----------------- FILE NUMBER 131----------------- 1. FLOW TITLE: CASE 0233; GILLIS, J. C., JOHNSTON, J. P. "TURBULENT BOUNDARY LAYER ON A CONVEX, CURVED SURFACE". 2. REVISION DATE: NOVEMBER 18, 1980 3. EVALUATORS: SIMON, T., HONAMI, S., STANFORD UNIVERSITY, STANFORD CA 94305 4. EXPERIMENT LOCATION AND DATE: DEPARTMENT OF MECHANICAL ENGINEERING, STANFORD UNIVERSITY, STANFORD, JUNE 1980 5. ABSTRACT OF EXPERIMENT: MEASUREMENTS WERE MADE IN A TURBULENT BOUNDARY LAYER ON A WALL WHICH HAD STRONG CONVEX CURVATURE. THE RADIUS OF CURVATURE WAS 0.45 M AND THE RATIO OF BOUNDARY LAYER THICKNESS TO RADIUS OF CURVATURE AT THE BEGINNING OF THE CURVE WAS 0.10. SECONDARY FLOWS WERE HELD TO A MINIMUM USING SIDEWALL SUCTION AND FENCES MOUNTED ON THE TEST WALL. THE TUNNEL HAD AN ASPECT RATIO OF 2.8; THE ASPECT RATIO DEFINED AS THE FENCE HEIGHT DIVIDED BY DISTANCE BETWEEN FENCES WAS 12.0. YAW MEASUREMENTS SHOWED THAT THE CONVERGENCE ANGLES WERE LESS THAN 2.5 DEGREES. THE TEST WALL STATIC PRESSURE WAS MAINTAINED CONSTANT IN THE STREAMWISE DIRECTION BY ADJUSTING THE OUTER (CONCAVE) WALL; SUCTION WAS APPLIED TO THE CONCAVE WALL AT THE START OF CURVATURE TO AVOID SEPARATION AND LOSS OF STATIC PRESSURE CONTROL. DATA TAKEN INCLUDE MEAN VELOCITY PROFILES AND PROFILES OF THE REYNOLDS STRESS COMPONENTS U1V1, U2, V2 AND W2. TURBULENCE DATA WERE TAKEN USING HOT WIRE ANEMOMETRY USING A ROTATABLE X-WIRE PROBE IN A CONSTANT TEMPERATURE MODE WITH ANALOG PROCESSING OF THE SIGNAL. THE LOCAL STATIC PRESSURE USED IN THE MEAN VELOCITY MEASUREMENT WAS DEDUCED FROM THE WALL STATIC PRESSURE BY USING THE EULER N-EQUATION ASSUMING POTENTIAL FLOW: (PTOT - PSTAT)/(PTOT - PSW) = (RAD/(RAD + N)) ** 2 WHERE PTOT IS THE LOCAL STAGNATION PRESSURE, PSTAT IS THE LOCAL STATIC PRESSURE, PSW IS THE WALL STATIC PRESSURE, RAD IS THE RADIUS OF CURVATURE OF THE TEST WALL AND N IS THE DISTANCE NORMAL TO THE TEST WALL. THEN : U ** 2 = 2 * (PTOT - PSTAT) / RHO. VISCOSITY FOR EACH PROFILE CAN BE CALCULATED FROM THE MOMENTUM THICKNESS, MOMENTUM THICKNESS REYNOLDS NUMBER AND THE POTENTIAL VELOCITY EXTRAPOLATED TO THE WALL (UPW) : RTHETA = THETA * UPW / XNU 6. REFERENCES: 1. GILLIS, J. C., JOHNSTON, J. P. "TURBULENT BOUNDARY LAYER ON A CONVEX, CURVED SURFACE", DRAFT OF TECHNICAL REPORT FOR NASA, LEWIS RESEARCH CENTER (PH.D. THESIS OF GILLIS, J. C., DEPARTMENT OF MECHANICAL ENGINEERING, STANFORD UNIVERSITY) 2. "EXPERIMENTS ON THE TURBULENT BOUNDARY LAYER OVER CONVEX WALLS AND ITS RECOVERY TO FLAT WALL CONDITIONS" 2ND SYMPOSIUM ON TURBULENT SHEAR FLOWS, JULY 1979 7. INSTRUMENTATION MEAN VELOCITY MEASUREMENTS: TOTAL PRESSURE WAS MEASURED WITH A PITOT TUBE OF 0.71 M.M. OUTER DIAMETER. STATIC PRESSURE MEASUREMENTS: STATIC PRESSURE PORTS IN THE TEST WALL WITHIN THE BEND AND IN THE SIDEWALL UPSTREAM AND DOWNSTREAM OF THE BEND WERE USED. FLUCTUATING VELOCITY MEASUREMENTS: HOT WIRE ANEMOMETERY USING AN X-WIRE IN A CONSTANT TEMPERATURE MODE. SIGNAL PROCESSING (LINEARIZATION AND TIME-AVERAGING) WAS DONE WITH ANALOG EQUIPMENT. HORIZONTAL WIRE DATA WERE ALSO TAKEN BUT NOT INCLUDED IN THIS DATA SET. 8. EXPERIMENTAL PARAMETERS TUNNEL HEIGHT AND SPAN ....... 0.19 M X 0.53 M DEL995/RADIUS OF CURVATURE AT BEGINNING OF CURVE ........ 0.10 RADIUS OF CURVATURE .......... 0.45 M TURNING ANGLE ................ 90 DEG DEVELOPING LENGTH UPSTREAM OF BEND ...................... 2.05 M REFERENCE VELOCITY - UPW...... 15.03 M/S 9. MEASURED VARIABLES EACH MEASURING STATION INCLUDES DATA FOR THE FOLLOWING MEASURED OR INFERRED QUANTITIES: S STREAMWISE DISTANCE. M (REF. TO START OF CURVE) CP COEFFICIENT OF PRESSURE. DEL995 BOUNDARY LAYER THICKNESS. M DELS DISPLACEMENT THICKNESS. M THETA MOMENTUM THICKNESS. M H NONDIMENSIONAL SHAPE FACTOR (DELS/THETA) UPW POTENTIAL FLOW VELOCITY EXTRAPOLATED TO THE WALL. M/S CFE SKIN FRICTION COEFFICENT. RTHETA MOMENTUM THICKNESS REYNOLDS NUMBER. N DISTANCE FROM THE WALL. M N/DEL995 DISTANCE FROM WALL/BOUNDARY LAYER THICKNESS. U/UPOT LOCAL VELOCITY/LOCAL POTENTIAL VELOCITY. U1V1/(UPW**2) NONDIMENSIONAL REYNOLDS STRESS. U2/(UPW**2) NONDIMENSIONAL REYNOLDS STRESS. V2/(UPW**2) NONDIMENSIONAL REYNOLDS STRESS. W2/(UPW**2) NONDIMENSIONAL REYNOLDS STRESS. 10. MEASUREMENT UNCERTAINTY: NONE SPECIFIED 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) THUS EACH NORMALIZED DATUM IS WRITTEN ONTO TAPE AS A VALUE BETWEEN 0.0 AND 1.0 ALL NULL DATA ARE WRITTEN AS 2.0 THE EQUATION DESCRIBING THE RELATIONSHIP BETWEEN ACTUAL DATA AND NORMALIZED DATA IS: X=XMIN + ((XMAX-XMIN) * XNORM) WHERE X, XMAX, XMIN AND XNORM ARE REAL NUMBERS. FILE # NREC CONTENTS FORMAT COMMENTS 1 TEXT FILE CONTAINS ITEMS 1 TO 11 OF THIS WRITE-UP 2 26 S,CP 2E13.6 RECORD 1:MAX VALUES S,CP 2E13.6 RECORD 2:MIN VALUES S,CP 2E13.6 RECORDS 3-26 NORMALIZED VALUES 3 28 S,DEL995,DELS, 4E13.6 RECORD 1:MAX VALUES THETA H,UPW,CFE,RTHETA 4E13.6 RECORD 2:MAX VALUES S,DEL995,DELS, 4E13.6 RECORD 3:MIN VALUES THETA H,UPW,CFE,RTHETA 4E13.6 RECORD 4:MIN VALUES S,DEL995,DELS, 4E13.6 ODD RECORD 5-27 THETA NORMALIZED VALUES H,UPW,CFE,RTHETA 4E13.6 EVEN RECORDS 6-28 NORMALIZED VALUES FILES 4-26 CONTAIN PROFILE DATA AT TWELVE STREAMWISE MEASURING STATIONS CORRESPONDING TO THE X STATIONS OF FILE 3. THE SECOND STATION CONTAINS ONLY TURBULENCE DATA WHILE THE REMAINING STATIONS CONTAIN MEAN AND TURBULENCE DATA. 4 23 N/DEL995,U/UPOT, 4E13.6 STATION: X=-0.2984 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-23 YPLUS,UPLUS NORMALIZED VALUES 5 24 N/DEL995,U/UPOT, 4E13.6 STATION: X=0.1039 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-24 YPLUS,UPLUS NORMALIZED VALUES 6 24 N/DEL995,U/UPOT, 4E13.6 STATION: X=0.2519 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-24 YPLUS,UPLUS NORMALIZED VALUES 7 24 N/DEL995,U/UPOT, 4E13.6 STATION: X=0.4148 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-24 YPLUS,UPLUS NORMALIZED VALUES 8 24 N/DEL995,U/UPOT, 4E13.6 STATION: X=0.6172 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-24 YPLUS,UPLUS NORMALIZED VALUES 9 24 N/DEL995,U/UPOT, 4E13.6 STATION: X=0.8847 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-24 YPLUS,UPLUS NORMALIZED VALUES 10 25 N/DEL995,U/UPOT, 4E13.6 STATION: X=1.0371 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-25 YPLUS,UPLUS NORMALIZED VALUES 11 25 N/DEL995,U/UPOT, 4E13.6 STATION: X=1.1895 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-25 YPLUS,UPLUS NORMALIZED VALUES 12 25 N/DEL995,U/UPOT, 4E13.6 STATION: X=1.3479 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-25 YPLUS,UPLUS NORMALIZED VALUES 13 25 N/DEL995,U/UPOT, 4E13.6 STATION: X=1.4943 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-25 YPLUS,UPLUS NORMALIZED VALUES 14 25 N/DEL995,U/UPOT, 4E13.6 STATION: X=1.6467 M YPLUS,UPLUS RECORD 1- MAXIMUM VALUES N/DEL995,U/UPOT, 4E13.6 RECORD 2- MINIMUM YPLUS,UPLUS VALUES N/DEL995,U/UPOT, 4E13.6 RECORDS 3-25 YPLUS,UPLUS NORMALIZED VALUES 15 16 N/DEL995, 5E13.6 STATION: X=-0.2984 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-16 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 16 19 N/DEL995, 5E13.6 STATION: X=0.00 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-19 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 17 19 N/DEL995, 5E13.6 STATION: X=0.1039 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-19 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 18 19 N/DEL995, 5E13.6 STATION: X=0.2519 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-19 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 19 19 N/DEL995, 5E13.6 STATION: X=0.4148 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-19 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 20 19 N/DEL995, 5E13.6 STATION: X=0.6172 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-19 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 21 20 N/DEL995, 5E13.6 STATION: X=0.8847 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 22 20 N/DEL995, 5E13.6 STATION: X=0.10371 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 23 20 N/DEL995, 5E13.6 STATION: X=0.11895 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 24 20 N/DEL995, 5E13.6 STATION: X=0.13479 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 25 20 N/DEL995, 5E13.6 STATION: X=0.14943 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 26 20 N/DEL995, 5E13.6 STATION: X=0.16467 M. U1V1/(UPW**2), RECORD 1- MAXIMUM U2/(UPW**2), VALUES V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORD 2- MINIMUM U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) N/DEL995, 5E13.6 RECORDS 3-20 NORMALIZED U1V1/(UPW**2), VALUES U2/(UPW**2), V2/(UPW**2), W2/(UPW**2) 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 BRC$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 VALUES OF ALL THE VARIABLES DIMENSION NDEL(30),U(30),YPLUS(30),UPLUS(30) READ (23,30) NMX,UMX,YPLSMX,UPLSMX READ (23,30) NMN,UMN,YPLSMN,UPLSMN WRITE (6,40) NMX,UMX,YPLSMX,UPLSMX WRITE (6,40) NMN,UMN,YPLSMN,UPLSMN C THE NEXT 22 RECORDS CONTAIN THE NORMALIZED PROFILE DATA DO 10 I=1,22 READ (23,30) NDEL(I),U(I),YPLUS(I),UPLUS(I) WRITE (6,40) NDEL(I),U(I),YPLUS(I),UPLUS(I) 10 CONTINUE 30 FORMAT (4E13.6) 40 FORMAT (1X,4E13.6) 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 131------------- ----------------- FILE NUMBER 132----------------- 0.189970E 01 0.250000E-01 -0.825500E 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