 .988 .993 .992 .994 .993 .991 .991 .199 .350 .476 .523 .550 .567 .588 .612 .636 .659 .682 .704 .723 .748 .776 .806 .837 .879 .168 .399 .484 .522 .557 .583 .600 .623 .646 .669 .690 .712 .730 .753 .780 .810 .846 .885 .927 .964 .986 .991 .991 .993 .992 .990 .990 .184 .333 .472 .522 .550 .561 .582 .609 .633 .654 .679 .701 .725 .747 .772 .802 .837 .879 .168 .389 .485 .522 .557 .581 .601 .622 .646 .667 .688 .710 .731 .753 .780 .811 .845 .883 .928 .962 .986 .992 .991 .992 .992 .989 .989 .211 .342 .472 .521 .547 .558 .584 .610 .632 .652 .679 .701 .723 .746 .771 .802 .838 .875 315.0 .168 .394 .479 .517 .555 .577 .599 .619 .646 .666 .689 .708 .729 .752 .780 .809 .845 .883 .928 .963 .985 .991 .990 .992 .991 .989 .989 .194 .341 .472 .518 .548 .559 .582 .606 .631 .651 .677 .703 .722 .742 .770 .799 .837 .874 ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~5. -5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. 000000000000000000000000000000000000000000000000 ~5 ~7. -3. ~9. ~10. ~11. ~12. ~13. .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 ~11. .82 .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .89 05 20 36 51 66 82 97 66 P‘P‘P‘ .920 .957 .986 .997 .998 .995 .995 .995 .991 .172 .364 .467 .515 .547 .565 .587 .609 .632 .654 .677 .697 .719 .742 .766 .797 .832 .870 .913 .953 .982 .000 .003 .003 .999 .998 .997 .167 .313 .426 .496 .534 .560' .585 .606 .627 .650 .673 .694 P‘P‘P‘P‘ .920 .959 .986 .996 .998 .996 .995 .995 .996 .167 .369 .473 .518 .547 .562 .586 .611 .632 .653 .677 .697 .717 .744 .767 .798 .831 .870 .916 .955 .986 .000 .004 .002 .000 .999 .998 .140 .313 .427 .501 .535 .562 .583 .605 .628 .655 .677 .693 Table D.15 (cont'd). P'P‘P‘P‘ .921 .959 .988 .998 .000 .997 .996 .996 .996 .141 .357 .468 .519 .551 .563 .589 .614 .635 .658 .678 .699 .720 .746 .771 .800 .834 .872 .916 .954 .986 .002 .005 .004 .001 .999 .999 .141 .315 .434 .504 .543 .565 .588 .611 .633 .657 .679 .699 F‘P‘P‘P‘P‘F‘ 152 .923 .960 .988 .999 .001 .998 .998 .997 .997 .172 .375 .477 .526 .559 .573 .591 .615 .641 .663 .683 .700 .727 .750 .773 .802 .839 .878 .922 .957 .989 .004 .007 .005 .003 .001 .000 .160 .329 .442 .510 .545 .574 .595 .614 .639 .661 .681 .706 P‘P‘ F‘P‘P‘F‘P‘F‘ .926 .964 .990 .000 .001 .999 .998 .998 .998 .172 .382 .477 .525 .556 .573 .597 .617 .639 .666 .684 .708 .729 .751 .779 .805 .839 .877 .924 .961 .990 .006 .009 .006 .004 .002 .001 .167 .338 .440 .517 .550 .575 .595 .622 .644 .664 .687 .706 P‘P‘F‘P‘P‘P‘ .924 .962 .989 .999 .001 .999 .998 .998 .998 .171 .382 .479 .526 .556 .573 .592 .616 .640 .663 .685 .702 .725 .751 .776 .804 .836 .878 .920 .960 .990 .005 .008 .006 .004 .001 .001 .158 .342 .445 .514 .544 .572 .595 .613 .642 .659 .685 .704 h‘h‘h‘h‘h‘h‘ .922 .960 .988 .998 .999 .997 .997 .997 .997 .185 .385 .478 .522 .546 .567 .591 .613 .638 .659 .679 .700 .722 .744 .770 .798 .833 .872 .919 .956 .987 .003 .006 .004 .002 .001 .000 .160 .323 .436 .503 .535 .562 .587 .609 .632 .653 .678 .698 r~r~r¢r~ .920 .959 .987 .996 .998 .996 .996 .996 .996 .173 .375 .473 .517 .546 .565 .585 .609 .634 .656 .678 .696 .719 .743 .767 .796 .827 .871 .914 .954 .984 .001 .005 .002 .001 .999 .999 .153 .307 .425 .498 .532 .558 .582 .604 .627 .649 .677 .691 F‘F‘P‘ .920 .959 .985 .996 .997 .996 .995 .995 .995 .167 .366 .468 .512 .544 .562 .587 .608 .630 .653 .672 .694 .717 .740 .764 .793 .828 .870 .913 .955 .984 .999 .003 .002 .000 .998 .998 .168 .325 .428 .498 .528 .558 .582 .602 .625 .644 .672 .692 ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~1. ~1. -1. ~1. -1. ~1. ~1. ~1. -1. ~1. ~1. ~1. -1. ~1. -1. ~1. ~1. ~1. -1. ~1. -1. ~1. ~1. ~1. -1. 000000000000000000000000000000000000000000000000 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 P‘F‘ P'P‘ .719 .741 .769 .798 .832 .870 .914 .953 .985 .998 .002 1. .002 1. .999 l. .999 .999 1. .165 .306 .453 .518 .553 .575 .594 .615 .637 .661 .680 .700 .720 .743 .768 .798 .830 .870 .912 .950 .981 .997 .001 1. .000 1. .998 .999 .999” .206 .364 .494 .540 .567 .591 .718 .739 .773 .802 .830 .871 .915 .955 .985 .999 002 002 001 .999 001 .156 .314 .460 .523 .560 .578 .600 .619 .643 .665 .683 .704 .722 .741 .771 .800 .830 .872 .912 .951 .982 .996 000 000 .999 .998 .997 .185 .374 .508 .548 .575 .595 Table D.15 (cont'd). P‘F‘P‘F‘P‘F‘ P‘P’ .722 .746 .773 .804 .837 .875 .920 .957 .986 .000 .004 .003 .002 .000 .002 .144 .314 .467 .529 .566 .585 .606 .630 .653 .673 .689 .710 .732 .751 .779 .808 .835 .871 .917 .953 .985 .998 .002 .001 .999 .998 .997 .172 .378 .524 .563 .586 .608 F‘h‘h‘h‘h‘h‘ h‘h‘h‘h‘h‘ 153 .729 .750 .778 .809 .838 .880 .926 .961 .989 .003 .006 .005 .004 .002 .003 .182 .339 .482 .547 .579 .595 .619 .643 .662 .683 .698 .718 .739 .759 .785 .814 .844 .881 .921 .958 .988 .000 .003 .003 .001 .000 .998 .191 .399 .535 .570 .600 .619 F‘F‘F‘P‘P‘P‘ F‘P‘F‘P‘F‘ .730 .757 .783 .809 .842 .882 .925 .962 .993 .004 .007 .007 .005 .003 .004 .191 .353 .491 .548 .580 .597 .620 .641 .663 .685 .704 .719 .743 .764 .788 .815 .848 .883 .925 .962 .991 .003 .006 .005 .003 .001 .999 .228 .414 .538 .580 .601 .621 P‘P‘F‘P‘P‘F‘ F‘F‘F‘F‘F‘F‘ .727 .751 .779 .807 .842 .879 .923 .963 .991 .005 .008 .007 .005 .003 .004 .179 .342 .475 .537 .568 .588 .609 .630 .655 .676 .693 .710 .732 .755 .779 .812 .844 .881 .922 .962 .991 .004 .006 .006 .004 .003 .001 .215 .398 .521 .561 .585 .603 P‘F‘F‘h‘h‘k‘ P‘P‘P‘F‘F‘F‘ .721 .746 .772 .802 .834 .875 .919 .959 .989 .003 .006 .005 .004 .003 .004 .161 .321 .461 .518 .554 .572 .595 .617 .639 .663 .682 .702 .724 .747 .771 .803 .833 .873 .916 .956 .987 .002 .006 .005 .004 .003 .002 .173 .368 .495 .538 .560 .584 F‘P‘F‘P‘P‘ F‘F‘P‘F‘F‘ .715 .744 .769 .797 .833 .869 .915 .953 .984 .999 .003 .003 .002 .001 .003 .167 .305 .447 .510 .550 .566 .585 .608 .633 .657 .675 .695 .717 .743 .766 .797 .828 .866 .911 .952 .983 .998 .003 .003 .002 .001 .000 .180 .363 .486 .532 .558 .582 P‘P‘P‘ .715 .741 .766 .797 .830 .866 .911 .952 .983 .998 .002 .002 .001 .999 .001 .169 .314 .451 .515 .548 .570 .594 .612 .632 .658 .676 .697 .716 .740 .765 .793 .828 .865 .908 .949 .980 .996 .000 .001 .000 .999 .998 .202 .375 .495 .540 .563 .583 UDP‘F‘F‘P‘F‘F‘P‘P‘F‘P‘P‘F‘P‘F‘F‘P‘F‘F‘P‘P‘F‘F‘P‘P‘F‘F‘ 00000000000000000000000000OOOOOOOOOOOOOOOOOOOOOO .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .58 .40 .21 .03 .12 .25 .40 .63 .79 .99 .24 .56 .95 .43 .03 .78 .71 .86 .02 .17 .32 .48 .63 .78 .94 .09 .58 P‘P‘P‘F‘P‘P‘ P‘P‘P‘P‘ .609 .628 .651 .673 .693 .711 .734 .755 .779 .806 .841 .876 .923 .960 .992 .006 .010 .008 .005 .005 .005 .051 .059 .056 .067 .132 .300 .518 .620 .652 .680 .703 .728 .753 .781 .808 .835 .864 .877 .906 .926 .955 .996 .004 .006 .006 .003 .100 P‘P‘F‘F‘P‘P‘ P‘F‘h‘h‘ .615 .637 .659 .675 .695 .712 .735 .757 .782 .810 .842 .879 .922 .961 .990 .005 .008 .007 .006 .006 .004 .053 .059 .063 .076 .145 .316 .522 .626 .653 .681 .707 .731 .753 .782 .810 .834 .860 .878 .905 .929 .955 .997 .003 .006 .005 .005 .107 Table D.15 (cont'd). P‘P‘F‘P‘P‘P‘ P‘F‘P‘P‘ .628 .650 .672 .690 .708 .725 .744 .765 .791 .815 .845 .883 .926 .964 .992 .007 .009 .008 .007 .006 .004 .063 .068 .071 .081 .151 .337 .547 .638 .668 .690 .717 .739 .764 .789 .814 .840 .866 .884 .909 .932 .957 .997 .004 .006 .005 .004 .100 P‘P‘F‘P‘P‘P‘ P‘P‘F‘F‘F‘ 154 .642 .656 .678 .694 .714 .732 .751 .771 .796 .823 .855 .891 .931 .971 .995 .009 .010 .009 .008 .006 .004 .058 .059 .061 .079 .164 .366 .566 .652 .679 .705 .729 .749 .774 .796 .824 .848 .873 .890 .914 .938 .960 .000 .007 .008 .006 .005 .118 P‘P‘P‘P‘P‘P‘P‘ P‘P‘F‘F‘F‘ .642 .659 .680 .700 .715 .734 .758 .778 .799 .830 .855 .895 .935 .973 .000 .012 .014 .012 .010 .008 .006 .072 .069 .066 .086 .185 .391 .580 .657 .684 .708 .732 .754 .774 .800 .827 .850 .877 .890 .919 .941 .964 .003 .009 .010 .008 .006 .138 F‘P‘P‘F‘h‘h‘h‘ F‘F‘F‘P‘P‘ .624 .642 .670 .687 .705 .726 .746 .769 .795 .823 .855 .893 .936 .973 .001 .013 .016 .014 .012 .010 .008 .084 .080 .080 .100 .179 .366 .560 .645 .673 .698 .721 .746 .769 .793 .823 .846 .875 .889 .919 .941 .966 .006 .010 .012 .010 .008 .137 F‘P‘P‘F‘P‘P‘ F‘P‘P‘P‘P‘ .607 .628 .652 .671 .691 .709 .736 .754 .783 .812 .847 .885 .928 .969 .998 .011 .015 .013 .012 .011 .009 .077 .077 .077 .097 .168 .333 .533 .625 .657 .683 .708 .734 .759 .781 .812 .838 .867 .884 .912 .937 .963 .004 .010 .012 .011 .009 .110 P‘F‘F‘F‘F‘P‘ P‘F‘F‘P‘ .602 .626 .647 .665 .685 .707 .731 .751 .777 .801 .841 .875 .923 .960 .994 .008 .012 .011 .010 .010 .008 .064 .066 .070 .085 .151 .312 .506 .610 .647 .671 .698 .725 .748 .772 .805 .834 .859 .879 .906 .930 .956 .999 .007 .010 .009 .008 .086 F‘P‘F‘P‘P‘P‘ F‘P‘h‘h‘ .602 .625 .650 .668 .687 .707 .730 .753 .775 .800 .837 .875 .919 .962 .989 .005 .009 .008 .007 .007 .005 .056 .059 .063 .079 .145 .303 .514 .610 .645 .669 .701 .724 .747 .775 .802 .831 .860 .878 .906 .928 .956 .996 .005 .007 .007 .006 .090 F‘P‘ oomummummummummmummuwu:mu:wwuwwwuwwwwwwwwwuwuwwwwww 000000000000000000000000000000000000000000000000 ~10 -4 ~13 .40 .21 .03 .12 .25 .40 .63 .79 .99 .24 .56 .95 .43 .03 .78 .71 .86 .02 .17 -9. 32 .48 ~11. ~12. ~13. ~15. 2. .01 .03 .96 -1. ~2. -3. .90 ~5. -5. ~7. ~8. -9. ~10. ~11. ~12. .78 ~14. ~15. ~16. ~17. .00 .87 63 78 94 09 00 94 93 92 89 88 86 85 84 82 81 79 76 75 74 72 P‘P‘P‘P‘F‘P‘ P‘F‘P‘F‘F‘P‘P‘F‘F‘F‘F‘ .107 .152 .228 .298 .369 .464 .591 .642 .675 .702 .726 .752 .774 .803 .830 .846 .904 .934 .987 .001 .009 .010 .008 .007 .004 .085 .093 .329 .688 .777 .821 .874 .909 .950 .976 .000 .007 .008 .007 .006 .004 .003’ .001 .000 .000 .000 .040 .041 P‘P‘P‘F‘h‘ P‘P‘P‘F‘P‘F‘P‘F‘P‘F‘ .111 .157 .241 .316 .387 .483 .607 .657 .683 .703 .729 .749 .777 .805 .830 .847 .904 .933 .987 .999 .010 .010 .008 .007 .004 .053 .059 .365 .679 .768 .816 .867 .904 .946 .973 .996 .004 .006 .005 .005 .004 .003 .001 .001 .001 .001 .032 .033 Table D.15 (cont'd). P‘P‘P‘P‘F‘P‘ P‘F‘P‘P‘P‘F‘ .113 .169 .262 .335 .409 .511 .620 .665 .687 .714 .736 .757 .783 .812 .838 .850 .906 .938 .989 .000 .009 .009 .007 .006 .003 .108 .107 .381 .689 .778 .823 .872 .907 .949 .974 .996 .002 .005 .004 .003 .001 .001 .999 .999 .999 .999 .032 .034 h‘h‘h‘h‘h‘h‘ P‘F‘P‘P‘h‘h‘ 155 .126 .186 .285 .362 .435 .535 .646 .687 .714 .732 .751 .771 .798 .817 .844 .858 .914 .939 .991 .003 .011 .010 .008 .006 .003 .130 .137 .407 .703 .784 .828 .878 .915 .952 .978 .998 .004 .006 .004 .003 .001 .000 .999 .998 I998 .998 .043 .048 F‘P‘P‘P‘P‘h‘ F'P‘F‘P‘P‘P‘F‘P‘ .141 .192 .281 .367 .444 .534 .653 .693 .719 .737 .759 .781 .802 .824 .849 .862 .917 .947 .994 .007 .014 .012 .010 .007 .004 .138 .144 .405 .715 .795 .834 .884 .920 .956 .983 .001 .007 .007 .006 .005 .003 .002 .000 .999 .999 .998 .044 .048 F‘P‘P‘P‘F‘F‘ h‘h‘h‘h‘h‘h‘h‘h‘h‘h‘h‘ .141 .177 .255 .326 .400 .493 .615 .666 .700 .723 .744 .769 .795 .818 .847 .858 .920 .946 .998 .008 .017 .015 .013 .010 .007 .112 .118 .349 .707 .799 .841 .891 .925 .960 .988 .007 .012 .013 .011 .009 .007 .005 .003 .002 .001 .001 .056 .062 F‘F‘P‘P‘F‘P‘ F‘F‘P‘P‘F‘P‘h‘h‘h‘h‘h‘ .119 .163 .233 .298 .366 .460 .581 .637 .678 .704 .733 .758 .784 .811 .840 .855 .916 .942 .996 .008 .017 .017 .015 .012 .009 .069 .089 .329 .687 .791 .835 .885 .921 .960 .989 .008 .014 .015 .014 .012 .010 .009 .006 .005 .004 .004 .063 .067 F‘F‘P‘h‘h‘h‘ P‘F‘F‘P‘P‘P‘F‘P‘P‘P‘h‘ .099 .146 .214 .283 .349 .447 .566 .628 .661 .692 .720 .745 .771 .800 .828 .846 .908 .938 .991 .005 .015 .015 .013 .011 .008 .039 .066 .319 .671 .780 .824 .877 .912 .956 .982 .005 .011 .013 .012 .011 .009 .008 .006 .006 .005 .005 .048 .047 P‘F‘F‘F‘P‘P‘ P‘P‘F‘F‘P‘F‘P‘F‘F‘F‘ .100 .145 .218 .291 .358 .454 .579 .632 .662 .689 .717 .743 .767 .801 .827 .841 .902 .933 .988 .000 .012 .012 .010 .009 .006 .030 .055 .333 .670 .772 .818 .871 .906 .950 .976 .998 .008 .009 .009 .008 .007 .006 .004 .004 .004 .004 .037 .037 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 25. 25. 25. 25. 25. 25. 25. 25. 000000000000000000000000000000000000000000000000 N090 ~5 ~6. ~7. ~9. ~10. ~11. ~12. .26 ~15. .79 ~18. ~19. .00 .45 .91 .36 .81 .27 .72 .82 ~14 ~16 I" NUU‘IGQO .75 .62 .51 ~1. ~2. ~3. ~5. ~6. ~7. ~8. ~9. ~10. ~11. ~12. ~14. ~15. ~16. ~17. .52 .00 .73 .47 .20 .93 .33 ~1. ~2. -4. .40 63 76 88 01 14 26 39 51 64 77 89 02 15 27 40 60 86 13 66 93 19 46 73 99 53 06 32 P‘F‘P‘F‘F‘ F‘F‘F‘P‘P‘h‘h‘ .065 .237 .555 .748 .810 .862 .909 .950 .983 .998 .003 .004 .002 .001 .001 .999 .998 .998 .997 .036 .037 .042 .082 .246 .501 .729 .811 .868 .919 .962 .990 .004 .004 .006 .004 .002 .001 .001 .999 .000 .034 .034 .036 .041 .070 .169 .353 .572 P‘P‘P‘F‘P‘P‘P‘P‘P‘ h‘h‘h‘h‘h‘h‘h‘h‘h‘ .062 .233 .553 .737 .801 .854 .902 .942 .977 .995 .001 .002 .002 .002 .001 .001 .000 .000 .001 .037 .035 .038 .077 .229 .470 .704 .794 .854 .906 .954 .986 .001 .005 .006 .006 .006 .005 .005 .005 .004 .077 .083 .092 .107 .132 .188 .325 .504 Table D.15 (cont'd). .073 .270 .587 .734 .797 .852 .899 .940 .975 .990 .996 .997 .997 .997 .996 .996 .996 .995 .997 .029 .029 .037 .088 .257 .502 .714 .793 .852 .902 .949 .979 .993 .996 .997 .998 .998 .998 .998 .999 .998 .063 .066 .070 .078 .095 .160 .299 .496 156 .085 .304 .611 .750 .806 .860 .904 .946 .977 .992 .996 .996 .996 .995 .994 .994 .993 .993 .994 .026 .028 .040 .107 .302 .559 .730 .803 .859 .906 .949 .977 .989 .992 .993 .994 .993 .993 .994 .994 .994 .044 .044 .044 .050 .079 .175 .350 .555 .095 .313 .624 .753 .812 .864 .909 .949 .980 .994 .998 .998 .997 .996 .995 .994 .994 .993 .994 .035 .039 .052 .125 .331 .575 .753 .814 .869 .918 .957 .982 .992 .994 .994 .994 .993 .992 .992 .993 .992 .028 .027 .030 .042 .092 .216 .415 .613 F‘F‘P‘P‘F‘ P‘F‘ .096 .306 .629 .778 .834 .883 .924 .960 .992 .003 .005 .004 .003 .002 .999 .998 .997 .996 .997 .040 .043 .055 .136 .334 .579 .757 .824 .878 .929 .969 .991 .999 .000 .000 .999 .997 .996 .995 .995 .994 .023 .024 .032 .051 .111 .247 .455 .666 P‘P‘F‘F‘F‘P‘P‘F‘P‘P‘P‘ P‘P‘F‘P‘F‘F‘h‘h‘h‘h‘ .091 .247 .556 .768 .836 .884 .929 .969 .000 .011 .014 .012 .010 .009 .006 .005 .003 .001 .001 .057 .063 .077 .123 .297 .563 .783 .857 .904 .947 .985 .007 .013 .013 .011 .009 .006 .004 .003 .002 .000 .034 .038 .045 .061 .125 .270 .479 .675 P‘P‘P‘h‘h‘h‘h‘h‘h‘h‘ F‘P‘F‘P‘P‘P‘P‘F‘F‘F‘ .067 .219 .519 .752 .819 .872 .921 .961 .994 .010 .014 .014 .012 .011 .008 .007 .006 .004 .004 .067 .073 .085 .116 .252 .474 .714 .832 .891 .943 .983 .011 .021 .020 .018 .016 .013 .011 .009 .007 .005 .053 .058 .066 .077 .121 .245 .447 .681 h‘h‘h‘h‘h‘h‘h‘h‘h‘h‘ P‘P‘P‘F‘F‘P‘F‘P‘F‘ .063 .222 .522 .740 .809 .861 .909 .950 .985 .003 .008 .009 .008 .007 .006 .005 .004 .003 .004 .053 .053 .056 .082 .215 .449 .691 .804 .865 .921 .967 .999 .013 .015 .015 .014 .012 .011 .010 .009 .007 .073 .081 .093 .111 .139 .212 .384 .595 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 00000000000000000O00000000OOOOOOOOOOOOOOOOO00000 .37 .92 .46 .01 .55 .10 .65 .19 .74 .29 .83 .38 .92 .00 .03 .07 .10 .13 .17 .20 .24 .27 .70 .66 .63 .60 .56 .53 .49 .46 .42 .39 .36 .32 .00 .47 .95 .42 .90 .37 .84 .32 .79 .26 .26 .79 .31 .84 H HHHH .766 .851 .914 .963 .993 .000 .000 .999 .997 .997 .996 .996 .993 .034 .034 .034 .036 .041 .060 .130 .264 .453 .661 .825 .917 .977 .001 .003 .002 .000 .999 .998 .992 .994 .036 .035 .035 .035 .036 .041 .061 .118’ .237 .396 .590 .781 .922 .988 P‘F‘P‘P‘P‘P‘P‘P‘F‘ P‘P‘P‘F‘P‘F‘F‘ .705 .843 .918 .975 .008 .019 .019 .017 .014 .011 .010 .007 .002 .055 .063 .077 .095 .108 .125 .212 .374 .599 .811 .936 .997 .033 .036 .028 .021 .013 .008 .003 .994 .997 .043 .044 .049 .058 .073 .097 .132 .200 .310 .452 .630 .774 .872 .911 Table D.15 (cont'd). P‘F‘P‘P‘P‘P‘ F‘F‘P‘F‘P‘P‘F‘P‘P‘P‘ .698 .811 .883 .944 .983 .997 .001 .002 .002 .001 .002 .000 .997 .078 .089 .107 .129 .148 .164 .219 .343 .525 .727 .890 .007 .055 .068 .057 .044 .032 .024 .017 .007 .007 .028 .027 .031 .042 .061 .090 .139 .233 .377 .548 .709 .825 .904 .930 1.001 1.081 1.047 P‘P‘P‘P‘F‘P‘F‘F‘ 157 .734 .751 .818 .828 .884 .390 .938 .941 .971 .968 .983 .976 .987 .930 .989 .981 .990 .982 .990 .983 .992 .985 .992 .985 .990 .983 .087 .081 .098 .089 .115 .102 .136 .117 .161 .135 .195 .162 .249 .204 .334 .271 .462 .397 .620 .555 .774 .727 .915 .355 .997 .942 .034 .986 .037 .998 .033 1.003 .026 1.003 .020 1.002 .015 1.001 .008 .998 .007 .999 .028 .048 .030 .054 .038 .066 .055 .034 .080 .109 .112 .128 .156 .134 .245 .182 .396 .339 .597 .551 .779 .747 .899 .906 .978 1.030 .791 .857 .910 .956 .977 .981 .983 .983 .982 .982 .984 .984 .981 .065 .070 .077 .087 .101 .122 .165 .261 .403 .590 .754 .855 .924 .960 .972 .980 .983 .985 .987 .985 .989 .065 .074 .088 .108 .132 .157 .172 .230 .358 .518 .675 .822 .950 .803 .871 .929 .970 .989 .993 .993 .991 .989 .988 .989 .988 .983 .045 .047 .051 .059 .072 .104 .185 .317 .490 .662 .787 .872 .930 .954 .964 .971 .973 .977 .978 .976 .982 .072 .081 .094 .113 .138 .167 .205 .268 .363 .482 .604 .734 .861 .976 F‘P‘F‘F‘F‘F‘ .834 .903 .956 .996 .014 .014 .011 .006 .002 .000 .998 .996 .990 .025 .026 .032 .044 .066 .113 .213 .379 .574 .733 .836 .906 .951 .965 .970 .974 .975 .977 .978 .974 .981 .069 .076 .087 .102 .122 .148 .186 .244 .320 .414 .531 .671 .824 .934 P‘F‘P‘F‘P‘P‘P‘P‘F‘ .792 .919 .971 .010 .030 .032 .027 .021 .015 .011 .009 .005 .999 .027 .033 .044 .061 .084 .127 .240 .432 .626 .776 .869 .937 .977 .987 ' .989 .989 .988 .987 .986 .981 .986 .058 .063 .070 .081 .097 .120 .154 .205 .284 .394 .529 .702 .839 .914 60. 60. 60. 60. 60. 60. 60. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. #94?##9##«8‘»Pk-I-‘kkb-P41>4‘k@000000000000000000000000000 .37 .89 .42 .95 .47 .00 .52 .47 .86 .24 .63 .01 .40 .78 .17 .55 .94 .68 .30 .91 .53 .14 .76 .37 .99 .60 .22 .83 .58 .37 .17 .97 .77 .57 .37 .17 .97 .77 .56 .64 .84 .04 .24 .44 .64 .84 .25 .25 P‘P‘P‘ .999 .000 .994 .994 .986 .988 .981 .000 .002 .003 .999 .981 .938 .862 .770 .664 .559 .457 .366 .281 .203 .149 .099 .070 .052 .045 .040 .038 .040 .042 .046 .055 .073 .101 .148 .205 .283 .360 .448 .547 .658 .771’ .867 .947 .985 .992 .992 .990 .931 .941 .949 .957 .957 .963 .962 .977 .972 .964 .943 .890 .823 .749 .678 .615 .556 .496 .439 .377 .321 .270 .225 .190 .165 .143 .125 .112 .054 .066 .081 .104 .133 .171 .222 .281 .361 .451 .550 .651 .748 .830 .899 .944 .965 .975 .980 .980 Table D.15 (cont’d). F‘F‘F‘F‘ 158 .946 1.003 .953 .997 .959 .993 .964 .991 .963 .982 .966 .982 .964 .977 .941 .930 .934 .923 .924 .913 .909 .899 .889 .883 .846 .860 .776 .825 .699 .775 .613 .702 .537 .617 .468 .528 .403 .438 .346 .367 .297 .299 .251 .245 .209 .198 .174 .160 .147 .131 .126 .110 .108 .090 .095 .077 .051 .063 .061 .071 .074 .083 .089 .094 .115 .113 .144 .134 .183 .173 .242 .248 .337 .359 .464 .485 .565 .567 .657 .653 .760 .761 .826 .820 .892 .880 .957 .931 .008 .983 .044 1.030 P‘P‘P‘F‘F‘F‘ .074 .051 .034 .022 .006 .001 .991 .955 .950 .944 .934 .921 .901 .874 .835 .774 .701 .619 .528 .438 .347 .273 .213 .163 .128 .102 .078 .063 .077 .086 .098 .112 .130 .160 .208 .292 .394 .499 .556 .618 .713 .768 .827 .884 .944 .993 .037 1.059 1.037 .037 1.059 1.037 P‘F‘P‘P‘F‘P' P'P‘P‘P‘F‘P‘ .080 .061 .043 .030 .016 .009 .998 .015 .022 .029 .031 .030 .010 .970 .914 .841 .750 .662 .561 .451 .351 .271 .214 .172 .141 .114 .086 .071 .086 .096 .110 .128 .152 .193 .241 .305 .387 .472 .519 .585 .656 .727 .792 .852 .914 .959 .993 .993 F‘P‘P‘P‘F‘P‘ P‘F‘P‘P‘F‘h‘ .028 .026 .019 .013 .005 .001 .992 .069 .086 .099 .091 .052 .000 .942 .882 .807 .722 .630 .529 .422 .302 .209 .154 .138 .131 .123 .107 .093 .086 .097 .115 .135 .164 .207 .252 .304 .374 .444 .509 .577 .645 .720 .787 .847 .899 .925 .947 .947 F‘P‘P‘P‘ .975 .983 .985 .987 .985 .986 .980 .071 .082 .076 .036 .978 .923 .870 .813 .752 .670 .588 .505 .424 .330 .245 .183 .151 .142 .132 .124 .112 .079 .092 .111 .134 .168 .210 .257 .309 .378 .442 .517 .593 .659 .743 .804 .845 .873 .891 .920 .920 P‘P‘P‘ .940 .952 .960 .966 .966 .972 .968 .029 .030 .021 .979 .913 .854 .795 .735 .683 .614 .547 .477 .410 .340 .276 .227 .192 .167 .149 .132 .120 .066 .081 .098 .124 .157 .199 .250 .308 .386 .454 .542 .633 .711 .777 .821 .854 .880 .901 .930 .930 159 Table D.15 (cont'd). 115.4 ~20.45 .990 .978 1.026 1.047 1.030 .992 .952 .926 .933 153.8 ~28.62 .979 .982 .960 .948 .953 .974 .999 1.011 1.004 153.8 ~25.51 .982 .987 .958 .941 .947 .976 1.010 1.025 1.015 153.8 -22.41 .985 .990 .955 .933 .941 .978 1.023 1.040 1.024 153.8 ~19.30 .992 .982 .948 .922 .934 .985 1.031 1.036 1.015 153.8 ~l6.19 .993 .948 .929 .908 .919 .980 1.014 1.002 .976 153.8 ~13.09 .982 .890 .883 .877 .894 .959 .966 .947 .911 153.8 ~9.98 .924 .822 .824 .837 .860 .903 .893 .870 .843 153.8 ~6.87 .820 .749 .744 .768 .802 .817 .808 .799 .772 153.8 ~3.76 .703 .688 .671 .684 .719 .710 .724 .727 .715 153.8 ~.66 .576 .599 .592 .602 .613 .584 .604 .629 .626 153.8 2.45 .457 .514 .513 .525 .521 .472 .467 .495 .516 153.8 5.56 .353 .442 .443 .446 .436 .388 .355 .378 .420 153.8 8.66 .271 .343 .367 .376 .365 .316 .272 .273 .310 153.8 11.77 .195 .273 .298 .312 .306 .271 .228 .216 .237 153.8 14.88 .133 .219 .236 .254 .254 .231 .203 .190 .200 153.8 17.98 .090 .176 .190 .200 .201 .185 .168 .160 .166 153.8 21.09 .062 .153 .158 .165 .166 .159 .146 .143 .148 153.8 24.20 .050 .130 .132 .135 .131 .124 .117 .119 .125 153.8 27.30 .045 .110 .110 .109 .104 .099 .097 .100 .105 153.8 30.41 .044 .091 .090 .090 .085 .082 .081 .084 .088 153.8 33.52 .043 .077 .077 .074 .070 .067 .067 .071 .075 192.3 43.46 .045 .069 .070 .071 .073 .075 .075 .073 .070 192.3 39.45 .046 .083 .084 .086 .088 .089 .089 .088 .086 192.3 35.43 .047 .114 .113 .112 .113 .117 .118 .118 .117 192.3 31.42 .051 .146 .143 .141 .145 .148 .151 .154 .151 192.3 27.41 .060 .194 .184 .180 .181 .187 .194 .196 .197 192.3 23.40 .082 .221 .209 .203 .208 .215 .226 .232 .230 192.3 19.38 .116 .260 .244 .235 .240 .250 .267 .274 .275 192.3 15.37 .182 .304 .279 .270 .275 .297 .322 .338 .332 192.3 11.36 .253 .341 .308 .302 .323 .351 .386 .403 .383 192.3 7.35 .349 .385 .349 .353 .396 .434 .459 .470 .444 192.3 3.33 .460 .439 .420 .448 .488 .513 .532 .530 .500 192.3 ~.68 .585 .550 .554 .586 .599 .601 .605 .610 .589 192.3 ~4.69 .715 .686 .701 .707 .710 .698 .689 .696 .701 192.3 ~8.70 .843 .806 .811 .812 .792 .772 .767 .787 .810 192.3 ~12.72 .941 .902 .894 .886 .863 .841 .837 .852 .886 192.3 ~16.73 .982 .963 .964 .949 .925 .904 .894 .897 .925 192.3 ~20.74 .990 .989 1.011 1.000 .979 .953 .932 .922 .943 192.3 ~24.75 .982 .989 1.017 1.019 1.000 .975 .949 .937 .952 192.3 ~28.77 .979 .984 1.009 1.016 1.002 .979 .957 .948 .958 192.3 ~32.78 .985” .990 1.006 1.010 1.001 .984 .968 .963 .971 192.3 ~36.79 .985 .987 1.000 1.004 .997 .984 .972 .968 .974 230.8 ~44.97 .985 .981 .977 .977 .983 .991 .996 .995 .989 230.8 ~40.05 .985 .982 .975 .975 .982 .994 1.001 1.001 .992 230.8 ~35.13 .987 .982 .970 .969 .980 .996 1.008 1.006 .996 230.8 ~30.21 .983 .971 .958 .957 .974 .998 1.010 1.005 .988 230.8 ~25.29 .986 .948 .939 .940 .966 .994 1.004 .991 .969 160 Table D.15 (cont'd). 230.8 ~20.37 .987 .916 .913 .923 .952 .975 .973 .957 .936 230.8 ~15.46 .956 .864 .868 .888 .914 .917 .914 .895 .876 230.8 ~10.54 .862 .794 .803 .824 .825 .826 .824 .815 .797 230.8 ~5.62 .733 .715 .722 .725 .710 .698 .708 .710 .715 230.8 ~.70 .593 .625 .638 .633 .593 .564 .574 .592 .609 230.8 4.22 .470 .540 .561 .558 .512 .464 .449 .473 .508 230.8 9.14 .359 .462 .484 .488 .461 .414 .389 .401 .432 230.8 14.06 .257 .396 .419 .429 .407 .374 .352 .351 .371 230.8 18.97 .165 .339 .359 .363 .353 .329 .311 .311 .319 230.8 23.89 .114 .289 .297 .303 .303 .288 .278 .277 .279 230.8 28.81 .075 .239 .243 .247 .246 .235 .232 .230 .231 230.8 33.73 .061 .195 .199 .200 .199 .194 .189 .188 .188 230.8 38.65 .053 .150 .151 .154 .151 .149 .146 .147 .148 230.8 43.57 .050 .110 .112 .111 .110 .109 .109 .109 .110 230.8 48.48 .049 .089 .089 .089 .087 .088 .087 .087 .088 x/Oo ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~30. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. O00000000000000000000000000000000000000000000 Unforced y/oo .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 ~11. ~12. .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 66 82 data .0739 .1039 .1013 .0956 .0888 .0838 .0820 .0791 .0782 .0777 .0770 .0746 .0737 .0725 .0694 .0668 .0649 .0589 .0513 .0376 .0211 .0118 .0070 .0061 .0054 .0054 .0052 .0888 .0989 .1003 .0921 .0878 .0850 .0829 .0807 .0794 .0780 .0761 .0755 .0733 .0718 .0694 .0664 .0646 .0607 0.0 .0576 .1031 .1052 .0946 .0874 .0828 .0822 .0794 .0793 .0771 .0774 .0745 .0731 .0709 .0696 .0662 .0650 .0600 .0505 .0371 .0216 .0103 .0076 .0062 .0058 .0057 .0054 .0746 .0973 .0986 .0927 .0869 .0826 .0826 .0793 .0785 .0766 .0781 .0752 .0746 .0721 .0692 .0681 .0624 .0591 161 Table D.16 ~ RMS velocity straight wire results Phase averaged data (at angle ¢) 90.0 135.0 180.0 225.0 270.0 45.0 .0519 .1064 .1024 .0960 .0887 .0843 .0825 .0798 .0767 .0765 .0754 .0753 .0739 .0724 .0707 .0677 .0644 .0599 .0510 .0388 .0202 .0110 .0080 .0061 .0056 .0055 .0054 .0689 .0984 .1015 .0924 .0889 .0849 .0831 .0812 .0782 .0760 .0781 .0750 .0733 .0714 .0693 .0672 .0663 .0616 .0536 .1046 .1005 .0947 .0875 .0846 .0816 .0805 .0789 .0777 .0780 .0746 .0726 .0710 .0708 .0686 .0645 .0596 .0511 .0375 .0228 .0105 .0078 .0061 .0057 .0056 .0054 .0711 .0995 .1001 .0891 .0863 .0849 .0323 .0794 .0792 .0762 .0754 .0737 .0727 .0714 .0684 .0683 .0636 .0610 .0545 .1042 .1002 .0967 .0886 .0829 .0830 .0788 .0774 .0764 .0746 .0749 .0735 .0712 .0708 .0675 .0650 .0604 .0515 .0373 .0226 .0116 .0082 .0061 .0058 .0056 .0054 .0671 .0982 .0991 .0918 .0875 .0831 .0820 .0791 .0776 .0764 .0747 .0758 .0741 .0712 .0702 .0685 .0633 .0607 .0651 .1042 .0982 .0956 .0878 .0873 .0815 .0791 .0778 .0787 .0748 .0767 .0731 .0732 .0680 .0674 .0635 .0589 .0519 .0385 .0226 .0118 .0079 .0060 .0056 .0056 .0055 .0733 .1006 .0986 .0912 .0889 .0860 .0822 .0811 .0793 .0770 .0781 .0749 .0739 .0693 .0700 .0672 .0649 .0616 .0644 .1055 .0995 .0944 .0869 .0831 .0820 .0804 .0781 .0769 .0762 .0747 .0745 .0711 .0701 .0670 .0628 .0586 .0508 .0367 .0212 .0124 .0078 .0061 .0056 .0055 .0054 .0692 .1007 .0962 .0940 .0867 .0823 .0812 .0802 .0791 .0784 .0760 .0760 .0750 .0743 .0701 .0666 .0652 .0597 .0677 .1056 .0998 .0924 .0896 .0835 .0817 .0798 .0778 .0786 .0756 .0766 .0732 .0717 .0700 .0680 .0637 .0593 .0488 .0388 .0210 .0103 .0077 .0060 .0056 .0056 .0054 .0822 .1023 .1001 .0931 .0865 .0841 .0830 .0811 .0809 .0790 .0751 .0768 .0742 .0710 .0704 .0703 .0652 .0595 315.0 .0662 .1048 .1011 .0955 .0866 .0839 .0817 .0786 .0793 .0770 .0770 .0748 .0716 .0713 .0709 .0664 .0639 .0594 .0498 .0362 .0207 .0098 .0078 .0061 .0055 .0056 .0054 .0790 .1004 .1003 .0897 .0882 .0872 .0818 .0799 .0769 .0755 .0751 .0751 .0728 .0728 .0679 .0677 .0631 .0606 ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~20. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. ~10. -5. -5, ~5. -5. ~5. ~5. -5. ~5. -5. -5. ~5. 000000000000000000000000000000000000000000000000 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .0533 .0429 .0267 .0139 .0085 .0069 .0063 .0056 .0059 .0603 .1023 .0999 .0923 .0869 .0841 .0808 .0796 .0784 .0763 .0758 .0745 .0735 .0704 .0694 .0677 .0642 .0610 .0541 .0451 .0313 .0174 .0098 .0070 .0061 .0056 .0052 .0648 .0967 .1020 .0938 .0875 .0840’ .0806 .0797 .0786 .0763 .0753 .0734 .0522 .0420 .0257 .0150 .0088 .0067 .0058 .0057 .0055 .0563 .1043 .0980 .0931 .0851 .0851 .0796 .0808 .0793 .0774 .0751 .0740 .0731 .0715 .0716 .0672 .0632 .0604 .0539 .0438 .0293 .0174 .0097 .0070 .0059 .0055 .0051 .0477 .0982 .1006 .0966 .0868 .0840 .0808 .0780 .0763 .0773 .0760 .0738 .0542 .0442 .0265 .0132 .0086 .0066 .0057 .0057 .0054 .0441 .0998 .0987 .0913 .0876 .0854 .0813 .0790 .0783 .0797 .0759 .0746 .0730 .0712 .0693 .0680 .0648 .0618 .0559 .0461 .0305 .0177 .0094 .0071 .0056 .0057 .0051 .0465 .0966 .1042 .0962 .0864 .0838 .0798 .0783 .0783 .0757 .0763 .0728 162 .0524 .0420 .0271 .0143 .0083 .0067 .0055 .0057 .0055 .0591 .1021 .0975 .0919 .0874 .0842 .0806 .0773 .0786 .0776 .0744 .0730 .0726 .0690 .0677 .0657 .0631 .0604 .0534 .0457 .0304 .0175 .0096 .0069 .0057 .0056 .0052 .0557 .0979 .1022 .0956 .0881 .0823 .0797 .0783 .0756 .0754 .0757 .0717 .0513 .0408 .0280 .0142 .0082 .0068 .0057 .0057 .0054 .0584 .1039 .0987 .0925 .0876 .0848 .0808 .0778 .0747 .0744 .0766 .0744 .0707 .0700 .0681 .0655 .0633 .0610 .0542 .0439 .0319 .0168 .0103 .0071 .0058 .0057 .0052 .0595 .1009 .1019 .0945 .0887 .0829 .0793 .0788 .0762 .0762 .0738 .0727 Table D.16 (cont'd). .0543 .0414 .0280 .0142 .0091 .0067 .0056 .0056 .0054 .0576 .1045 .1012 .0931 .0863 .0833 .0815 .0792 .0788 .0761 .0751 .0734 .0715 .0707 .0679 .0664 .0642 .0593 .0528 .0446 .0306 .0173 .0098 .0070 .0057 .0055 .0052 .0570 .1015 .1007 .0961 .0863 .0825 .0820 .0761 .0785 .0747 .0743 .0737 .0546 .0421 .0269 .0145 .0087 .0074 .0057 .0057 .0054 .0640 .1042 .0998 .0917 .0842 .0832 .0806 .0818 .0767 .0777 .0766 .0761 .0723 .0707 .0689 .0667 .0640 .0609 .0527 .0442 .0322 .0157 .0100 .0068 .0058 .0056 .0051 .0587 .0971 .0999 .0948 .0884 .0842 .0799 .0777 .0779 .0748 .0761 .0709 .0529 .0418 .0263 .0147 .0084 .0067 .0057 .0056 .0055 .0599 .1049 .0984 .0926 .0855 .0839 .0832 .0810 .0789 .0767 .0772 .0730 .0713 .0712 .0702 .0658 .0639 .0607 .0547 .0453 .0318 .0163 .0091 .0066 .0055 .0055 .0052 .0566 .0961 .1020 .0939 .0889 .0841 .0801 .0794 .0790 .0762 .0740 .0742 .0529 .0424 .0274 .0139 .0087 .0068 .0056 .0057 .0054 .0576 .1032 .1014 .0911 .0882 .0844 .0816 .0801 .0808 .0764 .0766 .0753 .0733 .0698 .0702 .0677 .0654 .0624 .0543 .0436 .0321 .0173 .0090 .0071 .0056 .0056 .0052 .0642 .1006 .1028 .0941 .0874 .0819 .0828 .0808 .0749 .0769 .0756 .0742 ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~5. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. ~1. COOO00000000000000000000000000000000000000000000 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .03 .09 .15 .21 .28 .34 .0729 .0702 .0685 .0671 .0637 .0600 .0547 .0453 .0312 .0175 .0095 .0068 .0060 .0054 .0055 .0512 .0921 .0999 .0916 .0851 .0820 .0779 .0784 .0762 .0752 .0734 .0733 .0704 .0696 .0683 .0661 .0635 .0595 .0538 .0449 .0318 .0179 .0096 .0065 .0060 .0058 .0059 .0731 .1018 .0972 .0927 .0864 .0828 .0720 .0700 .0684 .0671 .0663 .0586 .0532 .0442 .0310 .0171 .0084 .0066 .0058 .0057 .0055 .0471 .0925 .1006 .0896 .0845 .0827 .0795 .0747 .0769 .0770 .0747 .0727 .0733 .0701 .0660 .0669 .0629 .0604 .0531 .0451 .0304 .0175 .0103 .0070 .0054 .0055 .0051 .0631 .0973 .0979 .0909 .0854 .0830 .0711 .0706 .0689 .0674 .0634 .0602 .0525 .0459 .0311 .0187 .0087 .0066 .0058 .0057 .0055 .0416 .0899 .1007 .0914 .0868 .0810 .0776 .0766 .0735 .0755 .0722 .0721 .0719 .0697 .0674 .0668 .0646 .0597 .0529 .0454 .0305 .0174 .0090 .0066 .0054 .0055 .0053 .0572 .0972 .0962 .0890 .0855 .0824 163 .0707 .0676 .0679 .0662 .0653 .0602 .0530 .0439 .0318 .0172 .0086 .0066 .0059 .0057 .0054 .0553 .0949 .0997 .0914 .0835 .0795 .0790 .0765 .0758 .0735 .0722 .0725 .0703 .0674 .0678 .0651 .0634 .0579 .0525 .0438 .0297 .0163 .0087 .0067 .0053 .0055 .0053 .0640 .1001 .0970 .0898 .0832 .0810 .0714 .0717 .0694 .0659 .0658 .0601 .0533 .0447 .0297 .0190 .0090 .0068 .0059 .0058 .0055 .0601 .0966 .0982 .0891 .0807 .0798 .0789 .0759 .0755 .0735 .0738 .0700 .0696 .0695 .0664 .0659 .0622 .0603 .0524 .0428 .0298 .0178 .0092 .0064 .0054 .0055 .0053 .0739 .1017 .0961 .0876 .0834 .0805 Table D.16 (cont'd). .0721 .0697 .0665 .0671 .0625 .0604 .0545 .0434 .0307 .0156 .0088 .0072 .0059 .0057 .0054 .0566 .0978 .1006 .0909 .0827 .0798 .0772 .0767 .0752 .0730 .0730 .0724 .0699 .0695 .0672 .0648 .0644 .0576 .0527 .0439 .0305 .0174 .0098 .0069 .0055 .0057 .0053 .0762 .1063 .0994 .0921 .0896 .0809 .0725 .0689 .0681 .0659 .0633 .0597 .0523 .0441 .0299 .0167 .0093 .0066 .0058 .0056 .0055 .0527 .0975 .0986 .0913 .0857 .0807 .0787 .0791 .0744 .0741 .0729 .0718 .0714 .0705 .0668 .0661 .0644 .0596 .0542 .0441 .0320 .0175 .0083 .0067 .0055 .0056 .0054 .0679 .1042 .1005 .0935 .0887 .0849 .0731 .0714 .0673 .0647 .0633 .0615 .0551 .0459 .0316 .0178 .0089 .0066 .0063 .0058 .0055 .0556 .0933 .1014 .0925 .0853 .0816 .0793 .0774 .0772 .0783 .0761 .0750 .0707 .0690 .0660 .0662 .0635 .0601 .0514 .0433 .0324 .0196 .0101 .0067 .0054 .0056 .0052 .0683 .1068 .0993 .0927 .0916 .0839 .0728 .0709 .0684 .0649 .0649 .0611 .0541 .0459 .0308 .0173 .0091 .0068 .0059 .0056 .0056 .0550 .0948 .0994 .0922 .0872 .0823 .0781 .0797 .0780 .0753 .0739 .0724 .0706 .0714 .0677 .0661 .0641 .0602 .0521 .0442 .0317 .0182 .0094 .0066 .0056 .0055 .0053 .0745 .1033 .0959 .0928 .0883 .0840 c>c>c>c>c><>c>c>c>c>c>c>c>c>c>c>c><>c>c:c:c3c:cat:c><>c>c>c>E>E>E>E>E>E>c:c>c:c>c>c>c>c>c><>c>c> U’h‘h‘h‘h‘h‘h‘h‘F'F‘P‘P‘F‘P‘F‘F‘F‘P‘F‘F‘F‘F‘F‘F‘P‘P‘P‘ ~10 .43 .53 .66 .82 .02 .28 .59 .98 .46 .06 .81 .74 .89 .05 .20 .36 .51 .66 .82 .97 .12 .58 .40 .21 .03 .12 .25 .40 .63 .79 .99 .24 .56 .95 .43 .03 .78 .71 .86 .02 .17 .32 .48 .63 .78 .94 .09 .58 .0807 .0791 .0779 .0781 .0755 .0748 .0738 .0715 .0705 .0674 .0646 .0617 .0559 .0464 .0323 .0177 .0102 .0070 .0059 .0057 .0059 .0197 .0224 .0220 .0324 .0753 .1158 .1107 .0841 .0792 .0776 .0772 .0750 .0727 .0706 .0691 .0660 .0632 .0625 .0580 .0556 .0477' .0264 .0176 .0082 .0067 .0058 .0403 .0797 .0792 .0780 .0774 .0753 .0749 .0731 .0734 .0679 .0701 .0652 .0611 .0546 .0467 .0338 .0172 .0100 .0065 .0065 .0057 .0053 .0182 .0206 .0234 .0349 .0795 .1212 .1120 .0826 .0787 .0794 .0779 .0761 .0735 .0732 .0694 .0673 .0642 .0616 .0579 .0538 .0470 .0247 .0178 .0077 .0064 .0059 .0385 Table .0775 .0780 .0763 .0762 .0760 .0733 .0742 .0720 .0690 .0679 .0675 .0627 .0568 .0455 .0322 .0180 .0098 .0069 .0062 .0055 .0052 .0223 .0240 .0264 .0362 .0824 .1223 .1059 .0817 .0787 .0759 .0771 .0738 .0726 .0710 .0672 .0667 .0641 .0612 .0577 .0545 .0480 .0271 .0183 .0073 .0065 .0060 .0375 164 D.16 (cont'd). .0774 .0773 .0780 .0773 .0752 .0753 .0728 .0725 .0697 .0656 .0655 .0616 .0544 .0442 .0316 .0171 .0101 .0067 .0063 .0056 .0052 .0192 .0185 .0219 .0376 .0875 .1255 .1049 .0805 .0755 .0773 .0730 .0745 .0715 .0717 .0692 .0649 .0625 .0600 .0581 .0527 .0461 .0265 .0170 .0077 .0065 .0059 .0572 .0793 .0785 .0772 .0750 .0743 .0717 .0708 .0718 .0692 .0662 .0646 .0606 .0546 .0444 .0299 .0172 .0092 .0067 .0064 .0055 .0053 .0370 .0323 .0245 .0346 .0871 .1192 .0996 .0805 .0779 .0766 .0744 .0738 .0694 .0716 .0666 .0659 .0624 .0616 .0566 .0520 .0468 .0254 .0168 .0079 .0064 .0059 .0655 .0803 .0787 .0769 .0763 .0749 .0730 .0715 .0692 .0701 .0668 .0642 .0613 .0546 .0453 .0296 .0161 .0093 .0070 .0062 .0055 .0051 .0392 .0365 .0309 .0394 .0799 .1252 .1051 .0814 .0792 .0794 .0760 .0742 .0718 .0708 .0672 .0642 .0651 .0608 .0564 .0526 .0461 .0239 .0179 .0073 .0063 .0059 .0604 .0818 .0785 .0786 .0756 .0764 .0756 .0749 .0731 .0683 .0685 .0667 .0621 .0547 .0433 .0305 .0168 .0096 .0065 .0063 .0056 .0051 .0317 .0323 .0302 .0404 .0791 .1202 .1098 .0841 .0808 .0770 .0766 .0776 .0731 .0705 .0696 .0649 .0633 .0603 .0592 .0530 .0461 .0251 .0162 .0076 .0063 .0059 .0452 .0799 .0808 .0769 .0787 .0760 .0751 .0726 .0707 .0700 .0688 .0629 .0611 .0547 .0463 .0309 .0176 .0093 .0078 .0062 .0055 .0052 .0235 .0243 .0258 .0345 .0758 .1164 .1140 .0844 .0794 .0785 .0790 .0752 .0736 .0722 .0698 .0662 .0640 .0621 .0573 .0536 .0483 .0269 .0164 .0079 .0064 .0059 .0334 .0808 .0796 .0772 .0754 .0753 .0755 .0745 .0730 .0696 .0687 .0661 .0615 .0566 .0449 .0321 .0188 .0096 .0064 .0065 .0055 .0052 .0180 .0201 .0225 .0368 .0761 .1178 .1109 .0857 .0800 .0792 .0768 .0768 .0769 .0728 .0691 .0648 .0638 .0601 .0569 .0537 .0466 .0262 .0178 .0078 .0064 .0060 .0325 para oommmmummmmmmmmuu:mmmmuau:woowwwwwwwwwwwwuwwwwuwwwww 000000000000000000000000000000000000000000000000 .40 .21 .03 .12 .25 .40 .63 .79 .99 .24 .56 .95 .43 .03 .78 .71 .86 .02 .17 .32 .48 ~11. ~12. ~13. ~15. .00 .01 .03 .96 ~1. ~2. ~3. -4_ .89 ~6. ~7. ~8. -9. ~10. ~11. ~12. ~13. ~14. ~15. ~16. ~17. .00 .87 63 78 94 09 94 93 92 90 88 86 85 84 82 81 79 78 76 75 74 72 .0489 .0772 .1010 .1167 .1238 .1267 .1083 .0895 .0816 .0787 .0762 .0738 .0702 .0693 .0667 .0652 .0587 .0537 .0355 .0252 .0113 .0084 .0064 .0056 .0062 .0102 .0306 .1274 .0873 .0713 .0676 .0625 .0575 .0498 .0399 .0249 .0152 .0088 .0073 .0061 .0060 .0062 .0062 .0058 .0055 .0054 .0067 .0108 .0482 .0789 .1045 .1160 .1223 .1232 .1017 .0862 .0798 .0799 .0770 .0734 .0708 .0698 .0669 .0644 .0588 .0541 .0336 .0248 .0105 .0085 .0061 .0057 .0059 .0135 .0269 .1224 .0844 .0720 .0679 .0632 .0570 .0492 .0411 .0251 .0151 .0094 .0067 .0062 .0058 .0057 .0057 .0053 .0052 .0051 .0062 .0097 Table .0543 .0876 .1078 .1202 .1296 .1253 .1017 .0844 .0809 .0761 .0760 .0720 .0721 .0689 .0660 .0666 .0585 .0515 .0331 .0249 .0111 .0080 .0061 .0056 .0059 .0108 .0342 .1334 .0836 .0712 .0673 .0615 .0581 .0489 .0385 .0238 .0162 .0087 .0073 .0063 .0057 .0057 .0057 .0053 .0050 .0051 .0064 .0107 165 .0614 .0872 .1095 .1209 .1237 .1207 .0972 .0835 .0797 .0755 .0752 .0732 .0696 .0690 .0665 .0627 .0571 .0523 .0336 .0235 .0115 .0077 .0063 .0055 .0060 .0114 .0410 .1363 .0808 .0711 .0669 .0616 .0562 .0492 .0379 .0232 .0147 .0084 .0068 .0064 .0057 .0057 .0057 .0052 .0051 .0051 .0081 .0142 .0626 .0872 .1087 .1238 .1278 .1230 .0985 .0832 .0756 .0765 .0726 .0740 .0690 .0684 .0654 .0640 .0569 .0520 .0336 .0223 .0103 .0085 .0061 .0056 .0059 .0129 .0427 .1408 .0772 .0693 .0665 .0591 .0548 .0488 .0369 .0231 .0136 .0086 .0066 .0063 .0057 .0057 .0056 .0053 .0051 .0051 .0091 .0159 D.16 (cont'd). .0623 .0845 .1156 .1235 .1343 .1379 .1113 .0917 .0817 .0748 .0739 .0705 .0706 .0670 .0651 .0655 .0586 .0535 .0337 .0251 .0098 .0083 .0061 .0056 .0061 .0134 .0365 .1419 .0859 .0706 .0667 .0603 .0566 .0503 .0364 .0228 .0134 .0089 .0064 .0062 .0056 .0058 .0059 .0055 .0051 .0051 .0103 .0187 .0564 .0882 .1104 .1217 .1359 .1361 .1178 .0978 .0814 .0771 .0762 .0736 .0715 .0679 .0686 .0652 .0580 .0536 .0339 .0254 .0098 .0087 .0060 .0056 .0057 .0143 .0351 .1349 .0976 .0717 .0678 .0607 .0562 .0483 .0382 .0240 .0147 .0088 .0067 .0063 .0057 .0056 .0059 .0054 .0053 .0051 .0094 .0157 .0506 .0788 .1053 .1167 .1256 .1311 .1126 .0977 .0841 .0780 .0751 .0746 .0706 .0702 .0672 .0643 .0582 .0534 .0358 .0225 .0104 .0090 .0061 .0056 .0058 .0109 .0311 .1253 .0972 .0720 .0664 .0609 .0571 .0484 .0398 .0250 .0152 .0088 .0070 .0062 .0058 .0057 .0058 .0054 .0052 .0052 .0079 .0109 .0452 .0776 .1020 .1147 .1259 .1237 .1084 .0932 .0802 .0808 .0773 .0746 .0714 .0698 .0671 .0656 .0583 .0534 .0341 .0273 .0095 .0087 .0064 .0054 .0059 .0096 .0264 .1183 .0924 .0698 .0674 .0620 .0592 .0486 .0398 .0266 .0147 .0096 .0066 .0063 .0057 .0057 .0058 .0055 .0052 .0052 .0064 .0101 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 15. 25. 25. 25. 25. 25. 25. 25. 25. 000000000000000000000000000000000000000000000000 .75 .62 .51 .63 .76 .88 .01 .14 .26 .39 .51 .64 .77 .89 .02 .15 .27 .40 .52 .00 .73 .47 .20 .93 .33 .60 .86 .13 .40 .66 .93 .19 .46 .73 .99 .26 .53 .79 .06 .32 .00 .45 .91 .36 .81 .27 .72 .82 .0369 .1062 .1271 .0766 .0680 .0621 .0560 .0473 .0334 .0208 .0112 .0073 .0063 .0060 .0057 .0063 .0053 .0052 .0053 .0061 .0089 .0164 .0503 .1091 .1326 .0922 .0687 .0619 .0550 .0430 .0273 .0142 .0087 .0070 .0062 .0059 .0065 .0057 .0059 .0054 .0053 .0071’ .0103 .0164 .0421 .0888 .1253 .1318 .0385 .1055 .1220 .0765 .0686 .0630 .0558 .0487 .0338 .0198 .0107 .0073 .0061 .0057 .0058 .0057 .0052 .0052 .0050 .0056 .0076 .0153 .0505 .1092 .1334 .0976 .0709 .0626 .0558 .0448 .0294 .0147 .0081 .0067 .0057 .0057 .0057 .0055 .0053 .0054 .0071 .0076 .0112 .0162 .0278 .0551 .0987 .1258 Table .0501 .1162 .1172 .0769 .0695 .0621 .0552 .0476 .0328 .0189 .0100 .0070 .0061 .0056 .0058 .0057 .0051 .0051 .0052 .0053 .0075 .0163 .0563 .1129 .1330 .0906 .0691 .0622 .0547 .0432 .0285 .0147 .0082 .0068 .0056 .0059 .0058 .0056 .0053 .0054 .0067 .0069 .0097 .0133 .0253 .0724 .1204 .1440 166 D.16 (cont'd). .0507 .1172 .1150 .0751 .0679 .0617 .0544 .0462 .0319 .0180 .0100 .0069 .0062 .0057 .0058 .0058 .0053 .0052 .0052 .0055 .0086 .0211 .0698 .1232 .1266 .0817 .0705 .0621 .0531 .0421 .0255 .0139 .0079 .0067 .0057 .0057 .0056 .0054 .0052 .0053 .0058 .0068 .0087 .0138 .0463 .0983 .1303 .1318 .0579 .1218 .1151 .0729 .0657 .0620 .0552 .0448 .0312 .0182 .0103 .0071 .0060 .0058 .0058 .0058 .0052 .0053 .0053 .0072 .0121 .0240 .0724 .1202 .1276 .0800 .0664 .0586 .0511 .0398 .0259 .0117 .0077 .0067 .0059 .0059 .0056 .0056 .0055 .0054 .0047 .0052 .0076 .0217 .0665 .1130 .1350 .1189 .0497 .1240 .1245 .0742 .0653 .0595 .0533 .0457 .0288 .0176 .0096 .0071 .0063 .0059 .0058 .0057 .0051 .0052 .0052 .0087 .0137 .0266 .0832 .1241 .1258 .0774 .0674 .0610 .0513 .0384 .0233 .0125 .0076 .0068 .0059 .0059 .0057 .0055 .0055 .0053 .0056 .0064 .0120 .0305 .0741 .1148 .1305 .1136 .0387 .1004 .1355 .0832 .0657 .0620 .0547 .0462 .0304 .0179 .0108 .0068 .0062 .0058 .0058 .0059 .0053 .0053 .0052 .0088 .0144 .0297 .0650 .1158 .1312 .0919 .0683 .0597 .0516 .0403 .0247 .0130 .0080 .0065 .0057 .0058 .0058 .0056 .0055 .0054 .0084 .0103 .0163 .0314 .0746 .1150 .1337 .1143 .0332 .1053 .1361 .0851 .0670 .0627 .0549 .0464 .0322 .0187 .0099 .0072 .0062 .0057 .0058 .0059 .0052 .0053 .0054 .0079 .0120 .0215 .0412 .0999 .1305 .1127 .0716 .0598 .0541 .0429 .0265 .0133 .0084 .0068 .0058 .0060 .0058 .0056 .0053 .0054 .0091 .0124 .0188 .0317 .0688 .1094 .1343 .1181 .0360 .1038 .1271 .0807 .0680 .0632 .0576 .0491 .0333 .0204 .0113 .0076 .0064 .0057 .0059 .0057 .0052 .0053 .0053 .0067 .0097 .0159 .0433 .1054 .1383 .1095 .0713 .0635 .0543 .0436 .0281 .0136 .0094 .0068 .0059 .0061 .0058 .0055 .0052 .0053 .0076 .0102 .0156 .0264 .0454 .0736 .1175 .1320 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 25. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 40. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 60. 000000000000000000000000000000000000000000000000 .37 .92 .46 .01 .55 .10 .65 .19 .74 .29 .83 .38 .92 .00 .03 .07 .10 .13 .17 .20 .24 .27 .70 .66 .63 .60 .56 .53 .49 .46 .42 .39 .36 .32 .00 .47 .95 .42 .90 .37 .84 .32 .79 .26 .26 .79 .31 .84 .0911 .0658 .0554 .0420 .0230 .0108 .0073 .0063 .0062 .0054 .0054 .0054 .0050 .0043 .0056 .0076 .0100 .0150 .0325 .0746 .1146 .1360 .1274 .0858 .0581 .0387 .0172 .0097 .0072 .0067 .0059 .0055 .0060 .0054 .0038 .0048 .0061 .0081 .0104 .0159 .0333 .0689 .1078 .1314 .1379 .1097 .0618 .0326 .1189 .0766 .0563 .0432 .0276 .0117 .0077 .0066 .0059 .0054 .0052 .0056 .0053 .0085 .0113 .0160 .0230 .0385 .0610 .0994 .1254 .1304 .1069 .0714 .0520 .0313 .0153 .0092 .0081 .0071 .0061 .0059 .0065 .0058 .0056 .0062 .0070 .0085 .0118 .0173 .0364 .0855 .1248 .1387 .1115 .0728 .0445 .0220 Table .1059 .0712 .0588 .0451 .0252 .0123 .0078 .0065 .0061 .0055 .0053 .0056 .0052 .0081 .0110 .0148 .0216 .0368 .0539 .0730 .1020 .1181 .1304 .1109 .0688 .0436 .0194 .0095 .0075 .0066 .0058 .0058 .0061 .0054 .0058 .0058 .0078 .0120 .0205 .0397 .0789 .1220 .1434 .1261 .0847 .0580 .0328 .0188 167 .0882 .0659 .0558 .0413 .0231 .0106 .0076 .0061 .0060 .0055 .0051 .0054 .0051 .0069 .0090 .0116 .0158 .0248 .0362 .0527 .0680 .0901 .1128 .1191 .0814 .0487 .0243 .0113 .0078 .0070 .0061 .0059 .0059 .0053 .0062 .0078 .0123 .0185 .0319 .0516 .0819 .1158 .1277 .1146 .0877 .0643 .0423 .0215 .0800 .0657 .0550 .0382 .0202 .0101 .0073 .0061 .0059 .0057 .0053 .0055 .0052 .0062 .0077 .0088 .0112 .0149 .0203 .0325 .0559 .1021 .1269 .1133 .0728 .0471 .0233 .0115 .0083 .0071 .0061 .0056 .0058 .0054 .0059 .0074 .0106 .0166 .0275 .0427 .0565 .0870 .1216 .1228 .1213 .1091 .0762 .0369 D.16 (cont'd). .0748 .0617 .0527 .0352 .0180 .0095 .0076 .0062 .0063 .0056 .0055 .0056 .0055 .0058 .0069 .0078 .0099 .0131 .0199 .0506 .1010 .1344 .1298 .0888 .0615 .0429 .0188 .0102 .0080 .0070 .0061 .0055 .0057 .0053 .0051 .0066 .0095 .0145 .0259 .0430 .0586 .0776 .0935 .1025 .1115 .1136 .0986 .0632 .0740 .0603 .0504 .0342 .0171 .0096 .0072 .0062 .0062 .0057 .0055 .0055 .0055 .0054 .0064 .0078 .0105 .0163 .0498 .1006 .1360 .1401 .1157 .0754 .0548 .0333 .0147 .0094 .0078 .0068 .0061 .0057 .0060 .0054 .0046 .0057 .0083 .0120 .0191 .0312 .0449 .0599 .0721 .0873 .0937 .1024 .1047 .0661 .0779 .0629 .0519 .0379 .0171 .0093 .0071 .0062 .0063 .0057 .0055 .0055 .0055 .0046 .0057 .0084 .0160 .0365 .0754 .1176 .1393 .1312 .0940 .0666 .0480 .0275 .0138 .0091 .0079 .0071 .0064 .0061 .0063 .0056 .0047 .0058 .0079 .0100 .0137 .0210 .0309 .0456 .0578 .0751 .0968 .1120 .0963 .0504 .1128 .0703 .0544 .0417 .0237 .0100 .0070 .0062 .0060 .0055 .0052 .0057 .0055 .0067 .0100 .0144 .0236 .0446 .0800 .1207 .1366 .1268 .0845 .0628 .0455 .0262 .0118 .0084 .0079 .0069 .0062 .0061 .0064 .0057 .0051 .0059 .0074 .0088 .0112 .0160 .0234 .0377 .0753 .1111 .1253 .1099 .0641 .0319 60. 60. 60. 60. 60. 60. 60. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 76. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. 115. J-‘J-‘bp99pp##4-‘9‘Pbp9b99b0000000000000000000000000000 ~11. ~13. ~16. ~18. .47 ~24. ~26. ~15. ~13. ~12. ~10. ~9. .40 ~21 ~7 ~5. .17 .55 .94 .68 .30 .91 .53 .14 .76 .37 .99 .60 .22 .83 .58 .37 .17 .97 .77 .57 .37 .17 .97 .77 .56 .64 .84 .04 .24 .44 .64 .84 .25 .25 -4 oowuwwm 37 89 42 95 00 52 47 86 24 63 01 78 .0153 .0108 .0084 .0069 .0065 .0061 .0056 .0125 .0150 .0184 .0254 .0407 .0628 .0894 .1150 .1317 .1367 .1351 .1281 .1180 .0983 .0831 .0576 .0392 .0244 .0187 .0131 .0112 .0124 .0140 .0183 .0251 .0414 .0597 .0834 .0994 .1204 .1308 .1422 .1447 .1405 .1278 .1042 .0687 .0428 .0258 .0206 .0174 .0157 .0135 .0092 .0077 .0081 .0068 .0062 .0147 .0172 .0252 .0416 .0786 .0955 .1042 .1029 .0968 .0940 .0896 .0853 .0749 .0729 .0620 .0533 .0445 .0389 .0319 .0225 .0188 .0264 .0376 .0471 .0613 .0772 .0904 .1082 .1140 .1171 .1113 .1012 .0911 .0804 .0696 .0574 .0436 .0350 .0312 .0231 .0231 Table .0150 .0134 .0093 .0077 .0085 .0069 .0064 .0145 .0170 .0201 .0240 .0345 .0607 .0886 .1052 .1159 .1148 .1043 .0900 .0767 .0708 .0583 .0501 .0416 .0325 .0282 .0202 .0159 .0283 .0362 .0473 .0583 .0725 .0855 .0984 .1131 .1297 .1365 .1216 .1210 .1151 .1059 .0960 .0860 .0686 .0442 .0270 .0270 168 .0147 .0120 .0096 .0079 .0078 .0069 .0064 .0145 .0169 .0199 .0194 .0267 .0308 .0424 .0607 .0858 .1106 .1200 .1248 .1181 .1027 .0855 .0578 .0445 .0340 .0286 .0214 .0169 .0283 .0344 .0459 .0525 .0600 .0756 .0976 .1339 .1471 .1515 .1395 .1375 .1291 .1218 .1091 .1036 .0961 .0746 .0280 .0280 .0183 .0118 .0090 .0075 .0074 .0067 .0062 .0139 .0158 .0189 .0175 .0228 .0255 .0322 .0440 .0566 .0740 .0874 .1102 .1221 .1246 .1229 .1059 .0834 .0611 .0428 .0303 .0223 .0281 .0340 .0430 .0519 .0586 .0826 .1057 .1328 .1458 .1462 .1357 .1348 .1320 .1288 .1189 .1080 .0996 .0831 .0275 .0275 D.16 (cont'd). .0228 .0123 .0079 .0064 .0069 .0060 .0058 .0150 .0171 .0198 .0233 .0318 .0457 .0593 .0766 .0910 .0968 .1065 .1097 .1130 .1112 .1061 .0973 .0890 .0812 .0632 .0430 .0296 .0280 .0339 .0425 .0534 .0619 .0868 .1021 .1183 .1332 .1314 .1291 .1280 .1297 .1268 .1174 .1130 .0981 .0728 .0230 .0230 .0238 .0133 .0088 .0069 .0068 .0057 .0057 .0144 .0175 .0255 .0461 .0724 .0888 .0995 .1072 .1107 .1148 .1179 .1200 .1254 .1203 .0986 .0756 .0570 .0521 .0471 .0360 .0267 .0264 .0347 .0442 .0537 .0655 .0852 .0990 .1075 .1194 .1206 .1265 .1282 .1266 .1245 .1159 .1005 .0743 .0433 .0193 .0193 .0202 .0128 .0094 .0074 .0068 .0060 .0056 .0146 .0231 .0436 .0726 .0923 .0965 .1028 .1008 .1052 .1080 .1048 .1073 .1052 .1016 .0912 .0743 .0603 .0533 .0431 .0315 .0240 .0267 .0348 .0456 .0543 .0693 .0844 .0985 .1074 .1174 .1224 .1270 .1290 .1252 .1064 .0821 .0528 .0368 .0273 .0187 .0187 .0155 .0120 .0091 .0075 .0070 .0063 .0058 .0149 .0198 .0392 .0737 .0937 .1001 .0984 .0960 .0946 .0980 .0936 .0920 .0842 .0810 .0715 .0626 .0541 .0470 .0382 .0286 .0227 .0250 .0358 .0455 .0608 .0728 .0867 .1044 .1156 .1238 .1271 .1205 .1007 .0750 .0508 .0388 .0322 .0291 .0248 .0199 .0199 115. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 153. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 192. 230. 230. 230. 230. 230. oooooooooowwwuwwuwuwwwwwwuwwwuwooooooooooooooooooooooooooooooooooooooooook ~20. .62 .51 .41 .30 .19 .09 .98 .87 ~3. .66 .45 .56 .66 .77 .88 .98 .09 .20 .30 .41 .52 .46 .45 .43 .42 .41 .40 .38 .37 .36 .35 .33 .68 .69 .70 .72 .73 .74 .75 .77 .78 .79 .97 .05 .13 .21 .29 I I I I I I llHHI—‘NNN mcwmxommoo I II I I I I I I I I I UCU‘O-PO‘Nm‘I-‘OO‘N 45 76 .0148 .0131 .0162 .0199 .0240 .0339 .0532 .0929 .1290 .1423 .1495 .1443 .1334 .1209 .1028 .0773 .0523 .0321 .0201 .0152 .0126 .0113 .0109 .0127 .0155 .0197 .0297 .0505 .0688 .0952 .1198 .1395 .1536 .1532 .1496 .1298 .0910 .0541 .0345 .0245 .0184 .0138 .0126 .0125 .0147 .0177 .0227 .0320 .0216 .0119 .0178 .0287 .0555 .0932 .1263 .1431 .1524 .1592 .1608 .1627 .1640 .1480 .1250 .1063 .0877 .0789 .0682 .0575 .0456 .0368 .0433 .0540 .0737 .0885 .1114 .1169 .1203 .1261 .1272 .1240 .1329 .1424 .1370 .1111 .0913 .0637 .0453 .0364 .0283 .0237 .0205 .0109 .0151 .0174 .0405 .0762 Table .0225 .0115 .0138 .0187 .0373 .0647 .1068 .1302 .1535 .1545 .1579 .1605 .1558 .1482 .1342 .1153 .0976 .0807 .0694 .0566 .0448 .0362 .0433 .0537 .0729 .0896 .1028 .1072 .1105 .1155 .1136 .1252 .1497 .1686 .1575 .1346 .1229 .0968 .0642 .0447 .0312 .0242 .0214 .0105 .0131 .0170 .0252 .0523 169 .0204 .0141 .0161 .0187 .0261 .0350 .0612 .0908 .1294 .1534 .1591 .1609 .1517 .1446 .1367 .1199 .1058 .0897 .0725 .0594 .0487 .0363 .0431 .0553 .0701 .0849 .0963 .0990 .1085 .1112 .1190 .1430 .1708 .1839 .1704 .1493 .1366 .1145 .0823 .0518 .0305 .0218 .0192 .0137 .0163 .0181 .0232 .0355 .0168 .0177 .0203 .0224 .0289 .0323 .0396 .0516 .0785 .1089 .1366 .1445 .1432 .1404 .1307 .1214 .1101 .0929 .0759 .0594 .0489 .0374 .0456 .0561 .0703 .0814 .0966 .0990 .1078 .1150 .1309 .1561 .1745 .1804 .1673 .1532 .1404 .1224 .0887 .0542 .0280 .0186 .0153 .0176 .0206 .0233 .0289 .0377 D.16 (cont'd). .0140 .0214 .0258 .0292 .0344 .0398 .0507 .0699 .0887 .1028 .1213 .1302 .1257 .1208 .1137 .1102 .1011 .0949 .0738 .0576 .0486 .0365 .0456 .0544 .0701 .0852 .0982 .1039 .1113 .1280 .1427 .1633 .1726 .1701 .1643 .1574 .1465 .1232 .0857 .0455 .0241 .0148 .0114 .0200 .0237 .0276 .0351 .0491 .0154 .0237 .0283 .0335 .0402 .0639 .0881 .1077 .1210 .1269 .1433 .1506 .1380 .1128 .1001 .0983 .0892 .0838 .0647 .0583 .0485 .0363 .0455 .0557 .0722 .0860 .1044 .1095 .1218 .1425 .1539 .1626 .1681 .1641 .1647 .1563 .1361 .1030 .0618 .0339 .0172 .0124 .0100 .0200 .0238 .0279 .0386 .0620 .0161 .0217 .0269 .0335 .0556 .0875 .1115 .1305 .1445 .1541 .1681 .1680 .1663 .1276 .1016 .0912 .0831 .0783 .0660 .0551 .0463 .0371 .0445 .0552 .0736 .0889 .1047 .1150 .1280 .1455 .1562 .1608 .1623 .1604 .1542 .1326 .0971 .0627 .0352 .0219 .0176 .0150 .0126 .0177 .0215 .0263 .0454 .0760 .0175 .0167 .0226 .0333 .0634 .0989 .1246 .1392 .1474 .1522 .1669 .1671 .1702 .1429 .1131 .1001 .0859 .0791 .0660 .0545 .0454 .0376 .0444 .0577 .0740 .0895 .1081 .1179 .1280 .1405 .1426 .1466 .1457 .1441 .1289 .0969 .0682 .0479 .0365 .0281 .0223 .0198 .0168 .0141 .0170 .0236 .0498 .0811 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 230. 8 8 8 000000000000 ~20. .46 ~10. ~5. .70 .22 .14 14. 18. 23. 28. ~15 33 48 37 54 62 06 97 89 81 .73 38. 43. 65 57 .48 .0485 .0848 .1277 .1570 .1610 .1582 .1418 .1221 .0940 .0661 .0390 .0237 .0179 .0150 .0131 .1086 .1377 .1578 .1646 .1691 .1659 .1601 .1454 .1305 .1252 .1162 .1027 .0890 .0683 .0581 Table .0825 .1170 .1454 .1589 .1636 .1627 .1633 .1516 .1427 .1280 .1157 .1056 .0910 .0718 .0578 170 .0546 .0810 .1128 .1440 .1528 .1591 .1585 .1551 .1423 .1338 .1186 .1054 .0926 .0708 .0576 .0497 .0723 .1097 .1359 .1406 .1435 .1466 .1437 .1345 .1363 .1202 .1068 .0931 .0716 .0571 D.16 (cont'd). .0746 .1023 .1290 .1531 .1545 .1395 .1327 .1266 .1292 .1288 .1173 .1051 .0889 .0727 .0580 .0931 .1223 .1467 .1703 .1741 .1506 .1296 .1249 .1227 .1180 .1144 .1035 .0874 .0722 .0568 .1084 .1356 .1546 .1712 .1776 .1616 .1430 .1284 .1201 .1182 .1137 .1014 .0859 .0693 .0572 .1135 .1394 .1608 .1639 .1751 .1652 .1552 .1376 .1237 .1204 .1100 .0993 .0868 .0697 .0576 171 Table 0.17 - Entrainment Field E (o--60°) Unforced Phase averaged data (at angle ¢) x/oo y/0O data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0 107.7 17.54 .027 .033 .035 .038 .052 .079 .095 .078 .046 107.7 25.31 .012 .015 .017 .015 .016 .026 .035 .031 .019 107.7 33.07 .010 .008 .008 .007 .007 .011 .015 .015 .010 107.7 40.83 .010 .005 .004 .004 .005 .006 .007 .008 .006 107.7 48.59 .006 .003 .003 .004 .003 .004 .003 .003 .003 123.1 20.79 .021 .052 .033 .027 .027 .032 .042 .058 .064 123.1 30.00 .011 .021 .015 .013 .013 .012 .015 .021 .024 123.1 39.21 .011 .010 .008 .006 .005 .006 .007 .009 .010 123.1 48.42 .008 .004 .004 .004 .003 .004 .005 .005 .005 123.1 57.63 .003 .006 .005 .005 .005 .005 .005 .005 .006 138.5 24.04 .019 .052 .052 .045 .034 .029 .029 .034 .044 138.5 34.70 .012 .018 .019 .017 .014 .013 .012 .013 .015 138.5 45.36 .011 .006 .007 .007 .006 .005 .005 .005 .006 138.5 56.01 .007 .005 .005 .004 .004 .004 .004 .005 .005 138.5 66.67 .002 .005 .005 .005 .005 .005 .005 .005 .005 153.8 27.29 .019 .037 .042 .044 .046 .040 .036 .032 .034 153.8 39.40 .013 .014 .015 .017 .017 .016 .015 .014 .014 153.8 51.50 .011 .005 .005 .006 .006 .006 .005 .005 .004 153.8 63.61 .005 .005 .005 .004 .005 .004 .005 .004 .004 153.8 75.71 .003 .005 .006 .005 .005 .005 .005 .005 .005 169.2 30.54 .018 .036 .041 .043 .047 .047 .045 .044 .040 169.2 44.09 .013 .014 .014 .015 .015 .016 .016 .015 .015 169.2 57.65 .010 .004 .004 .004 .005 .005 .005 .005 .004 169.2 71.20 .005 .005 .004 .004 .005 .005 .005 .005 .005 169.2 84.75 .004 .006 .006 .006 .005 .005 .005 .006 .006 184.6 33.79 .019 .045 .042 .040 .045 .048 .051 .051 .048 184.6 48.79 .014 .014 .013 .013 .013 .013 .014 .015 .014 184.6 63.79 .010 .004 .004 .004 .004 .004 .004 .005 .005 184.6 78.80 .005 .005 .005 .005 .005 .005 .006 .005 .005 184.6 93.80 .006 .006 .005 .005 .005 .006 .005 .005 .005 200.0 37.04 .019 .055 .053 .049 .049 .050 .053 .055 .056 200.0 53.49 .014 .014 .014 .014 .013 .013 .013 .014 .014 200.0 69.94 .010 .004 .004 .004 .004 .004 .004 .004 .004 O 200. 86.39 .004 .005 .005 .005 .005 .005 .005 .005 .006 172 Table D.18 ~ Entrainment Field 0 (0-~60°) Unforced Phase averaged data (at angle ¢) x/oo y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0 107.7 17.54 .0243 .0351 .0356 .0427 .0538 .0569 .0546 .0511 .0433 107.7 25.31 .0081 .0143 .0161 .0166 .0162 .0180 .0194 .0195 .0160 107.7 33.07 .0038 .0079 .0102 .0109 .0105 .0101 .0107 .0100 .0071 107.7 40.83 .0029 .0059 .0076 .0082 .0078 .0074 .0068 .0063 .0055 107.7 48.59 .0023 .0054 .0065 .0081 .0072 .0062 .0059 .0049 .0045 123.1 20.79 .0176 .0434 .0362 .0316 .0337 .0379 .0408 .0471 .0478 123.1 30.00 .0070 .0169 .0148 .0129 .0144 .0159 .0156 .0167 .0178 123.1 39.21 .0037 .0080 .0071 .0082 .0090 .0092 .0086 .0083 .0085 123.1 48.42 .0030 .0062 .0064 .0068 .0080 .0086 .0079 .0071 .0065 123.1 57.63 .0031 .0060 .0061 .0068 .0075 .0073 .0070 .0061 .0060 138.5 24.04 .0162 .0446 .0464 .0425 .0381 .0356 .0360 .0377 .0435 138.5 34.70 .0064 .0156 .0156 .0154 .0142 .0140 .0149 .0149 .0154 138.5 45.36 .0036 .0081 .0076 .0076 .0077 .0082 .0088 .0089 .0085 138.5 56.01 .0034 .0078 .0075 .0071 .0073 .0077 .0084 .0089 .0084 138.5 66.67 .0034 .0075 .0076 .0074 .0077 .0077 .0079 .0083 .0081 153.8 27.29 .0136 .0435 .0459 .0459 .0466 .0439 .0422 .0399 .0402 153.8 39.40 .0058 .0154 .0163 .0166 .0158 .0156 .0152 .0154 .0161 153.8 51.50 .0040 .0093 .0091 .0087 .0082 .0079 .0082 .0085 .0090 153.8 63.61 .0040 .0096 .0091 .0084 .0080 .0077 .0083 .0087 .0090 153.8 75.71 .0044 .0093 .0094 .0089 .0083 .0078 .0083 .0087 .0089 169.2 30.54 .0129 .0466 .0495 .0500 .0524 .0510 .0507 .0508 .0485 169.2 44.09 .0061 .0162 .0172 .0171 .0166 .0159 .0164 .0156 .0166 169.2 57.65 .0047 .0092 .0100 .0100 .0094 .0087 .0083 .0086 .0089 169.2 71.20 .0044 .0090 .0092 .0092 .0088 .0081 .0077 .0076 .0083 169.2 84.75 .0054 .0099 .0106 .0106 .0099 .0093 .0089 .0089 .0090 184.6 33.79 .0132 .0492 .0504 .0486 .0512 .0533 .0539 .0535 .0529 184.6 48.79 .0068 .0162 .0155 .0164 .0162 .0163 .0164 .0160 .0163 184.6 63.79 .0051 .0092 .0096 .0093 .0095 .0096 .0086 .0085 .0087 184.6 78.80 .0047 .0086 .0091 .0092 .0091 .0086 .0084 .0081 .0083 184.6 93.80 .0065 .0096 .0101 .0102 .0100 .0097 .0093 .0090 .0091 200.0 37.04 .0132 .0571 .0563 .0557 .0548 .0532 .0538 .0557 .0566 200.0 53.49 .0070 .0164 .0155 .0164 .0170 .0167 .0163 .0165 .0161 200.0 69.94 .0057 .0085 .0089 .0087 .0089 .0089 .0089 .0086 .0084 0 86.39 .0046 .0087 .0091 .0092 .0095 .0090 .0088 .0087 .0087 200. 173 Table D.19 ~ Entrainment Field 3 (0-~60°) Unforced Phase averaged data (at angle d) x/60 y/fio data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0 107.7 17.54 ~.047 ~.094 ~.088 ~.099 ~.120 ~.120 ~.099 ~.085 ~.094 107.7 25.31 ~.023 ~.032 ~.038 ~.054 ~.066 ~.065 ~.053 ~.037 ~.031 107.7 33.07 ~.020 ~.021 ~.027 ~.035 ~.042 ~.043 ~.037 ~.028 ~.022 107.7 40.83 ~.022 ~.024 ~.028 ~.033 ~.036 ~.036 ~.033 ~.028 ~.024 107.7 48.59 ~.024 ~.028 ~.030 ~.032 ~.035 ~.035 ~.033 ~.030 ~.028 123.1 20.79 ~.036 ~.076 ~.072 ~.068 ~.073 ~.085 ~.095 ~.095 ~.085 123.1 30.00 ~.021 ~.036 ~.031 ~.033 ~.039 ~.047 ~.052 ~.051 ~.043 123.1 39.21 ~.022 ~.028 ~.026 ~.027 ~.031 ~.035 ~.037 ~.037 ~.033 123.1 48.42 ~.024 ~.031 ~.029 ~.029 ~.031 ~.034 ~.035 ~.035 ~.033 123.1 57.63 ~.028 ~.033 ~.032 ~.031 ~.032 ~.033 ~.034 ~.035 ~.034 138.5 24.04 ~.033 ~.083 ~.081 ~.076 ~.074 ~.072 ~.076 ~.082 ~.084 138.5 34.70 ~.021 ~.044 ~.040 ~.035 ~.033 ~.036 ~.040 ~.045 ~.046 138.5 45.36 ~.023 ~.035 ~.033 ~.030 ~.028 ~.029 ~.032 ~.035 ~.036 138.5 56.01 ~.027 ~.034 ~.033 ~.031 ~.O30 ~.030 ~.031 ~.033 ~.034 138.5 66.67 ~.030 ~.035 ~.035 ~.034 ~.033 ~.033 ~.033 ~.034 ~.035 153.8 27.29 ~.030 ~.084 ~.084 ~.083 ~.080 ~.079 ~.077 ~.078 ~.081 153.8 39.40 ~.023 ~.045 ~.045 ~.043 ~.039 ~.036 ~.037 ~.039 ~.042 153.8 51.50 ~.025 ~.034 ~.034 ~.033 ~.031 ~.029 ~.029 ~.031 ~.032 153.8 63.61 ~.029 ~.034 ~.034 ~.034 ~.033 ~.032 ~.031 ~.032 ~.033 153.8 75.71 ~.032 ~.035 ~.035 ~.035 ~.035 ~.034 ~.034 ~.034 ~.035 169.2 30.54 ~.028 ~.088 ~.087 ~.088 ~.087 ~.086 ~.087 ~.087 ~.087 169.2 44.09 ~.023 ~.039 ~.041 ~.042 ~.041 ~.039 ~.037 ~.037 ~.038 169.2 57.65 ~.027 ~.032 ~.033 ~.034 ~.033 ~.032 ~.031 ~.030 ~.031 169.2 71.20 ~.031 ~.032 ~.033 ~.033 ~.033 ~.032 ~.032 ~.032 ~.032 169.2 84.75 ~.033 ~.035 ~.035 ~.035 ~.035 ~.034 ~.034 ~.034 ~.035 184.6 33.79 ~.027 ~.089 ~.089 ~.089 ~.090 ~.092 ~.091 ~.089 ~.089 184.6 48.79 ~.025 ~.037 ~.038 ~.039 ~.040 ~.040 ~.039 ~.038 ~.037 184.6 63.79 ~.029 ~.030 ~.030 ~.031 ~.031 ~.031 ~.031 ~.030 ~.030 184.6 78.80 ~.032 ~.032 ~.032 ~.032 ~.032 ~.032 ~.032 ~.032 ~.032 184.6 93.80 ~.034 ~.034 ~.034 ~.034 ~.034 ~.034 ~.034 ~.034 ~.034 200.0 37.04 ~.028 ~.095 ~.093 ~.094 ~.095 ~.097 ~.095 ~.096 ~.096 200.0 53.49 ~.026 ~.038 ~.038 ~.038 ~.039 ~.O40 ~.040 ~.040 ~.039 200.0 69.94 ~.030 ~.030 ~.030 ~.030 ~.030 ~.030 ~.030 ~.030 ~.03O 0 200. 86.39 ~.033 ~.033 ~.033 ~.033 ~.032 ~.032 ~.032 ~.032 ~.033 x/0 107. 107. 107. 107. 107. 123. 123. 123. 123. 123. 138. 138. 138. 138. 138. 153. 153. 153. 153. 153. 169. 169. 169. 169. 169. 184. 184. 184. 184. 184. 200. 200. 200. 200. 000000000NNNNN00000U‘UUUU‘HHHHHVVVNN 174 Table D.20 ~ Entrainment Field 3 (0-~60°) Unforced Phase averaged data (at angle ¢) MO 17. 25. 33. 40. .59 20. 48 30 48 57. 24. 34. 45. .01 66. 27. .40 51. 63. 75. 30. 44. 57. 71. .75 33. 48. 63. 78. 93. .04 56 39 84 37 53. 69. 86. 54 31 07 83 79 .00 39. .42 21 63 04 70 36 67 29 50 61 71 54 O9 65 20 79 79 79 80 80 49 94 39 data .0308 .0113 .0064 .0044 .0030 .0232 .0097 .0059 .0039 .0032 .0222 .0091 .0053 .0039 .0028 .0183 .0080 .0050 .0038 .0029 .0167 .0079 .0052 .0040 .0029 .0168 .0083 .0055 .0042 .0029 .0160 .0080 .0057 .0038 0.0 .0648 .0203 .0121 .0091 .0062 .0452 .0207 .0110 .0079 .0049 .0404 .0197 .0126 .0081 .0054 .0435 .0238 .0124 .0076 .0057 .0531 .0219 .0123 .0068 .0056 .0612 .0242 .0110 .0064 .0054 .0605 .0241 .0108 .0065 45.0 90.0 135.0 .0535 .0214 .0144 .0100 .0067 .0490 .0202 .0110 .0078 .0048 .0477 .0194 .0119 .0078 .0054 .0444 .0225 .0124 .0076 .0059 .0506 .0228 .0126 .0070 .0059 .0611 .0238 .0111 .0065 .0055 .0606 .0241 .0106 .0065 .0545 .0235 .0151 .0105 .0073 .0448 .0213 .0122 .0083 .0052 .0496 .0188 .0112 .0072 .0050 .0476 .0228 .0120 .0075 .0057 .0509 .0224 .0127 .0070 .0057 .0567 .0242 .0113 .0066 .0055 .0636 .0249 .0105 .0065 .0554 .0222 .0149 .0105 .0073 .0432 .0226 .0133 .0090 .0056 .0501 .0188 .0112 .0070 .0050 .0488 .0220 .0113 .0071,. .0054 .0493 .0233 .0127 .0070 .0057 .0550 .0244 .0115 .0067 .0057 .0618 .0250 .0105 .0067 .0500 .0199 .0134 .0098 .0069 .0432 .0226 .0139 .0095 .0060 .0447 .0209 .0118 .0073 .0050 .0521 .0211 .0108 0069 .0051 .0513 .0236 .0122 .0069 .0056 .0561 .0242 .0116 .0067 .0056 .0624 .0256 .0106 .0066 .0461 .0184 .0122 .0089 .0063 .0435 .0215 .0136 .0094 .0061 .0421 .0219 .0125 .0079 .0052 .0491 .0223 .0108 .0069 .0052 .0554 .0219 .0118 .0066 .0054 .0564 .0228 .0115 .0066 .0054 .0586 .0250 .0108 .0065 180.0 225.0 270.0 .0448 .0188 .0113 .0082 .0058 .0465 .0198 .0127 .0091 .0058 .0401 .0223 .0131 .0083 .0056 .0469 .0227 .0113 .0071 .0052 .0587 .0226 .0115 .0064 .0053 .0578 .0235 .0113 .0066 .0053 .0572 .0256 .0109 .0066 315.0 .0601 .0202 .0106 .0081 .0056 .0452 .0190 .0118 .0085 .0052 .0385 .0213 .0131 .0083 .0056 .0439 .0233 .0120 .0075 .0054 .0577 .0226 .0123 .0065 .0053 .0595 .0235 .0111 .0065 .0053 .0585 .0259 .0108 .0065 x/0 107. 107. 107. 107. 107. 123. 123. 123. 123. 123. 138. 138. 138. 138. 138. 153. 153. 153. 153. 153. 169. 169. 169. 169. 169. 184. 184. 184. 184. 184. 200. 200. 200. 200. 000000000NNNNN00000U’IMMWU‘HI—‘I—‘HHVNNNN Table D.21 - Unforced y/oo 17 25 30 48 57. 24. 34. 45. 56. 66. 27. .40-. .0000 .0000 39 51. 63. 75. 30. .09-. .65 44 57 71. 84. 33. .79-. .0001 .0000 48 63. 78. 93. .04-. .49-. 69. 86. 37 53 .54-. .31-. 33. 40. 48. 20. .00-. 39. .42 07-. 83 59 79-. 21-. 63 04-. 70-. 36-. 01 67 29-. 50 61 71-. 54-. 20 75-. 79-. 79 80 80-. 94 39 data 0034- 0000-. .0005 .0003 .0001 .0060- 0001-. .0001 .0000 .0000 .0045- .0009- .0002 .0001 .0002 .0067- .0004- .0004 .0004 .0004 .0059- .0005- .0005 .0004 .0005 .0124- .0010- .0005 .0003 .0004 .0150- .0010- .0005 .0003 0001 .0000 .0000 0014- 0000 .0000 .0000 0010- 0001- 0000 .0000 .0000 0003- 0001- 0000 0001- 0001- .0000 .0000 0001 0002- 0000- 0001 0000- 0000- .0001 .0000 0.0 .0088-. .0013 .0009 .0004 .0001 .0060-. .0003 .0002 .0001 .0001 .0058-. .0008-. .0001 .0001 .0002 .0064-. .0006-. .0003 .0003 .0004 .0075-. .0002-. .0005 .0004 .0005 .0122-. .0005-. .0006 .0004 .0005 .0165-. .0004-. .0005 .0004 0001 0005- 175 Entrainment Field u'v' (0--60°) Phase averaged data (at angle d) 90.0 135.0 180.0 225.0 270.0 315.0 45.0 0063-. .0012 .0011 .0004 .0002 0051-. .0000 .0006 .0002 .0002 0066-. 0007-. .0004 .0002 .0002 0085-. .0003- .0006 .0002 .0001- .0002 .0001 .0002 0063-. 0010-. .0003 .0003 .0003 0073-. 0007-. .0004 .0004 .0005 0103-. 0009-. .0006 .0004 .0005 .0006 .0004 .0005 0137-. 0011-. .0005 .0005 .0005 .0004 0086- 0042- .0007 .0007 .0003 .0002 0059- 0003- 0078- 0009- .0002 .0002 .0003 0083- 0010- .0004 .0003 .0004 0101- 0006- 0143- 0005-. .0083-. .0003-. .0001 .0001 .0001- .0054- .0004- .0006 .0003 .0002 .0040- .0003 .0005 .0002 .0003 .0086- .0008- .0003 .0002 .0002 .0091- .0012- .0003 .0003 .0004 .0124- .0006-. .0005 .0003 .0004 .0127-. 0007-. .0005 .0004 0080-. 0002-. .0000 .0001 .0001-. .0050-. .0002-. .0004 .0001-. .0002 .0035-. .0001 .0005 .0003 .0003 .0082-. .0008-. .0004 .0003 .0003 .0087-. .0009-. .0004 .0002 .0004 .0130-. 0008-. .0005 .0003 .0004 0122-. 0007-. .0005 .0004 0087-. 0001-. .0002 .0001 0000 0131 0003 .0001 .0001 .0000 0082-. 0007-. .0000 0001-. .0001 0063 0008 .0000 0001 .0000 0045-. .0001-. .0005 .0003 .0003 0052 0004 .0003 .0001 .0002 0049-. 0002-. .0005 .0003 .0003 0052 0001 .0005 .0003 .0003 0124-. 0009-. .0004 .0002 .0004 0129-. 0006-. .0004 .0003 .0004 0113 0009 .0004 .0003 .0004 0147 0009 .0005 .0003 .0004 0133-. 0010-. .0005 .0003 0145 0010 .0004 .0003 x/0 107. 107. 107. 138. 138. 138. 169. 169. 169. 200. 200. x/0 107. 107. 107. 138. 138. 138. 169. 169. 169. 200. 200. 00NNNU1LnU|\J\J\J CONNNUIMUINVN 176 Table 0.22 - Entrainment Field 3 (a--45°) Unforced Phase averaged data (at angle ¢) y/a0 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 17.54 .028 .050 .053 .058 .062 .076 .092 .088 33.07 .012 .015 .018 .016 .014 .015 .017 .016 48.59 .013 .012 .012 .010 .008 .007 .007 .009 24.04 .020 .059 .061 .055 .047 .045 .047 .049 45.36 .015 .011 .012 .012 .013 .013 .013 .012 66.67 .010 .007 .007 .007 .007 .008 .007 .007 30.54 .019 .058 .060 .064 .067 .068 .064 .061 57.65 .015 .013 .012 .012 .012 .012 .012 .012 84.75 .009 .007 .007 .007 .007 .007 .007 .007 37.04 .020 .073 .070 .067 .068 .068 .071 .073 69.94 .014 .012 .012 .013 .012 .012 .012 .012 Table 0.23 - Entrainment Field 6 (o--45°) Unforced Phase averaged data (at angle 6) y/oO data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 17.54 .0208 .0380 .0325 .0348 .0379 .0432 .0441 .0451 33.07 .0048 .0069 .0084 .0091 .0085 .0090 .0090 .0078 48.59 .0039 .0056 .0060 .0059 .0051 .0043 .0041 .0048 24.04 .0114 .0421 .0435 .0439 .0400 .0379 .0348 .0364 45.36 .0062 .0071 .0071 .0067 .0070 .0074 .0077 .0072 66.67 .0041 .0038 .0040 .0043 .0045 .0045 .0044 .0041 30.54 .0111 .0490 .0497 .0525 .0548 .0559 .0524 .0506 57.65 .0070 .0077 .0074 .0073 .0070 .0071 .0071 .0074 84.75 .0039 .0042 .0043 .0043 .0043 .0044 .0044 .0043 37.04 .0104 .0627 .0614 .0609 .0600 .0612 .0620 .0629 69.94 .0078 .0070 .0072 .0073 .0073 .0070 .0069 .0070 315.0 .060 .013 .010 .054 .011 .007 .058 .013 .007 .074 .012 315.0 .0443 .0057 .0053 .0383 .0072 .0039 .0488 .0077 .0042 .0628 .0070 Table Unforced x/Oo y/00 data 107.7 17.54 -.029 - 107.7 33.07 -.018 ~ 107.7 48.59 -.024 - 138.5 24.04 -.023 - 138.5 45.36 -.024 - 138.5 66.67 -.028 - 169.2 30.54 -.024 - 169.2 57.65 -.027 - 169.2 84.75 -.030 - 200.0 37.04 -.026 -. 200.0 69.94 -.030 -. Table Unforced x/Oo y/0O data 107.7 17.54 .0218 107.7 33.07 .0083 107.7 48.59 .0048 138.5 24.04 .0164 138.5 45.36 .0073 138.5 66.67 .0038 169.2 30.54 .0168 169.2 57.65 .0073 169.2 84.75 .0036 200.0 37.04 .0162 200.0 69.94 .0074 177 0.24 - Entrainment Field 3 (o--45°) .053 .013 .021 .062 .031 .031 .061 .025 .030 061 023 0.25 - Entrainment Field 3 (o--45°) 0.0 .0421 .0117 .0084 .0351 .0136 .0059 .0441 .0127 .0052 .0459 .0119 Phase averaged 0.0 45.0 90.0 .056 .017 .022 .054 .028 .031 .064 .026 .030 .059 .022 .067 .027 .025 .048 .024 .030 .064 .027 .029 .061 .022 135.0 .086 .035 .029 .045 .022 .029 .063 .027 .030 .062 .023 data (at angle d) 180.0 225.0 270.0 .091 .071 .046 .038 .033 .024 .031 .030 .027 .047 .053 .060 .023 .026 .030 .029 .030 .030 .061 .058 .058 .026 .025 .024 .030 .029 .030 .064 .065 .064 .024 .024 .024 Phase averaged data (at angle d) 90.0 135.0 45.0 .0377 .0148 .0093 .0348 .0128 .0058 .0446 .0130 .0053 .0435 .0118 .0397 .0163 .0093 .0359 .0122 .0057 .0435 .0131 .0055 .0446 .0118 .0404 .0163 .0083 .0352 .0120 .0058 .0407 .0130 .0055 .0456 .0119 .0373 .0149 .0074 .0343 .0128 .0060 .0413 .0126 .0055 .0458 .0121 .0339 .0130 .0068 .0369 .0137 .0062 .0413 .0123 .0054 .0452 .0123 180.0 225.0 270.0 .0327 .0112 .0066 .0375 .0141 .0062 .0428 .0122 .0052 .0435 .0123 315.0 .047 .016 .023 .065 .032 .031 .059 .024 .030 .063 .024 315.0 .0349 .0098 .0071 .0364 .0141 .0061 .0425 .0124 .0052 .0449 .0121 178 Table D.26 - Entrainment Field u'v' (0--45’) Unforced Phase averaged data (at angle 8) x/oO y/oo data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0 107.7 17.54-.0019-.0096-.0046-.0028-.0006 .0005 .0013-.0007-.0054 107.7 33.07 .0001 .0004 .0008 .0010 .0007 .0001-.0001 .0001 .0002 107.7 48.59 .0002 .0005 .0006 .0006 .0004 .0003 .0003 .0003 .0004 138.5 24.04-.0004-.0022-.003l-.0050-.0050-.0048-.0038-.0025-.0033 138.5 45.36 .0002 .0004 .0004 .0005 .0006 .0007 .0007 .0007 .0006 138.5 66.67 .0001 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0002 169.2 30.54-.0004-.0052-.0052-.0034-.0040-.0058-.0058-.0070-.0065 169.2 57.65 .0003 .0007 .0007 .0007 .0007 .0007 .0007 .0007 .0007 169.2 84.75 .0001 .0002 .0002 .0003 .0003 .0003 .0003 .0002 .0002 200.0 37.04-.0001-.0073-.0068-.0107-.0069-.0069-.0069-.0067-.0086 200.0 69.94 .0004 .0007 .0007 .0007 .0007 .0007 .0007 .0007 .0007 x/0 107. 107. 107. 138. 138. 138. 169. 169. 169. 200. 200. 00NNNU|LBU1\I\I\I x/0 107. 107. 107. 138. 138. 138. 169. 169. 169. 200. 200. 00NNNU‘U‘U'INNN 179 D.27 - Entrainment Field 5 (0--90°) D.28 - Entrainment Field 3 (0--90°) Table Unforced y/0O data 17.54 -.005 .027 33.07 .012 .007 48.59 .007 .001 24.04 .004 .006 45.36 .011 .006 66.67 .007 .006 30.54 .008 .011 57.65 .009 .006 84.75 .007 .009 37.04 .011 .014 69.94 .009 .005 Table Unforced y/0o data 0.0 17.54 .0391 .0452 33.07 .0093 .0139 48.59 .0012 .0037 24.04 .0264 .0509 45.36 .0050 .0123 66.67 .0014 .0049 30.54 .0208 .0475 57.65 .0028 .0099 84.75 .0018 .0050 37.04 .0164 .0516 69.94 .0029 .0087 Phase averaged 0.0 45.0 90.0 135.0 .024 .006 .002 .004 .006 .005 .011 .006 .010 .015 .006 .027 .005 .002 .005 .005 .006 .006 .006 .009 .015 .006 .002 .005 .001 .011 .002 .006 .007 .004 .009 .013 .006 data (at angle d) 180.0 225.0 270.0 315.0 .035 .038 .002 .006 .010 .012 .001 .003 .003 .010 .006 .004 .001 .001 .002 .007 .008 .007 .009 .011 .012 .004 .004 .005 .009 .009 .009 .011 .010 .010 .006 .006 .005 Phase averaged data (at angle d) 90.0 135.0 45.0 .0496 .0127 .0039 .0502 .0121 .0050 .0491 .0097 .0051 .0509 .0088 .0584 .0127 .0039 .0483 .0113 .0052 .0486 .0095 .0050 .0491 .0088 .0729 .0135 .0044 .0448 .0114 .0052 .0493 .0093 .0050 .0497 .0089 .0763 .0157 .0051 .0429 .0108 .0052 .0501 .0098 .0051 .0498 .0086 .0704 .0174 .0053 .0407 .0106 .0050 .0512 .0096 .0052 .0500 .0087 180.0 225.0 270.0 .0579 .0172 .0050 .0434 .0114 .0049 .0494 .0096 .0052 .0508 .0087 .031 .010 .001 .003 .004 .006 .010 .006 .009 .013 .005 315.0 .0499 .0156 .0044 .0478 .0116 .0048 .0471 .0104 .0051 .0519 .0088 Table Unforced x/9 y/oo data 107.7 17.54 .097 107.7 33.07 .024 107.7 48.59 .023 138.5 24.04 .061 138.5 45.36 .024 138.5 66.67 .027 169.2 30.54 .045 169.2 57.65 .029 169.2 84.75 .029 200.0 37.04 .036 200.0 69.94 .031 Table Unforced x/0 y/oO data 107.7 17.54 .0596 107.7 33.07 .0094 107.7 48.59 .0028 138.5 24.04 .0413 138.5 45.36 .0061 138.5 66.67 .0027 169.2 30.54 .0275 169.2 57.65 .0053 169.2 84.75 .0027 200.0 37.04 .0186 200.0 69.94 .0050 180 D.29 - Entrainment Field 3 (0--90°) .135 .037 .025 .116 .039 .033 .113 .033 .032 .127 .027 0.30 - Entrainment Field 6 (o--90°) 0.0 .0786 .0190 .0063 .0667 .0142 .0044 .0683 .0118 .0043 .0798 .0100 Phase averaged 0.0 45.0 90.0 .131 .034 .026 .117 .036 .032 .115 .034 .032 .124 .027 .150 .036 .029 .112 .034 .031 .116 .034 .032 .122 .027 135.0 .177 .041 .031 .103 .034 .031 .119 .033 .032 .120 .028 data (at angle 6) 180.0 225.0 270.0 .186 .171 .156 .047 .050 .047 .031 .029 .027 .095 .093 .099 .036 .039 .041 .032 .032 .033 .120 .120 .118 .032 .032 .032 .032 .032 .032 .119 .122 .125 .028 .029 .029 Phase averaged data (at angle d) 90.0 135.0 45.0 .0812 .0203 .0068 .0707 .0142 .0041 .0693 .0122 .0043 .0808 .0097 .0941 .0200 .0068 .0738 .0138 .0039 .0674 .0124 .0043 .0783 .0098 .0925 .0196 .0064 .0682 .0143 .0040 .0709 .0118 .0043 .0753 .0102 .0832 .0182 .0057 .0628 .0144 .0043 .0749 .0118 .0042 .0742 .0109 .0771 .0181 .0053 .0579 .0148 .0046 .0797 .0120 .0041 .0763 .0111 180.0 225.0 270.0 .0713 .0179 .0053 .0579 .0148 .0047 .0780 .0123 .0041 .0761 .0102 315.0 .150 .042 .025 .109 .042 .033 .114 .032 .032 .127 .028 315.0 .0750 .0181 .0058 .0610 .0144 .0046 .0728 .0119 .0042 .0783 .0103 x/O 107. 107. 107. 138. 138. 138. 169. 169. 169. 200. 200. 00NNNU'IUIUINNV Table D.31 - Unforced y/oo 17. 33. 48. 24. 45. 66. 30. 57. 84. 37. 69. 54 07-. 59-. 04 36 67-. 54 65-. 75 04-. 94-. data .0105 0002 0000 .0036 .0000 0000-. .0012 0001 .0000 0004 0001 0.0 .0202 .0002-. .0001 .0100 .0000 0000-. .0081 .0005 .0000 .0209 .0003 .0189 .0001 .0133 .0001 .0093 .0004 .0000 .0219 .0003 181 Entrainment Field u'v' (0--90°) Phase averaged data (at angle d) 45.0 90.0 135.0 180.0 225.0 270.0 315.0 .0265 .0257 .0001-.0003- .0001 .0157 .0001 .0000 .0181 .0125 .0003-.0001 .0000-.0001-.0001 .0132 .0073 .0020 .0002 .0002 .0002 .0000 .0001 .0001 .0073 .0109 .0167 .0176 .0004 .0002 .0003 .0002 .0000-.0000-.0000-.0000 .0191 .0145 .0156 .0147 .0004 .0004 .0004 .0003 .0151 .0004 .0000 .0001 .0013 .0034 .0000-.0000 .0000-.0000 .0149 .0118 .0003 .0004 .0000 .0000 .0159 .0200 .0003 .0003 .0226 0001 .0002 0000 182 List of References Ali, S.K., Klewicki, C.L., Disimile, P.J., Lawson, I. and Foss, J.F. "Entrainment Region Phenomena for a Large Plane Shear Layer", Turbulent Shear flows V, 1985, pp. 3.7-3.12. Clauser, 6.8. [1954] "Turbulent Boundary Layers in Adverse Pressure Gradients", Journal of Aeronautical Science, vol 21, pp 91-108. Coles, D. [1962] "The Turbulent Boundary in a compressible fluid", Rand Corp., Rep. R-403-PR. Disimile, P.J. [1984] "Phase Averaged Transverse Vorticity Measurements in an Excited, Two-dimensional Mixing Layer", Phd Thesis, Michigan State University. Disimile, P.J. [1986] "Phase Averaged Transverse Vorticity Measurements in an Excited, Two-dimensional Mixing Layer”, AIAA Journal, vol. 24 No. 10, pp. 231-269. Fiedler, 8.8. and Mensing [1985] "The Plane Turbulent Shear Layer with Periodic Excitation", Journal of Fluid Mechanics, vol 15, pp281-309. Fiedler, H.E. [1988] "Coherent Structures in Turbulent Flows", Prog. in Aerospace Sciences, vol. 25, pp. 231-269. Foss J.F., Davis, E.D. Haw, R.C. and Ali S.K. [1987] "Coherent Motion Induced Fluctuations in the Primary Transition Region of Plane Shear Layer", Forum on Turbulent Flows, ADME FED - vol. 51, pp. 1-13. Haw R.C., Ali S.K., and Foss J.F. [1987] ”Gravitationally Defined Veloci- ties for a Low Speed Hot-wire Calibration", Symposium on Thermal Anemometry, ADME FED - vol. 53, pp. 7-13. Hussain, A.K.M.F. [1983] "Coherent Structures - Reality and Myth”, Phys. Fluids, vol. 26, pp.2816-2850. Hussain, A.K.M.F. [1986] "Coherent Structures and Turbulence", Journal of Fluid Mechanics,vol. 173, pp. 303-356. Klebanoff, P.S. and Diehl, 2.0. [1951] "Some Features of Artificially Thickened Fully Developed Turbulent Boundary Layers with Zero Pressure Gradient", NACA Technical note 2475. "7'1111111'1‘111111ITS