----------------- FILE NUMBER 105----------------- 1. FLOW TITLE: CASE 0232, 0231; HOFFMANN, P.H. & BRADSHAW P. "TURBULENT BOUNDARY LAYERS ON SURFACES OF MILD LONGITUDINAL CURVATURE" 2. REVISION DATE: NOVEMBER 1, 1981 3. EVALUATORS SIMON, T. AND HONAMI, S., STANFORD UNIVERSITY 4. EXPERIMENT LOCATION AND DATE IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY DEPARTMENT OF AERONAUTICS LONDON, ENGLAND. 1978 5. ABSTRACT OF EXPERIMENT MEASUREMENTS WERE MADE IN THE TURBULENT BOUNDARY LAYER ON A WALL WHICH HAS MILD CURVATURE. THE BOUNDARY LAYER THICKNESS TO RADIUS OF CURVATURE RATIO AT THE START OF CURVATURE WAS APPROXIMATELY 0.01 . THE DATA INCLUDES PROFILES OF MEAN STREAMWISE VELOCITY AND THEIR INTEGRAL PARAMETERS FOR FIVE STREAMWISE STATIONS AND PROFILES OF SECOND AND THIRD ORDER FLUCTUATING VELOCITY QUANTITIES. FOURTH ORDER QUANTITIES WERE PUBLISHED BUT NOT ENTERED ON THIS FILE. THE TUNNEL HEIGHT WAS 0.127 M AND THE SPAN WAS 0.762 M. THE LOCAL STATIC PRESSURE USED IN THE MEAN VELOCITY MEASUREMENT IS DEDUCED FROM THE WALL STATIC PRESSURE BY USING THE EULER-N EQUATION ASSUMING POTENTIAL FLOW: (PTOT-PSTAT)/(PTOT-PSW)=EXP(-2*Y/R) AS DONE BY SO AND MELLOR. THEN: U**2=2*(PTOT-PSTAT)/RHO WHERE PTOT IS THE LOCAL TOTAL PRESSURE, PSTAT IS THE LOCAL STATIC PRESSURE, PSW IS THE WALL STATIC PRESSURE, Y IS THE DISTANCE NORMAL TO THE WALL AND R IS THE RADIUS OF CURVATURE OF THE WALL THE AUTHORS PRESENT PROFILES UPSTREAM OF CURVATURE. THE UPSTREAM PROFILE ON THE WALL WHICH BECOMES THE CONCAVE WALL IS LABELED PRE-CONCAVE AND THE PROFILE ON THE WALL WHICH BECOMES THE CONVEX WALL IS LABELED PRE- CONVEX. THE PRE-CONVEX DATA ARE FOR MEAN VELOCITY ONLY, WHEREAS PRE-CONCAVE DATA INCLUDE MEAN AS WELL AS FLUCTUATING QUANTITIES. THE PRE-CONCAVE FLUCTUATING QUANTITY PROFILES ARE REPRESENTATIVE OF THE CONVEX WALL AS WELL. THE PRESSURE COEFFICIENT DATA AND THE SKIN FRICTION COEFFICIENT DATA WERE DIGITIZED FROM GRAPHS USING A HOUSTON INSTRUMENTS HI-PAD. 6. REFERENCES 1. HOFFMANN AND BRADSHAW, "TURBULENT BOUNDARY LAYERS ON SURFACES OF MILD LONGITUDINAL CURVATURE", JFM, VOL. , PART , PP - , 198 . (TO BE ASSIGNED) 2. HOFFMANN AND BRADSHAW, "TURBULENT BOUNDARY LAYERS ON SURFACES OF MILD LONGITUDINAL CURVATURE", IMPERIAL COLLEGE AERO REPORT #78-04, DEC. 1978. 3. MERONEY AND BRADSHAW, "TURBULENT BOUNDARY LAYER GROWTH OVER A LONGITUDINALLY CURVED SURFACE", AIAA JOURNAL, VOL. 13, NO. 11, PP 1448-1453, NOV. 1975. 4. WEIR AND BRADSHAW, "APPARATUS AND PROGRAMS FOR DIGITAL ANALYSIS OF FLUCTUATING QUANTITIES IN TURBULENT FLOW", IMPERIAL COLLEGE AERO REPORT #74-09, 1974 7. INSTRUMENTATION THE MEAN VELOCITY MEASUREMENTS WERE TAKEN BY USING A STAGNATION TUBE TO MEASURE THE TOTAL PRESSURE. STATIC PRESSURE PORTS IN THE TEST WALL WERE USED TO MEASURE WALL STATIC PRESSURE. FLUCTUATING QUANTITIES WERE MEASURED WITH CROSS-WIRE CONSTANT TEMPERATURE HOT-WIRE ANEMOMETRY. LINEARIZATION OF THE SIGNALS WAS DONE DIGITALLY. 8. EXPERIMENTAL PARAMETERS 1. TUNNEL HEIGHT AND SPAN ....... 0.127 BY 0.762 M 2. DEL995/RADIUS OF CURVATURE AT BEGINNING OF CURVE ........ 0.01 3. RADIUS OF CURVATURE .......... 2.54 M 4. TURNING ANGLE ................ 30 DEG 5. DEVELOPING LENGTH UPSTREAM OF BEND ...................... 1.45 M 6. REFERENCE VELOCITY ........... 30.5 M/SEC 9. MEASURED VARIABLES EACH MEASURING STATION INCLUDES DATA FOR THE FOLLOWING MEASURED OR INFERRED QUANTITIES: XS STREAMWISE DISTANCE. M (REF. TO START OF CURVE) CP NONDIMENSIONAL PRESSURE COEFFICIENT. CF NONDIMENSIONAL SKIN FRICTION COEFFICIENT. DEL995 BOUNDARY LAYER THICKNESS. M UPW POTENTIAL FLOW VELOCITY EXTRAPOLATED TO THE WALL. M/S DELS DISPLACEMENT THICKNESS. M THETA MOMENTUM THICKNESS. M Y/DEL995 DISTANCE FROM WALL. U/UPOT LOCAL VELOCITY/LOCAL POTENTIAL VELOCITY. U2/(UPW**2) REYNOLDS STRESS. V2/(UPW**2) REYNOLDS STRESS. U1V1/(UPW**2) REYNOLDS STRESS. U2V1/(UPW**3) TRIPLE PRODUCT. U1V2/(UPW**3) TRIPLE PRODUCT. U3/(UPW**3) TRIPLE PRODUCT. V3/(UPW**3) TRIPLE PRODUCT. 10. MEASUREMENT UNCERTAINTY ESTIMATED: +-5% ON U2. +-10% ON OTHER REYNOLDS STRESSES. +-15% ON TRIPLE PRODUCTS. 11. TAPE ORGANIZATION THE TAPE IS A 2400 FOOT, 9-TRACK, ODD PARITY, PHASE ENCODED, UNLABELLED TAPE WRITTEN AT A DENSITY OF 1600 BITS PER INCH ACCORDING TO EBCDIC CODE. THE RECORD FORMAT IS FIXED AND BLOCKED; RECORD LENGTH = 80 BYTES; 100 RECORDS PER BLOCK; BLOCKSIZE = 8000 BYTES. NORMALIZED DATA ARE CREATED FROM MEASURED DATA AS FOLLOWS: XNORM=(X-XMIN)/(XMAX-XMIN) NORMALIZED VALUES ARE INTEGERIZED BY MULTIPLYING BY 10000 AND ROUNDING UP OR DOWN TO NEAREST INTEGER. IXNORM=XNORM * 10000. THUS EACH NORMALIZED DATUM IS WRITTEN ONTO TAPE AS AN INTEGER VALUE BETWEEN 0 AND 10000. ALL NULL DATA ARE WRITTEN AS 20000. THE EQUATION DESCRIBING THE RELATIONSHIP BETWEEN ACTUAL DATA AND NORMALIZED DATA IS: X=XMIN + (((XMAX-XMIN) * IXNORM) /10000.) WHERE X, XMAX AND XMIN ARE REAL AND IXNORM IS INTEGER. FILE # NREC CONTENTS FORMAT COMMENTS 1 TEXT FILE CONTAINS ITEMS 1 TO 11 OF THIS WRITE-UP 2 14 XS,CP 2E13.6 RECORD 1:MAX VALUES- CONVEX XS,CP 2E13.6 RECORD 2:MIN VALUES XS,CP 2I6 RECORDS 3-14 NORMALIZED VALUES 3 14 XS,CP 2E13.6 RECORD 1:MAX VALUES- CONCAVE XS,CP 2E13.6 RECORD 2:MIN VALUES XS,CP 2I6 RECORDS 3-14 NORMALIZED VALUES 4 7 XS,CF 2E13.6 RECORD 1:MAX VALUES- CONVEX XS,CF 2E13.6 RECORD 2:MIN VALUES XS,CF 2I6 RECORDS 3-7 NORMALIZED VALUES 5 7 XS,CF 2E13.6 RECORD 1:MAX VALUES- CONCAVE XS,CF 2E13.6 RECORD 2:MIN VALUES XS,CF 2I6 RECORDS 3-7 NORMALIZED VALUES 6 7 XS,DEL995,UPW, 5E13.6 RECORD 1:MAX VALUES- DELS,THETA CONVEX XS,DEL995,UPW, 5E13.6 RECORD 2:MIN VALUES- DELS,THETA CONVEX XS,DEL995,UPW, 5I6 RECORDS 3-7 :NORMALIZED DELS,THETA VALUES- CONVEX 7 7 XS,DEL995,UPW, 5E13.6 RECORD 1:MAX VALUES- DELS,THETA CONCAVE XS,DEL995,UPW, 5E13.6 RECORD 2:MIN VALUES- DELS,THETA CONCAVE XS,DEL995,UPW, 5I6 RECORDS 3-7 :NORMALIZED DELS,THETA VALUES- CONCAVE FILES 8-26 CONTAIN PROFILE DATA AT FIVE STREAMWISE MEASURING STATIONS CORRESPONDING TO THE XS STATIONS OF FILES 6 AND 7 RESPECTIVELY. THE FIRST STATION, LABELED PRE-CONVEX, CONTAINS ONLY MEAN DATA AND THE REMAINING STATIONS (WITHIN BEND) CONTAIN MEAN AND TURBULENCE DATA. 8 28 Y/DEL995,U/UPOT 2E13.6 STATION: PRE-CONVEX RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-28 NORMALIZED VALUES 9 28 Y/DEL995,U/UPOT 2E13.6 STATION: CONVEX-1 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-28 NORMALIZED VALUES 10 30 Y/DEL995,U/UPOT 2E13.6 STATION: CONVEX-2 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-30 NORMALIZED VALUES 11 30 Y/DEL995,U/UPOT 2E13.6 STATION: CONVEX-3 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-30 NORMALIZED VALUES 12 31 Y/DEL995,U/UPOT 2E13.6 STATION: CONVEX-4 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-31 NORMALIZED VALUES 13 16 Y/DEL995, 4E13.6 STATION: CONVEX-1 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-16 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 14 17 Y/DEL995, 4E13.6 STATION: CONVEX-2 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-17 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 15 17 Y/DEL995, 4E13.6 STATION: CONVEX-3 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-17 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 16 17 Y/DEL995, 4E13.6 STATION: CONVEX-4 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-17 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 17 26 Y/DEL995,U/UPOT 2E13.6 STATION: PRE-CONCAVE RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-26 NORMALIZED VALUES 18 30 Y/DEL995,U/UPOT 2E13.6 STATION: CONCAVE-1 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-30 NORMALIZED VALUES 19 31 Y/DEL995,U/UPOT 2E13.6 STATION: CONCAVE-2 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-31 NORMALIZED VALUES 20 32 Y/DEL995,U/UPOT 2E13.6 STATION: CONCAVE-3 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-32 NORMALIZED VALUES 21 31 Y/DEL995,U/UPOT 2E13.6 STATION: CONCAVE-4 RECORD 1- MAXIMUM VALUES Y/DEL995,U/UPOT 2E13.6 RECORD 2- MINIMUM VALUES Y/DEL995,U/UPOT 2I6 RECORDS 3-31 NORMALIZED VALUES 22 14 Y/DEL995, 4E13.6 STATION: PRE-CONCAVE U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-14 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 23 16 Y/DEL995, 4E13.6 STATION: CONCAVE-1 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-16 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 24 17 Y/DEL995, 4E13.6 STATION: CONCAVE-2 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-17 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 25 18 Y/DEL995, 4E13.6 STATION: CONCAVE-3 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-18 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) 26 19 Y/DEL995, 4E13.6 STATION: CONCAVE-4 U2/(UPW**2),V2/(UPW**2), RECORD 1- MAXIMUM U1V1/(UPW**2) VALUES U2V1/(UPW**3), 4E13.6 RECORD 2- MAXIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 4E13.6 RECORD 3- MINIMUM U2/(UPW**2),V2/(UPW**2), VALUES U1V1/(UPW**2) U2V1/(UPW**3), 4E13.6 RECORD 4- MINIMUM U1V2/(UPW**3),U3/(UPW**3), VALUES V3/(UPW**3) Y/DEL995, 8I6 RECORDS 5-19 U2/(UPW**2),V2/(UPW**2), NORMALIZED VALUES U1V1/(UPW**2),U2V1/(UPW**3), U1V2/(UPW**3),U3/(UPW**3), V3/(UPW**3) A SAMPLE PROGRAM FOR READING FILE 8 AND PRINTING IT IS SHOWN BELOW. THE JCL IS FOR THE STANFORD CIT FACILITY. CHECK WITH YOUR OWN COMPUTER FACILITY FOR THE EXACT JCL NEEDED. //TAPE JOB TWS$NJ /*SETUP TAPE=1,INPUT=(LIBRARY NUMBER ASSIGNED TO TAPE) // EXEC FORTCG //FORT.SYSIN DD * C TO READ FILE 8 OFF TAPE AND C PRINT THE MAXIMAS AND MINIMAS OF ALL THE VARIABLES AND PRINT C THE NORMALIZED AND INTEGERIZED VALUES OF ALL THE VARIABLES INTEGER YU(30),U(30) READ (23,30) YMX,UMX READ (23,30) YMN,UMN WRITE (6,50) YMX,UMX WRITE (6,50) YMN,UMN C THE NEXT 27 RECORDS CONTAIN THE NORMALIZED PROFILE DATA DO 10 I=1,27 READ (23,40) YU(I),U(I) WRITE (6,60) YU(I),U(I) 10 CONTINUE 30 FORMAT (2E13.6) 40 FORMAT (2I6) 50 FORMAT (1X,2E13.6) 60 FORMAT (1X,2I6) STOP END //GO.FT23F001 DD UNIT=T1600,VOL=SER=(TAPE LIBRARY), // DISP=(OLD,KEEP),DCP=(RECFM=FB,LREC=80,BLKSIZE=8000,DEN=3), // LABEL=(8,NL) // -------------- END OF FILE NUMBER 105------------- ----------------- FILE NUMBER 106----------------- 0.107018E 01-0.205000E 00 -0.119250E 00-0.336000E 00 0 10000 459 9924 693 8321 924 7710 1261 7023 1681 6260 2364 5191 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