Investigation of Blockage Effects on Circular Cylinders in a Two-Dimensional Wind Tunnel Citation Pounder, Edwin (1951) Investigation of Blockage Effects on Circular Cylinders in a Two-Dimensional Wind Tunnel. Engineer's thesis, California Institute of Technology. doi:10.7907/1F84-BB81. https://resolver.caltech.edu/CaltechETD:etd-03312009-085215 Abstract These investigations include some experimental and theoretical studies upon blockage effects in a two-dimensional wind tunnel. The shape chosen to represent a body in the tunnel is that of a circular cylinder since such a body will eliminate circulation as a variable and will produce large blockage effects. In experimental studies, three cylinders of different size are tested in a two-dimensional tunnel. It is found that interference effects are of such a magnitude that it is impossible to obtain two-dimensional flow with the basic models. Two-dimensional flow is obtained through the use of separation devices, but a quantitative blockage study is not attained. The theoretical work attempts to show the blockage effects of a two-dimensional tunnel upon a circular cylinder of arbitrary size with and without a wake. The potential flow theory is used throughout, and some correlations with the experimental data are indicated. Item Type: Thesis (Engineer's thesis) Subject Keywords: Aeronautical engineering Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Bell, Richard William Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 January 1951 Record Number: CaltechETD:etd-03312009-085215 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03312009-085215 DOI: 10.7907/1F84-BB81 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1229 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 31 Mar 2009 Last Modified: 04 May 2023 17:12 Thesis Files Preview PDF (Pounder_e_1951.pdf) - Final Version See Usage Policy. 104MB Repository Staff Only: item control page

INVESTIGATION OF BLOCKAGE EFFECTS ON CIRCULAR CYLINDERS IN A TWO-DIMENSIONAL WIND TUNNEL Thesis by Edwin Pounder In Partial Fulfillment of the Requirements: for the Degree of Aeronautical Engineer California Institute of Technology Pasadena, California 1951 ACKNOWLEDGEMENT The author wishes to express his appreciation to Mr. Richard W. Bell, Mr. Josiah E. Smith and Mr. Lowis Schmidt for their com- ments and assistance during the course of this investigation. He is greatly indebted to the members of the GALCIT ten-foot wind tun- nel staff for their work in the preparation of the figures and the manuscript. wel Jo ABSTRACT These investigations include some experimental and theoretical studies upon blockage effects in a two-dimensional wind tunnel. The shape chosen to represent a body in the tunnel is that of a circuler cylinder since such a body will eliminate circulation as a variable and will produce large blockage effects. In experimental studies, three cylinders of different size are tested in a two-dimensional tunnel. It is found that interference effects are of such a magnitude that it is impossible to obtain two= dimensional flow with the basic models, Two-dimensional flow is ob-= tained through the use of separation devices, but a quantitative blockage study is not attained. The theoretical work attempts to show the blockage effects of a two-dimensional tunnel upon a circular cylinder of arbitrary size with and without a wake. The potential flew theory is used through- out, and some correlations with the experimental data are indicated. ~Lii- TABLE OF CONTENTS Index of Runs . .. . +» 2 6 » © » » © s © mw wa we Index of Figures . . ® . e e e ® s * 2 @ Table 1. A. Nomenclature ° . ° @ © © © 8&8 # © » #® 8 @ © B. Notation Used to Describe Configurations Tested G. Notation Used for the Theoretical Analysis Table 2. Text: I. Introduction. .. 0... 0s ee ee II. Physical and Calibration Data... TIT. Data Presentation . . « « « « = 5s « IV. Discussion of Experimental Results. Important Physical Data ...... 2 e e @¢ 8 # 8 @ * a oe 4 V. Theoretical Considerations on Two-Dimensional Blocking in Channel Due to the Presence of A Circular Cylinder. Bibliography 2... es ee ee eee Figures 1-76 o @ @® 8 @© © ¢€ 6© 8 © © @® #8 © « * ° * e @ ¢ @e@ ® ee ee © @ @ e@ «© Page 10 13 16 18 19 22 25 29 38 64, 05 INDEX OF RUNS Date Run | Configuration Test dose a, Remarks t 3= 30248 1 | Clear Tunnel PitP, 10 # 2 " t " + tt 20 t 3 " " Li ff 40 " L 8 8 1 + tt 80 a0 4ole48 5 Gy PtP, Vary | -4.37 : " " 6 6, +R, PL tPa4P, 80 Li 7 bi] 4 Ry Py Le Ly " 8 " of R, tt " " f 9 + Ry bf " tt " 10 " + Re tt t ft " LL " + Re t tt Les a 12 Ly a Ry ot if it An2-48 | 13 | 0, P, " i" " 5a | om P " 0° |Repeat of Run 5 ata = 0° g " 4 C, + tT + Ry P)tPotP, " " # 15 # + ft “f Ro P, " Li " 16 Le on Ry ft tt t 4e5e4B] TT] " + T, Py " " " ij," + T, + Ry PitPotP, " " INDEX OF RUNS (Continued) Date Run| Configuration Test Io vee a, Remarks An5e48 | 19 | C) +7, P,+P,(Vis.)} 80 0° 20 it + ff + R, P, " w uw : al 8 + We + Ry 8 Li Lil L=b=L8 2) t 4 T, 4+ u " " it Lif " n 23] " +" +R, |P,+P, (Vis.) tt t" 24) " +" +R, | PyaPi4P, " it 25 Li + w P, Lt] # " 26)" +7, PotP, (Vis.)} " q " 27 | Clear Tunnel Po Vary AnTnk8 | 28 | Co P, " 0° f " 29 GC. + Ry PLtPotP, 10 woe Show " " hmSnh8 30 C. + Ry PS t 31 " P, bs] ot tt wt " 32 | 8 + Ts + Ry PitPotPs " " 33 |" em 4 Ry P, it W 34 Li +H P, t " Li " 35 +Tg +R, | PLP, " " " 36, * + Ty +" PyAPotPs " " ow rot n AnQohB 37 + +R, P, " f " 38 | t 48 P, " " INDEX OF RUNS (Continued) Date Run Configuration Test 1b Toft? Remarks Aa 2BuL8 Am 2Qnh8 Li hn 3048 Ly 39 40 43 45 46 A6A 47 48 Clear Tumnel CG, +R 1 3 " +R, nog Ry uoo+ Ry Lis +R # - " + Ry Press, P, (Vis. ) " 8 | 80 " Li Lis Li Lu t % w Li Calibration of Rake Staties Model. Orifices Taped Model Orifices Taped Model Orifices Taped Model Orifices Taped, Tape on Model in Front of Rake Model Orifices Taped, Tape on Model in Front of Rake Cylinder Orifices Waxed Cylinder Orifices Waxed Gylinder Orifices Waxed, Wiped Model of Surface Oxidation Cylinder Orifices Waxed Cylinder Orifices Waxed INDEX OF RUNS (Continued) Date Run| Configuration Test 4, 9Be2 g Remarks An30-48 | 484) C, + Ry P, gO 0° |Cylinder Orifices Waxed " 49 |" +R, P (vis. ) " " 8 , 3 ° 5el-4S 50," + Tg + Rg " " " Sandpaper Separa-| tion Strips Blew Loose " SOA; *" +8 458 i " " Repeat of Run 50 " Sl, 4+ Ty + a 8 i " 5a ZLB 52 |" + Ty ot " P3(Vis.)+P, " " End Plate Unseal- . ed " 49A| " + Ry "+f " " Gylinder Orifices Waxed, End Plate Unsealed n A9B) " +8 n 4i t n Cylinder Orifices Waxed, End Plate Sealed t 53," + Xy + Ra " . pit " 8 8 8 s Lid Lis 54 |" +" + Ry P,(Vis.) i ff " 13 if Bahn S 55 + 8, + Re ; u Li " 56)" + Ry Pot u 57 # + Rg " + # Lie $f n 58 [m+ R. P (vis.) " " 9 3 8 " 49G)}" + Ry " " " Cylinder Orifices Waxed, End Plate Sealed, Repeat of Run 49B INDEX OF RUNS (Continued) lb Date Run| Configuration Test do? Pte o, Remarks 5e5e48 | 59) 0, +1, +R, PatP, 80 o° u 60 |" +" +R P, i tt i él |" +0, +" Pp+P, " i" " 62," +8 + Re P, " " " 63 |" + Ty, +8 PoAP, " " i 64 |" +" +R P, " tt Sabah S 65 Cy + Ro P 4 24 " " 66 |" +8 P)+PotP, ] " n 67 Gy P, Vary tt " 68 |" +R, BaP, 2h " 5a Toh S 69 |" + T3437 Ry P)+P, +P, " n g " 70; " +" +Ry Pp#P, " " : " TL |" + Ty ot ® | Fi tPotP, " " " 7)" +" +R, PotP t i" 5-48 73 C, + Ry noaye 10 8 t q Th, Cy +H PotPotP, 80 " n 75 |" +R, P,(Vis.) | M" mbuo INDEX OF FIGURES Miscellaneous Page Sketches 1. Sketch Showing Two-Dimensional Working Section... ++ 65 26 " of Circular Cylinders . . 2.6 6 2 6 eo es ee ae 66 36 " Showing End Plate Orifice Locations ....... 67 Calibrations he Two-Dimensional Tunnel Velocity Calibration. . ... +. «+ 68 56 " " it Reference Pressures ......- + 69 66 " Statie Pressure Survey Across Tunnel... 2 0 we eee 70 7° " ut " Along Tunnel Floor and Gelling. . 71 8. Variations Between Wall and Centerline Reference Pressures . . + « + + 6 » re 7-4 96 Calibration of Rake Static Pressure Tubes. ...... - 73 Wake Surveys, Cylinder C, 10=10j. Cylinder C1, x/d = 3.108....... bee eee ee 7h, 11-Lle. nm oo , Orifices Waxed, x/d = 3.108.......-. 85 12-12e. " , a Taped, " = " .,. 2.2 2 eo 2 » 8 13-13}. " Hy " Plugged, x/d = 3.108. ...... 93 l4-lg. moot, x/d = 4.927, 52837, 6.746. 2 ee ee ees 103 I-l5e, =" 0 + Ty, x/d = 3.108, 4.927, 6.746, 2/d = -.910 11 16~-16e. "6, + Ts xf/d = 3.108... .-2 5004 eee - iy 17-17e. moot a ty fd = 56837. - ee ee tee eee 119 Is-18f, "0, + T,, x/d = 36108... tee ee ee BL - 19=19¢. ho ot 40. x/d = 5.837. ...65 52 se ee ee 130 i wo ry 2 i 20-20, tt CG. + Ts x/d = 3,108. ....- 2.2068» see « 137 INDEX OF FIGURES (Continued) Page ai~2if. Gylinder C, + T,, u/d = 5.837, 60o7Th0. 2 ee ee te ee “U3 Wake Surveys, Cylinder Co 22—22f, Cylinder Cos x/d = 1.626. ... 0.0 0 we ew ee ee we 150 23-23f. mo MM 5 B,053. ee 157 Qhm2NE« "6, 4+ Typ x/d = 1.626. ...6005 020 .. . 164 25_25£. Hoo om 4m 5 HM = 3,053. ....4. ct eh ee ee 172 26—26f'. M Cy + Troy " = 1,626. .--.---.4. rn 180 27-278 » 2c PO. 188 Wake Surveys, Cylinder G. 28-281. Cylinder C3, xf/d = 1,150, 1.823 . 2... 2.0.0.0 ee eee 196 29. "63 + Tey x/d= 1.150 ......2:. cee eww 2 206 30. " Hoa , x/d = 1.823 -- - eee eee ee ew ee BOF 31. " C, + Tas x/d = 1150-1 2 ee ee ew ee ew ee « 2B 326 moo 4M e/g = 16823 2 ee wo 2D Static Pressure Distributions on Models 33~=33d. Cylinder C, (Reynolds Number Effects) ....... -... 210 3he a re 2 35. mo G+ Tye eee tw et ee wt ee ae ae ALS 36. HG, +E. eee vce tw we te tt es 216 37. " C,+T, te ee ewe a 38. " GC, +T,... oe ee oe we te ee 2 eee 2 218 39=39e. a c, (Reynolds Number Effects) - - +--+ +s - wee 6 ALO 40. n Hee a ct te eh ee es coe eee 2228 Al. oe Se be ee eee BBB «As es a 2 Lh 3C. "Cy (Reynolds Number Effects)... 2.5 +e ees 225 w=Shen INDEX OF FIGURES (Continued) Page Lhe Cylinder Cy + + ose ee eee eee ee ee ee - » 228 15. a » «229 Abe Fe ee eo 230 47. " i 2 6 23L Static Pressure Distributions on North Ind Plate 48» Circular Cylinder in Potential Flow... 2 2 6 e+ 6 0 2» 232 L9e Combined Survey from Cylinders C, and Cy. 6 es ee se ee 233 50. Cylinder 0, + Tig ste et et et te ee ee ee o » 234 Static Pressure Distributions of the Tunnel Floor and Ceiling 51. Cylinders ©, , Gy', C, + 13, C,+T,. ra <>) 526 rt Cy, Cp + Tye Cot Bp eee ee ee ee eee + 236 536 u Ca, Cs + T, er 237 Averaged Data on Wake Patterns 5he Maximum Wake Losses for Cylinder CC]. + + + 2 + eee « . . 238 55~55b. Average Wake Pattern, Cylinders Cy + Ty, 0, + Toe - seo 239 56~56b, " " ny Cylinder Cy + T3- re 2 » 241 57=57b. 7 " u, Cylinder 0, + Ty. se te ee tw 8 w RAB 58, Maximum Wake Losses for Cylinder C., ve eee see ee 245 59=59b. Average Wake Pattern, Cylinder CG, + Ty, - +0 ee eee 246 60-60b, 1" i to, oe . . 248 61. Maximum Wake Losses for Cylinder CG, . . ce ee es - » 250 Results. of Drag. Computations 62. Effects of Reynolds Number on Drag Coefficient for Cylinder Cj - + + + ee ee ee es ce ee es oe ew ee S51 63. Table of Pressure and Wake Drag Coefficient for Two- Dimensional Wake Configurations .... 0 +s 0s 6+ +s 6 208 wom 7 INDEX OF FIGURES (Continued) Results of Analysis Oh. 65. 666 67. 68. 70. 71. 726 73.0 The 756 76. Doublet Strengths, Gase 2.» « » 2 » © © » © © @ © © Gylinder Ordinates, Case 2 . « 6 © « © © © © © # © © » © Without Wake . . «+ « © 2 « » Qf Blockage Factor at x u " "uo y=O " er Comparison Between Experimental and Potential Pressures on Body, Using Equation (12) and Figure 35... «+s. Comparison Between Experimental and Potential Pressures on Body, Using Equation (13) and Figure Al. re Comparison Between Experimental and Potential Pressures on Body, Using Equation (13) and Figure 42. . 2.» » + « Strength of Doublet “', Case 4 «2 0 2 6 © ee ee ew we Gylinder Ordinates for Source Flow in Channel, Case 4 .» e Comparison of Leading Edge Ordinates With and Without Wake. Blockage Factor at xX = 0 With Wake. e ¢ ® ® @® 6 ® #® & & *# ® Comparison Between Experimental and Potential Pressures at Wall of Channel, Co + Tay Pr er er Comparison Between Experimental and Potential Pressures at Wall of Ghannel, 6, + T 2 12 a &® ® @® ® &® © # @© &® 8 @ 253 254 255 256 257 258 259 260 261 262 263 264 265 oat | Qee TABLE 1 A. NOMENCLATURE Definition of Tests PL = Static pressure measurements made on cylinder using cylinder orifices. Measurements were recorded photographically. P, (Vis.) = Visual ebservation and recording of Py pressure neasurenents. PS = Static pressure measurements made at floor and ceiling of test section using flush mounted orifices which were coincident. with vertical plane through tunnel centerline. Measurements were indicated on a multimanometer and recorded photographically. { P, = Pp static pressure measurements made visually using a Zahm type precision micromanome ter . Ps = Stetic and total head measurements of the wake made using the survey rake. Measurements were indicated on a multi-= manometer and recorded photographically. P,(Vis.) = Visual observation and recording of P, pressure measurements. P. = Visual observation and recording of static pressures on cylinder endplate support as indicated on a multimanometer. Definition of Anguler and linear Measurements a =Angle of attack of reference. cylinder diameter with zero defined by rotating the cylinder in the windstream until orifice number 1 indicated that it was measuring the forward stagnation pressure. Positive angular displacement occurs when the nose is raised or trailing edge is lowered {as s tunnel cbserver would see it). @ = Anguler measurement of point on cylinder relative to reférence dianéter (when model isata= 00), See sketch U_, to right. O oF on | |= TABLE 1 (Continued) x = Distance from trunnion axis measured in direction parallel to tumnel centerline. Positive value corresponds to downstream direction. y = Distance from trunnion axis measured in vertical direction. Positive value corresponds to measurement above trunnion axis. Distance from tunnel centerline measured parallel to trunnion axis (i.e. horizontal). Positive valve eorresponds to measurement to left (North) of tunnel centerline (observer looking upstream), s i d = Diameter of cylinder. Definition of Coefficients C_ = Total or static pressure coefficient. Figures on which the scales are labeled C, have the curves marked so as to identify the pressure coefficient presented. P-P |. H ~P x re GC = f, or = ref. Pp do Io R = Reynolds number = Pao 7, Where the foregoing coefficients are associated with the following quantities: gq. = Dynamic pressure in clear tunnel test section’ as indicated when using calibrated tunnel piezometer rings. (1/2 pUg? in lb/ft.) qg= Ho P, = True dynamic presstire measured in tunnel when model i8 present (1/2 pu? in 1b/ft.2) r H.. = Total head as indicated by measurements made using the rake. P_ = Static pressure measurements made at "x" where subseripts used are: TABLE 1 (Continued ) x = denotes location of static pressure orifice as indi- cated on figures. (i.e. Rake, model, or endplate static orifices) w = denotes static pressure measurement made on the wall (floor and ceiling) when medel is present in tunnel. P :. = Reference static pressure measurement where subscript Tere tref 3 may be: 20 ~ denotes static pressure measurements made at the 20 ft. piezometer ring 3-1/2 ~ denotes static pressure measurements made at the 3-1/2 ft. piezometer ring o ~ denotes static pressure measurements made at the intersection of the tunnel centerline with the trumnion axis when no model is present ¢ ~ denotes static pressure measurements made when no model is present at points on the tunnel centerline other than at intersection with the trumion axis Wy~ denotes static pressure measurements made on the wall (floor and ceiling) when no model is present Us = Freestream velocity when no model is present. u = Local velocity when model is. present. . P = Mass density of air (note: A correction is applied in the tunnel airspeed calibration so that in the above formulae p is to be taken as the free air density unaffected by compressibility). 4 /# = Absolute viscosity of air (for T= 15° C., h = 760 mm.) = -? lb - wet x sec In addition to the preceding definitions, new definitions are given in the text when they occur in conjunction with derivations, etc. B. TABLE 1 (Continued) NOTATIONS USED TO DESCRIBE CONFIGURATIONS TESTED Cy = R = R, = Steel cylinder machined and ground to a high polish. Length is 36.0 inches and diameter is 6.598 inches. It is equipped with 20 static pressure orifices made by installing 3/32" 0.D. copper tubing flush to the surfaces. Orifices are spaced evenly apart with number 1 orifice being on the leading edge. The orifices were mounted on tunnel centerline in an unstaggered (axially) position, Cy with static pressure orifices filled in with brass red. Slight surface irregularities still existed.- Steel cylinder similar to C, but of 12.613 inch diameter. It is equipped with 36 static pressure orifices mounted in a vertical plane coincident with the tunnel centerline. Steel cylinder similar to Co but of 17.838 inch diameter. Standard 80 tube GALCIT traversing total head rake installed so as to make a vertical total head survey 20-1/2 inches aft of the trunnion axis and 6 inches South of tunnel center- line. Rake also equipped with static pressure tubes. Rake mounted 32-1/2 inches aft ofthe trunnion axis and 6 inches South of tunnel centerline. Rake mounted Ahn /2 inehes aft of the trumnion axis and 6 inches South of tunnel centerline. Rake in same axial position as Ry, but mounted 12 inches South of tunnel centerline. Rake in same axial position as Ry but mounted on tunnel centerline. Rake in same axial position as Ry but mounted 6 inches North of tunnel centerline. Rake in same axial position as Ry but mounted 12 inches North of tunnel centerline. Rg = Ty = TABLE 1. (Continued) Rake mounted 20~1/2 inches aft of trunnion axis. Differs from previous rake notation in that this location allows a complete horizontal traverse in addition to the vertical traverse. Actual position of rake in traverse plane is noted on pressure data. Rake Rg with total head tube mounted on outside of static pressure tube mount so as to permit total head measurements to be taken close to the South tunnel wall. (Total head tube was mounted on South side of rake). Rake Rg with total head tube mounted to flanges on North side of rake so as to permit total head survey close to the North wall. Rake mounted 38-1/2 inches aft of trunnion axis, Similar to Rg in that notation is used to denote rake being used for complete traverse with actual rake position noted on pressure data... with total head tube mounted as in Ri so as bo permit. total ead. survey near South wall. 0.041-inch diameter (piano wire) separation strips taped spanwise on model at @ = £ 65°. Used in conjunction with cylinder Cy. 0.018-inch diameter (piano wire ) separation strips taped spanwise on cylinder Cy at @ = = 65°, Separation strips similar to T, except taped at @ = + 350, tT. + Ty. 0,039~inch diameter (piano wire) separation strips taped spanwise on cylinder C3 at @ = £ 650. 0.0675—inch diameter (welding rod) separation strips taped spanwise on cylinder C3 at @ = + 55°, Separation strips similar to T, except taped at @ = + 85°, 19 x H ~L5= TABLE 1 (Continued) One-inch wide chordwise separation strips (sandpaper) mounted on each end of cylinder. Extended around leading edge from 6 = + 100° to @ = - 100°, 0,0675-inch diameter (welding rod) separation strips taped spanwise on cylinder C, at 6 = = 65°, Separation strips similar to Tg but modified such that they only extended to within 2 inches of each wall. 0.0675-inch diameter (welding rod) separation strips taped spenwise on cylinder Cy at © = F 65°. 0,0675-inch diameter (welding rod) separation strips taped spanwise on cylinder 0, at @ = + 65° and + 85°. 1/2- inch wide cellulose tape strips mounted parallel to chord plane of cylinder Cy and spaced 3 inches apart across the span. Wax fillet installed at intersection of front side of cylinder Cy and North tunnel wall. Clear Tunnel = Test section of wind tunnel devoid of models so as to permit preliminary calibrations of air flow. =] Ge TABLE 17 (Continued ) C. NOTATION USED FOR THE THEORETICAL ANALYSIS ¢ x = r cos 9 = coordinate in direction of (sy) undisturbed flow A y =r sin © = coordinate perpendicular 7. 4 to undisturbed flow \l2,-2) ag r =\\x" + y” = polar coordinate i) = tan™) z = polar argument Zz =x +iy = re’? = complex coordinate . d = diameter of circular cylinder b = radius of circular cylinder a = height of channel c = polar distance of wake source from origin ye Q = angular location of wake source from origin V u = undisturbed velocity C Ak, 2 U Arf u = velocity in x direction — Me pb v = tt "oy " "9 7 x u, = radial velocity u, = tangential velocity wz) =u- iv = (a, -iu)e ~te . complex velocity F(z) = § + 4¥ = complex potential G = velocity potential, ¥ = stream function = 00. ov = @ . 2 oy ox By YS By * 7 OX ad 1,2 = strengths of doublets for the cylinder without wake in the channel strength of Xn = OF strength of strength of oo | J om TABLE 1 (Continued) doublet which corrects wake disturbance at doublet for the cylinder with wake in the channel sources. which simulate wake TABLE 2 IMPORTANT PHYSICAL DATA Cylinder d a b Span (inches) a a a Cy 6-598 ° 06468 ° 03234, 5.46 C, 12.613 12366 06183 2685 C, 17.838. 17488 | .08744 | 2.02 APPROXIMATE REYNOLDS NUMBERS, R x 1079 1/tt? e "8 "3 2 201 5 308 5eh, 10 Bel 567 125 | 305 15 307 7.0 10.3 1705 Aol a 20 hed Sel 114 24 ; 30 54 909 A605 40 6.2 60 76 80 APPROXIMATE MACH NUMBERS q(1b/ft*) M 10 082 24, 2128 80 0235 ~19= I__INTRODUCTION | The following is a summary of some experimental and theoretical studies of flow about right circular cylinders in a two-dimensional wind tunnel, The attempt is made to draw some conclusions concerning the effects of tunnel walls upon the flow, In the absence of any circulation about the body in the tunnel, all such effects are gener= ally grouped together under the term "blockage effects", and the effects will be so designated hereafter in this report. The reason for interest in blockage effects is simply that in all wind-tunnel tests the data obtained in the tunnel must be applied. to cases in free aire Gonsequently, such data must be corrected for the effects of the tunnel if they are to be used with assurance. Gorrec=- tions, associated with circulation, are based on a well developed theory which has been checked by experiment with some success; while corrections for blockage effects are not so well developed or so thoroughly substan= tlated by experiment. It has always been eustomary to keep all corrections as small as possible by keeping the sizes of the models small in comparison to the tunnel dimensions, but if the corrections were well understood large models would be desirable for many reasons. As Mach numbers increase, this consideration becomes even more critical, since all corrections increase markedly with M. The present investigation was undertaken with these things in mind. It was decided to use a large two-dimensional wind tunnel and to use as models three right circular cylinders of different diameters, each span= ning the tunnel working section. All models were to be tested at the -20— same Reynolds number and at low Mach mmbers. The cylinder shape was chosen to eliminate circulation as a variable, and the two-dimensional flow was used because of the comparative simplicity and because most of the detailed theory is for this case. Comparatively large cylinder diameters were chosen to assure large wakes and large blockage effects. Comprehensive pressure surveys were taken in the flow about each model, and it was believed that the differences in data between models would be solely due to blockage effects, Therefore, these data could be used to check the theoretical treatments. Wake sizes were to be varied by the use of devices to induce separation. As it turned out, the experimental work was complicated by some unforeseen circumstances. It was found that the flow about the models was far from two-dimensional, with the interference between the boundary layers on the tunnel walls and the cylinder surface having a profound effect on the wake pattern. Since the ratio between cylinder diameter and span was different for each model, this interference varied greatly between models and made direct. two-dimensional flow correlation impossible In addition, some static pressure tubes set flush in the model surfaces induced early separation, and any surface irregularities such as small spots of corrosion, which were almost imperceptable, had similar effects. As a consequence of these troubles, a good deal of the testing time was spent in studying and eliminating their effects, It was found that reasonably good two-dimensional flows could be obtained by moving the general location of the separation forward. This was done by laying wires spanwise along the model surface upstream of the maximum thickness point, and several of these configurations were =D] = tested. Sets of data for all models with wires located in similar positions are available and can be compared for blockage effects. How- ever, the data from the clean models cannot be compared at ail in this sense. Some attempts were made to eliminate the wall interference by fillets and similar devices, but it is quite clear that the only effec- tive method would be to remove the wall boundary layer just ahead of the cylinder through a porous surface or a slot. In addition to these experimental surveys a theoretical study was made of the potential flow about a circular cylinder in a tunnel with and without singularities downstream to simulate wake effects. The experimental data which were obtained and a summary of the theoretical treatment are presented here, along with a general discussion of results. A complete outline of the tests is presented in the Index of Runs, and the definitions of model configurations and test nomenclature are found in Table I. The experimental setup and instrumentation are de~ scribed in Section II, and the methods of data reduction and presenta- tion are outlined in Section III. =—22e ID PHYSICAL AND CALTBRATION DATA A, Physical, Data The facility used for the experimental studies is the GALCIT 10- Foot Wind Tunnel with the two~dimensional working section installed. A complete description of this installation is given in References (1) and (2). The working section is three feet wide, eight feet high and ten feet long, and models are mounted horizontally between two end plates which are set flush to the walls. The contraction ratio is about 12-1/2 to 1, and five turbulence sereens are provided in the settling section between the last turn and the contraction section. A very snooth flow is achieved with a turbulence level (ratio of the root mean square of velocity fluctuations to mean velocity) of 0.08% parallel to and 0.12% perpendicular to the flow direction. The models consisted of three 36.0 inch lengths of steel tubing ground to an accurate circular shape on a centerless grinder, and finished to a high polish. Their diameters were 6.598, 12.613, and 17.833 inches, and they were mounted between the standard end plates. Each model was equipped with a chordwise row of static pressure orifices located at the center of the span and extending around the entire cir- cumference. _ Wake surveys were made with the standard survey rake for the two- dimensional tunnel. This rake consists of 80 total head tubes mounted 0.1 inches apart and of 5 static pressure tubes mounted on the side of the rake frame. The rake mount incorporates horizontal and vertical leadscrews to facilitate surveys, while fore and aft movenent, of the rake must be accomplished by unclamping the rake support strut from the mount and moving it manually. = 230 Static pressure surveys on the working section floor and ceiling were made using 38 orifices set flush in the walls on lines defined by the intersection of the fore and aft vertical plane of symmetry with the floor and ceiling. The north end plate was equipped with 27 static pressure orifices, from which data were taken during several runs of the test. All pressure tubes were connected by rubber tubing to back-lighted multi=manometer banks, and most of the data were recorded photographic~- ally from these banks. In several instances, where interest centered on only a few readings, data were taken visually. The floor and ceiling pressures were recorded both from the multi=manometers and from a pre- cision micro-manometer, since it was found that pressure differences were often too small to record accurately from the former. The wake rake was in general too short to cover the large wakes encountered, and so surveys were taken in two or three steps with the rake moved about two thirds of its length across the wake for each step. Several pictures were taken during each reading so that the continually fluctuating wake pattern could be satisfactorily averaged. The wake patterns all fluctuated about 5 or 10% about their mean values, and were in no cases unstable or subject to violent variations with time, so that this survey procedure was considered adequate. A drawing of the working section is presented in Figure 1 which shows the model support system, the wake rake mount, and the locations of the floor and ceiling orifices. Figure 2 shows the cylinders and Figure 3 the location of the end plate orifices. B. Tunnel Calibrations - The results of the clear tunnel flow calibrations are shown in Figures 4 through 9. 2h The tunnel flow parameter to which all data are referred is the free stream dynamic pressure q,, which is completely defined in Table I. This dynamic pressure was set during the testing by measuring the static pressure difference between two sets of pressure orifices in the settling and contraction sections of the tunnel. The calibration between this pressure difference and q, was obtained by taking simultaneous measure- ments of the two, using a standard pitotestatic tube located at the reference point to measure q,. A compressibility correction was applied, so that the true q, was known at all times. The calibration is shown in plotted form in Figure 4. Figures 5 through 8 illustrate the clear tunnel variations in statie pressure along the reference axis in the working section and along the fleor and ceiling. It should be noted that at the farthest aft rake position (4-1/2 inches aft of trunnion axis) q had varied only 1% from q,. Since this was so, dg was used as. the reference value in the denominators of all pressure coefficients. In general, static pressure references were taken from the calibration plots at the place in the working section where the measurements were taken. Figure 9 illustrates the calibration of the static pressure tubes on the wake rake. No calibration was made for the total head tubes. IIl__DATA PRESENTATION All experimental data presented in this report were obtained from p¥essure. measurements. They are all reduced to the form of pressure coefficients by subtrecting the value of a suitable reference pressure and dividing the difference by the dynamic pressure, q,, which was used when the data were taken. Definitions of the coefficients used are , found in Table I. All space coordinates are made dimensionless by dividing them by the diameter, d, of the cylinder to which they refer. The coordinate system used is shown at right and is defined completely in Table I. (4- 7) All. data are shown in plotted form, fe aa . Ss with the type of plot depending on the . : : : . ae a kind of data in question. Essentially LONG, TUBINAL SSeS reerow four kinds of data were recorded as aw follows: % “0 | (+ Dowy (& NORTH) STREAM) a) Wake surveys behind the models. | b) Static pressure surveys around the models at their midspans. ec) Static pressure surveys on the tunnel wall near the tunnel- model intersection. d) Static pressure surveys along the fleor and ceiling covering the length of the working section. The data in each of these categories are presented together, and the presentation of each group will be described separately in the following discussion. a) Wake Surveys: Wake data are presented in Figures 10 to 32. - In general, surveys were taken vertically through the wake. A series wn 2bun of such surveys taken at a given distance downstream (x/d) and at several spanwise stations (z/d) are considered a complete picture of the wake at that value of (x/d). These groups are presented to- gether, each under one Figure number. In some cases, only one span= wise station was studied and in these instances the plots usually appear individually. Each vertical survey is plotted on a separate sheet. Plotted are H = p20 , P~ Pao and Pé ~ P20 vs. (y/a) Qo do do Also, indicated is the value of Py 7 Pa9 existing at the floor and Go ceiling at that value of (x/d). The points without symbols represent experimental values of H = Pag and the circled points values of P= P20, Go q In some cases where the amount of data is insufficient, no fairing has been shown for the static pressure curves. It is to be noted that, for this tunnel contraction ratio, Ho 7 Pao = .0064 or about 1/2 mm. on these plots, so that the coefficients are ° nominally referenced to Ho: The difference between the static pressure and total head curves is essentially g/a,. In several cases, groups of surveys are cross-plotted to show contours of constant total head values at a given value of (x/d) (a few cross plots of static pressure also appear). These cross-plots illus- trate the three dimensional character of the wake when transition wires are not used, and the two dimensional qualities when they are. In the case of cylinder Cy two detailed total head surveys were made near the model~wall, intersection and these are included on the appropriate cross- ~27- plots (Figures 10 and 14). b) Static Pressure Surveys on Models: These data are presented in Figures 33 to 47, and were obtained from static pressure orifices located around the cylinders at their midspan. Plotted is F—Pe vs, 8. a ° In cases where no differences existed between corresponding orifices on the top and bottom of the model only one point is plotted. When differ- ences did exist, the data for the lower surface are given tagged symbols. The dotted line on each plot represents the static pressure distribution on a cylinder in potential flow (no walls). It may be noted here for reference later that the pressure drag coefficient can be computed from these data using the relation: 2ir co eLillIPZPo|ecse@d9 --=--= (1) Di 2 Q ° fe) c) Surveys on the End Plates: Here several complete surveys were taken, and results are plotted as lines of constant static pressure in Figures 49 and 50. It was found that differences between eylinders Gy and Co were slight in this case and so data taken in these cases are plotted together in Figure 49. No data appear for C. since this model covered most of the orifices. Figure 48 presents the potential flow solution corresponding to these plots. The points shown on these Figures are not experimental values but are obtained from cross-plotting the data and picking even values of p-p “o Yo e a) Floor and Ceiling Surveys: Data from these studies are plotted oe on Figures 51, 52 and 53. They are presented as “ta VS. x/d for a series of model configurations. Each curve is an average of floor and ceiling pressures, with values of the reference pressure, Pury? being taken from Figure 7. The curves are a combination of data taken on both the multi- manometer and a micro-manometer. The latter was used to accurately establish the level of the readings, since in some cases the differ- ences were quite small and hard to read from the manometer film. The velocities at the wall can be computed from the relation 1 ~ DH Pie | ae -~---- (2) “Mtg 1 ~ vo ~ Bo =-29— IV DISCUSSION OF EXPERIMENTAL RESULTS The experimental data will be discussed qualitatively here, and some of the difficulties encountered will be pointed out in detail. Wake surveys, model pressures, and floor and ceiling data will be discussed separately, and then some general results con- cerning drag and blockage will be indicated. a) Wake Surveys: The data on configurations without separation strips may be considered first. These are presented in Figures 10-14, 22, 23 and 28 The first thing to notice is the interference due to the wall-model intersection (see the cross plots of constant total head decrements). For all three cylinders, an area of large total head loss exists adjacent to the wall, and outside this area a region of almost negligible total head loss exists. The center of the latter area is at about one diameter from the wall in every case, and the amount of loss depends only on the distance x/d downstream of the model. The ratio of cylinder diameter to span is never small enough for effects of this interference to be very well defined farther than one diameter from the wall, but presumably, if the cylinders were longer the effects would die out and a predominately two- dimensional wake would be established at two or three diameters dis- tanee. Some probing at the intersection indicated that a double | vortex is formed off the top and bottom of the model, and evidently this forces high energy air down into the wake at about one diameter out causing the low loss observed at that point. =30= The data also show that the static pressure orifices caused some wake distortion by moving the point of separation at the center of the span somewhat forward. This effect is not nearly as well defined as the wall intersection interference, since it is a weaker disturbance and occurs close to or within the area in which the wall effect predominates. Figures 11-13 illustrate attempts to eliminate orifice interference by waxing, taping, and plugging the orifices as smoothly as possible. It is seen that the waxing (Figure lie) and plugging (Figure 13f) were effective, but that the taping (Figure 12e) was not. In the first two cases, there is still an area of larger total head loss at the center, but this mst be mainly caused by the attempt of the wake to form in a two-dimensional manner since the wall effect is comparatively small at center of the span for this case. The remaining Figures in the group illustrate the effects of _ the separation wires, and it is apparent that all these configurations have wakes which are predominately two dimensional. Separation wires at 85° have the least effect; those at 65° are intermediate; and those at both 65° and 85° develop the largest wakes. It was found that the size of wire was relatively unimportant. Note that in all cases the spanwise variations in static pressure are comparatively minor, but that through the wake vertically, large gradients are exhibited which are of the same order of magnitude as those in total head pressure. b) Static Pressure Surveys on Models: The data under this Category are shown in Figures 33-47. Reynolds number comparisons are presented in Figures 33, 39 and 43 for the cylinders without -31= separation strips, and a table of R is included in Table 2. It is apparent that a marked change in pressure distribution occurs at a value of R of about 3.7 x 10°, and this is to be expected as a manifestation of the transition from laminar to turbulent separation which oceurs in the flow over any smooth body. Most of the data in this thesis were taken at a Reynolds number of about 8.6 x 10° so as to be well above this critical range. Sinee none of these data were taken with separation strips, the pressures shown are only good at the center of the model spans. It 5 is seen that the region of separation below R = 3.7 x 10° is at about @ = 90°, while after transition separation occurs at about © = 115°. This leads to the possibility that the wakes below R = 3.7 x 10° might be much more two dimensional than those which were observed for the cases without separation strips, but since no wake surveys were - actually made at the low Reynolds muibers this cannot be proved. Such tests would be interesting if any further experimental surveys are undertaken on the cylinders, as wakes of a somewhat different nature would certainly be produced. The remaining Figures illustrate pressure distributions with the separation strips in use, and it may be reasonably assumed that these surveys apply across the model spans. Note that as the cylinder size — inereases for a given separation strip location (cf. Figures 36, 41 and 45) the point of separation remains reasonably constant while the peak negative pressure (point of highest velocity) increases somewhat. Such behavior can be considered as a bonafide effect of blockage. =32= One other fact is worthy of note here. Figure 43 shows data on eylinder Gy and it will be remembered (cf. Figure 28) that these data are taken in the region of minimum total head loss mentioned previously as being associated with the wall interference. Figure 43 shows that the separation point is moved back to about @ = 140° for this case and that the peak negative pressure is very large. This can only occur if high energy air is being forced over the back side of the cylinder to delay the separation, since the blockage itself does not move the sepa- ration point appreciably. Presumably then, the delayed separation is due to the formation of the double vortex which was observed in the visual studies. However, the whole interference pattern is surprising and still somewhat obscure. ec) Surveys on The End Plates: These data are shown on Figures 49 and 50 and may be compared with the potential distribution (in free air) shown on Figure 48. As they are made on the wall surface, they represent the static pressure distribution as observed through the boundary layer and wall interference effect. Therefore, they are of qualitative inter- est only. The effect of the separation strip is seen to be very large (Figure 50) in that the static pressure behind the model is considerably reduced. ad) Floor and Ceiling Surveys: Floor and ceiling pressure distri- butions are shown in Figures 51, 52 and 53 for the three models with and without separation strips. The separation strips increase the distur- bance at the wall as expected due to the increased wake sizes. At about four diameters upstream of the cylinders the disturbence is about -.02 in all cases. The peak change occurs slightly aft of the cylinders, m3 Jam moving forward and increasing markedly as the ratio de increases. Downstream, the curves all tend to some final negative value which indicates a higher velocity than that in the free stream, and this may be considered as an indication of the wake blockage. However in no case was the final value of static pressure established, so that it: is clear that the working section was somewhat short for these investi- gations. e) Other Observations: Figures 54~61 summarize the data on the wakes which were considered to be two-dimensional. Averages of the wake surveys are shown, and plots of maximum wake losses as functions. of x/d are presented. Figures 54, 58 and 61 show the latter. It is seen here that at about six diameters downstream when the wake is perhaps three diameters wide, the velocity recovery in the center of the wake is almost complete, so that the losses apparently | appear almost immediately as decreases in static pressure and not as velocity gradients as is usually the case. This is an unexpected result, and must mean that the wake is diffusing into the tunnel free stream flow ina manner quite different from that‘of the usual wakes observed in two-dimensional work. In Figure 61 no fairing was attempted since it is clear that the rake was too close to the model to allow the total head tubes to function properly. This highlights another difficulty encountered which may be mentioned here. Ideally the wake surveys should have been taken at the same values of x/d for all cylinders, but this was impossible because of the relatively short working section length. From the experience here it would seem that values of about 4, 6 and 8 for x/d would be ahout right. 3c Because such a procedure could not be adopted with the model sizes used; exact wake correlations are impossible. Figures 62 and 63 show results of some drag coefficient computations made from the experimental data. The first figure is a plot of °D, vs. R for cylinder Cy» computed from equation (1). The data are taken from Figures 33-38. This again illustrates the critical Reynolds number effect at about R = 3.8 x 10°, which is typical for such cases. For Cy without the separation strips the values of C5 are of qualitative 1 interest only, because of the interference effects. .The effect of the separation strips on °p, is clearly indicated here. Figure 63 is a tabulation of pressure and wake drag coefficients computed for the cases with two-dimensional wakes. Here °D, was again computed from equation (1) using Figures 35-47. These values indicate that “D, generally increases as cylinder size increases for a given separation strip, but there is too much scatter for any exact correlations considering the number of values available. The values of CD are computed from the averaged wake plots, Figures 55—60, using a relation derived in reference 3), page 128, from the momentum equation. This relation was chosen because it restricts the computations to the region of the wake, and is presumably quite general. In the nomenclature used here, the equation can be written as fH =H a2 [PSJeqp-[egi] -----0 where qn a. x ( a refers to data in the wake The values, thus computed, do not correlate very well with corre- sponding values of Ch >» nor do values for the same cylinder at different 1 values of x/d correspond. In general, the values of SD are slightly W less than those of Cy and decrease somewhat as x/d increases. This 1 probably means that equation (1a) cannot be accurately applied so close to the body and/or that the data are not accurate because of instrument errors close to the body. No values of Cy were computed for C. since the wake surveys were made at very small values of x/d for this model. In summary then, it is plain that the drag data are not adequate for any quantitative blockage study, although the general trends are in the correct direction. This is due in part to the lack of complete similarity between the cylinders, and also due to the manner in which ‘wake data were taken. f) Comment on the Tests: As a result of the experience gained from these investigations, several rules concerning experimental techniques may be laid down which should aid in any future studies of this nature. First, geometric similarity must be maintained to a higher degree than was possible here. Ideally, of course,the only geometric para- meter to be varied should be d/a, with the ratio of span to diameter and the values of x/d at the wake rake stations held constant. If this Could be done, good quantitative results could almost certainly be obtained, but several working sections of different dimensions would be required, and this would introduce many new difficulties. The alter- natives are either to eliminate the wall interference effect so that the Span to diameter ratio would lose its significance or to make the ratio 36m quite large (at least 10) to reduce the importance of the wall inter- ference. Either approach should give essentially two-dimensional wakes. The wall effects could be presumably eliminated by boundary layer re- moval on the wall just upstream of the model either through a slot or @ porous surface. Second, the practice of using a complete ring of orifices to measure pressures on the model is not too sound, and a much better approach might be to use one orifice and rotate the model. However, the latter approach would require much more testing time for equiva- lent results, so a probable compromise might be to locate a row of orifices on a helical line around the model. The orifice size should also be reduced to as small a diameter as possible (the model orifices used here had diameters of about 3/64") and the orifice holes should be drilled directly into the surface of the model and connected to pressure tubing on the inside. Third, the use of separation wires to vary the wake size is well established by these tests, and the locations for maximum effectiveness are pretty well fixed as between 6 = 65° and 35°. If similar strips are to be used on several cylinders as was done for this report, some care should be taken to see that all strips are fastened in the same manner with as much geometric similarity between models as possible. The variations in wire size which were investigated (ef. Table 1B) did not seem to be very important as far as wake size was concerned, but it would probably be wise to use geometrically similar diameters. 37m Fourth, the surface condition of the cylinders is of extreme in~ portance, and any practice leading to the possibility of corrosion should be avoided. It might be well to use some kind of a lacquer to insure complete uniformity of the surface over a reasonable period of time. | Fifth, it might be very interesting to study the wall-cylinder interference effect in some detail, so that it can be defined and understood completely. The two primary variables if compressibility is neglected should be R, the Reynolds number of the cylinder and Ry the Reynolds number along the wall (Ry would define the character of the wall boundary layer in the vicinity of the wall-cylinder intersection if the cylinder were not present). If the effect is completely defined as a function of R and Ry , it should be easy to eliminate it or at least exercise some measure of control. If the above points are considered, it is reasonably certain that good quantitative data on the basic two-dimensional blockage effects can be obtained with circular cylinders. These points must therefore be considered as the main results of the experimental part of the thesis, as they indicate the way to the final solution of the problem as originally outlined. It is now pertinent to pre- sent the theoretical considerations which may also act as a guide in any future experimental work. ~38= V. Theoretical Considerations on Two Dimensional Blocking in a Ghannel Due to the Presence of a Circular Cylinder The two dimensional flow around cylinders has been treated ex- tensively both for the cases with and without channel walls. Some elaboration will be given here with special emphasis on circular eylinders of comparatively large dimensions. The two dimensional potential theory is employed throughout, and correlation with the experimental data is discussed wherever necessary. The analysis is presented in four parts for reasons of clarity. These are: 1). Flow about a circular cylinder without a wake in free air (rectilinear flow). 2). Flow about a circular cylinder without a wake in a channel. 3). Flow about a circular cylinder with a wake in free air (rectilinear flow). 4). Flow about a circular cylinder with a wake in a channel. The presence of the wake is simulated by a suitable arrangement of sources. The two primary purposes of the analysis are first to simulate the wake by a potential flow, and second to preserve the shape of the body in the channel as completely as possible. 1). Cylinder without wake in a simple rectilinear flow.—This Case is derived by combining a doublet with rectilinear flow and is well known. The results will simply be listed here without derivation for a circular cylinder at the origin of the coordinate system (the cylinder will be maintained at this location throughout). =39— The complex potential is Cc F(z) = Uz += and if we let the doublet have the strength = m2 ¢ = Tr ™ Ub then b- F(z) =U a+ ~---- (3) The potential is _ Zz Glug) =e Jl +Zzl =e - (3a) x +yY a and the stream function is pe V@y) = Uy Jl =f rr re (3b) x + y7! The streamline ¥ = 0 lies along the x axis and on a cirele of radius be The velocities are u., VG? - 2) y= 2b" ? . (2 + y?)? © Ge + y*)? -~-- (4) tr . |, -/b) 7 |, , Be. b) 7] 7 - | (2) Joos © _ --h+Q) sin © On the cylinder r = b and =O 3; = «2 sin O oF be) U The pressure coefficient is obtained from the incompressible Bernoulli equation as 2 2 2/2 — oA\_>4 4 2 Cp ey. ot, aoe - yo’. /b fe 25. cane P . me (x2 + ¥2)2 (2) + 2(2) (eos*O - sin”@) and on the cylinder C= 1-4 sin“ =A,0= 2). Cylinder without wake in a channel of height a.--This case is obtained approximately by placing an infinite row of doublets on the y axis and combining the resultant flow with rectilinear flow (©). If the doublets are spaced a distance, a, apart, the wall boundary con~- | dition at y = = 5 is satisfied, but a slightly distorted circular cylinder is created. Here the complex potential is al i F(z) Un + a7 2 Fs ina 1S - ina = Uz +z coth & “-=-=- (5) The potential is _ sinh on G UK bn (5a) cosh a - Gos ale and the stream function is , & sin i (5) = Uy ~ a a 5b cosh alz ~ Cos ame condition. The velocities may be written as fa ~- cosh ans cos 2s] sinh Eb s sin ay = 93 EL ae Ua [eosh ans - cos az) u Ua [eos ae = cos om We now wish to evaluate X which determines the size of the cylinder in relation to the channel. Probably the most critical dimension when comparing this case with case 1 is the thickness or . Maximum y coordinate, so we would like to maintain this at a constant ~il= value, be To do this, use equation (5b) letting ¥ = 0, x = 0 and y = b and solve for“. Then rigorously (4), = ati 2 tan (") meee (7) Ua a gives the result desired (the form for the doublet strength parameter used here is written because of its convenience later). If this ex- pression is expanded and only the first term written, the strength is we) Ua which is the value used in reference (5). If (7a) is used the y semi- , an* ( B/? ----- (7a) diameter varies with ( ) and this variation can be expressed by the relation 2 a a a In any case the x semi-diameter is given by the relation fe] Be(B) coat [AE ea] wee e yo ) Equations (7), (7a), and (8) are plotted in Figures 64,65 and here the doublet strength required and the distortion of the cylinder as a function of b| are clearly shown. To further study the shape of the cylinder expand (5b) for ¥ = 0. 20x .. amy , |e | a any. Here cosh a cos “2 + |e |x sin a and if this expression is expanded and rewritten, we get + shy ea lis.a (z)* ~ 12.2 () ee, | If the size of the cylinder is such that anywhere on it ae <i (a maximum value for this report is 0-01) then ote is of the same order, from equation (7), and the following can be said. On the right-hand side of the above expression the 445 order terms are the only ones of any importance, and they have a maximum value of about 3% of the terms on the left. On the left, therefore, since Eas 1-is the equation of a figure very near to a circle of radius b = VaR. This gives a physical interpretation to the value for 4 given in (7a) i.e., 2 _ eu Aw TEe The velocities 5 and q are not so easy to interpret in relation to those of case (1), but if they are expanded in power series, the second order terms give expressions identical to those of case (1) with pps) order terms providing the first corrections. 2a). A comparison between velocities in cases (1) and (2).--Velocities on the lines x = 0 and y = 0 can be profitably compared here as an indi- Cation of the blockage. The doublet strength ez) will be used here Va i for complete generality, and in fact will be used exclusively hereafter. u) _ /2 u a ah Let a( 7] = ( 3) el -(G) ain tet of channel. walls Then . rb , . A(z) = 2a a ated, u X=0 a fa ~- COs ar] vra pe (9) end y(z) = (e/a)? - 20> _ tan “e A Tao (x/a)2 a [cost aie . 1 5 where we are interested in the regions 0 <y/a < 1/2, 0< x/a<od, O0=b/a<1/2. Since these quantities obviously approach 0 as (v/a)? > 0, a more significant form can be written as P 1b | 2 27 tan — ) ai) ~ UT ba =| ie coo - Gye on ten TEI = = = = (9) 2 {27 tan ane (2) (5) 0° ba = 1. — atx * AY. In addition when considering small values of x/a and y/a it is convenient to expand (9b) in power series with the result that Tb , 2 tan 2 |tan — 20 a By . le LC 1 Te |e 2n a a M=/ and 4. (9¢) a\2/x) __ |e 1, 72 tera S 2n (3) (8) 7 m ~*) GAR S wm |e Kan (x/a)” a a fcc where C,,, and K,, are constants of the expansions. Using (9b) and (9c) the two functions have been computed over the range of interest and are presented in plotted form in Mgures 66 and67, | The limits: shown there at x/a = y/a = 0 can be clearly seen in (9c), since, if we let b/a approach zero faster than y/a or x/a both limits are ah ipo (Foi). (8) (Bp = & ta=% Y=? 4-0, 4-0 but if b/a, y/as x/a all approach zero at the same rate then the limits become ‘ay? fa on? a\=,/a The range of practical interest on the Figures lies in the areas U oO where y/a and x/a are larger than b/a, since elsewhere the coordinates are inside the body. The effects which are indicated. are generally referred to as "solid blockage", when b/a = 0. Although these expressions specifically represent results for a circular cylinder, they may be used to illustrate the general effect of finite body sizes and can be compared directly with results given in Reference (4) which has considered "solid blockage" for a general body shape in the limiting case of very small size. For instance Figures 66and 67 may be compared directly with Figures 6 and 7 of Ref- erence (4). It is seen that the curves for b/a = O correspond directly to the blockage increments (Fo) indicated there, but that as soon as finite size is considered marked differences occur. The most notable is in the velocity increment at the maximum thickness of the body, which differs from the value at b/a = 0 (the ‘reference would show this) where b/a. is finite. Such differences are of considerable im- portance when high subsonic Mach mumbers are considered. 3). Cylinder with wake in a simple rectilinear flow.--The real flow behind a cylinder cannot be represented by the potential theory since the irrotationality condition is not maintained throughout. However, the . effects of the wake upon the irrotational part of the real flow can be ~/,5 approximated by the introduction of singularities near the body on its downstream side. These create a "displacement thickness" behind the body, which influences the rest of the flow in a manner similar to the way the wake influences the rest of the real flow. However, the pressures and velocities in the potential flow downstream of the cylinder become meaningless in any region where the wake has been dissipated into the real flow to an appreciable extent. Considering circular cylinders, the addition of singularities in the free stream (rectilinear flow) is easy, because a system of sources and sinks, say, can be set up which have a circle as a stream=- line, and then this solution ean be superimposed on that in part (1) using a circle of the same radius. Because of the linearity the circle streamline will be retained in the combined solution. In the channel case however, the source sink solution will give a body streamline slightly distorted from a circle and different from that of part (2). Therefore, superposition of these solutions will not necessarily yield results which can be compared directly with the free air case. If the two shapes are not grossly different, the super- position is plausible. In this regard, the effect of one source behind the cylinder is first investigated, and then a pair of sources on the cylinder surface are studied. It will be shown that the latter can be matched to the experimental results much more closely. In this section the problem will be studied in free air and in the following section, part (4), the channel case will be attacked. ~hb= The flow about a circular cylinder due to a source of strength Q@ at 2 = ¢ has the complex potential F(a) =Qin(2-c)+Qin(g-%)-Qmz 2 ----- (10) The potential is L i Ce ee and the stream function is t= tna & -~-=--= (10d) where v4 . 2 2 2 4 =r cos 0 (r* +b”) - 2(e +8") ¢ Bay (x +y~-b*) =r sine (r= b ‘as / 2) we Of ul y When r = b or y = 0, x<e The velocities are 7 2 2 we. 8.2 =[,8 S O°" "Bs pe fo $2 - 9 33 These solutions can be immediately added to those of part (1) to Give the result desired, as follows: 2 a re) = 0 (2 El om le =o @-%) i 2 Vo2 + p2 = b at + foe he get) van ee Y= Ai a *Q@tant & = Uy - 3+ Q tan a eats a) 4 fog tw ane i i) + he? el Le o La sa) ---- (12) the cylinder (r = b) =o. Wee 3 ¢ = 05 U 2 sin © b BET ae os The body downstream of the cylinder formed by the source is defined af og os by the streamline ¥ =7Q, and as x+oo, the value of y for this stream- line approaches EB, so that the width of the so-called displacement thickness becomes: ais far downstream from the body. This fact gives a method of picking a value of Q/U to match experimental data, obtained by wake surveys, from which a pseudo displacement thickness can be computed. When Q/U has been picked in an attempt to simulate a real flow by the above equations, the only remaining unknown is ce Therefore, one more condition in the real flow can be matched in the potential flow, and since ¢ is the location of the source, the logical thing to do is to match some pressure on the cylinder surface. This pressure mst be upstream of the separation point but should be close enough to it to be influenced profoundly by the wake presence. A convenient point to use is the maximum thickness point where @ = 7/2. ~L8= For this case from equation (12) we can write me) 2. (thy ~ p+ iy = -\/1 = Cy (72) (§) which ean be solved for c/b since & and c,,( 7/2) ave picked from experimental data. This method and several variations of it were used in attempting to match the experimental data of this report (Figures 33-47) and a sample result is shown in Figure 6& It was soon apparent that to match the pressure distributions on the cylinder using one source is generally not feasible; the closest approach is to let c = b as was done in the example, but even here the matching cannot be complete. This last statement can best be illustrated by a variation of the above method. Here, match the following experimental quantities C,,(8) at © = 7/2 and C,(0) at 0 = Oo where @, = angle at which separation occurs. Then from equation (12), it ean be shown that (o/o)= a+ Va = 2 | 1 2h - reba i= Spd] one 0 A Sana Ma =o (Z) - ate, a= 0a] Now obviously A must be greater or equal to one, and a few where Computations will quickly show that for the data of this report at . least, Gg in the above expression for A mst always be smaller than the observed Qs if A21. When A = 1 the closest matching is obtained, but it 1s still not very good. Therefore, the best possible position for the single source is at c/b = 1. =, Je Since one source fails to match the wake influence properly, the next step is to try two sources on the downstream surface of the cylinder, symmetrically spaced about the x axis. They will be lo- cated by the coordinates (b, + )» and the velocity on the surface can be obtained immediately by the simple @ = 6° - @ (see diagram) / From equation (11) t ¢ (=) - sin 8 6! Qh4 "b= bcos 8 C) so that g * q (22_] _ sin (0 = 9) x' Qh, b = bcos (e' ~ g) nb Dropping the prime on the new coordinate system and using two sources and the rectilinear flow we get (52) e=m2einge+& : sin (9-9) , sin (0 +9) | bU 1-cos (@=-G) l-=-eos (6 +¢ = : lL --20m0 [1-8 | cagteas)| ~--- (3) In matching this new flow to a real case, two parameters are again available; a and §. Therefore, for example, the displacement thickness and Cy ( 7/2) can be matched as was done previously (these seem to be the most logical quantities to use for this purpose, and so will be employed exclusively hereafter). Since the displacement thickness is © to be used to find the source strength, it might be well to write down in detail here the relations concerning the displacement thickness which will be employed. For the potential flows, the displacement thicknesses are clearly defined by the following equations =50= (& _ }? se 2b! pree air 2b 5 B 2k |2mng|/_2 |. 2b | 2nng] || a 2b channel. 2b u 1 + ate ab u 4 where n = number of sources used to simulate the wake Jo= dynamic pressure far ahead of the body q,= dynamic pressure fer behind the body The second equation can be derived easily from relations appearing later. n is of course 2 for the case under consideration. For the real flow in the wind tunnel it will now be assumed that where here Go = free stream dynamic pressure without cylinder qy dynamic pressure downstream of cylinder outside of wake Further, it will be assumed that the ratios do/a, in the potential and real flows are equivalent for the matching to be done. Therefore, we can immediately write from the above relations & i dh, bU 2TIn(b/a) Io 1 x 2a. \ oF “ia” “1 an - 1 which will be used to pick the wake source strength in the potential flow from the measurements in the real flow. The value of q/qo to be used in an actual case must of course be picked with care, but no basic difficulty should exist if the working section is reasonably long. If the wake has entirely dissipated, the ratio must be 1 with the velocity increment being replaced by a static pressure loss, and here the simile breaks abe down. Probably the only thing to be done here is to replace a; /a 3 Po = Pi a by 1 + where p is the downstream value of static pressure. To return to the main discussion, Q/bU may be picked from (14) and then § may be chosen if C,( 11/2) in free air is known. This can be computed from the expression Qfot a nem (15) E - 1/2 (= CTP} which can easily be derived from (13). The only restriction here is cos G = that eos @=1 so that as G,,( 1/2) approaches-3, the theoretical value for no wake, Q/bU mist approach zero faster than the denominator in (15). For the experimental data available, this condition is easily met. In Figures 69 and 70, two cases are presented in which experimental and potential pressure distributions are compared using the method just outlined. It is seen that the matching, up to the area of sep~ . aration, is quite good, and that further consideration of the wake Simulation by this method is probably justified. Therefore, the general velocity expressions will be worked out, and the correspond- ing case in the channel considered. The complex potential for this soures flow can be expressed as F(z) _ kn ES e i(6) + Go = *) 2Q r where 1s Tos 9,5 G, are related as follows (see diagram) r? = x + pe ~ 2rb cos (@ =f) 3 r/ry * an (a ~ a 5 =r +b -2rbcos (+9) 3 x/ry = == ee a (X,4) The potential is Ms yh Z . rz ¢ 2. Ln r The stream function is 3 oe b Q> The velocities can be obtained easily from the transformation of g equation (11) lettingr =r',c=b,9=0 -@. First let c =b, whereupon Uy/Q and ue/Q become ur r= be . be . 2b sin 0 , Q r(r2+b2-2rbcos 9) ”* & (c* + BY - 2 rb cos 0) then apply the transformation and drop the prime to get. Ur re -b? Ye _ 2p sin (0-9) Q 2 * Q 2 rr rl Adding this flow to its image in the x-axis and adding the rectilinear flow solution (4), we get the general velocity expressions ~ 2 7 iz 2 _ x r r Ur (2)? 29 (z) -1 (E)"+ 1 - 2 £ cos 0 cos g 7 = [4 -\z) | cos © +i x3 r/b ry r 172 dL = | p(16) 2 | (2) *, 1) cos $f - 2 = cos 6 | wee (a+ (2 sin 9 + £2 2 sin 6 b b we which represent the velocities in free air of the flow proposed to Similate the real flow with wake. The next step is to investigate the Similar flow in the channel, after which the two can be compared. =5 3m 4)e Gylinder with wake in a channel of height a.~=-To determine the flow in the channel, the precedure must be as follows. First, set up a system of sources like that proposed in section 3) with appropriate images. Then the complex potential will be #@) SS fa| (2 =» cos 8) - 4 (o sin # + na)| 22270 + fa[ (2 ~ bcos @) +4 (b sing ~ na)| ~ fo| 2-4 nal This will give a body in a channel of width a, due to the source flow. Next, another system similar to that of section 2) must be added to cancel out the flow at x = ~codue to the infinite row of sources, since ‘the disturbance at -oomust vanish to satisfy the boundary condition. Finally, the solution in section 2) can be added to give the complete solution. The main problem is to adjust the solutions so that the shape of the final body will be as close to the circular cylinder of radius b as possible. Now consider the complex potential given here. If we let it Z, = z= bcos $= ib sin g Zo =2=becos $ +i b sin g we can write F(z) as Fa). hy sinh 2a ln sinh 12. fy sinh M2 (17) and writing the real and imaginary parts we get ee (y = b sin p)} a +3 3 f cosn 27 x - bcos #) - cos 2 y +b sin p)|-(272) 3 fa & a 31 cosh = ans = COS arr} =5 hn and 4 “1 ten a 5 Y= b sin 9) =i | tan q (y+b sin ¢) | 3g * tan tanh & if [x - b cos 9) * tan tenh J (x - b cos 9)| ai tan ue ~ (17b) ~ tan tanh 1 a The velocities in the x and y directions can be written as : al ~~ au. sinh = a abst am Q [cosh 4 aN xb cos s @) - cos 22 = (geb sin 9) sinh & ( x - b cos gb) fe a cosh aD (nb eos ~) ~- cos an (y+b sin #) sinh aa ” faneh Sts any cosh a 7 cos | 5 Soto (28) tr : 2u. sin 4 (y ~ b sin 9) 7 27 8 [eosh 22 xt cos $) ~ cos an (y-b sin 9) sin = an (y +b sin 9) fe mee — cosh 2 (ab cos %) = cos an (y+b sin 9) sin atte ~ aux. aay [cosh a 7 60s a ~ When y = a) x =} 3 and at y = 0 and on the cylinder to the Source singularities = =fT> To get an equation which represents the shape of the cylinder, we must let ae Tl and combine terms in (17b). When this is done, the following relation is obtained. ~55e tanh” (x-b cos @) + tan” TB sin a) a(t ) = a 2 tan 2/" 1+ tan (2 sin 9) tanh” x (x-b cos 2) -~ == (19) 2 ten tanh (x-b eos ) E + ten (2 sin 2) et 1 + ten®(@ sin $) tank E(x-b cos 9) This gives the relation between x and y on the body in terms of b, @ and a. In the strict sense of the derivation it only applies for x<b cos 9 but it can easily be shown that it actually applies to the whole body. The intersections of the cylinder with the coordinate axes can be obtained from the relations 2 = 9? 45% [te CF), 1 +g? end + 2A + 2 t 2 2 Yy*0- — — (19a) ’ 2F(1 +77) _ where ¥? = tanh” (tb/a\ cos g) and 7° = ten” (/b/a sin g) Two things should be noted here. First, we now have a body sym= metrical about the x-axis but not about the y-axis, and second, the size of the body relative to a cannot be adjusted by varying the source strength, since Q does not appear in (19). Since Q is assumed invariant from the free air to the channel case anyway, it does not matter. ‘The cylinder size can be adjusted in the next step, as will soon become apparent. Equation (19a) is plotted on Figure 72to indicate the body shape. =56— Once the flow due to the source system is know, the rest of the flow can be constructed. From equation (18) it is seen that, at very lerge negative values of x, the velocity u approaches =< a8 while v¥ approaches zero- Sothe first thing to do is to cancel out this velocity, since the disturbance at x = -comist be zero for the final flow. This is done by superimposing a system similer to that of section 2) upon the source system. The velocity of this system at x = ~cowill be H amg and the doublet strength in it, “, will be undetermined. Therefore its complex potential will be F(z) = + eth ww ee (20) The shape of the body produced by this potential in the channel will be close to a circular cylinder, ‘but will be unlike the shape from the source system. Therefore, the addition of the two systems will produce a third body of still a different shape which will also be slightly distorted from the circle. On this last cylinder, we would like to have y = b when x = O, and this can be done by picking it as follows. | The complex potential for the combined flow is (17) + (20) or F(z) 12, & coup UZ 4 m2 son 22 ey ay = 2 + & coth 1 + A sinh + & sinh = - A sinh ™ ~(21) The stream function is s Sy Y ¢ Ae (4) sin © + tent tan © (y - b sin 9) & 2Q cosh FE ~ cos A tanh © (x - b cos 6) — (21a) wr Ty tan = (y + b sin 9) tan + ten” a gp - ten a tanh © (x - b cos 9) tanh =5J= and on the body when xb cos @ , ¥/2Q =1T Now letting x = 0. y = b, 0/2Q =71, we ean rewrite (21a) as a 2 7, 1 _ =1 -1 =1 ee 2 +2 5 — sam Tl & Vii» & | + +t where ~F = tanh (~ a cos $)s 7 2s tan? ( sin f), V= _ Thus, the value of doublet strength which is desired can be written as U 7 = tan 2 a wtan | FAA] aaf |] ----- (22) efi +z] | ‘ g Some representative values of /_/2Q have been computed and are : g plotted on Figure 71. Note that for ¢ ~ 90°, //2Q has a finite limit as b/a—~1/2. This limit ean be expressed simply as fla +74 él, va “Faye ep a) Q°-2 This means that we can construct a flow with a finite doublet strength in which the cylinder actually touches the walls. This naturally cannot be done when the velocity U has been added to the system. To get the x coordinate of this body for y = 0 and x < 0 we let y—~-0 in the expression for the stream function. Then for very small y the expression becomes 1 an or 20 tanh E (xb cos 9) [ a+tan?(rib sin 0) Tey(Z)- y i +y| 3 ib ] cosh = “1 tanh” E(x cos ¢) + tan ony sin 9) ~5Sa which can also be written as an 4. 29 |g y(Z)+ y| cosh SE. 3 3 tanh a tanh a (x-b cos @) E + tan“("2 sin 9)] tanh* = (xb cos g) + tan” (tb sin @) a -¥ -Ti =! + 2TI Finally canceling out the y's we obtain (Ss (a 1 2 tanh Dxeb cos 2) E + ten? sin ) sinh “(He ) tanh us tenh” E(xeb cos %) + ten sin ~) a which gives x/a in terms of b/as p and <=. 20° The resulting value of x is the coordinate of the leading edge of the body. We now have produced the desired source flow in a channel about a slightly distorted circular cylinder, and must now add the free stream velocity U. This is equivalent to adding in the solution from section 2) and now the complete complex potential becomes F(z) = [ + an | z + {Ay ou" ] coth ™ + 2Q EE sinh Ed +n sinh =2 fy sinh end the stream function becomes ; +, SI a 1 +28/z -\/2 +( (2) sin = Ua Ua arg cosh amix - COs any. a a 1 : AY & tanh es cos 9) tanh xb cos §)| (24) ~ ear an - - (24a) TIX tanh 2 5 Qen and on the body when x< b cos q, a = qa 2 The ordinates of this final body can be immediately defined. (7) 20 = b by definition since the doublet strengths have been picked with this as a criterion. Noting that (24a) is of exactly the same form as (21a) we can write an equation like (23) by inspection which defines (x)y29 on the body when x=< 0. This is th Va, al) \ Ua st wh” (=) Va t anh 2 ° 2 tanh zg (x=b cos %) [2 + tan @ sin d) | tanh” yi (x<b cos f) + ten (2 sin @) 211Q + Va -~(25) which gives x/a in terns of b/a.g, and Q@ No attempt is made to write the explicit relation x/a (b/a, g, Q) but a typical solution is presented in Figure 73 compared with the solution of equation (8). This indicates that while the body is slightly more distorted than for the case with no wake simulation, the increase is not significant. The velocities for this final configuration may be most con= veniently written as pales ay -[2 +] anf + (4) (38) co oe 2 (a, 28) Ua Ua 2N1Q/ \ Ua [cos - cos any] anh SUE asp SW b= ol = (a) (28) | re + ew) 4 @ a [cosh = cos S| -~=-=- (26) To check experimental data, 0. and Q must be picked as in the free air case. Q may be computed from the equation Ya 2 Io - ~60~ and @ mst be found by solving [| yzo Using an experimental value of =6 ¢.,(17/2). The doublet strengths for any case may be taken from Figures 64, and G7 or computed from the equations. Once a solution is computed in the channel, it should be compared with the free air case using the same values of @ and @. Time was not available to include any extensive computations of this sort in this thesis, but they are quite important in testing the validity of the method, and should be carried out to some extent at least. Two short calculations were made and their results are indicated in Figures 74, 75 and 76. Figure 74 illustrates a typical blockage calculation at x = 0 with wake. Note that the parameter (a/b)Au/U is used rather than (afo)*a u/t which was used for case 2. This is done because the latter parameter has a singularity at b/a = 0 due to the wake terms. Notice that here there is a double limit as y/a and b/a approach zero, which can be compared with 2119 Tb? and this the double limit in Figure 66. At b/a = 0s (243), = in conjunction with equation (14) gives the result that [42 | zi = Tly-0 472 U %=0 where u, is the velocity outside the wake downstream of the cylinder. However, if 2 and z approach zero at the same rate (243) x20 an or twice the above value. More calculations of this nature should be made to illustrate the general effects of wake size on the rest of the flow. ~6l= Figures 75 and 76 illustrate two comparisons between the measured pressure distribution at the channel wall and the theoretical value computed from equation (26). The correlation is reasonably good although not perfect by any means. It was found in computing such examples from the data that the quantity 41/deis often not well defined numerically, and this fact contributes to the differences on the Figures to a large degree. It would be well to make similar computa~ tions on the remainder of the data available to further check the correlation. =62— & Gheck on the Importance of Gylinder Distortion Since the circular cylinder is distorted slightly in the channel by the analysis given here, the effect of distortion on velocity should be cheeked. This may be done by considering the flow over an elliptic cylinder. Using elliptic coordinates, the potential flow about an elliptic cylinder in a rectilinear flow can easily be derived. On the surface Vn Vg of the cylinder, the velocity can be expressed as | ¥ To 2 oe ~ (b + ¢) siny it |®° cos*y +e ain?’ — - —~ QO He where the semi major axis c fe) al the semi minor axis it coordinate perpendicular to the cylinder surface xy So ii = ¢ cos » y = b sin For our purpose it is sufficient to check the velocity at x = 0, y = bs 7= 1/2. Here, the velocity becomes - 7 = Bis Uv e and to check the distortion effect, let ¢ = b (1 +7) whereT< i. Under this condition the velocity becomes, with higher terms neglected Vv - | = (2 =7+ 2) <2 72 and the pressure coefficient is C, (3) =-3 + 47-527 =63= Thus a 1% distortion in shape will create about 0.5% velocity distortion on the surface and a 1.5% Cp distortion. For our case a 1% shape distortion cceurs when b/a = 0.2, and for such a size the change in velocity due to the blockage is about 30%. Therefore, it is clear that the amount of distortion introduced is quite negligible. Le Re Ae De 7° De ~bh= BIBLIOGRAPHY Description of the GAICIT 10' Wind Tunnel, The Model Suspension System, General Facilities and Model Specifications, Revised September 10, 1942 (Unpublished) GALCIT Two-Dimensional Tunnel Installation and Test Procedures (Unpublished) Prandtl, L. and Tletjens, 0.G., "Applied Hydro- and Aeromechanics", MeGrew-Hill, 1934 Thom, Ae, "Blockage Corrections in a Closed High-Speed Tunnel", R.& MeNo. 2033, Now, 1943 Streeter, V.L., "Fluid Dynamics", MeGraw-Hill, 1948 Goldstein, S., "Modern Developments in Fiuid Mechanics", Oxford, 1938 Thom, A., "An Investigation of Fluid Flow in Two Dimensions", R. & M. No, 1194, Nov. 1928 Lock, G.N.H., "The Interference of a Wind Tunnel on a Symmetrical Body", Ro & M. No, 1275, Oet. 1929 Allen, H.J, and Vincenti, W.G., "Wall Interference in a Two-Dimen- sional Flow Wind Tunnel with Gonsideration of the Effect of Gompressibility", A.R.R. No. 4K03, Dee. 1944 “252- Cylinder Separation CDi Cp, at x/d C, +7, 65 2759 m+, 6 tee | 387 | Base G, +7 85 603 wits ae c+ 4, 65 and 85 -907 ers ae C+ Thy 65 mu | 1a | 3055 Co + TM. 65 and 85 1.243 use oss C, +f, 65 oThT C. + 1, 55 2805 C, +1, 85 2632 Cp, = pressure drag coefficient ( equation (1)) Cp, = wake drag coefficient ( equation (1a) Figure 63 TABLE OF PRESSURE AND WAKE DRAG COEFFICIENTS FOR TWO-DIMENSIONAL WAKE CONFIGURATIONS | ~—65- : “ Pf } | a | eae | , wee —— | ed oe L811 NGS POAPTING | | patito cf ita es | AOSUSTOBL E ‘ ‘ re ) ¢ 1 Bo . at \ 1 ~ A, LLL Le. C- OWA FECTION TO | calf 17K INS ae og aa te Ribs hiaclacael icy esa: " Sag MEERUT ’ i a : ZALLLIALLLV A LIV LL ALT ALLL. cae Z. cule wanay AFA ae VS AF AE Ge (LLL LZ ' rr waa nro she prc Pena PME FT L — ~~ ECT/ON fi ae CEILING: L h | | STANOARRO TUNNEL io oe Vo Ly \ : 4 : t ) ile tee | Og Nc eae LTE ahs fee 3 | i |€% | ee ; | ‘% | . | oe ) | | ' ad 4 | | | | | | ~~ ‘ | YO 42? PZOW SF INOICA TE . x >> Ody : é 4 ae ITATIC OR FICE) LOCATIONS | “f 4 cA | | | | x Ons , ay TT & 3 4 et ie (Fi 008 é Ceydsve) is ee « ellneeen ~ “~S | / | | | | 5 RT : : 7 } ees, | | | STRUTS \ h / Oo Tle | GLO I /\\ WINE WAKE SURVEY NS | | I { / | i | | | / v4 Ne | /RaKE \ lM Sraric OeMrr1c€ | = =| Ibe # i Ve A Se I \\yb Lacariow | U M Y | we iy | Tea RE e + | j ; j | GEARING POIUSTIIEN T aie j i un i | ~ ae \ | -F y jy . alt JeVvew Hl] | Sov 5 7A86 E Vi \ LOCATION OF Piet i | ® N DEP fe { at |) TATHC CR1FICE ; a4 ( | REVOLVING a {ma \ va i RIAN f faus | END PLATES ) HO] ea att. « ee | \ 7 v sf iS . ys : GL AOIUS TAE L. & i \ Z a . . 7 4 sae: of I ee i | | ; { ; ; 4 4 we we | eis | 4 sé f } ye $ we Z Ba ie Lake SUPPORT FRAME | | | ‘ | (o) ms a | | | 4 : ise | : be a 9° 0 lg st ae | y | | Ye / LERO SCREW ; Eee i ee ‘ | | ae i Be | eve he Se 1 ; to v4 : ficor \ i { | / ae a 1 ( asad x ieee f f { ITANOARO tae eth 4 mo = {- ; as A “ Pd: et tt 77 PIT IVI WI VII Tt ZLLELZATYTAZATZ ILA ZL IV ALAC L LZ LV ZZ LAZIZ IILALIL IV LI JO’ WorRKING FECTION ea Tee ke Ne BNE tea i at ag pa] Bch z } tate r | : Lap a Eee 2 aii { ; | 3 } ‘ — Hl] <enee oF Verric At , \ Le he. , ae | DEFLECTOR VANE , te OR | 30 : ae peared 4-4 | | ; Fe oe eo ' : FROT YUNNEL g t. t | C/F/2E } TOLERANCES + .010 on - 4 Vt STANOARO TUNNEL tan | ; UNLESS OTHERWISE NOTED J ; ie! | FHF Scace: Ha'=/ : oe Seeocker & CHAIN Seace: f= 7" if ee : | “o/ee/ ge AN0 NOTED ay 7E VV ; i v \TERIAL MISH |HEAT TREAT] ORARTSMAN | CHECK APPROVED | DOWN STRER IA Mi i $ Bem GOLCIT Owe | MATERIAL Fl ee AT AT fi AFTSMAN | CHECKED ENGINEER a i Ng TE ed Th ae: a | GUGGENHEIM AERONAUTICAL | CALE ea ee SSE ae i’ ra Piedad 7WO- LIA EN SIONAL TUNNEL ; ; ; Hj a * CALIFORNIA INSTITUTE OF | Seercr SHowive Twoe-Wnens/Onal WoRkINe IECT/ION ee Cane Feat lAbGEMOLY fee ai TECHNOLOGY Tauie SS care ¥ . a } ae Le ie — TUNNEL WALL CIRCULAR CYL INDER- | | 18.0 Vv grt Tt PRESSURE ORIFICES 36.0 TOP VIEW I~ at > a5 fe 12 Nore: ALL DIMENSIONS END PLATE iF Are In INCHES CYLINDER C, Pig. 2 Sketch of Circular Cylinders a SIDE VIEW W/ND —— eee DIRECTION 7B oO fo) Oo 0-—0-- o—o—- ro) fo) \ ° ° Lf Awe 4-6 TOP ROW SECOND ROW MIDDLE _ 12) | oO | ~* | © | ° Row FOURTH ROW BOT TOM ——— ROW Oo— oO 4- NORMAL END PLATE ORIENTATION DIMENSIONS (N INCHES O ~ ORIFICE Fig. 3 Sketch Showing Endplate Orifice Locations Se Sense epens Mawes Fame! rea, Soa F, i ht i fe or Ens Fete a re cpg ce a pocorpet on on ion eer ewes a t ies sare fed oe eres wid wld i LING. ¢ CUAIAL EAR Ed. ich g MOUNTED 4 GA NG tA B fe i i ‘ sient tate efecee + ae i ! + RSE i i | f é oe fap AS TRAVE: 4 i ’ OUT Hi, Se FY PRE e PRAMO FE On. os RR ele a = i 3 nt et a ae on r £ gm ard - 4 Fig ae Si a Se Betceee i tt is esed neue 7 itt see teheaunal i f i t ' check ~73>- oh & JAX CA habia AAs LIAN ERS! a we ON AR VBE} BURE OL ny a4 i fee pe... caeep tga mane § i i: it ae omen 4 ‘o- 2 4 t ag My £ 4 t ‘ ci £ i ue SAT? i H : is 3 aK E: 2 Be VN ’ fog Of Rake Static Pressure Tubes * Calibration 757 geass Gate errniaeses seszeczssee Seas skeen eee eats ceges tncaraecce saeeeess ee sages aes Eeeee + {4 cpirhht rT ereagseee ieee einai mee et sosteene wes a4 + TE sib be ~7 9 a + tt i af Es + ~“G2- peatned t 1 J. +H ana if ty 2 BRA is LETT . eb eaaea ao wae mat iviear an i 1 i is I 1 tft ti EEE EEE ET ee se es WO: Hy. on ay, ey ‘s Wb aaeess Bere eEaE apiereaar -~87- yee ped Gane as Ht ate -89- ya F asd he CES: f. 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