RETURNING MATERIALS: }V1531_] Place in book drop to remove this checkout from w your record. FINES will _ be charged if book is returned after the date stamped below. .OI’I‘E'OOIIO ....... CHANGES IN THE TURBULENT BOUNDARY LAYER STRUCTURE ASSOCIATED WITH NET DRAG REDUCTION BY OUTER LAYER MANIPULATORS By Nasser Rashidnia A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 1985 Copyright by Nasser Rashidnia 1985 ABSTRACT CHANGES IN THE TURBULENT BOUNDARY LAYER STRUCTURE ASSOCIATED WITH NET DRAG REDUCTION BY OUTER LAYER MMNIPULATORS By Nasser Rashidnia A specially designed wind tunnel was used to examine the effects of tandemly-arranged parallel plate manipulators (TAPPMs) on turbulent boundary layer structure and the associated drag. Momentum balances and use of the velocity gradient near the wall were used to obtain the net drag and local skin friction changes. Measurements showed that local skin friction reductions were found from 2050 to as far as 1206,. Two sets of plates, identical except for thickness were used. Results with .003" plates produced a maximum net drag reduction of 10% at 5880 using momentum balance. Downstream of this position the drag began to relax back to its unmanipulated level. and returned to normal by 1005,. The wall friction coefficient (obtained from mean velocity gradients near the wall referred to as the "Cfn") remained below normal. The net drag calculated from Cfn' taking the device drag into account. resulted in a 2% drag reduction at 1205.. The difference in the net drag results obtained from the two independent methods suggests difficulty detecting three-dimensional effects due to the wake of the TAPPM. At 205.. simultaneous laser sheet flow visualization and hot-wire anemometry were' used to conditionally sample the u'. v', and u'v' information of the large eddies in both manipulated, and normal boundary layers at y/5 = .4 and .6. (The TAPPM was located at y = .850). The Reynolds stress in the large eddies was significantly reduced at 206,, but substantially recovered at 515,. This was verified using spatially separated temporal correlations of u', v'. and u'v' at the two locations. The frequency of occurrence of the footprints of the bursting process was also measured using flow visualization from a sublayer slit. The mean frequency of occurrence of the "pockets" decreased when scaled with both outer and inner variables urn (where uTu obtained from near wall mean velocity gradient was used). but increased when scaled with “16 (obtained from momentum balance). . The outward normal velocity of the inner region was significantly decreased at 205,, while the thickness of the sublayer increased by 10-20% throughout the 13080. ACKNOWLEDGEMENTS I would like to acknowledge the support of the NASA Langley Research Center (Contract NAG-1-302). grant monitor: Dr. D.M. Bushnell. and the support of AFOSR (Contract F49620-85-C-0002) for part of the last phase of the data acquisition of this experiment. I would also like to express gratitude to my advisor, R.E. Falco, for his advice and guidance throughout my graduate research studies. Many thanks is due to my committee members, in particular C.A. Petty and R.W. Bartholomew for their constructive comments and assistance. To Douglas Little for writing and modifying most of the computer programs and to Nancy Dawson for processing photos as well as their friendship. my deepest appreciation and thanks. The assistance of many students and technicians who contributed to the construction of the facility and many other areas of this project must not be forgotten. On a final note I would like to thank such colleagues as Mr. Kue Pan, C.C. Chu. and Marwan Zabdawi for their friendship and support. Lastly. a special thanks to Jan Cilla-Rashidnia for all the moral support she provided. THANK YOU TO ALL. TABLE OF CONTENTS Page LIST OF FIGURES...................... ..... ......................... vii LIST OF TABLES..................................................... xvii LIST OF SYMBOLS ................ . ..... ..............................xviii CHAPTER 1. INTRODUCTION................................................... 1 2. DESCRIPTION OF EXPERIMENTAL FACILITIES AND TECHNIQUES.......... 6 2.1 Facilities........ .......... ............................... 6 2.1.1 Wind Tunnel......................................... 6 2.1.2 Measurement Stations, Probe Support, Traverse Mechanism, and Positioning Instrument (Cathetometer)...................................... 8 1.3 Tunnel Inlet.... ........ ............................ 10 .1.4 Exit Diffusers......... ............... .............. 12 2.2 Experimental Apparatus................ ...... ...... ..... .... 12 2 1 Static Pressure Probes.............................. 12 .2 2 Traveling Preston Tube.............................. 13 .2.3 Boundary-Layer Manipulators and Tripping Device..... 14 2 4 Hot-wire Anemometry and the Data Acquisition System. 15 2.2.4.1 Single Probe Hot-wire........................ 15 2.2.4.2 Twin-x-wire'Probe............................ 16 2 2 5 Flat Pitot-tube..................................... 17 2.2.6 Flow Visualization.................................. 18 2.2.6.1 Smoke Fog.................................... 18 2.2.6.2 Smoke-Wire................................... 19 2.2.6.3 Titanium Tetrachloride (TiCl4)............... 19 2.3 Experimental ProcedureOOOOOOICOIOO.OOOOOOOOOOOOOOOOOOOOOOOO 19 2.3.1 Visual Data Acquisition............................. 20 2.3.1.1 Tunnel Preparation Visualization............. 20 2.3.11.2 TAPPM Wake and Wall-Layer Visualization...... 22 2.3.1.3 Wall Layer "Pocket Module" Event Visualization................................ 24 2.3.2 Mean Velocity and Combined Hot-wire and Laser Visual Data Acquisition Systems............... 25 iv 2.4 Data Reduction and AnaIYSis.OOOOOOOOOOOOOOOOOOOOIO00.0.0.0. 2.4 1 Streamwise Pressure Gradient and Skin Friction Data. 2.4.2 Mean Velocity Profile Data.......................... 2.4.3 Twin-x-wire Probe Data Processing and Analysis...... 2.4 4 Conditional Sampling of Probe Date With M The Aid of Film Data................................ RESULTS.eeeeeeeaeeeaeeeeeeeeaeeeeeeeeeeeeae eeeee eeaeeeeeeaeeeee 3.1 Flow Field conditions.............o........................ 3.1.1 Pressure Gradient Along the Centerline of the Test Wall.................................... 3 1 2 Two-dimensionality of the Boundary Layer............ 3.1.3 Turbulence Intensity of the Wind Tunnel............. 3 1 4 Smoke Flow Visualization of the Laminar Flow on the Test Wall....................................... 302 "can VCIOCity PIOfileSeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea 3.2.1 Mean Velocity Profile and Integral Parameters in Experiment I........................................ 3.2.2 Mean Velocity Profile and Integral Parameters in Experiment II....................................... 3.2.3 Skin Friction and Net Drag Results of Experiment 1.. 3.2.4 Skin Friction and Net Drag Results of Experiment II. 3.3 Flow Visualization Results.OOOIOOCOOOOOIOOCOOOOOI.000...... 3.3.1 Flow Visualization on Manipulator Plates ...... . ..... 3.3.2 Sublayer "Bursting” Results From Falco "Pocket" Flow Modules......................... 3.4 Correlation of Fluctuating Component Results............... 3.4.1 Correlation of Fluctuating Components Normalized with Their Respective RMS Values.................... 3.4.2 Correlation of Fluctuating Components Nermalized 'ith FreeStrem velocity (Um)OOOOOOOOOOOOOOOOOOOOOOO 3.5 Conditionally Sampled Large-Scale Motions (LSMs)........... 3.6 Accuracy................................................... DISCUSSION..................................................... 4.1 Flow Condition and Time-Averaged Integral Characteristics of Regular and Manipulated Boundary Layers Based on the moment“ Balance AnaIYSiSeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeee 28 28 3O 34 38 42 42 42 43 44 45 45 46 49 54 56 57 58 59 60 60 62 64 69 72 72 4.2 Large Eddy Characteristic Changes Associated with Drag Reduction in Manipulated Boundary Layers.................. 76 4.3 Characteristics of Regular and Manipulated Boundary Layers Seen from the Perspective of the Wall-Friction Velocity (urn) Obtained by Local Means............................. 79 5. mNalUSIONSOOOOO ........ O0.0.0.000...00....OOIOOIOOOOOOOOOOOOO 82 FIGURES.OOOOOOOOOOOOOOOOO0.0.0....OOOOOOOOOOOOOOOOO0.0.00.00.00.00. 85 TABLES.... ......... ..... .............. ............................. 189 APPENDIX A.... ........ . .......................... ........... ...... . 191 APPENDIX B........ ...... . ........... ..... ......... . ...... .......... 225 BIBLIOGRAPHY.. ............................................... . ..... 227 vi Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 2.4 2.6 2.10 2.11 2.12 2.13 2.14 LIST OF FIGURES Schematic of the low-speed wind tunnel............ ..... . Schematic of boundary layer test wall showing the TAPPM and measurement stations.......................... Honeycomb; Top picture shows the cell size. Bottom picture shows the uniformity of the lower edge of cells that rest on the lower side of the honeycomb box flush with the surface of the test wall at the leading edge............................................ Schematic of honeycomb-screen arrangement used for experiment I.0.0...000......00......COCOOOIOOOOOIOOOOOOO Schematic of honeycomb-screen arrangement used for experiment II...OOOOOOOOOOOOOOOOOOOOOO0.0000000000000000 Variation of freestream turbulent intensity rms(u')/U¢ versus x for both experiments: I (4.), II (1)000000000000000OOOOOOOOOOOOOOO A snap-shot of the freestream and the boundary layer smoke-wire flow visualization around x = 210". (flow is from right to left).................. Schematic of the movable (modified) Preston tube pIObe.O...00.......0....ICOCCOOOOOCOOOOOOOOO0...... Schematic of twin-x-wire array probe...... ........ ...... Schematic of the Pitot static tube probe used in velocity profile survey in experiment I..0.OOOIOOCOOOOOOOOOOOOOO.0.0.0.0...0.0.0... Schematic side view of laser optics and data acquisition streamwise region of inner wall flow visualization with Titanium tetrachloride (TiCl4) flow marker.OOOOOOOOOOOOOOOOCO0.00.00000000000000000000...0.. Velocity and calibration data acquisition. reduction. and analysis program sequence................ Twin-x-wire array probe calibration. data acquisition. reduction, and analysis program sequenceOOOIOOOOOIOOCOOOOOOOOOOOOIOOOOOOO0...... Block diagram of data acquisition and proce881n8 ‘ystwOOOOOO0.00.00.00.00.00......00.0.0.0... vii 85 86 88 89 90 91 92 93 94 95 96 97 98 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 2.15 2.16 2.17 2.18 Smoke-wire flow visualization with high-speed movie camera at x = 520" (13.2m); straight streaklines (tap); wavy streaklines in the freestream flow due to passage of large scale motions...0.0.0.0000.........OOOOCOOOOOOOO0.0.0.0000... Schematic of laser optics and x-wire array probe arrangement used in simultaneous visualization and anemometry at 2050.00.00.00000000......IOOOOOOOOOOOOO......OOOOOOO Smoke flow visualization around the downstream plate of TAPPM device (h = .880) at z = 0 (top); 2 = 30.5cm in the turbulent boundary layer.................................. ..... .. An example of a large eddy structure striking the probe in a turbulent boundary layer................ 3.1 Variation of differential pressure gradient 3.2 3.3 3.4 3.5 de/dx per foot vs x.............OOOOOOOOOOOOOOI0...... Preston tube calibration data (0). compared to Patel's (1965) empirical relation: . y = 0.8287 - 0.1381: + 0.1437: 1 - 0.0060: ’ (solid line)................................. ....... ... Spanwise variation of the local skin friction measured by Preston tube at different streamwise stations; 0 (o). A (+). C (‘). and K (x), with a sand paper (36 grit) tripping device and inlet No. 1 configuration............................. Spanwise variation of the local skin friction measured by Preston tube at different streamwise stations; 0 (o). and K (x). with a 1/16" threaded rod tripping device for inlet No. 1 configuration..... (bmparison of spanwise variation of the local skin friction measured by Preston tube at station 0 (x = 179") with a 1/16" threaded rod tripping device (at x = 13.5") for inlet No. 1 (+) and inlet No. 2 (x) configurations................. Non-dimensional mean velocity profiles (y/O vs 5/0,) at various streamwise stations in regular boundary layer from experiment I........................................... Clauser plot for mean velocity profiles (U/Um vs pUQy/p) at various streamwise stations in regular boundary layer from experiment I................................ viii 99 100 101 102 103 104 105 106 107 108 109 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 Wall- unit non-dimensionalized mean velocity profiles (U/uw vs pyu 9/") at various streamwise stations in regular boundary layer from experiment I................................ 110 Variation of (U -U)/u19 vs (yu ”9/8 U ) at various streamwise stations in regular boundary layer from experiment I................................ 111 Wake function profiles (W vs y/5) at various streamwise stations in regular boundary layer from experiment I. (Solid line : W= 28in (fly/28))... 112 Non-dimensional mean velocity profiles (y/O vs 0/05) at various streamwise stations in manipulated boundary layer from experiment I.......OOOOOIOOOOOOOO0.0.0.000... 113 Clauser plot for mean velocity profiles (U/Uco vs pUgy/p) at various streamwise stations in manipulated boundary layer from experiment I....................... ......... 114 Wall-unit non-dimensionalized mean velocity profiles (U/u 16 vs pyutelu) at various streamwise stations in manipulated boundary layer from experiment I........ ...... . ..... ... 115 Variation of (Uan — U)/ur6 vs IS “U ) at various streamwise stat?onson in manipulated boundary layer from experiment1.0.0.0000...00.000.000.00. 116 Wake function profiles (W vs y/8) at various streamwise stations in manipulated boundary layer from experiment 1. (Solid line : w = zsin’(ny/2s))... 117 Comparison of streamwise momentum thickness distributions (6 (In.) vs x (In.)) for regular (open) and manipulated boundary l'yers from experiment I.......OOOOCOOOO......OOOOOOOO 118 Streamwise variation of "law of the wall" (u+ = Alog1.(y+) + B) parameters (A and B) in manipulated boundary layers from experiment I....... 119 NonZdimensional mean velocity profiles (y/O vs U/Ua) at various streamwise stations in regular boundary layer from experiment II........... 120 Clauser plot for mean velocity profiles (U/U‘ vs pUay/u) at various streamwise stations in regular boundary l‘yer from experiment IIOCCOOOOOOOCOOOOO0.0.0.0........ 121 ix Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 Wall-unit non-dimensionalized mean velocity profiles (fi/“re vs p elp) at various streamwise stations n regular boundary layer from experiment II...................... Variation of (U5 - fi)/“re vs (yut ldec) at various streamwise stations in regular boundary layer from experiment IIOOOOOOO...O.......OOOOOO0.0.0.0000...0.... Wake function profiles (W vs y/5) at various streamwise stations in regular boundary layer from experiment II. (Solid line : W = 28in’(ny/28)).. Wall-unit non-dimensionalized fluctuating velocity profiles (rms(u’)/ute vs pyut In) at various streamwise stations in regu ar boundary layer from experiment II...................... Variation of rms(u')/U, vs y/O at various streamwise stations in regular boundary layer from experiment II...................... Near wall variation of rms(u')/U§ vs y/O at various streamwise stations in regular boundary layer from experiment II...................... Near wall variation of rms(u')/ute vs pyute/p at various streamwise stations in regular boundary layer from experiment II........... Near wall mean velocity profiles (y vs U) at various streamwise stations in regular boundary layer from experiment II...................... Non-dimensional mean velocity profiles (y/O vs U/Um) at various streamwise stations in manipulated boundary layer from experiment II..................................... Clauser plot for mean velocity profiles (U/Ug vs pUgy/u) at various streamwise stations in manipulated boundary layer from experiment II............................... Wall-unit non-dimensionalized mean velocity profiles (Flute vs pyutelu) at various streamwise stations in manipulated boundary layer from experiment II...................... Variation of (Uw - U)/ute vs (yut lde,) at various streamwise stations in manipulated boundary layer from experiment II..................................... X 122 123 124 125 126 127 128 129 130 131 132 133 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.41 Wake function profiles (W vs y/8) at various streamwise stations in manipulated boundary layer from experiment II. (Solid line : W = 28in’(ny/25)).. Wall-unit non-dimensionalized fluctuating velocity profiles (rms(u')/ut9 vs p elu) at various streamwise stations in man pulated boundary layer from experiment II...................... Variation of rms(u')/U; vs y/O at various streamwise stations in manipulated boundary l.yer from experiment II............OOOOOOOOOOOOOOOOOO. Near wall variation of rms(u')/U; vs y/O at various streamwise stations in manipulated boundary layer from experiment II...................... Near wall variation of rms(u')/ure vs pynte/u at various streamwise stations in manipulated boundary layer from experiment II....... Near wall mean velocity profiles (y vs U) at various streamwise stations in manipulated boundary layer from experiment II...................... Comparison of streamwise momentum thickness distributions (0 (In.) vs x (In.)) for regular (open) and manipulated boundary layers from experiment II.......................................... Streamwise variation of "law of the wall" (u+ = Alog"(y+ + B) parameters (A and B) in manipulated boundary layers from experiment 11...... Comparison of streamwise sublayer thickness distribution (68 vs t) in regular (x). and manipulated (o) boundary layers. (The ends of error bars represent distances of the data points below and above the chosen sublayer thickness shown in the figure)................ Wall-unit non-dimensionalized ratio of sublayer thickness [psslurn/"lman./[paslutn/nlreg. vs £................................................... Near wall mean velocity profiles (y vs U) at various streamwise stations (0. ArB) used to measure the dU/dy' and the sublayer thickness in regular boundary layer from experiment II........... Near wall mean velocity profiles (y vs U) at various streamwise stations (A-J) used to measure the dU/dyw and the sublayer thickness in manipulated boundary layer from experiment II....... .xi 134 135 136 137 138 139 140 141 142 143 144 145 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.48 3.49 3.50 3.51 3.52 3.53 3.54 Streamwise variation of the C 9/Cfc in regular boundary layer for experiment I................ Streamwise variation of the non-dimensional net drag ratio (NDR) (0- 9 °)Man [(0- 9°)Reg.’ for experiment I.......OOOOO:OOOOO......OOOCOOOOOOOO... Comparison between streamwise variation of the nonrdimensional net drag ratio (NDR) (0- 0 )M Ma [(0- 0. )R (+). and the local skin friction oratio (C 9)Man. /(Cf6)Re (x) both obtained from momentum galance in experiment 1.... ComparisonC between streamwise percent variation of (C - ) / C from fM CRg fRe momeggum ba agce (x). and from slope of mean velocity pofile at the wall (dU/dy') (+) in experiment IOCCCCCCCCOOCCIOCCCCOCOO OOOOOOOOOOOOOOOOO Streamwise variation of the Cfe/Cfc in regular boundary layer for experiment 11 ............... Streamwise variation of the non-dimensional net drag ratio (NDR) (0- 9 0)Man /(0- 9°)Reg. for experiment II.....0.0.0.:000000000000000 ..... .00... Comparison between streamwise variation of the non-dimensional net drag ratio (NDR) (9 M) Ma /(0- M) 08 (+). and the local skin friction ratio (Cf6)Man [(CfO)R (I) bOth obtained from momentum baffince in experiment II................. Comparison between streamwise percent variation of (C ) / C fM . R R . from momgntum Cga Ignce (x§.e§£d from slope of mean velocity at the wall (dU/dy') (+) in experiment II.0.00.00.........O.........OOOOOOOOOOOO Streamwise percent variation of (C ) l C obtained WnM f from slope offl megn velocIty8 at the wall (dU/dy') in experiment II.......OOOOCOOOCOIO......OOOCOOOOOOOOOO Streamwise variation of ratio (Cf 9)“ n / C ) obtained in manipu ated {om Maary layer in experiment II............ A snap-shot of the turbulent boundary layer downstream of the second manipulator plate. (Flow is from right to left)..... ....... . ...... xii 146 147 148 149 150 151 152 153 154 155 156 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.55 3.56 3.57 3.58 3.59 3.60 3.61 3 .62 3.63 3.64 3.65 3.66 Snap-shots of manipulators wake interaction with wall-layer fluid upstream plate in place (top). and both plates in place (bottom) at C = 20 (center of the pictures).................... Snap-shots of wall-layer normal transport of fluid marker (TiCl4) into outer region at t = 20 (center of the pictures). regular (top). and manipulated (bottom) boundary layers......... ...... Probability distribution of normal transfer of flow marker (TiCl4) into the wall region measured over 33.380 around t = 20 for regular and manipulated boundary layers............ Plan view of smoke-filled turbulent sublayer showing the "pocket" flow modules. which result from the interaction of outer layer typical eddies with the sublayer region................ ........ Variation of Rv' . /rms(v',)rms(v',) versus 1 for regufaf (x). and manipulated (+) boundary l‘yers at g =510.00.00.00000000000000.... Variation of Ru' . /rms(u'1)rms(u',) versus r for regfiraf (x). and manipulated (+) boundary layers at t = 51...... ........................ Variation of Ru' . /rms(u',)rms(v',) versus 1 for regulai (x). and manipulated (+) boundary layers at 6 = 51.................. ............ Variation of R(uovo) /rms((u'v')1)rms((u'v')3) versus t(¥o¥ ilgular (x). and manipulated (+) boundary layers at C = 51.............................. Variation of RV. . /rms(v'1)rms(v', versus 1 for regulai (x). and manipulated (+) boundary layers at C = 20.............................. Variation of Ru. . /rms(u'1)rms(u',) versus 1 for regulai (x). and manipulated (+) bound‘ry l'yers ‘t:g20......C.................OCCCOC Variation of Ru' . lrms(u'1)rms(v',) versus 1 for reguYaf (x). and manipulated (+) boundary layers at C = 20.............................. Variation of R a a . . /rms((u'v') )rms((u'v') ) vggs:8)t(?o¥ iigular (x). :nd manipulated (+) boundary layers at C = 20.............................. xiii 157 158 159 160 161 162 163 164 165 166 167 168 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3. 67 3.68 3.69 3.70 3.71 3.72 3.73 3.74 3.75 3.76 Variation of R v' IU; versus 1 for regular (x).1and manipulated (+) boundary layers at t = 51.............................. 169 Variation of R o . IU; versus 1 for regular (x).1and manipulated (+) boundary layers at §= 51.............. ...... . ......... 170 Variation of R v' IU; versus 1 for regular (x). and manipulated (+) boundary layers at §= 51......... .......... ...... ..... 171 Variation of R( IU; versus 1 for regular 2). add manipulated (+) boundary l‘yers 'tg=510.000.000.000...0.0.0..0...... 172 Variation of R v' IU; versus t for regular (x). and manipulated (+) boundary layers at §= 20.......... ............ ... ..... 173 Variation of R u' IU; versus 1 for regular (x3. and manipulated (+) boundary l‘yers at§= OOOOOOIOOOOIOOOCOOOCOOOC......COO ..... O. 174 Variation of R v' /U; versus 1 for regular (13.: and manipulated (+) boundary 1ayersat§= ......OICOOOO......OOOOOOO ........... 175 Variation of R( H, versus 1 for regular W( ). afldU manipulated (+) boundary layers at t = 20..... ..... ...... .............. 176 Schematic of an ideal large-scale motion in turbulent boundary layer used to estimate the position of the lower x-wire array signals with respect to 'front' and 'back' of the structure in the ensemble average results. The dashed lines indicate the y location of x-wire arrays.......................................... 177 Ensemble averaged v'. u'. and u'v' signals conditionally sampled to large scale motions and normalized by “r0 in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y= al' The vertical axes correspond to the normalized large eddy smoke boundaries. Zero lines are represented by three dots with a space between them ( ... ...). The average of the signals are shown by very close dotted lines. and the standard deviation of the normal boundary layers are shown by two lines with rather spaced dots. This convention is same for the following ensemble average signals in next sevenfigures......... ...... .... 178 xiv Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.77 3.78 3.79 3.80 3.81 Ensemble averaged v'. u'. and u'v' signals conditionally sampled to large scale motions and normalized by “16 in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y = .48........ ....... Ensemble averaged v', u'. and u'v' signals conditionally sampled to large scale motions and normalized by D; in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y = .65 ...... ......... Ensemble averaged v'. u’. and u'v' signals conditionally sampled to large scale motions and normalized by U; in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y = .48.................... Ensemble averaged v', u', and u'v' signals conditionally sampled to large scale motions and normalized by their respective rms values in regular (solid line signals) and manipulated (light dashed line signals) boundary layers ‘ty=068......0.0.0.000...0.000000000000000. ....... O. Ensemble averaged v', u'. and u'v' signals conditionally sampled to large scale motions and normalized by their respective rms values in regular (solid line signals) and manipulated (light dashed line signals) boundary layers aty= .48....0.0.0..............OOOOCOOOOOOCOOOO...... Ensemble averaged v'. u'. and u'v' signals conditionally sampled to large scale motions and normalized by u in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y = .65........ ....... Ensemble averaged v'. u'. and u'v' signals conditionally sampled to large scale motions and normalized by u in regular (solid line signals) and manipulated (light dashed line signals) boundary layers at y = .48............... Variation of C 9 versus (x-x.)/xo for regular and manipulated boundary layers and comparison with other investigators' results.OI...CO.........OCOOOOOOOOOOOOOOO.....OCOOOOOOO Variation of {C - l/C fM fReg versus (x-xo)/xo :gtained Rvia different techniques.......OOOOICOCCOC......CCOCCOOOO00.0.0000... XV 179 180 181 182 183 185 186 187 Figure 4.3 Streamwise comparison between non-dimensional net drag ratio (NDR) (6 - 90)Man./(e - 9°)Re . obtained from momentum balance, End direct measurement of dU/dy' in experiment II................. ............ xvi LIST OF TABLES Table 3.1 Mean boundary layer characteristics and wall-layer statistical information of visualization experiment ‘tg=20.0.0000000000000..........IOOOOOOOOOOOOOO0.0... 189 Table 3.2 Mean boundary layer integral characteristics............ 190 xvii fa LIST OF SYMBOLS Coles (1968) "law of the wall" parameter = 5.61 Coles (1968) "law of the wall" constant = 5.0 Skin friction coefficient = cw/(1/2pU’w) where a=c ; tw is obtained from Clauser plot. a=n 3 1w is obtained from dU/dyw, (Newtonian) a=9 3 tw is obtained from momentum balance Equilibrium shape factor Height of manipulator plates away from wall Shape factor = bdle Von Karman's constant = .41 Chord dimension of parallel plate manipulator Reynolds Number = pUmG/p Streamwise spacing between tandem manipulator plates Space-time correlation of functions p' and q' where p' is used as the reference function Tandem arrayed parallel plate manipulator Time period between wall burst events ("Pockets") Streamwise velocity component = U + u' Fluctuating velocity component in the x direction Ensemble averaged of u' in the large scale motions (LSM) Time-averaged mean of streamwise velocity component Time-averaged freestream velocity U/ “1 Wall shear velocity = (rw/p)°'s where a=c ; t' is obtained from Clauser plot. a=n 3 7w is obtained from dU/dyw, (Newtonian, a=6 ; tw is obtained from momentum balance Fluctuating Reynolds shear stress Ensemble average of u'v' in the large sale motions (LSM) Fluctuating velocity component in the y direction xviii 80) where skin friction coefficient decreased for the second time. no longer fit the curve of the regular boundary layer. This phenomenon can be interpreted as boundary layer flow in an adverse pressure gradient. This is similar to the pipe flow results by Clauser (1954). which showed lower skin friction for corresponding mean velocity profiles. The wake law profiles in the manipulated boundary layer are somewhat scattered around the Coles wake function law. There is a trend of low skin friction profiles (8 < 70) positioned above. high skin friction profiles (6 > 80) below. and profiles with the same CfO values of their corresponding regular boundary layer collapsed on the Coles wake function curve. Thus, the wake profiles in the manipulated boundary layer do significantly change. 3.2.2 Mean Velocity Profile and Integral Parameters in Experiment II Since no net drag reduction occurred in Experiment I (refer to 50 Figure 3.44), it was decided to use the thinner manipulators (t = 0.003”; t/8o = 0.00095) based on the Anders et al. (1984). Each velocity profile in Experiment II was made up of 50 discrete data points. These profiles were taken at several stations (refer to Figure 2.2). The data processing procedure is explained in Chapter 2. Table 3.2 contains some of integral characteristics of the boundary layers in Experiment 11. Figures 3.18 to 3.25 show the non-dimensionalized velocity profiles in Experiment 11 for regular boundary layers at various stations. Figure 3.18 shows y/O vs U/UQ. Figure 3.19 displays the Clauser plot of velocity profiles from which Cfc were estimated for the regular boundary layer case. This figure represents filug vs Rey. where Rey = prm/p. The straight lines plotted in this figure represent various Cfc uniformly ranged (with 0.00025 between two consecutive lines) from 0.00100 to 0.00575. as used in Experiment 1. Information (Cfc) from this figure is used in the results to be presented in Section 3.2.3 for a comparison with momentum balance and skin friction coefficient results obtained from the slope of the mean velocity close to wall (for ”Newtonian fluid"). Figure 3.20 is a representation of the wall-unit non-dimensional mean velocity profiles (u+ vs y+). A solid straight line. Coles "law of the wall". u+ = 5.6llog,.(y+) + 5.0). and u+ = y+. viscous-sublayer region are also plotted in the same figure. It is clear that the regular boundary results in this figure. all fit the solid line in the "log law" region to a large extent. This is a good representation of the fully-developed turbulent boundary layer in the unmanipulated case. The equilibrium condition of the boundary layer is also shown in 51 Figure 3.21. This figure shows (U5 - U)/ut vs yut/8dUo. Figure 3.22 displayes the wake function W vs y/8. For comparison purposes the wake function W = 2sin’(ny/28). suggested by Coles (1968). is also plotted in the same figure. Figures 3.23 to 3.26 show the non-dimensional streamwise component of fluctuating mean velocity profiles at different stations. Figure 3.23 of this group shows rms(u')/ut vs y+. Figure 3.24 shows rms(u')/U; vs y/O for the mean velocity profile, and Figure 3.25 shows close to wall data normalized in the same way as in Figure 3.24. Due to the thick boundary layer in this experiment. velocities very near the surface of the wall could be measured using the single hot-wire probe. The probe could reach as low as one wall unit (y+ = 1) close to the wall (refer to Figures 3.20. 3.26, and 3.27). This can also be seen in Figure 3.27, which shows the dimensional mean velocities close to the wall in the regular boundary layer at various stations. It is important to note that each profile has at least 10 points which fit a straight line passing through the origin (y = 0.0 and U = 0.0 in Figure 3.27). This confirms the linearity condition in the sublayer region of the mean velocity profiles. These results were also used to obtain the thickness of the sublayer region. Notice that the resulting local skin friction coefficients from the slope of the velocity profiles are different from both Clauser Cfc and from ch presented in this experiment. Details of the discrepancies between local skin friction coefficients obtained by different methods are discussed in chapter 4. In Experiment II, with manipulators in position. a similar non-dimensionalization procedure was used. Corresponding velocity profiles are presented in Figures 3.28-3.36 in the same order as for the 52 regular boundary layer case discussed above. In Figure 3.28. velocity profiles are non-dimensionalized by the outer parameters (6 and Ug). This figure shows y/O vs U/U; at various stations. Only two profiles of stations A (t = 19.3) and B (C = 34.81) show the effect of wake of the manipulator plates. Figure 3.29 diplays the data plotted in the Clauser plot. This figure is presented here to demonstrate the inadequacy of the Clauser plot method for the manipulated boundary layer. Results of local skin friction coefficients obtained from this figure are discussed in the following section. Using the friction velocity obtained via the momentum balance + vs y+) results. The trend of the profiles method. Figure 3.30 (u position in this figure follows the variation of CfO at different stations. Notice that the parameters A and B (refer to equation u+ = Aloslo(y+) + B) are obtained by fitting a straight line through the data in the log region. This line fit was normally located at 30 < y+ < 500. Parameters A and B at (various stations) are shown in Figure 3.39. Cf6 results are also discussed in the following section. The equilibrium condition of the boundary layer is also shown in Figure 3.31. This figure shows (0; - U)/ut vs yuT/8dUg. Similar to Experiment I, this figure shows that at stations where the skin friction drag is reduced. the profiles demonstrate a deviation from the other profiles. leading to a pressure gradient-like effect in the manipulated boundary layer (Clauser 1954). The wake function of the manipulated case is shown in Figure 3.32. In this figure, there is a large profile deviation from the Coles wake function. This reflects the presence of the manipulators in place. demonstrating a significant change in the 53 wake region. Figures 3.33 to 3.36 show the non-dimensionalized streamwise component of the fluctuating velocities at different stations. Figure 3.33 of this group shows rms(u')/ut vs y+. At low skin friction stations. there is higher rms(u')/u in the inner region (also refer to t Figure 3.36), and lower rms(u')/ut in the outer region of the manipulated boundary layer. in comparison to their corresponding regular boundary layers. Figures 3.34 and 3.35 show the same effect when the rms(u'). and y are non-dimensionalized by the outer region parameters 0; and 0. Figure 3.37 shows the dimensional mean velocity profiles close to wall in the manipulated boundary layer at various stations. Similar to regular boundary layer, each profile has 10 points which fit a straight line passing through the origin (y = 0.0 and U = 0.0 in Figure 3.37). This confirms the linearity condition in the sublayer region of the mean velocity profiles. Notice that the resulting local skin friction coefficients from the slape of the velocity profiles are different from Clauser Cfc and CfO presented in this experiment. Details of the local skin friction coefficient results obtained through different methods are presented in the following section. Furthermore. using the calculated 0 from the velocity profiles at various stations for both regular and manipulated boundary layers. Figure 3.38 (0 vs x) was constructed. It was then used to obtain CfO and “10' which were finally used to normalize the velocity profile data in this experiment. This figure shows that at station A (t = 19.3). 0 overshoots (due to device drag) and then relaxes back (with a lower 0 gradient than the regular boundary layer). This 0 gradient stays low, even after 9 54 reaches values less than those of the regular boundary layer. This reflects a net skin drag reduction (lower 0). At about station D (C > 60). the momentum thickness gradient increases sharply. and after 8 = 94 it levels off with the regular boundary layer to almost no net drag reduction. The results of Figures 3.37 and 3.27 were also used to obtain the thickness of the sublayer region. Individual near-wall velocity profiles for regular and manipulated boundary layers appear in Figures 3.42 and 3.43. Streamwise sublayer thickness variation for both regular and manipulated boundary layers are shown in Figure 3.40 (dimensional). In dimensional form. the manipulated boundary layer has. on average. a 17% thicker sublayer. For reference. the streamwise variation of ratio of the non-dimensional sublayer thickness (normalized by u rn obtained from the slope of the mean velocity profile near the wall) is shown in Figure 3.41. Overall, this indicates a similar increase in sublayer thickness. On the other hand. when the sublayer thickness is normalized by “TO (obtained from the momentum balance). it must show sharp variations, as seen in Cf9 vs :. 3.2.3 Skin Friction and Net Drag Results of Experiment I Using the information from Figure 3.16 (0 vs x). the local skin friction coefficient Cfo (by a graphical differentiation; Cfe = 2dO/dx) and the non-dimensional net drag (Ox - 0x.)Man./(e - 01.)R°8- along the x centerline of the test wall were calculated. These parameters combined with the results discussed above were used to obtain Figures 3.44 to 3.47. Figure 3.44 shows CfO/Cfc vs 5. which is an example of high 55 consistency between momentum balance CfO and the Clauser Cfc results in the regular boundary layer. The net drag result in Experiment I is shown in Figure 3.45 (Ox — 9x°)Man./(ex - 01°)Reg. vs 8. The net drag increase is at its highest value at 8 = 25. This is reduced to zero at 8 = 80. and again increased to higher values (10%) at stations farther downstream. Thus no net skin drag reduction was obtained in Experiment 1. However. it is concluded that if there are to be beneficial effects of TAPPMs. these will be limited to 8 = 80 (Rashidnia and Falco. 1983). Figure 3.46 is a replot of the same result in addition to the streamwise normalized local skin friction variation (CfO)Man./(CfO)Reg. vs 8. At 8 ( 80. where net drag has increased. the local skin friction is reduced, (CfO)Man./(ch)Reg. < 1.0. The two curves cross (8 = 80) and the ratio (CfO)Man./(ch)Reg. stays above 1.0. As a result of the sharp increase in gradient of 9 in the range of 80 < 8 < 120. (CfO)Man./(Cf0)Reg. increases and reaches its peak (2 1.4). In addition, net drag increases from zero to 10% in the same distance range. Then net drag tends to relax back to regular boundary layer very slowly. while'the ratio (ch)Man./(CfO)Reg. sharply decreases to about 0.7 at 8 = 188.4. In Experiment I, the slope of the mean velocity profile near the wall was obtained by a single hot-wire probe at two stations 8 = 44 (a decreased local skin friction station) and at 8 = 121 (an increased local skin friction station). The result is shown in Figure 3.47 for comparison with momentum balance Cf65 changes. The magnitude of changes in these two methods is not the same. yet they demonstrate similar trends of local skin friction variations. 56 3.2.4 Skin Friction and Net Drag Results of Experiment 11 Using the information from Figure 3.38 (9 vs x) local skin friction coefficient CfO (by a graphical differentiation; CfO = ZdO/dx similar to Experiment I) and the non-dimensional net drag (Ox - ex.)Man./(ex - exo)Reg. along the centerline of the test wall were calculated. These parameters combined with previously explained results. were used to obtain Figures 3.48 to 3.53. Figure 3.48 shows cfe/Cfc vs 8. which is an example of consistency between momentum balance CfO and the Clauser Cfc results with the same percentage variation obtained in Experiment I. The non-dimensional net skin drag result in Experiment 11 is shown in Figure 3.49 (Ox - exo)Man./(ex - ex,)Reg. vs 8). The net drag was at its highest value at 8 = 20. This was reduced to zero at 8 = 45. and reached its minimum at 8 = 58.2; i.e.. a 10% net drag reduction resulted. This net reduction relaxed back to normal boundary layer drag at 8 = 94. and remained at its normal value (zero net drag change). However, in Experiment II. a net drag of 10% was obtained. This is only up to 60 boundary layer thicknesses downstream of the manipulator. Figure 3.50 is a replot of the same result. in addition to the streamwise normalized local skin friction variation. (Cf9)Man./(CfO)Reg. vs 8. In the range of 8 < 45. where no net drag reduction is obtained. there is still a significant reduction in the local skin friction coefficient CfO (2 45%); i.e.. (CfO)Man./(cf0)Reg. = 0.55. At 8 =58.2. where the maximum net drag reduction is achieved. the local skin friction reaches its regular boundary layer value. The peak of the Cf9 increase is reached at 8 = 66. where the momentum thickness gradient has its maximum in the manipulated boundary layer. The two curves meet 57 again at 8 = 93. where net skin drag and local skin friction coefficient changes are almost nonexistent. This condition (ratio (CfO)Man./(ch)Reg. = 1) follows to the last measuring station. In Experiment 11, the near-wall slope of the mean velocity profile was obtained by a single hot-wire probe at several stations. Figure 3.52 shows the streamwise percentage local skin friction coefficient variation ((Cfn)Man. - (Cfn)Reg.)/(Cfn)Reg. vs 8. For comparison, similar parameters obtained from the momentum balance method ((Cf9)Man - (CfO)Reg.)/(cf6)Reg. are also plotted in Figure 3.51. This figure does not show a general correlation between the two curves. except in the local wall-skin friction (8 < 50). where both methods show different level of reduction in the manipulated boundary layers. The difference between the above independent techniques in the local skin friction coefficient amounts to 50% in upto 5080. Figure 3.53 shows the ratio (CfO)Man./(Cfn)Man. vs 8. This indicates that the Cfn obtained from the slope of the mean velocity profile near the wall is not consistent with the Cfe obtained from the momentum balance method. 3.3 Flow Visualization Results This section consists solely of visualization results obtained with the second TAPPM configuration. unless otherwise specified. 58 3.3.1 Flow Visualization on Manipulator Plates The results of boundary layer drag relaxation (refer to Figures 3.49 and 3.50) cast some doubt on the possibility of flow separation around the TAPPM plates. Careful flow visualization around the manipulator plates was conducted and checked. and no evidence of any sort of flow separation was observed. An example of this check is given in Figure 2.17. During the process of separation detection. further flow visualization was conducted downstream of the plates. Figure 3.54 presents an example of the manipulated boundary layer, with the wake of plates present along with the rest of the layer structures. These pictures necessitated a study of the plates' wake by themselves. A combination of wake and wall region flow visualization around 8 = 20 sparked new evidence of wake interaction with wall region flow. As many as 200 snapshots of this experiment were taken. A study of two cases (upstream plate alone and both plates in place) indicated that when two plates were in place the structures in the wake of the plates were coherent for longer downstream distances than the one-plate case. The mixing of wall region flow and wake structure was also reduced around 8 = 20. This is shown in Figures 3.55(a) and 3.55(b). Figure 3.55(a) shows the one-plate case. and 3.55(b) shows two plates in place. It was then decided to obtain quantitative results regarding the flow marker (TiCl4) normal distance rise at this station (8 = 20). To this end, a number of rolls of film were taken from this region. Under similar visualization conditions. the last two rolls with 39 frames of film were used for the final analysis. Figure 3.56 presents an example of the film used to measure the normal values of the marker lifted up 59 into the wall region. The y values obtained from similar films were statistically analyzed. The experimental setup appears in Figure 2.11. The results of this analysis are presented in Figure 3.57. The mean value of y+. averaged around $3.38.. shows a 25% reduction in the manipulated case. Table 3.1 displays the mean characteristics of the boundary layers at 8 = 19.3 in this experiment. It is also interesting to note that the flow marker (TiCl4). which was originally painted on the test wall surface. travelled in the normal direction upto y+ = 240 in the regular case and y+ = 180 in the manipulated boundary layer. It covered a large portion of the logarithmic region within a range of 6 boundary layer thicknesses to the leading edge of the flow marker on the wall. 3.3.2 Sublayer "Bursting" Results From Falco "Pocket" Flow Modules The results of the interaction of "typical eddies" with the sublayer flow leading to the "pocket" module were obtained at the station (8 = 51) where the maximum ch reduction occurred. Using this information. along with the duration of experiment and the frame rate of the movies. a calculation of the burst rate of wall events in both regular and manipulated boundary layers was possible. Figure 3.58 gives an example of the "footprints” of this interaction (referred to as the "pocket module"). This sublayer structure was originally observed by Falco (1974). and is one of the strongest bits of evidence of turbulence production structure in the turbulent boundary layers. It was found that the frequency of occurrence of footprints of the bursting process was significantly changed. This frequency increased (from 0.6905 to 60 1.033) when scaled with outer variables (TBU§/8), but decreased (from 29.670 to 21.699) when scaled on inner variables (pThu;9/u). When the period TB was normalized by “tn (obtained from mean velocity gradient at the wall) and u/p. a 28% increase in pThu;n/u was obtained. 3.4 Correlation of Fluctuating Component Results Based on the skin friction results and wall bursting results obtained through "pocket" flow module visualization at station C (8 = 51). it was decided to do a space-time correlation analysis of the fluctuating components obtained from twin-x-wire array. A similar correlation analysis was conducted at station A (8 = 20). These results were obtained for both regular and manipulated boundary layers. 3.4.1 Correlation of Fluctuating Components Normalized with Their Respective RMS Values Results of the analysis on u'. v'. and u'v'. when normalized with their respective rms values. are presented as follows. Figures 3.59 to 3.62 represent the results at 8 = 51. and Figures 3.63 to 3.66 show similar results at 8 = 20. Notice that all the peaks in these figures are shifted to the right side of r = 0. where t = (t - to)U°/5Reg.' This is the result of the streamwise separation (O'sslocal) of the two x-wire arrays. Figure 3.59 shows the rms normalized correlation of vertical velocity components at .68 and .48 (Rv.1v.z/rms(v'1)rms(v',) vs 1). 61 Signals of the top x-array (subscript 1) are used as the reference in the correlation calculation. Note that the peak values for both cases were positive. There was a little change in the peak of [the normal fluctuations (8.75% reduction). No other significant differences are indicated in this figure. Figure 3.60 shows the rms normalized correlation of streamwise fluctuations for both regular and manipulated boundary layers (Ru.1n.z/rms(u'1)rms(u',) vs t). When there is a 10.8% reduction in this correlation. the peak is narrowed a small amount. Therefore. a relatively small change appears in the large-scale motions (LSMs). as a result of the presence of the TAPPM's wake on the manipulated boundary layer. At about one 5100.1 to left of the peak. the correlation is closer to the zero value. This may be a sign of alteration of the flow in the valleys between the two consecutive LSMs at this station. At the same station. cross correlation of the signals. R u.Iv.z with a negative peak. hardly shows a peak value change in Figure 3.61 (Ru. .z/rms(u'1)rms(v',) vs 1). This correlation on the left-hand side 1 v of the peak shows a minor positive correlation in the manipulated case. which could be an indication of the manipulator's wake. A correlation reduction of 9.4% occurred in the peak of Reynolds stress signature (R(u.v.):(u.v.)3/rms((u'v')1)rms((u'v')3) vs t). This reduction was of the same order as the normal and streamwise components previously indicated. Figure 3.62 shows the correlations with positive peaks. In the rms normalized form at station C (8 = 51). results of temporal correlations did not reveal significant changes. It was 62 therefore, prOper to conduct the same analysis on the data obtained at 8 = 20. where the effect of the manipulator was expected to be more active. Using the same procedure applied to the data at 8 = 51. Figures 3.63 to 3.66 were obtained. Figure 3.63 indicates a 6.4% reduction. not noticeable. in the peak of normal velocity correlations. Streamwise fluctuating temporal correlations are significantly changed. Figure 3.64 (R . . /rms(u' )rms(u’,) vs 1) indicates a similar result, along u 1‘1 z 1 with a 30% narrower peak in the manipulated than the regular boundary layer case. The cross-correlation at this station (Ru' . /rms(n'1)rms(v'z) vs 1v 3 r. at 8 = 20). shows a 13% reduction and a 25% narrower peak. This is shown in Figure 3.65. This effect is more pronounced in the Reynolds stress correlation (R(u.v.)1(u.v.)3/rms((u'v')1)rms((u'v’),) vs r. in Figure 3.66. which indicates a 48% lower and 30% narrower peak when compared with the regular boundary case. 3.4.2 Correlation of Fluctuating Components Normalized with Freestream Velocity (0;) Although the traditional normalization in space-time correlation showed the presence of some structures in both regular and manipulated boundary layers, it was not easy to observe a clear picture of flow alterations due to the TAPPM. For reference, the aforementioned fluctuating correlations were non-dimensionalized with the freestream velocity (0;). which was held constant for all cases. Results of this analysis on u'. v'. and u'v' are presented as follows. Figures 3.67 to 3.70 represent the results at 8 = 51. and 63 Figures 3.71 to 3.74 show similar results at 8 = 20. Notice that all the peaks are again shifted to the right-hand side of t = 0. as was the case in Section 3.4.1. This was explained as the result of streamwise separation of the x-wire arrays. Figure 3.67 shows the correlation of vertical velocity components at .68 and .48 (Rv.1v.z/U: vs 1). The subscripts used were similar to those in the previous section. as explained above. There are no significant differences in the temporal correlations at station C. Figure 3.68 (Ru'xu'3/U: vs 1) shows the correlation of streamwise fluctuations for both regular and manipulated boundary layers. A small amount of correlation reduction is observed in the peak value shown in Figure 3.68. In general. no significant change is indicated in that correlation. At the same station. cross-correlation of the signals Ru'zv'1/U: with a negative peak. shows little peak value change in Figure 3.69 (Ru.1v.z/U; vs 1). The only apparent change in the 51) is shown in Figure 3.70 for correlation at this station (8 Reynolds stresses, with a 7.5% peak increase and a 30% peak width increase. The average Reynolds stress correlation farther outside the peak also stayed above the regular boundary layer. Thus. the correlation functions. when normalized by the freestream velocity at station C (8 = 51). again showed no significant change. Similar normalization was applied to the signatures at station A (8 = 20). Figures 3.71 to 3.74 present these results. Figure 3.71 (R . [0: vs r) shows a 48% reduction in the peak correlation of F v 1v 1 normal fluctuating velocities. A 60% reduction in the streamwise correlation of u' signals (Figure 3.72. Ru' .3/0: vs r) was obtained. 1 u 64 This is a major difference that was not so obvious in the rms normalized correlations in the previous section. Cross-correlation results at this station are shown in Figure 3.73 (Ru'1v'3/U: vs 1). This figure shows a 54% reduction in peak value. which has narrowed the same amount in width. It is interesting to note that the correlation function is very close to zero for the most part at values 1 ( 0 for the manipulated boundary layer, in comparison to the regular case with a positive value of 0.00004 in a relatively long range negative 1 (-O.6 > r ) -2.0). The most striking change in the entire correlation occurred in the Reynolds stress signatures (Figure 3.74. R .) IU; vs r). The 3 (u'v')1(u'v major changes in these correlation results are an 84% reduction in peak and a 97.2% reduction for the rest of this correlation function. It is clearly evident that this result demonstrates the fact that there is hardly any correlation between the two Reynolds stresses at .68 and .48. In other words, in addition to the results in previous figures. one might be convinced that u' and v' signals are decoupled a great deal. This will be further explored in the conditionally sampled results of the large-scale motions. presented in the following section. 3.5 Conditionally Sampled Large-Scale Motions (LSMs) This section is devoted to a description of the results of the conditionally sampled large-scale motions (LSMs) and the ensemble averaged data of these structures' signatures for both regular and manipulated boundary layers. These were obtained by simultaneous hot-wire anemometry and laser flow visualization performed at station A 65 ( 8 = 20). Note that three signals, u'. v'. and u'v'. are discussed here. Note also that based on better visibility of the tap x-wire array. the data were sampled with signals of the probe, which was located at y=0.68. The lower x-wire array was located at .48 and was .58 downstream of the top array. In order to find the upstream and the downstream border of the signals related to the averaged LSMs passing by the probe located at y=.48. a simple geometrical analysis on an ideal LSM was performed. To this end. a sketch of the side view of a LSM was plotted, and using the suggested 33° angle (Falco. 1974) of the upstream side of an ideal large eddy structure and the average convective velocity of a typical LSM at the probe position, the approximate location of front and back of the averaged scales was estimated. A schematic of the LSM used for the above procedure is shown in Figure 3.75. In order to demonstrate the changes in motions in the large-eddy structures when the turbulent boundary layer was manipulated, the abovementioned signals from both cases were conditionally sampled. The method of sampling from movies is explained in Chapter 2. The sampled data were then averaged and plotted, mainly to observe the dynamics of the flow inside the bulges (refer to Falco. 1977 for details of this technique) and outside the bulges in the ”valleys". Ideally. a large eddy in the turbulent boundary layer is assumed to look from a side view like the structure shown in Figure 3.75. with the flow moving from right to left. The fluctuating velocity and Reynolds shear stress signals. when normalized by friction velocity ure (see Tennekes and Lumley. 1972). are shown in Figure 3.76 with separate horizontal axes. The two 66 vertical axes in the middle portion of the signals represent the boundaries (upstream = right-hand side. and downstream = left-hand side) of the large eddies sampled in this experiment. Therefore. the distance between these two vertical axes represents a normalized streamwise length of the LSMs at the probe location. The signals outside these two lines indicate the average activity of the flow upstream and downstream of the LSMs in this experiment. For comparison. signals of the top x-wire probe for both regular and manipulated boundary layers are shown in the same figure. Figure 3.77 shows similar signals obtained with the lower x-wire probe located at y = .48 (and .58 downstream of the top x-wire array). A comparison of the ensemble-averaged signals when normalized by u.c both at .68 and .48 indicates a significant reduction in the transfer of low momentum fluid into the high momentum fluid region when the manipulators were present. The distribution of (u') and 3 in the same region of the large eddy. caused a reduction of the Reynolds stress inside these large motions. The downstream boundary of the LSM shows a 75% reduction in the streamwise velocity. An overall result marks a total of 30% reduction in the long time average Reynolds stress in the signature shown in Figure 3.77. A comparison of the ensemble-averaged signals, when normalized by the freestream velocity (0;) inside the large scale motions (LSMs) both 68 at .68 and .48. indicates the same picture. but with somewhat large shifting in the Reynolds shear stress signals. Figure 3.78 shows a 29% and 50% increase of wallward normal motion in the upstream portion and boundary. and a 15% increase in the downstream portion. along with no change in this boundary of the LSM's. The ensemble-averaged streamwise velocity at .68 changes are as follows: a 30% increase in upstream portion with no change in this boundary. and a 27% decrease in the upstream valley of the LSM. The unchanged downstream portion and boundary of the average LSM is indicated in Figure 3.78. The Reynolds stress (u'v')1 associated with the above sweeps show a 35% reduction in the upstream boundary. along with a 50% reduction inside the average LSM as indicated in this figure. A 10% Reynolds stress reduction in the downstream boundary of the average LSM, along with a 39% reduction in the overall long time average inside and outside of these scales. is important to note. Notice that the signal demonstrates a flat signature for a good portion of the average LSM. Although no significant change occurs at the boundary. the downstream portion shows a sharp negative peak. This is the same peak mentioned earlier in the “to normalized signals which is difficult to understand. The ensemble-averaged signatures of LSMs at y = .48. normalized with the freestream velocity. are shown in Figure 3.79. Similar changes to those found in .68. but with higher magnitudes. are also observed in these signals. The most dramatic change occurred in the Reynolds stress signal. with a 60% reduction in the entire length of ensemble-averaged signal at .48; inside and outside the averaged LSM (refer to Figure 3.79). The strong change of the wallward normal motion a in the 69 downstream boundary of the LSM indicates a 48% reduction. An average of 35.5% decrease in the central portion of the LSM is shown in the same figure. This. combined with a 37.5% reduction in the streamwise velocity (u')3 in the same region of the large eddy, resulted in the loss of the Reynolds stress signal inside these large motions. The downstream boundary of the scale shows a 75% reduction in the streamwise velocity. This marks a total of 60% reduction in the overall Reynolds stress in the signature shown in Figure 3.79. When the signals were normalized by their respective rms values. they appeared similar to the comparisons with urO' These signals are shown in Figures 3.80 and 3.81. In addition. for reference purposes. the signals were normalized by the friction velocities (u ). which were tn obtained from the slope of the mean velocity near the wall in each case. These results are presented in Figures 3.82 and 3.83. They appeared similar to the comparison with 0;. It is therefore also shown here that the conditionally sampled data are consistent with the space-time correlation results at 208.. 3.6 Accuracy In this section a brief discussion of the maximum errors resulting from instrumentation and calculation will be presented. Errors resulting from the conditional sampling (670 samples in each case) technique have not been calculated. The errors due to sampling. however. are assumed to be small. This assumption is based on a comparison with similar results in regular boundary layers obtained by 7O Falco (1983) from his LSMs. It appears that Falco's ensemble-averaged signals at y = '75510cal are in consistent with the signatures obtained at y = '6blocal in this experiment. Notice that the sample size in the present experiment was one order of magnitude larger. It has been shown that the ensemble-averaged signatures in LSMs do not depend on R9 over a range of 730 < R9 < 3116. This was substantiated for R9 = 2542 in the present experiment. The AID was tested with a 3.75-volt input. The output was 3.75 r .002 volts. or t .006% in converted anemometer voltages. This error converts to 1.1% and .6% error in the streamwise and normal velocity components. respectively. The pressure transducer contributed a maximum of 1% error to the freestream velocity. The error of the A/D due to sampling rate is about .01%. which is negligible. The errors due to the calibration curve (using the Collis and Willams parameters) were .002% in velocity form. The sum of the above errors is at most 2.4 and 1.9 for the streamwise (u') and normal (v') velocity components respectively. This amounts to a 2% error for components. Based on the above error in u' and v'. the error in u'v' was estimated to be less than 4%. The error in local skin friction measurements obtained from the slope of the mean velocity profiles at the wall was calculated. The error bars on the most important factors which influence the measurement of the slape of the mean velocity profile at the wall were determined as follows: 1) measurement of probe position 3.% change in Cfn‘ 2) hot-wire wall effects for the insulating test wall showed up 71 only below y+ = 2 (in excellent agreement with the work of Bhatia el al. 1982). and hence did not affect the measurements in this experiment; 3) the accuracy of the calibration from day to day of a burned-in hot-wire resulted in a 1.5% changes in cfn‘ temperature changes during a run, t .2%; and the accuracy of the curve fit. a .3%. Thus. the overall measurement accuracy of the wall slape technique is estimated to be r 3.5%. In an attempt to eliminate the effect of changes in wire calibration in the Cfn calculation. a procedure was devised in which a calibration is made when a profile was taken. The wire was recalibrated after the profile data was taken. Minute changes in the calibration constants were always noted. However. this procedure reduced the overall error by another 0.5% to = 13% at the expense of much time and effort. CHAPTER 4 DISCUSSION In Chapter 3 flow conditions and the consequences of manipulating the outer layer flow structures in turbulent boundary layers were presented. In this chapter these results will be examined and interrelated in order to demonstrate this effect of the manipulation on the physical mechanisms involved in the associated drag reduction and relaxation to the normal (unmanipulated) boundary layer situation. To this end. it is appropriate to place emphasis on the detailed study of large scale motion alterations and the role of the TAPPM wake in interrupting the interaction of outer layer fluid with near-wall layer fluid. Based on the difference between the values of “re and “r it is n' helpful to discuss the effect of each separarately. In cases of correlation. they are referred to accordingly. This analysis is an attempt to correlate the detail structural changes in large eddy geometry and the dynamics which resulted from the presence of the TAPPM in the boundary layer. Results of other investigations will be referred to whenever appropriate. This will corroborate the conclusions drawn in the present discussion. 4.1 Flow Condition and Time-Averaged Integral Characteristics of Regular and Manipulated Boundary Layers Based on the Momentum Balance Analysis The two major changes in Experiment II namely freestream turbulence level and thickness of the TAPPM plates _ played an important 72 73 role in changing the net drag reduction from zero in Experiment I to 10% at 8 = 58.23 in Experiment II. The lower turbulence intensity (refer to Figure 2.6) is the key to the improved two-dimensionality of the turbulent boundary layers (Bradshaw. 1965) developed on the test wall (refer to Figure 3.4). This plus reduction in thickness of the plates suggested by other investigators (Corke. 1981; Hefner et al.. 1983; Anders et al., 1984; Plesniak et al.. 1984). resulted in the successful net drag reduction mentioned above. It was shown that any beneficial effects of the TAPPMs occur at downstream distances greater than 50-808o (Rashidnia and Falco. 1983). This proved to be the case for a second time in the present experiments. resulting in a 10% net drag reduction at 8 = 60. Similar trends of local skin friction reduction. overshoot. and relaxation were obtained by Anders et al (1984). Figure 4.1 shows the streamwise variation of CfO vs 8. However, assuming a two-dimensional flow in the manipulated boundary layers. which might have suffered from some three-dimensional effects (difficult to avoid). skin drag results in different laboratories do not seem to show a unified trend. One may therefore speculate that when the TAPPM is in place. the development of the manipulated boundary layer is susceptible to three-dimensional flow caused by some kind of very small irregularity (e.g. angle of attack. spanwise and/or streamwise ripples. burrs at upstream/downstream edges of the plates) in the device which. in turn, develops a separation around itself. The skin friction drag evolution for similar flow conditions of several investigators has been also discussed by Anders (1985). It is thus necessary to examine the skin drag directly measured by different independent techniques available 74 today (e.g.. Westphal, 1985; Immay et al.. 1985; Mumford and Savill. 1984; Lynn and Screenivasan. 1985). The visualization results presented in Chapter 2 (refer to Figure 2.18). did not show separation. (Note. however, that the resolution of this technique is not high enough to detect long thin separation regions of thickness the order of a few thousandths of an inch). It is of interest to note that the spanwise Cf results from Preston tube measurements indicated rather similar percentage variations in their peaks about their averages in the manipulated case. (They were not presented here because of their dependence on the universal law of the wall). Using the momentum balance. present results indicate a Cf9 reduction comparable to other investigators for up to about 5180 (Corke, 1981; Bertelrud et al.. 1982; Anders et al.. 1984). Figure 4.1 show even higher reduction. up to 45%, in local skin friction coefficient. This plus the results of the visualization experiment indicate that the sublayer fluid moved 25% less distance into the outer layer region (reduced from yReg. = 240 to yMan. = 179, over a range of 13.38. around 8 = 20). In addition. burst frequency in absolute value was reduced at 8 = 51. It therefore justified the maximum ch reduction in the region. On the other hand, it was shown that the sublayer thickness increased from 15-20% (refer to Figure 3.40) over the major downstream distance of the test wall after the TAPPM in the manipulated boundary layers. The increase in sublayer thickness was hypothesized by Corke (1981). but not supported with data. Corke's estimate was that sublayer thickness increased by 17%. From the present experimental results. it is now strongly evident for the first time. that the sublayer thickness in the 75 manipulated boundary layers does indeed increase (refer to Figures 3.40 and 3.41). This is consistent with the drag-reducing effects of riblets (Walsh. 1980 and 1982) which in fact increase the thickness of the sublayer. In the case of the TAPPM, the sublayer thickens for at least the first 50-608.. This in turn makes the interaction of typical eddies with a thick sublayer somewhat less chaotic (Falco, 1983). leading to local skin friction reduction. The Typical Eddy/wall interactions with a thick sublayer are labeled type 1 and type 2 (as described by Falco). Type 1 was visually observed in a vortex ring/moving wall interaction experiment in the TSL which involved a rearrangement of sublayer fluid without the break-up of the typical eddy (in this case the vortex ring; also see Liang. 1984). In type 2. this interaction lifts the sublayer fluid up into the logarithmic region without the breakup of the Typical Eddy itself. However, the thickened sublayer does not appear to be the main physical mechanism behind the reduced skin drag. Otherwise. the relaxation to the normal situation after 8 = 75 (obtained from the momentum balance) would not have occurred (refer to Figure 3.49). The footprint (wall event) of the typical eddy is called the "pocket" flow module (Falco. 1980), showed that this interaction was weakened at 8 = 51 when TAPPMs were present. The wall event mean period TB, when sealed with inner layer variables (“r and u/p) over a range of Reynolds numbers (738 < R9 ( 4000). has been shown by Falco (1983) to be pThutezlu = 30 in regular boundary layers. Results of a similar experiment in the normal boundary layer (using “re for non-dimensionalization of the burst period) confirms this number (T5 = 29.67) at R9 = 3495. Similar normalization in the manipulated case 76 indicated T; = 21.7. The reduction of the inner wall normalized burst rate implies more wall interaction at this station. although in absolute value the number of wall events was reduced by 40%. On the other hand, when these mean periods were scaled with the outer layer variables (0; and 510ca1)' they indicated 50% fewer bursts ("pockets"). consistent with the maximum skin friction reduction at this station. This conclusion takes into account Rao's (Rao et al.. 1971) outer-layer scaling results. from which he concluded that the wall bursts scale with outer-layer parameters. Overall. interpreting these results in terms of the skin friction changes obtained from the momentum balance does not lead to a constant picture. 4.2 Large Eddy Characteristic Changes Associated with Drag Reduction in Manipulated Boundary Layers A comparison of fluctuating components in boundary layers indicated that distinct changes occurred in the LSMs when TAPPMs were present. Temporal correlations at 8 = 20 were significantly modified. The reduction of streamwise velocity components inside and outside the large-scale motions, represented by ensemble-averaged signals at both y = .48 and .68 with the x-wire arrays. confirmed the reduction of the rms of the same signal in the fluctuating velocity profile results. These results are presented in Figures 3.33 and 3.34 from the independent measurement in Experiment II. Farther downstream. at 8 = 51, the correlations returned closer to their normal boundary layer level. This indicates that the LSMs regained most of their strength. The downstream relaxation of fluctuating components were also investigated by 77 Guezenenec et al. (1985). Their results showed that at 8 = 45 (close to station C in the present experiment) u'. v' and u'v' had a small amount of overrelaxation. This. interestingly. supports the mean velocity and space-time correlation results at 8 = 51. There is. however. a significant difference in the net drag reduction and its relaxation farther downstream. The IIT research team's net drag results (in particular, refer to Plesniak, 1984) did not show a sharp relaxation to normal boundary layers when the manipulators were present. Thus there is a significant difference in the net drag reduction and its relaxation results between the present results and the ongoing experiments at IIT. It is therefore concluded in accord with Hefner et al. (1983). that the resultant relaxation disturbances become significant by the order of 50-80 boundary layer thicknesses downstream of the manipulators. This conclusion refers the three-dimensional effects discussed earlier, and suggests the develonment length needed before they become important. A detailed study of the ensemble-averaged signals in the LSMs indicate a significant reduction in the sweeps at .48 in their upstream and downstream portions. and large reduction in the Reynolds stress inside bulges at both heights (.4 and .68) when the TAPPM was in place. Despite these large signal changes. it is not hypothesized that the large scale motions lose their identity. The ensemble-averaged u' and v' signals are almost identical to those of Falco's (1977 and 1983) results in the unmanipulated boundary layers. These signals, in general. did not lose their unique dynamic characteristics. when compared to their regular boundary layer counterpart (see Falco. 1977). 78 indicating their intact coherent structure at 8 = 20 in the manipulated case. However. there is a phase shift in (v') with respect to (u'). which reflects the diminished correlation between u' and v'. thereby reducing (u'v'). Visual data from movies also supports this conclusion. In addition to the thick sublayer mechanism previously discussed, many mechanisms have been hypothesizes to be responsible for skin drag reduction in the manipulated boundary layers. These claims have not, however. been supported by data. Based on the sublayer flow visualization. and in light of the large-scale motions data at 8 = 20. and to the wall event visualiation at 8 = 51, following it is concluded here: a strong inhibition in the interaction of the inner and outer layer flow structures is another important mechanism responsible for the skin drag reduction in manipulated boundary layers. This has been further supported by the evidence that the wake of the manipulator plates maintains a strong coherence at 8 = 20, but by 8 = 51 is distributed throughout the turbulent boundary layer and reaches the wall. In other words. the relaxation of the skin friction drag in the manipulated boundary layer to normal conditions by about 6080 is essentially unavoidable. unless the TAPPM is redesigned to generate a stronger. coherent wake. three-dimensionalities are created in the flow to prevent the relaxation. Alternatively. a second TAPPM may be placed upstream of the relaxation region. 79 4.3 Characteristics of Regular and Manipulated Boundary Layers Seen from the Perspective of the Wall-Friction Velocity (urn) Obtained by Local Means The results of skin friction measurements obtained from” the mean velocity gradients near the wall indicated a 15% to 25% lower local skin friction than that of the Clauser plot counterparts in the regular boundary layers. However. they were reduced in the manipulated case. The change in Cfn is shown in Figure 4.2. For comparative purposes. results obtained by other inestigators are displayed in the same figure. Note that they were obtained through different measurement techniques (both used a skin friction balance). All the results indicate lower skin drag in the manipulated boundary layers with a gradually lower relaxation pattern. A 2% net drag reduction was obtained when the Cfn were used in a simple drag analysis. The formulation is shown in Appendix B. Notice that a linear extrapolation was made to estimate the O at the trailing edge of the second plate of the TAPPM and to calculate the device drag. The resultant net drag from momentum balance and the local skin friction integration are shown in Figure 4.3. It is more likely that direct measurements are not biased by the three-dimensional effects mentioned above. This is in agreement with the thickened sublayer results achieved in the present experiment. Furthermore. the wall event ("pocket" module flow) period in absolute value. Th, in wall-unit normalized (pThutnzlu). and in outer-layer-unit non-dimensionalized (pThUg’lp) form all indicate 38%. 28%. and 55% increases respectively. The longer periods between the wall events indicate that fewer pockets are forming. which is consistent with a thicker sublayer. They also indicate and slightly reduced strength of 80 the large-scale motions at this station. where Cfn is reduced 5%. Thus the difference in momentum balance results and direct skin drag measurements seems to support the suggestion that downstream three-dimensionality develops in the manipulated boundary layer. Further investigation is needed in order to answer this question. CHAPTER 5 CONCLUSIONS The results and conclusions presented in the previous chapters address several interrelated subjects of this experimental investigation. First, the objective of the flow facility design. construction. and performance was to develop a thick two-dimensional boundary layer (up to 10") low freestream turbulence intensity flow visualization wind tunnel. with high-quality hot-wire measurements. Next, net drag reduction in the manipulated boundary layers was obtained. This confirmed the ongoing research activities of others in the field. yet revealed sharp skin drag relaxation to unmanipulated case. Last, the detailed investigation of structural changes which were presented in the space-time correlations and the conditionally ensemble-averaged large scale motions were discussed. The major findings of the three phases of this experimental project may be summarized as follows: 1) A high-quality flow wind tunnel with a unique (no-contraction) inlet. long enough to study the relaxation of manipulated turbulent boundary layers. was constructed. It appears possible to expand the improvements on this type of inlet configuration to achieve a wind tunnel with a low turbulence intensity and higher velocities. while avoiding a high cost contraction. This also reduces the possibility of generating streamwise G8rtler vortices on the test wall. 81 2) 3) 4) 82 Two sets of very thin tandemly-arranged parallel plate manipulators (TAPPMs). were used in an attempt to reproduce the results of other net drag reduction investigations and to study the downstream evolution of the drag changes. It was found that the thickness of the manipulator plates was of importance to both the skin friction change and the device drag. Also, the experiment with thinner plates (.003") resulted in a 10% net drag reduction only at 58.238o downstream of the TAPPM. which relaxed by 1008.. In each of the two separate experiments (I and II). a similar drag evolution was obtained, although the thick plates (.03”) did not reduce the net drag. The local skin friction coefficient (CfO) was reduced 30-45% for up to 50-8580 downstream of manipulators in both experiments. The local skin friction obtained from mean velocity gradient near the wall was reduced by 10-20%. but did not show a sharp overrelaxation as it did when calculated from the momentum balance. A 2% net drag result was obtained from Cf”, taking the device drag into consideration. but no overrelaxation was shown. No separation of flow was detected (to within the order of a few thousandths of an inch) over the manipulator plate surfaces. A laminar boundary layer was developed on both plates which were parallel to the test wall in the experiments. The Coles constant in the "law of the wall” also underwent a sequence of changes. It increased in the CfO reduction range 5) 6) 7) 8) 9) 10) 83 region. then decreased. and finally relaxed back to the normal value (B = 5.) after 908,. The "law of the wake" portion of the mean velocity profiles also incurred some changes. which were similar to the variations in the Coles constant B. The sublayer thickness increased 15-20% throughout the length of the test wall for the manipulated layers. The burst frequency in the sublayer decreased by a 38% in absolute value. and by 55% when normalized by outer layer variables. It increased by 27% when normalized by the inner variables (p/p. neO” When the burst frequency was non-dimensionalized by u it reduced by 28%. rn' The outward normal distance that the sublayer fluid travelled into the logarithmic region decreased 30% or 11.4% around the region of 8 = 20 when it was normalized by are or utn respectively. The dynamics of the large-scale motions changed. but LSMs did not lose their uniqueness in geometry and the flow patterns within. The Reynolds stress of the LSMs was reduced significantly. although it increased in the "valleys". The space-time correlations changed at 8 = 20. with significant reductions in the Reynolds stress and the streamwise components of temporal correlations. The large-eddy motions regained most of their strength by 5180 downstream of the manipulators. 84 In summary. when all the information presented above are combined. it becomes clear that the TAPPM acts as a passive suppressor of the large-scale motions up to about 605.. In that same downstream distance. TAPPMs interrupt interactions of the scales from the outer region with the inner-region-scale motions. In contrast to Corke's (1981) ”aging". and NASA group's "break up" of the large eddies speculation. the large-scale motions neither "break up" nor do they lose their strength, but reappear after that distance (6080). FIGURES 85 Hos—=5 v53 mmoamlsofl wzu mo uauflumxom H.N ounwfim {3 Ancmnmnoc Heaven gonzo Heccnn can: men on concEnncm "3mH>-moe cow umum Zoe; \\\\\\ Ancnnmaon onocnmv eHx * I “87 E @ . /: :mwnum muooo mmoou< * ennene Ancnnmanc nnxc Hnoxn nnnzv Henson can; ens no connsnncmnzmH>Imon .nmo one cannons Le m N C . Hon n c H3// or A 1' n n. #095 .33 prmzmwwo meévHme 6 / I HQWDMMHD t I 1-1. 11.. ....J a Flu. rIL rlL . Eh . rfi . nsouzoco: ucfioh. Memo: cam monouom “3.:on xom coouum can 6 9:093:02 ”.wa . :Nec . = = e wcofiocu .ncn. .ueowoauu adoleuuaaol we. 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IT 000. v .11. moo. .LI opo. mAxv __ “25 .A+v _ Ea; 'dx3 ‘ 4ugn .1er (,n)st 'dx3 ‘(+) I (X) H 91 .Aeaom cu uzmmu Eoum mm 3o_mv .:o- u x tuneua :o_«mN_—a:m_> 30". ohmsloxosm uo>a~ >uauanon 9:“ can Euouamouuc 0:“ mo eczmlaacm < h.~ ”unwed 92 FLEXIBLE TYGON TUBES T0 PRESSURE TRANSDUCER TRAVERSE MECHANISM 1" Dia. STATIC PRESSURE --————\ g PROBE (United Sensor) _ 7-7 ’ fl E{.9.£L (jELow -——«C:\ 1" [3* i1 1 l fifil f SIDE VIEw TEST WALL MKS ELECTRO—MOTO PRESSURE DISA TSI DIGITA TRANSDUSE INTEGRATO VOLTMETER 36" 48" I Aafiiii= <3FLOW 12H PLAN VIEW Figure 2.8 Schematic of the movable (modified) Preston tube probe. 93 .onoua Manna uumtnunamiu no omuaaonom a." ouaumm 3mH> hoe x JMHHHHHHHHHTH “ M SMH> mnHm N HNN\\4\N NKUNNKNNNNKNN‘NNNB J N /AA<3 HmMH a w. h :# 304m . WV 94 .H ucmEHnmaxm a“ >m>u=m mawmoua mufioon> CH com: mnou afiumum acufim mo ofiumamzum 0H.~ muawfim & Dawz Dona aunt Madam uo «canon coats-ouuu domuuuquvoa gang and «omega Henna mo nom> on“. emu-nonom HH.N ounnam on u u S _ u: T 238m 832m $sz Eu: _ .ooa.» ‘14 V—fi /// oHsam mm>u A - 96 CALIBRATION PROGRAMS Data Acquisition ALEXZ computer and A/D synchronization RUNTST collects u-wire and pressure trasducer calibration data Data Reduction CONVOL converts bits/millivolt to voltages Data Analysis CALlWIRE determines Collis and 'illiams parameters IULPLT plots calibration data for a visual check of the result IEAN VELOCITY PROFILE PROGRAMS Data Acquisition ALBXZ computer and A/D synchronization RUNTST collects velocity profile data Data Reduction CONVOL converts bits/mollivolt to voltages (mean and fluctuations) and merges with probe positions in one data file Data Analysis in Batch Form: CALANL command file for analysis and plotting programs VELPRO converts voltages to velocities and processes the velocity profile for four plots IULPLT plots the output of VELPRO as follows: 1) mean velocity profile close to the wall in the sublayer region (y vs U) for velociy slope estimation at the wall 2) y vs U of the entire velocity profile 3) Clauser plot to obtain Cfc based on Coles ”law of the wall" parameters VELPR3 analyses the data and calculates the boundary layer velocity profile parameters. non-dimensionalizes the velocity profile based on two different estimations of the wall shear stress (dU/dy at wall (C n). and Cf or dOIdx). and finally stores them with the rest nof the information in one master data file IDLPLT plots the output file of VELPRS: 4) y/O vs WU. 5) u... vs_ Y based on both “10 and “to 6) (U. - U)/ut vs yut/de. 7) lake part of the velocity profile vs y/b 8) rms(u' )lut vs y+. also for near wall region 9) rms(u')/Ug vs y/O. also for near wall region Figure 2.12 Velocity profile and calibration data acquisition. reduction. and analysis program sequence 97 CALIBRATION PROGRAMS Data Acquisition ALEXZ computer and A/D synchronization RUNTST collects twin-x-vire and pressure trasducer calibration data Data Reduction CDNVOL converts bits/millivolt to voltages Data Analysis CALFIT determines Collis and Williams parameters IULPLT plots calibration data for a visual check of the result T'IN-X-WIRE PROBE PROGRAMS Data Acquisition ALEXZ computer and A/D synchronization RUNTST collects twin-x-wire probe data Data Reduction CONVOL converts bits/mollivolt to velocities CPCN calculates the CP and CH parameters for the x-vires VEL4 calculates the long time record of fluctuating quantities TIMPLT plots long time records of fluctuating quantities OORRELATE3 computes space-time correlations of fluctuating quantities OORAVG averages the space-time correlation output files of CORRELAIB3 IULPLT plots the space-time correlations ENSMBL selects, scales and averges the segments of the data records produced by VEL4 which correspond to large eddies striking the twin-x-wire arrey probe NORMALIZE, non-dimensionalizes the long records of data Figure 2.13 Twines-wire probe calibration. data acquisition. reduction, and analysis program sequence nor-va PROBI-Zj DIGITAL [Error TDDE] Doom HIGH SPEED DDVIE DISA DOT-IRE i IRS HESSURE» ANEnouETERs 1 TRANSWCER A TSI _ '{oscnwsooPEJ J TSI VOLTRETER ' ' ' I VOLTIETER cusmu RADE PDP 11/ 23 111.02 16 CHANNEL 16 BIT Dst All) CONVERTER T-11 srs mIVE Arrangement of instruments used for hot-wire anemometry and simultaneous visual data acquisition. 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On. .00000— mall-I mllul. mos x oo .00000— .H acoamuoquo scum unhau Penance; Housman :« anemone» unmeauouau unodua> an A:\m80Q a> aaxpv ao—muoun hamoo~o> neoa uou ao—a avocado P. .0000— .0000F >mwfi .000F .000? m ousmmm .n:0F OCH 2; A31 .2955 Jd .oum ._ gamma .n:UF 0.0 F.0 N.0 0.0 ¢.0 0.0 0.0 N.0 0.0 0.0 0.— —.F N._ 0.P ¢.F win JaAo Joqn 110 .n «no! woman low we»: hue—.55.— uonn-ou mm 233:. again-cu: «not: an 2: was up 0 \E aonquoua Magoo—o» coo.- vouqnaoomauomuuhou 3.31—us. u.m one...»— + .A 000p 00, OF P o o o m 0P 0P moo". mmaoo mp m— om 0N mm mm 9N < On. a: 0 on A2? .2055 .40 .00». ._ P631950 00 00 000— 00— 0— P n 111 .H anoaquonuo aouu woke" Pueuuooa ungauou om anomaeum ommsaaouum mnemua> an A8060\0P=P0 u> 0P:\Am I 800 0o aomuemua> m.m ousmmm :c_:_..mmoco_o_cP.om_ov eo>o A 3003:: 00.0 00.0 0N0 0N0 n 9.0 0 F .0 00.0 00.0 0 1:; P P P P P P — P P P P — P P P k h F P P P o A ”a. H 1 9N“? T 1 Jg r ... I @r... T n 1 .H .. .. . 1 . ....o‘ I. I a 1 T 0- l I 0.. 1 T I so . x x n. 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No— OOP 000 000 000 000 00+ 00+ 000 000 00N 00H 00* 119 .H aaoamuoano aouu «woman huauasoa voaauaamqaa a“ An vac oamtaaouum h~.m ouammm 03.00 ..o>O AOxlxv on. 8. on o FF b b b x— LlL b b — b p - n b b - plL xF - F b F P P b b r — o - I I I I —‘ q I I I _ I d I I ‘ I I a I dl I I I I ‘ q I I I N \«//.f + fix; ¢\ ,llm/ \l/[LTXIX1IL‘ , \\ // \_ o O— MOI—50] 4o wapwmod a pup v 120 o— p— N— HH «aoamuonuo Baum nomad macaques unnswou cm anomaaa» onmsaaouuu anomua> as Aa§\= m> @\hv moummoun humoo~u> duos uaGOMmcoEmvtaoz an.m ouammu ES 35 :5: p.— o;_ may use hgu mg. may tau ngv NA. fie “Ho h b b h - p n b P — n u b p .b p b p - p p b h - h P n p . II ... . , “a,“ o u a rcm.. n .I. I x. 1 II F 1 . . \ .Q r 1 Luqu u u an. . ...... ........... T N u -.w‘. n L. ...... F n 1 . . n I. 1.30 T 1 l c u .; m 1 3 . , I11- L a; m. n H J. ong ..+ < w .11 r... . a .I I .. oox‘ “V e P.o n ...... 33 .u a . n l v .0 ..u a}. neon . u > II N. u ......u. 93... . o 0 WV . ...u .d A: oxhn .o nu - o l ». 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"rm _ OQDODBOQ : o k u N l D < 0.2... . o o m L 2.8 .< o O — I with u . _ L I A2? .2225 L Jd .ouz .a ...zuafiumxu n qII-qd‘j-IdfiddId-I-‘Iddfil-IjI-dqdu-JJWII-wfiduldl.1dd|ld‘.jd*qqldId-I‘41q4-Ilqd n w; n; N4 —é 6; Q6 Q6 D6 Q6 06 .To Q6 N6 fio Q6 anoM uonounj 125 nfio 6.P m.. nHN mHN awn ma” AH¢ .HH aaoawuonuo Baum uo>a~ unavasca unanmou cm anomauam oumtaaouum «acmua> as A accpaha m> @P:\A.avmauv onmuoua hamoo~o> unmaasaoauu cosmuanommsoamulao: «maalfiuai m~.m ounmmm fl . r I 0.23 6.3 n69 ndon 660m n.5nn odou ndnu with. Azsx o 6P 6' egg 0A6 6._ m.F mfim Dan Dan AH¢ S LU J JaAO n noun 126 .HH uuoamuonuo scum woman muannacn uaunmou am anamaauu oawtaaouam msomua> «a th m> 8=\A.=vmau mo nomuamua> v~.m magnum 0605p _o>o > N— —— 6— m 6 h m 0 ¢ n N p 6 0°. l—IPLDIL pL-L—Irl— Pl—r_ phrP—lplb rP- Fr-Ltrblr—h — - nbbbblr—b-p- pi nibICu—t 0°. 9% goat en 9m .H. 0 £090 8. 8» fig 6. mo. fill"! '19]. llllaJ. 665* . I d 6.3+ . 0 0 6600 . ... 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JaAo (,n)st Julfl 128 ommsaaouum asomu¢> an ARC flag 6; 6; .HN ON 65” 6A” 96 6N .Hm aaoawuuquo aouu unma— huanaaoa unmamuu um anomauua 6N +> m— 6— m Lpr—ppi—pppFrPhp-—r—PLlehplP—b-bphpprhthbnpu» 6.65? 663‘ 666* 6.666 6.666 6.566 6.66N 6.66N 665— Azcx JL1L1L4L11111111L11L11LJ111111111llllll a,» fiazaa!|-t;---:4 . I o OK>Eleq O @p=\A.=6mau no nomuumuu> uuut uaoz e~.m ouammm Q6 6; mé ON 66 65” 06 6%. JaAo (,n)quJ ldlnolf‘l 129 06fi3360h¢6 690MH6> “6 A: 6D 66. 56. .HH aucfimuonuc Baum nomad huucaaon uafiauou am mnemaaaa 3&6 L2.: 96 né. 66. 65” n26 MHN AHN 6;. 64 6A6 hPPL-pt-pnbp-nbbbr-hp—nppp-pn-b-ppPp-hbbp—h—Pb-pbpb-b-np-nphh-pp-p-pb-p-pbbp—n-t-ppnn-nhnb-h-n Q6 o o Mu oo emhw o a? o 00 an 0 o 'lVll.‘ . I. of; . ed: . Eu 8Q 39 . «v 2.3 . 0.23 . 3.3 . 0 063 . n63 . oOGDODEJQQJ 6 ‘< m c: a mu m c: I a 645 p . 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P66 Nun. mwfiu ¢xnv 6.6 mwgu mung mwgu mwgu nip P.F mu? 6.? ¢xP QDODEledNfl mm mo Joqn 132 .II unuamuonuo How u a $§6P§3 u> NF 5— NN 5N N6 56 w... 666p 666— 66F 66p 6— 6— uohau huauaaop unauIanmuoa am anomaauu oumtaaouaa m:o¢u¢> 9\66 ao—Iucun humooIo> anus conflunaommaosmvnao: «6:: AwwaIv 66466 1|!" ...: IIIIJ . 6666 a _ 6.6 —6 6.656 669' 6.63 . 6.666 6.666 6.566 <: D <> D E] e «a N .. 666N . nsu .< “V faz¥_.z@2mW!- .46 .23. ... #26236va -44.: an.m ouammm NF 5— NN 5N N6 56 n 133 .mm «coamuoquo scum noun" macaque: coca—squads um «comaauu oumtauouuu maomua> an A8666\6p§56 m> @path I 866 mo acquamua> Im.m ousmmm :c_:_..mmocv_o_np.am_ov ..m>6 A 3066:: 66.6 66.6 6N6 6N6 6 — .6 6 p .6 66.6 66.6 h {—IF 5 h b hr h p L P o _L l 6— 1 J l L 6.666 . ... 1 6, 90:" . L afic. . L “23+ . o~.1 ea: . L nag" . 6.666 . 1 6.566 . 6N l Odom . 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ON! m—l OF... 0— @— ON (queued) 69303) .1er [69503) — 'u0w(;3)] 188 .mu adoluuoano a. thu\bu a aaoauuuucom «conga an. 32.3.: Isa—.23.. Iona 03.3.3 mad..@ I d: nasao¢ lug Amnzv emu-u want «on undo.uaolmvnaaa dootoop nauduualoo undulaouum m.¢ ouauqm 00:00 Lm>O noxle on. mm. 00. mm on mm o — L p p h — p r FL — r L p F — p p P b — p L! p h — p p h _ fl . a 1 a W q 1- q q d u a 1 4 _ . J a u — q 4 . J H J 4 . d -r lrl -T F Tu; L. L. P 1 ‘41 q - 41 If r. Net Drag (Obtained from Cfn Integration [*] ) 1 HTTIT IT r' I r1 m6 m6 0.. N.— Y. o.— m; ON [+] “693(0019qi—01eql) .1er ‘UDW(0019H1—019q1) TABLES 189 Table 3.1 lean boundary layer characteristics and wall-layer statistical information of visualization experiment at t = 20. B. L. Parameters Regular lanipulated 6 (IN) 4.16 4.17 0 (IN) 0.4988 0.5550 a 1.4116 1.3594 R0 2542 2991 Cf0 0.003144 0.001914 Cfn 0.002473 0.002125 Statistical information of outward normal travel (y+) of fluid corresponding to the figure 3.56. lean (y+) 240.3 179.1 Std. va. ' TIME :'(TIME)' RUN BY :'USERNM' COMMENTz'COMNT' .DISABLE DATA .RETURN .MESANS: .ENABLE DATA MEASURED EXPERIMENTAL CONDITIONS BARO PRESS :'BARO' BARO STATUS:'BAROST' TEMP :'TEMP' KIN. VISC. :'KVISC' HUMIDITY :'HUMID' WIND SPEED :'WNDSPD' WIND DIRECT:'WNDDIR' .DISABLE DATA .RETURN .VELANS: .ENABLE DATA EXPERIMENTAL VARIABLES B0 FROM VEL FUNCT :'BO' Bl FROM VEL FUNCT :'Bl' SAMPLES per DATA POINT :'PTINTK' STATION DIST from inlet :'STDIST' TRIP DIST from inlet :'TPDIST' TRIP DESCRIPTION, SIZE :'TPDESC' FAN SETTING :'FANSET' ZERO VELOCITY VOLTAGE :'ZROVOL' AID VOLTAGE RANGE :'ADRNGE' .DISABLE DATA 200 .RETURN .IBUANS: .ENABLE DATA TAPPM DIST from inlet :'IBDIST' TAPPM HEIGHT (inches) :'LBHIGH' TAPPM PLATE SEPERATION inz'LBPLAT' .DISABLE DATA .RETURN .CALANS: .ENABLE DATA OF WIRES ON PROBE : 'NWIRES' .DISABLE DATA .RETURN .PDLSLP: .DATA 'SLPFIL' .DATA -/TIT2....DAT/.. .DATA TIT2RAW DATA FILE :'FILNAM' .DATA / .RETURN .INDEX: .SETS 81 ”'FILNMl'" .SETS S2 "." .SETN I 1 .BEGIN: .IF 82 <) SllI:I] .GOTO ELSE .SETN PERIOD '1' .RETURN .ELSE: .INC I .GOTO BEGIN 0 PROGRAM VELPRO LOCAL VARIABLES HWAVG(I) = HOTPWIRE AVERAGE VOLTAGE (RMS) EWRMS(I) = HOT-WIRE RMS VOLTAGE (RMS) PRESS(I) = PRESSURE TRANSDUCER VOLTAGE DIST(I) = DISTANCE above the wall of the hot-wire measurement UBAR(I) = MEAN VELOCITY FROM HOT WIRE URMS(I) = RMS VELOCITY FROM HOT WIRE UINF(I) = VELOCITY FROM PRESSURE TRANSDUCER AVGU = AVERAGE UINF FOR DATA RUN RMSU = RMS UINF FOR DATA RUN it asks for the datafilename and the number of points in the data file. the barometric pressure and the temperature. These are read in, manipulated, and written out to a file with the format: OOGOOOOOOOOCOOOOO 201 PARAMETER ASIZE=100 IMPLICIT REALM-Z) REAL BO , Bl ,TEMP, BARO, KVISC. EXPONT, RTEMP, SUM. SUMSQ REAL HWAVG(ASIZE) .HWRMS(ASIZE) .PRESS(ASIZE) .DIST(ASIZE) REAL BCONST, UFINAL. UBAR (AS IZE) . URMS (ASIZE) . UINF(ASIZE) REAL UoUINF (ASIZE) . CNT. AVGU, RMSU. REY(ASIZE) .YOFF INTEGER ImUNT. I CHARACTER INFIL‘30. 0UTFIL‘30, TAG‘l, COMNT‘80 . J'DATE‘9. ITIME‘8 LOGICAL‘l PROCES DATA ImUNT. I/0.1/ C C START MAIN ROGRAM C .... .— CALL GETCMD(PROCES, INFIL) IF(PROCES)THEN READ 9, BO READ 9, Bl READ 9. BARO e a READ . TEMP READ . KVISC READ 9, YOFF READ 700. INFIL READ 700. OUTFIL ELSE TYPE ‘, 'ENTER BO---FROM VEL".45 BO + Bl‘VOLTS”2' ACCEPT *, BO TYPE 9. 'ENTER B1---FROM VEL“.45 ACCEPT ‘, Bl TYPE 9. 'ENTER BAROME'IRIC PRESSURE' ACCEPT ’. BARO TYPE 9. 'ENTER TEMPERATURE IN DEGREES F' ACCEPT 9, TEMP TYPE 9. 'ENTER KINEMATIC VlsmSITY' ACCEPT ‘. KVISC TYPE ‘, 'ENTER THE Y OFFSET' ACCEPT ‘5 YOFF 8 TYPE ‘. 'ENTER INPUT DATA FILE :' ACCEPT 700.INFIL 9 TYPE ‘. 'FNTER OUTPUT DATA FILE :' ACCEPT 700. OUTFIL BO + Bl ‘VOLTS“2 ' ENDIF OPEN(UNIT=1.NAME=INFIL.STATUS='OLD'.ERR:520) OPEN(UNIT=2.NAME=OUTFIL.STATUS='NEW'.ERR353O) 15 READ(1.950.ERR=20.END=30) TAG. EWAVG(I). HWRMS(I). + PRESS(I). DIST(I) ‘ IF(TAG .EQ. '3') THEN 20 WRITE(2.960) TAG.COMNT READ(1.955) TAG.COMNT IF(TAG .NE. ';')GOTO 20 ELSE I =I+l ENDIF GOTO 15 202 c manipulation esssassssaasoseesassassasaseessassoaseasaass 30 ICDUNT = I-l RTEMP = TEMP+459.7 SUM = 0.0 SUMSQ = 0.0 BCONST = 0.00535774 UFINAL = (80 + Bl’(HWAVG(ICOUNT)l1000.0)"2)“(l./.45) D0 100 I = ICOUNT.1r’1 IF(HWAVG(I) .EQ. 0.0) GOTO 100 lzero is passed over HWAVG(I) =HWAVG(I)/1000.0 lconvert to millivolts PRESS(I) =PRESS(I)/1000.0 UBAR(I) = (HO + Bl‘HWAVG(I)“2)"(1./.45) SLOPE = 2.0/.45‘(BO+B1‘HWAVG(I)“2)“((1./.45)-l)‘B1‘HWAVG(I) URMS(I) = SLOPE ' HWRMS(I)/1000. UINF(I) = 15.9‘SQRT(RTEMP‘PRESS(I)‘BCONST/BARO) SUM = SUM + UINF(I) SUMSQ = SUMSQ + UINF(I)"2 100 CONTINUE C this routine for calculating u infinity C DO WHILE USUM=0.0 I=ICOUNT 7O UMEAN = (USUM+UBAR(I))/(ICOUNT>I+1) DIFF = UMEAN-UBAR(I) IF (DIFF .GE. .Ol‘UMEAN) GOTO 75 USUM = USUM + UBAR(I) I=I-1 GOTO 70 C ELSE C D0 WHILE LT ICOUNT 75 I=I+l UBAR(I)=UMEAN IF(I .LT. ICOUNT) GOTO 75 C ENDIF C continue with calculations DO 175 I=1.ICOUNT DIST(I) DIST(I) + YOFF REY(I) UFINAL‘DIST(I)/(XVISC’12.0) UoUINF(I) UBAR(I)/UFINAL 175 CONTINUE CNT FLOAT(ICOUNT) AVGU SUM/CNT RMSU SQRT(ABS(SUMSQ‘SUM“2/CNT)/(CNT‘I)) c output aasesssosessassasssassseeaaaassesssssssaassassasss CALL TIME(JTIME) CALL DATE(JDATE) WRITE(2.900) JDATE.JTIME.INFIL.OUTFIL WRTTE(2.905) HO.Bl.TEMP.KVISC WRITE(2.910) ICOUNT.AVGU.RMSU WRITE(2.915) D0 150 I=1.ICOUNT WRITE(2.920) HWAVG(I).HWRMS(I).PRESS(I).DIST(I) 150 CONTINUE 203 WRITE(2.925) WRITE(2,930) DO 200 I=1.ICOUNT WRITE(2.935) UBAR(I).URMS(I).UINF(I).DIST(I).REY(I). + UoUINF(I) ZOO CONTINUE CALL EXIT C C FORMAT STATEMENTS C 700 FORMAT(A) 900 FORMAT('O'.T5.'VELPRO OUTPUT -- JULY-1'84 VERSION'l ' '.T7,'DATE :',A/ ' '.T7,'TIME :'.A/ ' ',T7,'INPUT FILE NAME:'.A/ ' ',T7,'OUTPUT FILE NAME:',A) 905 FORMAT('O'.T5,'VELPRO INPUTS'/ ' '.T7.'BO from VEL Fu. :',F10.5/ ' '.T7,'Bl from VEL Fu. :',F10.5/ ' '.T7 TEMPERTURE (F) :',F5.2/ ' '.T7,'KIN. VISC. :'.F10.7) 910 FORMAT('O'.T5,'VELPRO OUTPUT'I ' '.T7,'POINTS IN FILE :',I$/ ' '3T7.'AVG UINF (PRESS):'.FIO.7/ + + + + + + + + + + + ' ',T7,'RMS UINF :'.F10.7) 915 FORMAT( '0'.T5.'VELPRO INPUT DATA '/ + ' '.T7.' AVG-(V) RMS-(MV) PRES-(V) DIST>(IN)') 920 FORMAT(T7.4(F8.3.2X)) 925 FORMAT(' '.'VELPRO OUTPUT DATA'./ + T7.'UBAR',T16,'URMS',T25,'UINF',T34,'DIST', + T45,'REY',T52,'UoUINF') 930 FORMAT(' '.T7.'F/S',T16,'F/S',T25.'F/S',T34,'IN'/';') 935 FORMAT('RD', F8.3. ',' ,F8.5, ',' ,F8.3. ',' .F8.3. '.' + ,F10.2, ',' ,Ffi.3) C15 READ(1.950.ERR=20.END=30) TAG. HWAVG(I). HWRMS(I), PRESS(I). DIST(I) 950 FORMAT(A1.4(1X.F8.3)) 955 FORMAT(A1.A60) 960 FORMAT(' '.A1.A60) C C ERROR CONTROL 520 TYPE 522.INFIL 522 FORMAT(' '.'ERROR OPENING FILE:'.A.'PLEASE REENTER') GOTO 8 530 TYPE 522.0UTFIL GOTO 9 END SUBROUTINE GETCMD(CMDFIL.INFIL) C LOCAL VARIABLES CHARACTER‘l CMDLIN'40.INFIL'3O LOGICAL‘I CMDFIL INTEGER IDS.LENGTH DATA CMDLINl' '/ CALL GETMCR(CMDLIN.IDS) 204 C SCAN COMMAND LINE FOR (DMMAND FILE NAME LENGTH=INDEX(CMDLIN, ' . ') C IF(LB‘JGTH.NE.0)THEN D TYPE 100,CMDLIN(1:LENGTH+3) OPEN ( UNIT=1 . NAME=CMDLIN(1:LENGTH+3) . STATUS= ' UNKNOWN' . ERR=15) CMDFIL=.TRUE. INFI L=CMDLIN ( 1 :LENGTH+3) ELSE CMDFIL= . FALSE. 15 TYPE ‘, 'WMMAND FILE NOT FOUND REVERTING TO MANUAL (DNTROL' ENDIF RETURN END C PROGRAM VELPR3 C C CALCULATES: C DELTA C DISPLACEMENT THICKNESS C MOMENTUM 'mICKNESS - POINTS DO NOT HAVE TO BE C EQUALLY SPACED - BUT THE NUMBER OF DATA POINTS (N) C MUST BE AN ODD NUMBER C" LOCAL SKIN FRICTION (DEFFICIENT -- CfNTN C‘ FRICTIN VEL.(based on CLAUSER PLOT) -- UTAUCR SHAPE FACTOR -- H INTEGRAL -- G (BASED ON (lAUSER _DUDY) (OLES FACTOR -- PI ( B . O . CLAUSER _DUDY) OOOOOOOOOOOOOOOOOCOOOOOO RESR RESISTANCE RATIO USED FOR H.W ANELDMETRY TRPS TRIP SIZE(OR GRIT OF SAND PAPER) HLB HEIGHT OF LEBU DEVICE FROM WALL(IN(HES) RHDLTA RATIO OF HLB AND DELTA(B.L.Thickness at the lst LEBU) IETAH RATIO OF DITANCE FROM 2nd LFBU AND HLB S DISTANCE BETWEEN LEBU DEVICES(inches) CfCLR LOCCAL FRICTION (DEFF. FROM CLASER VEL-PLOT FTN2.VPR changed to FTN2.LVP UINF FREE STREAM VELOCITY ABOVE THE B.L. (FT/ SEC) N THE NUMBER OF DATA POINTS (ODD INCLUDING 0.0.0.0) NFNL THE FIRST _THE LAST POINT THAT DUDY IS ESTIMATED FROM VEL HOT-WIRE READING IN (FT/SEC) Y POSITION OF PROBE (DISTANCE FROM WALL INCHES) DELT99 CHOSEN PERCENATGE VALUE FOR "ENE" OF THE BDL. USUALLY .99 OR .995 (INPUT) DELTA CALCULATED B.L. THICKNESS BASED ON DELT99 UTAUNTN FRICTION VEOCITY(CLR:CLASER And NTN=NEWTONIAN.sub's) (ifhflffi C‘P“ ‘ CfNTN LOCAL SKIN FRICTION COEFF.(B.O. DUDY AT Y=0) 205 XNU KINEMATIC VISCOSITY--NU (FT‘92/SEC) DISP DISPLACEMENT THICKNESS THETA MOMENTUM THICKNESS RTHETA REYNOLDS NUMBER BASED ON THETA C‘I FOR USE IN QUAD: (3C3CICDC1CICDCDCDCDCDCD(1C3(if) CDCDCDCIC5(fiffiffitfitfitfitfitfitfitfitfitfi NOMENCLATURE VEL 1.0-(VEL/UINF) AND (VEL/UINF)‘VEL YDIST POSITION OF PROBE THE VELOCITIES MUST BE (FT/SEC). THE POSITIONS MUST BE (INCHES) GCLR = G based on UTAUC ANU = Kinematic viscosity ft‘2/sec YPLUSC(I) = Y‘UTAUCLAUSER/ANU YPLUSN(I) = Y'UTAUN/ANU UTAUN utau Newton UTAUC utau Clauser THETA momentum thickness YOTHET(I) = YYTHETHA DELTAS = displacement thickness YODSTR(I) = Y/DELTAS DELT99 = 99% thickness YOD99(I) = Y(I)/DELT99 UOUINF(I) U/UINF UOUTAN(I) U/UTAUN UOUTAC(I) U/UTAUC UMUOUN(I) (UINF-UBAR)/UTAUN UMUOUC(I) (UINF-UBAR)/UTAUC UPOUIN(I) RMSU/UINF UPOUTN(I) RMSU/UTAUN UPOUTC(I) RMSU/UTAUC . YROTAC(I) (Y‘UTAUC)/(DELTAS'UINF) YROTAN(I) (Y‘UTAUN)/(DELTAS‘UINF) 0.0..OOOOOOOOOOOOOOOOOOOOCO.........OOOOOOOOOOOOOOOOO0.00.. REAL DUDYWL.CfCLR.KVISC.UBAR(100).URMS(100).UPRES(100) REAL DIST(lOO).REY(100). UoUINF(100) REAL UINF.UTAUN.UTAUCR.CfNTN.SLOPE.X.DELTA.VEL(100) REAL YDIST(100).DISP.THETA.DELTA3.RTHETA.SHAPE.GDUDY REAL GCLR.PItemp.PI,PICLR.VEL99 REAL YPLUSC(lOO).YPLUSN(100).YOTHET(100).YODSTR(100) REAL YOD99(100).UOUTAN(100).UOUTAC(100).UMUOUN(100) REAL UMUOUC(lOO).UPOUIN(100).UPOUTN(100).UPOUTC(100) REAL YROTAC(100).YROTAN(100).WAKET(100).WAKEC(100) REAL WAKEN(100) INTEGER ICOUNT.I.J CHARACTER OUTFIL‘30.INFIL‘30.TAG‘1.COMNT‘60.JTIME‘8 CHARACTER JDATE‘9 LOGICAL‘l PROCES itCOO...0.000030000000000.........OOOOOOOOOO. 206 COMMON lQPARM/ VEL.YDIST DATA (DMNT /' '/ C C START MAIN PROGRAM C CALL GETCMD(PROCES, INFIL) IF(PROCES)THEN READ (l.‘) DUDYWL READ (1.") CfCLR READ (L‘) KVISC READ 700. OUTFIL ELSE TYPE ‘. 'ENTER DUDY AT THE WALL' ACCEPT 9. DUDYWL TYPE ‘, 'BJTER CfCLR' ACCEPT ‘, CfCLR TYPE '5 'ENTER KINEMATIC VISCOSITY' ACCEPT l'. KVISC 8 TYPE 9, 'ENTER INPUT DATA FILE :' ACCEPT 700.INFIL 9 TYPE ‘. 'ENTER OUTPUT DATA FILE :' ACCEPT 700. OUTFIL OPEN(UNIT=1 . NAME=INFIL. STATUS= 'OLD' . ERR=520) ENDIF OPEN(UNIT=2 , NAME=OUTFIL. STATUS= 'NEW ' . ERR=530) I=1 15 READ(1.702,ERR=20.END=30) TAG, UBAR(I). URMS(I). UPRES(I). + DIST(I). REY(I). UoUINF(I) IF(TAG .m. ';') THEN 20 WRITE (2.960) TAG.CDMNT READ (1.705) TAG,(DMNT IF(TAG .NE. '3')GOTO 20 WRITE (2,960) TAG,(I)MNT ELSE WRITE(2.965) UBAR(I). URMS(I). UPRES(I). DIST(I). + REY(I). UoUINF(I) I =I+1 ENDIF GOTO 15 C Cass MANIPULATION asasssaasasasteatsssassasasasssaaesassssaas C C Calc of velocity profile experimental quantities 3O ImUNT = I-l VISC = KVISC‘12.0 UINF = UBAR(ICDUNT) lfix to reflect average of final c points within 1% of delt99 UTAUN = SQRT(VISC‘DUDYWL) UTAUCR = UINF‘SQRT(CfCLR/ 2.0) CfNTN = 2.‘(UTAUN/UINF)”2 I = ImUNT+1 200 I = I-l IF(VEL99 .LT. UBAR(I)) GOTO 200 225 250 275 207 (VEL99-UBAR(I)) / (UBAR(I+1)-UBAR(I)) DIST(I+1)-DIST(I) SLOPE ‘ X + DIST(I) 1.0 - UBAR(I)/UINF DIST(I) = UBAR(J)‘VEL(J)/UINF SLOPE = x = DELTA = VEL(1) = 1.0 YDIST(1) = 0.0 no 225 J=2.ICOUNT VEL(J) = YDIST(J) = CONTINUE CALL QUAD(ICOUNT.DISP) VEL(1) = 0.0 no 250 J=2.ICOUNT VEL(J) CONTINUE CALL QUAD(ICOUNT.THETA) DO 275 J=2.ICOUNT VEL(J) = 1.0 - (UBAR(I)/UINF)“2 CONTINUE CALL QUAD(ICOUNT.DELTA3) RTHETA = (UINF‘THEIA)/(VISC) SHAPE = DISP/THETA GDUDY = (SHAPE-1.0) ‘ UINF/ (UTAUN ‘ SHAPE) GCLR = (SHAPE-1.0) * UINF/ (UTAUCR * SHAPE) PItemp = O.41‘(UINF‘DISP/VISC-65.0) PI = (PItemp ‘ VISC/ (DELTA ‘ UTAUN)) -1.0 PICLR = (PItemp * VISC/ (DELTA ‘ UTAUCR)) -1.0 C nondimensionalize the measured values using the calc values DO 300 I=1.ICOUNT 300 YPLUSC(I) YPLUSN(I) YOTHET(I) YODSTR(I) YOD99 (I) UOUINF(I) UOUTAN(I) UOUTAC(I) UMUOUN(I) UMUOUC(I) UPOUIN(I) UPOUTN(I) UPOUTC(I) YROTAC(I) YROTAN(I) WAKECU) WAKEN(I) WAKET(I) CONTINUE output DIST(I)‘UTAUCR/VISC DIST(I)‘UTAUN/VISC DIST(I)/THETA DIST(I)/DISP DIST(I)/DELTA UBAR(I)/UINF UBAR(I)/UTAUN UBAR(I)/UTAUCR (UINF-UBAR ( I) ) IUTAUN (UINF-DEAR ( I ) ) IUTAUCR URMS(I)/UINF URMS(I)/UTAUN URMS(I)/UTAUCR (DIST(I)‘UTAUCR)/(DISP‘UINF) (DIST(I)‘UTAUN)/(DISP‘UINF) (UOUTAC(I)-(5.61'ALOGIO(YPLUSC(I)))-5.0)‘.41/.6 (UOUTAN(I)-(5.61‘ALOGIO(YPLUSN(I)))-5.0)‘.41/.6 2‘(SIN((3.1416/2)‘YOD99(I)))“2 COOOOOOOO......OO0.0.0....OOOOOOOOOOOOOOOOOOOOOQOO CALL TIME(JTIME) CALL DATE(JDATE) WRITE(2.900) JDATE.JTIME.INFIL.OUTFIL WRITE(2.905) DUDYWL.CfCLR.KVISC WRITE(2.910) ICOUNT 208 C----- WRITE(2.920) VEL99.UINF.DELTA.DISP.THETA.DELTA3.RTHETA. + SHAPE.GDUDY.GCLR.PI.PICLR.CfNTN.UTAUCR.UTAUN WRITE (2,921) WRITE(2.922) DO 390 I=1.IOOUNT WRITE(2.925) YPLUSC(I). UOUTAC(I). UPOUTC(I). + YPLUSN(I). UOUTAN(I). UPOUTN(I). + UOUINF(I). YOTHET(I). UPOUIN(I) 390 CONTINUE WRITE(2,930) DO 400.I=1.ICOUNT WRITE(2.935) YROTAC(I). UMUOUC(I). YROTAN(I). UMUOUN(I). + YOD99(I). WAKET(I). WAKEC(I). WAKEN(I) 400 CONTINUE WRITE(2.945) CLOSE (UNIT=2) C OUTPUT MULPLT DATA FILES C output YOTHVSUUI plot file OPEN(UNIT=3.NAME='YOTHV.DAT'.STATUS='NEW') WRITE(3.941) ( UoUINF(I).YOTHET(I). I=l.IOOUNT) CLOSE (UNIT=3) C output innerlaw plot file OPEN(UNIT=3,NAME='ILAWC.DAT'.STATUS='NEW') WRITE(3.941) (YPLUSC(I). UOUTAC(I). I=1.IOOUNT) CLOSE (UNIT=3) OPEN(UNIT=3.NAME='ILAWN.DAT'.STATUS='NEW') WRITE(3.941) (YPLUSN(I). UOUTANIRMSN(I). I=1.ICOUNT) CLOSE (UNIT=3) C output YROTTA plot files OPEN(UNIT=3.NAME='YROTC.DAT'.STATUS='NEW') WRITE(3.941) (YROTAC(I). UMUOUC(I). I=1.ICOUNT) CLOSE (UNIT=3) OPEN(UNIT=3.NAME='YROTN.DAT'.STATUS='NEW') WRITE(3.941) (YROTAN(I). UMUOUN(I). I=1.IOOUNT) CLOSE (UNIT=3) C output WAKE plot files OPEN(UNIT=3.NAME='WAKEC.DAT'.STATUS='NEW') WRITE(3.941) (YOD99(I).WAKEC(I). I=l.IOOUNT) CLOSE (UNIT=3) OPEN(UNIT=3.NAME='WAKEN.DAT'.STATUS='NEW') WRITE(3.941) (YOD99(I).WAKEN(I). I=1.IOOUNT) CLOSE (UNIT=3) 0PEN(UNIT=3.NAME='WAKET.DAT'.STATUS='NEW') WRITE(3.941) (YOD99(I).WAKET(I). I=1.IOOUNT) CLOSE (UNIT=3) C output OUTER RMS plot files OPEN(UNIT=3.NAME='ORMS.DAT'.STATUS='NEW') WRITE(3.941) (YOTHET(I). UPOUIN(I). I=1.IOOUNT) CLOSE (UNIT=3) C output INNER RMS plot file C output WALL RMS plot files OPEN(UNIT=3.NAME='IRMSC.DAT'.STATUS='NEW') 209 WRITE(3.941) (YPLUSC(I).UPOUTC(I).I=1.ICOUNT) CLOSE (UNIT=3) OPEN(UNIT=3.NAME='IRMSN.DAT'.STATUS='NEW') WRITE(3.941) (YPLUSN(I).UPOUTN(I).I=1.ICOUNT) CLOSE (UNIT=3) TYPE ‘,'PROGRAM VELPR3 NORMAL TERMINATION' CALL EXIT C C FORMAT STATEMENTS C C read formats 700 FORMAT(A) 702 FORMAT(A,1X,F8.3,1X,F8.5.1X,F8.3.1X.F8.3.1X.F10.2,1X,F8.3) 705 FORMAT(ZA) C write formats 900 FORMAT( '; '/ '0'.T5, 'VELPRB OUTPUT -- JULY-1-84 VERSION'/ ' '.T7.'DATE :'.A/ ' '.T7.'TIME :',A/ ' '.T7.'INPUT FILE NAME: '.A/ ' '.T7. 'OUTPUT FILE NAME: '.A) 905 FORMAT(‘O'.T5.'VELPR3 INPUTS'I ' '.T7. 'DUDY at the wall:'.F10.5/ ++++ + 4' ' '.T7.'CfCLR :'.F10.5/ + ' '.T7.'KIN. VISC. :'.F10.7) 910 FORMAT(‘O'.T5.'VELPR3 OUTPUT'/ 4' ' '.T7.'POINTS IN FILE :',IS) 920 FORMAT( 'O'.T5, 'VELPR3 OUTPUT INFORMATION: ' 1 /.' '.T7.’ m99--- -— ---='.F5.2.' FT/SEC' 1 /.' '.T7. ' UINFINITY ='.F5.2,' FT/SEC' 1 I, ' '.T7. ' B.L.THICKNESS-- DELTA - ='.F5.2, ' INCHES' 1 /.' '.T7.’ DISPLACEMENT THICKNESS ='.F7.4.' INCHES' 2 /. ' '.T'I.’ MOMENTUM THICKNESS- ='.F7.4.' INCHES' 2 /.' '.T7.’ ENERGY THICKNESS ='.F7.4.' INGES' 3 /.' '.T7. ' REYNOLDS NUMBER (RTHETA) -------='.F8.2 4 /.' '.T7.’ SHAPE FACTOR H ----='.F7.4 5 /.' '.T7.’ INTEGRAL (B.O DUDY) ---- G ----=',F12.8 6 I.' '.T7.’ INTEGRAL(B.O CLAUSER) ----- GCLR--=',F12.8 7 l.’ '.T7. ' (DLES FACTOR(B.O DUDY) - PI --='.F8.4 8 /.' '.T7.’ (DLES FACTOR(B.0 CLAUSER)--PICLR ='.F10.4 9 /.' '.T7.’ LOCAL SKIN FRICTION (DEFF. CfNTN ='.F8.6 + /. ' '.T7. ' FRC.VEL.(C1auser Plot) UTAUCR---='.F6.4.' FT/SEC' + l.’ '.T7. ' UTAUNTN(From DUDY) ='.F7.4.' FT/SEC') 921 FORMAT( '0 ' . T5 . ' NONDIMSIONALIZED VALUES ') 922 FORMAT( '0 ' . + T6.'Y+ C',T20, 'U'. T31. 'URMS'. T41.'Y+ N'. + T57. 'U'. T68. 'URMS'. T81. 'U'. T95. 'Y'. T108.'URMS'/ + 0+0, ns’v—v.'r30'o—o' + T56. '_'.T67, '_'.T80. '_'.T93. '_'.T108. '_'/ + ' ' T18.'UTAU C'.T30.'UTAU C', + T56.'UTAU N',T67.'UTAU N',T80.'UINF'.T93.'THETA'.T108.'UINF'//) 925 FORMAT(' '.2(F9.4.4X.F9.6.4X.F9.7.4X).F9.7.4X.F9.6.4X.F9.7) 930 FORMAT(’0'. + ' Y’UTAUC', T16,'UNIF-UBAR'.T29,'Y‘UTAUN'. 210 ' '.‘DISP‘UINF', T16.’ UTAU C'. T29.'DISP‘UINF'. T42,’ UTAU N', T55.'DEL99'/) " 935 FORMAT(' '.2(F9.6.4X. F9.4.4X). F9.6.4X. 3(F9.5.4X)) 941 FORMAT((ICOUNT)('RD'.2(GIS.5)/)) 945 FORMAT(';') 960 FORMAT(ZA) 965 FORMAT('RD', F8.3. '.' ,F8.5. '.' .F8.3. '.' .F8.3. '.' + .F10.2. ',' .F8.3) C ERROR CONTROL 520 TYPE 522.1NFIL 522 FORMAT(' '.‘ERROR OPENING FILE:'.A,'PLEASE REENTER') GOTO 8 530 TYPE 522.0UTFIL GOTO 9 END SUBROUTINE GETCMD(CMDFIL.INFIL) C LOCAL VARIABLES CHARACTER’l CMDLIN‘40.INFIL‘30 LOGICAL‘l CMDFIL INTEGER IDS.LENGTH DATA CMDLINI' '/ CALL GETMCR(CMDLIN, IDS) C SCAN COMMAND LINE FOR COMMAND FILE NAME LENGTH=INDEX(CMDLIN.'.') + T42.'UNIF-UBAR' ,T55.’ Y'. T68.'WAKE T'. + T81.'WAKE C'.T94.'WAKE N'./ + 0+0'l 0, T16’l I, 129'! I. + T42.‘ '. T55.'_'/ 4. + C IF(LENGTH.NE.O)THEN D TYPE 100.CMDLIN(1:LENGTH+3) OPEN(UNIT=1.NAME=CMDLIN(1:LENGTH+3).STATUS='UNKNOWN',ERR=15) CMDFIL=.TRUE. INFIL=CMDLIN(1:LENGTH+3) ELSE CMDFIL=.FALSE. 15 TYPE I'.'COMMAND FILE NOT FOUND REVERTING TO MANUAL CONTROL' ENDIF RETURN END SUBROUTINE QUAD (K. OUT) REAL DU(100).UU1(100) COMMON/QPARM/DU.DUI TOT=0.0 K3=K-1 DO 30 I=2.K3.2 E1=DU(I+1)-DU(I-1) E2=DU(I)-DU(I-1) V1=DU1(I+1)“2.0-DUl(I)“2.0 V2=DU1(I+1)-DU1(I-1) V3=DU1(I)“2.0-DU1(I-1)992.0 V4=DUl(I)-DUI(I-1) 30 211 A= ( V4 ‘El-VZ I'EZ ) / (V1 I'V4--V3 9V2) B=(E2-A“V3)/V4 C=DU(I)-A‘DU1(I)“2.0-B’DU1(I) TOT=TOT+A‘(DU1 (1+1) “3 .O-DU1(I-1) "'3 .0) /3.0+B‘ (DU1 (1+1) 9‘2 .O-DU1(I-1) eez .0) /2.0+C"(DU1(I+1)-DU1(I-1) ) CONTINUE OUT=TOT RETURN END C PROGRAM CALFIT COOOOOOOOOOCOOOOOOOOOOOOOO.....OOOOOOOOOO.....OOOOOOOOOOOOOOOOOOOOOO... Q Q (5000009006000OGOOOOOOOOOO000600000000 VERSION 5 CALFIT TAKES THE OUTPUT OF AVGVOL AND PRODUCES A U-WIRE CALIBRATION CURVE BY PERFORMING A LEAST SQUARES FIT ON THE DATA. THE INPUT FILE IS CURVE.DAT THE OUTPUT FILE IS CALCRV.DAT MODIFIED BY NASSER RASHIDNIA SPRING 1984 TO ELIMINATE MILLIVOLT TO VOLTS CONVERSION ERROR AND TO ELIMINATE INCORRECT AREA RATIO THE CURRENT VERSION USES A PRESSURE TRANDUCER OUTPUT FOR THE VELOCITY REFERENCE. THIS INPUT MUST BE FROM THE MKS BARYTRON AND THE INPUT VOLTAGES EXPRESSED IN MILLIVOLTS MODIFIED TO PRODUCE A FILE CALLED CALPLT WHICH IS USED BY THE CALPLOT PROGRAM WHICH ALLOWS THE USER TO INSPECT THE LINEARITY OF THE DATA MODIFIED 14-OCT-81 TO IMPROVE READIBILITY EXPAND PROGRAM TO ALLOW UP TO 16 SWSORS. CORRECT FOR STANDARD DEVIATION INACCURACY AND TO ALLOW THE USE OF A CALIBRATED HOT WIRE AS A VROCITY REFERENCE. MODIFIED 28-NOV-81 TO ALLOW THE FLUIDS LAB PRESSURE TRANSDUCER MILLIVOLTS TO BE INPUT INTO THIS PROGRAM MODIFIED 5-DEC-81 TO ALLOW THE PROGRAM TO LOOK FOR EXPONENTS (N) UP TO .64 THE PREVIOUS UPPER BOUND WAS .54 MODIFIED WED-16-DEC-81 TOALLOWNTOBEUPTO .99 MODIFIED SUN-3-J'AN-82 TO OUTPUT THE PARAMETERS A. B. STD.N OF THE CHANNEL TO BE PLOT'TED TO THE LAST LINE OF FILE CALPLT. DAT. 9" ALSO. ALL WIRE VOLTAGES ARE NOW OUTPUT TO CALPLT.DAT SO THAT CALDRW CAN BE RUN FOUR TIMES (ONE/WIRE) FOR EACH RUN OF CALFIT MODIFIED DDN-4-J'AN-82 212 TO OUTPUT ALL A. B. STD. N. FOR ALL WIRES AND ITERATIONS MDIFIED TUE-ZG-JAN-BZ RELKWED OLD (ODE (ONCERNING WHICH WIRE TO PLOT(SEE P” ABOVE) IMPROVED READABILITY OF COMMENT STATEMENTS WITH ------ (DRRECTED TEMP (DNVERSION (NEW: TR=459.7+TF) (OLD: TR=459.3+TF) THIS IDDIFICATION CHANGED THE P.T. VELOCITIES ’ BY LESS THAN 0.01 FT/SEC eeeeteoeeeeeatetaeeeeeeeeaaeeeeeeeaeeeeaseeeeeteeeeeeteetesteeeeeeaeeee DIMENSION XN(4) .EW(16. 85) .EP(85) .QP(85) . 1 A(16).B(16) REAL NCOWIL (DMMON IDEV/ STDEV(70) .STD(16) .OPXN( 85) .AITER(75) . 1 BITER(75).EWSQ(16.85).NVELS.J Ofififififififi INPUT SECTION ACCEPTS NUMBER OF SENSORS. COMPUTES NUMBER OF WIRES. TYPE OF VELOCITY REFERENCE. (IF REFERENCE IS A HOT WIRE IT ACCEPTS THE COLLIS AND WILLIAMS (DEFFICIENTS A. B. AND N) THE TEMPERATURE. BAROMETRIC PRESSURE THE NUMBER OF SPEEDS AND A GANNEL TO BE PLOT'TED ON A VOLTS SQUARED VERSUS VELOCITY TO THE N AXIS. 00006000 TYPE a. 'ENTER 1 FOR DEBUG mUATIoNS' ACCEPT ., DEBUG TYPE 10 10 FORMAT(IX. 'BNTBR NUMBER OF SENSORS') ACCEPT ‘.NSENSO NWIRES=NSENSO-l TYPE 12 12 FORMAT(lX. 'IS VELOCITY REFERENCE A BUT WIRE Y/N ') ACCEPT 13.ANSWER 13 FORMAT(Al) IF(ANSWER.NE.'Y') GOTO 14 TYPE a. 'INPUT A 0F CDLLIS AND WILLIAMS LAW FOR REFERENCE WIRE' ACCEPT a, ACDWIL TYPE a, 'INPUT B OF COLLIS AND WILLIAMS LAW FOR REFERENCE WIRE' ACCEPT ., BCDWIL TYPE t, 'INPU'T N OF COLLIS AND WILLIAMS LAW FOR REFERENCE WIRE' ACCEPT -. NCDWIL _ Go To 18 14 TYPE 15 15 FORMAT(lX. 'ENTER TEMPERATURE IN DEGREES F') ACCEPT ’.TEMP TYPE 17 17 FORMAT(lX. 'ENTER BARGMETRIC PRESS IN INCHES OF HG') ACCEPT ‘.RARO 18 TYPE 20 20 FORMAT(IX. 'ENTER NUMBER OF FAN SETTINGS') ACCEPT ‘.NVELS TYPE ‘. 'IF THE BAROTRON HESS. TRAN. WAS USED' TYPE ‘.'MAX VEL < 12.0 FT/SEC . m 1' TYPE 9. ' IF FLUIDS LAB P.T. WAS USED' 213 TYPE ‘.'1.0 INCH WATER = 5.0 VOLTS. ENTER 2' ACCEPT l'.PI'RAN C ______ C OPEN THE AVERAGE VOLTAGE FILE CURVE. DAT AND READ IN C THE AVERAGES FOR EACH CALIBRATION SPEED C__...._.. OPEN( UNIT=1 . NAME= ' CURVE. DAT' . FORM= 'FORMATTED' . 1 TYPE= ' OLD' . REAWNLY) DO 30 I=1.NVELS READ(1. ‘) (EW(J. I) .J=1.NWIRES) .EP(I) D WRITE(7.‘) (EW(J.I).J=1.NWIRES).EP(I) 3 O CONTINUE C..___..... C CONVERTS MILLIVOLTS AS OUTPUT BY (DNVOL TO VOLTS C__.._.__ DO 31 I=1.NVELS EP(I)=EP(I)/1000.0 DO 31 J=1.NWIRES EW(J.I)=EW(J.I)/1000.0 31 (DNTINUE D TYPE ‘. 'THE FOLLOWING IS EW.EP VOLTS' D TYPE ‘.EW.EP CLOSE(UNIT=1) C ______ C CALCULATE THE REFERENCE VELOCITY C C ______ IF(PTRAN.m.2.0)GOTO 50 IF(PTRAN.m.1.0)GOTO 32 IF(PTRAN.NE.1.0)TYPE ‘. 'YOU DIDNOT ENTER PROPER P.T'RAN. mNTROL' GOTO 18 C 32 D0 40 I=1.NVELS IF(ANSWER.EQ.'Y') GOTO 35 C..--- C THE MUATION BELOW IS GOOD ONLY IF EP(I)=1 VOLT/MM HG C...—_._ QP(I)=15.9‘SQRT(((TEMP+459.7)‘(EP(I)’.01‘.53682)) 1 /(BARO)) GO TO 40 35 CALL WIRCAL(QP(I).EP(I).ACDWIL.B(DWIL.N(DWIL) 4O (DNTINUE GOTO 60 50 TYPE '. 'ENTER SLOPE(SLOPE) AND Y-INTERCEPT(YINTER)' TYPE ‘. ' OF FLUIDS LAB P.T. CALIBRATION' ACCEPT ‘.SLOPE.YINTER m 55.K=1.NVELS EP(K) = (EP(K)-YINTER)/SLOPE D TYPE ‘. 'THIS IS EP IN INCHES OF WATER' D TYPE ‘.EP QP(K)=15.9‘SQRT(EP(K)‘(TEMP+4$9.7)/BARO) 55 mNTINUE 214 D TYPE ‘. "THIS IS THE VELOCITY BASED ON THE P.T. ' D TYPE ‘.QP C 60 OPEN(UNIT=2.TYPE='NEW'.NAME='CALPLT.DAT') DO 70 I=1.NVELS WRITE(2.‘)(EW(J.I).J=1.NWIRES).QP(I) 70 CONTINUE ------ CLOSE(UNIT=2.DISPOSE='SAVE') C C C CALCULATION OF COLLIS AND WILLIAMS COEFFICIENTS FOR C EACH WIRE USING STANDARD DEVIATION SUBROUTINE CALCAB TO FIND C THE TWO COEFFICIENTS A AND B WHILE N RANGES FROM .3 TO C .54 (.99) AND THEN USES SUBROUTINE SMALL TO SELECT THE THREE C COEFFICIENTS ASSOCIATED WITH THE SMALLEST STANDARD DEVIATION C THE COEFFICIENTS ARE THEN OUTPUT'TO THE LIST DIRECTED FILE C CALCRV IN ASCENDING ORDER C ______ OPEN(UNIT=1.NAME='CALCRV.DAT'.FORM='FORMATTED'.STATUS= + 'UNKNOWN') OPEN(UNIT=9.NAME='CDEFF.DAT'.FORM='FORMATTED'.STATUS= + 'UNKNOWN') DO 300 J=1.NWIRES XN(J)=.29 D0 200 ITER=1.70 XN(J)=XN(J)+.01 D0 100 K=1.NVELS EWSQ(J,K)=EW(J,K)”2 QPXN(K)=QP(K)“XN(J) 100 CONTINUE CALL CALCAB(ITER.DEBUG) WRITE(9.150) J.ITER.AITER(ITER).BITER(ITER).STDEV(ITER).XN(J) 150 FORMAT(2X.'WIRE '.Il.’ ITER '.IZ.’ A='.F6.3.' B='.F6.3. 1 ' STD='.F8.6.' N='.F4.2) 200 CONTINUE CALL ISMALL