----------------- FILE NUMBER 2----------------- 1. FLOW TITLE: CASE 0111; PO, J. K., LUND, E. G. AND GESSNER, F. B.; DEVELOPING FLOW IN A SQUARE DUCT (SECONDARY FLOW OF THE SECOND KIND). 2. REVISION DATE: OCTOBER 30, 1981. 3. EVALUATOR: GESSNER, F. B., UNIVERSITY OF WASHINGTON, DEPARTMENT OF MECHNICAL ENGINEERING, FU-10, SEATTLE, WASHINGTON 98195. 4. DATE AND LOCATION OF EXPERIMENT: UNIVERSITY OF WASHINGTON, DEPARTMENT OF MECHNICAL ENGINEERING, SEATTLE, WASHINGTON, 1975. 5. ABSTRACT: THIS EXPERIMENT IS CONCERNED WITH TURBULENT FLOW IN A CONSTANT AREA SQUARE DUCT WHICH DEVELOPS IDEALLY FROM A ZERO TURBULENCE LEVEL, UNIFORM MEAN FLOW AT THE DUCT INLET (U = UB , V = W = 0). THE BULK REYNOLDS NUMBER MAY BE REGARDED AS BEING SUFFICIENTLY HIGH TO INITIATE TURBULENT BOUNDARY LAYER DEVELOPMENT AT THE DUCT INLET (X/DH = 0). A UNIQUE FEATURE OF THIS FLOW IS THE STREAMWISE DEVELOPMENT OF TWO SECONDARY FLOW CELLS IN EACH QUADRANT WHICH ARE CENTERED ABOVE THE CORNER BISECTOR. THESE CELLS CORRESPOND TO A FLOW PATTERN FORMED BY THE VECTOR SUM OF THE TRANSVERSE MEAN-VELOCITY COMPONENTS (V AND W) WHICH CAN BE REGARDED AS BEING SUPERIMPOSED UPON THE PRIMARY MEAN FLOW. THE FORMATION OF THESE CELLS IS THE DIRECT RESULT OF REYNOLDS STRESS GRADIENTS ACTING IN THE CORNER REGION WHICH ARE NOT PRESENT IN TWO-DIMENTIONAL BOUNDARY LAYER FLOWS. RESULTS WERE OBTAINED IN THE NEAR ENTRANCE REGION OF THE DUCT IN ORDER TO DETERMINE INLET FLOW CONDITIONS. THE VIRTUAL ORIGIN OF THE WALL BISECTOR BOUNDARY LAYER WAS FOUND BY EXTRAPOLATING VALUES OF DEL EVALUATED AT X/DH = 0.2, 1, 2, AND 4 FROM VELOCITY PROFILES MEASURED AT THESE LOCATIONS. THE VIRTUAL ORIGIN WAS LOCATED AT XS/DH = - 0.65, WHICH INDICATES THAT FLOW AT X/DH = 0 IS ESSENTIALLY UNIFORM. TURBULENCE INTENSITY MEASUREMENTS IN THE NEAR ENTRANCE REGION INDICATED A CORE FLOW TURBULENCE LEVEL LESS THAN 0.0035 THE ISOTACH PATTERNS MEASURED IN A QUADRANT OF THE FLOW AT X/DH = 8, 16, 24, 40, AND 84 EXHIBIT EXCELLENT SYMMETRY ABOUT THE CORNER BISECTOR AND ARE INDICATIVE OF THE PRESENCE OF TWO SECONDARY FLOW CELLS CENTERED ABOUT THE BISECTOR. 6. REFERENCES: 1. BEAVERS, G. S., SPARROW, E. M., AND MAGNUSON, R. A.; EXPERIMENTS ON HYDRODYNAMICALLY DEVELOPING FLOW IN RECTANGULAR DUCTS OF ARBITRARY ASPECT RATIO, IJHMT, VOL. 13, 1970, PP. 689-702. 2. GOLDSTEIN, R. J., AND KREID, D. K.; MEASUREMENT OF LAMINAR FLOW DEVELOPMENT IN A SQUARE DUCT USING A LASER-DOPPLER FLOWMETER, J. APPL. MECH., TRANS. ASME, VOL. 34, 1967, PP. 813-818. 3. GESSNER, F. B.; FINAL REPORT: CORNER FLOW DATA EVALUATION, DEPARTMENT OF MECHNICAL ENGINEERING, UNIVERSITY OF WASHINGTON, 1980. 4. PO, J. K.; DEVELOPING TURBULENT FLOW IN THE ENTRANCE REGION OF A SQUARE DUCT, MS THESIS, DEPARTMENT OF MECHNICAL ENGINEERING, UNIVERSITY OF WASHINGTON, 1975. 5. LUND, E. G.; MEAN FLOW AND TURBULENCE CHARACTRISTICS IN THE NEAR CORNER REGION OF A SQUARE DUCT, MS THESIS, DEPARTMENT OF MECHNICAL ENGINEERING, UNIVERSITY OF WASHINGTON, 1977. 6. EPPICH, H. M.; DEVELOPMENT OF A PRESSURE- STRAIN MODEL FOR TURBULENT FLOW ALONG A STREAMWISE CORNER, MS THESIS, DEPARTMENT OF MECHNICAL ENGINEERING, UNIVERSITY OF WASHINGTON (IN PREPARATION). 7. GESSNER, F. B., PO, J. K., AND EMERY, A. F.; MEASUREMENTS OF TURBULENT FLOW IN A SQUARE DUCT. IN TURBULENT SHEAR FLOWS I (EDITED DY DURST) SPINGER-VERLAG, NEW YORK, 1979. 8. GESSNER, F. B., AND EMERY, A. F.; THE NUMERICAL PREDICTION OF DEVELOPING TURBULENT FLOW IN RECTANGULAR DUCTS, SYMPOSIUM ON TURBULENT SHEAR FLOWS, VOL. II, IMPERIAL COLLEGE, LONDON, 1979, PP. 17.1-17.6. 9. EMERY, A. F., NEIGHBORS,P. K., AND GESSNER, F. B.; THE NUMERICAL PREDICTION OF DEVELOPING TURBULENT FLOW AND HEAT TRANSFER IN A SQUARE DUCT, J. HEAT TRANSFER, TRANS. ASME, VOL. 102, 1980, PP. 51-57. 7. INSTRUMENTATION: STATIC PRESSURE TAPS WERE LOCATED ON OPPOSITE WALLS OF THE DUCT AT 1-DH INTERVALS BETWEEN X/DH = 1 AND X/DH = 26, AND THEN AT 2-D INTERVALS BETWEEN X/DH = 26 AND X/DH = 84. AXIAL MEAN VELOCITIES WERE MEASURED BY MEANS OF A MINIATURE KIEL PROBE (UNITED SENSOR KAC-8) IN CONJUNCTION WITH A WALL STATIC PRESSURE TAP. DIFFERENTIAL PRESSURES WERE MEASURED WITH AN E. VERNON HILL TYPE A MICROMANOMETER WITH MINOR SCALE DIVISIONS OF 0.0254 MM. TURBULENCE MEASUREMENTS WERE MADE WITH HOT-WIRE PROBES SIMILAR IN DESIGN TO CONFIGURATIONS RECOMMENDED BY COMTE-BELLOT AND HER CO-WORKERS, FOR MINIMAL PRONG INTERFERENCE EFFECTS. THE SENSING ELEMENT OF EACH PROBE WAS TUNGSTEN WIRE, 3.8 MICROMETER (0.00015 IN.) IN DIAMETER, AND WIRE LENGTH-TO-DIAMETER RATIO VARIED BETWEEN 250 AND 450. THE LONGITUDINAL NORMAL STRESS COMPONENT WAS MEASURED BY MEANS OF A SINGLE WIRE NORMAL TO THE FLOW WHICH WAS CALIBRATED BEFORE AND AFTER EACH DATA RUN IN THE POTENTIAL CORE OF A FREE JET. THE REMAINING RENOLDS STRESS COMPONENTS WERE MEASURED BY MEANS OF A SINGLE INCLINED WIRE ORIENTED AT THE NOMINAL ANGLE OF 45 DEGREES RELATIVE TO THE AXIAL FLOW DIRECTION. THE HOT-WIRE PROBES WERE OPERATED BY MEANS OF A THERMO-SYSTEMS, INC. MODEL 1010 CONSTANT TEMPERATURE ANEMOMETER. THE KIEL PROBE AND HOT-WIRE PROBES WERE MOUNTED ON A TRASVERSING MECHANISM FOR PROBE TRANSLATION IN THE Y-Z PLANE. PROBE POSITIONING IN THE Y- AND Z-DIRECTIONS WAS ACCURATE TO WITHIN +/- 0.1 MM. BOTH NORMAL AND INCLINED WIRE PROBES WERE MOUNTED WITH THE PROBE STEM PARALLEL TO THE AXIAL FLOW DIRECTION. BY MEANS OF A BEVEL GEAR ARRANGEMENT THE INCLINED WIRE PROBE WAS ROTATED IN 45-DEGREE INCREMENTS TO ORIENT THE WIRE IN THE X-Y AND X-Z PLANES, AND IN THE PLANES WHICH BISECT THESE PLANES (8 ANGULAR POSITIONS). THIS ARRANGEMENT PERMITTED V2, W2, UV, UW, AND VW TO BE MEASURED SIMULTANEOUSLY AT EACH POINT WHERE WALL INTERFERENCE EFFECTS ARE NEGLIGIBLE (Y/A >= 0.05, Z/A >= 0.05), NO CORRECTIONS WERE APPLIED TO MEASURED REYNOLDS STRESS VALUES. 8. EXPERIMENTAL PARAMETERS: THE TEST FACILITY CONSISTED OF A FORMICA-LINED SQUARE DUCT APPROXIMATELY 22 M IN LENGTH. THE DUCT WAS PRECEDED BY A CONTRACTION AND A SETTLING CHAMBER WITH SCREENS, FILTERS, AND HONEYCOMB. THE JOINT BETWEEN THE CONTRACTION AND DUCT WAS SMOOTH, AND NO TRIPPING DEVICE WAS INSTALLED AT THE DUCT INLET. THE DISTANCE BETWEEN OPPOSITE WALLS OF THE DUCT WAS MAINTAINED AT 0.254 M +/-0.025 MM OVER THE LENGTH OF THE DUCT, AND ADJACENT WALLS WERE SET PERPENDICULAR TO WITHIN +/- 0.05 DEGREE. THE BOTTOM WALL WAS MAINTAINED LEVEL TO WITHIN +/- 0.4 MM OVER ITS LENGTH. THE TOP WALL WAS MADE OF REMOVABLE SECTIONS SO THAT A TRAVERSING MECHANISM CAN BE POSITIONED AT DIFFERENT STREAMWISE LOCATIONS. DUCT DIMENSION: A = 0.127 M (5.000 IN.) L = 22 M DH = 2A = 0.254 M (10.000 IN.) (X/DH)MAX = 84 OPERATING CONDITIONS: UB = 15.2 M/SEC. (50.0 FT/SEC.) REB = 2.5*10**5 9. MEASURED AND INFERRED VARIABLES: X,Y,Z CARTESIAN COORDINATES. YPRIME,ZPRIME DIAGONAL COORDINATES WITH ORIGINS AT THE DUCT CORNERS MEASURED POSITIVELY TOWARD THE DUCT CENTER. XS STARTING LENGTH. L LENGTH OF THE DUCT, (M). A HALF WIDTH OF THE DUCT, (M). DH HYDRAULIC DIAMETER OF THE DUCT (DH = 2A), (M). APRIME DIAGONAL HALF WIDTH OF THE DUCT, (M). DEL BOUNDARY LAYER THICKNESS, (M). NU KINEMATIC VISCOSITY. CP PRESSURE COEFFICIENT ( CP = (P0 - P)/(1/2*RHO*UB**2) ). CPWA PRESSURE COEFFICIENT AT WALL A CPWB PRESSURE COEFFICIENT AT WALL B P MEAN STATIC PRESSURE. P0 MEAN STATIC PRESSURE AT X = 0. REB BULK REYNOLDS NUMBER (REB = UB*DH/NU) U, V, W MEAN-VELOCITY COMPONENTS IN X, Y, AND Z DIRECTIONS, RESPECTIVELY, (M/SEC.). UB BULK VELOCITY, (M/SEC.). UC AXIAL CENTERLINE VELOCITY, (M/SEC.). USTAR FRICTION VELOCITY (USTAR =SQRT(TAW/RHO), (M/SEC.). U0 MEAN CENTERLINE VELOCITY, (M/SEC.). VPRIME MEAN-VELOCITY COMPONENT IN YPRIME DIRECTION, (M/SEC.). YPLUS DIMENSIONLESS COORDINATE (YPLUS = Y*USTAR/NU). EPSILON DISSIPATION VISCOSITY RATE OF TURBULENT MOTION, (M**2)/(SEC.**3). RHO FLUID DENSITY. TAUW LOCAL WALL SHEAR STRESS. TAUWBAR SPANWISE AVERAGED VALUE OF TAUW. U2, V2, W2 REYNOLDS NORMAL STRESS COMPONENTS REFERRED TO THE X,Y,Z COORDINATE SYSTEM. U*V,U*W,V*W REYNOLDS SHEAR STRESS COMPONENTS REFERRED TO THE X,Y,Z COORDINATE SYSTEM. UB2 REYNOLDS NORMAL STRESS IN THE X-DIRECTION. H1 HORIZONTAL TRAVERSE ONE. H2 HORIZONTAL TRAVERSE TWO (OPPOSITE WALL). H1R REPEAT OF H1. VERT1 VERTICAL TRAVERSE ONE. VERT2 VERTICAL TRAVERSE TWO. D1 DIAGONAL TRAVERSE ONE. D2 DIAGONAL TRAVERSE TWO. D1R REPEAT OF D1. Y/A NONDIMENSIONAL DISTANCE. YPRIME/APRIME NONDIMENSIONAL DISTANCE. Z/A NONDIMENSIONAL DISTANCE. X/DH NONDIMENSIONAL DISTANCE. U0/UB NONDIMENSIONAL VELOCITY U/UB NONDIMENSIONAL VELOCITY. V/UB NONDIMENSIONAL VELOCITY. VPRIME/UB NONDIMENSIONAL VELOCITY. TAUW/TAUWBAR NONDIMENSIONAL SHEAR STRESS. U/UC NONDIMENSIONAL VELOCITY. K TURBULENT KINETIC ENERGY 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; 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 THE 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 RELATION BETWEEN ACTUAL DATA AND THE NORMALIZED DATA ON TAPE IS X = XMIN + (((XMAX - XMIN) * IXNORM)/10000.) WHERE X, XMAX AND XMIN ARE REAL AND IXNORM IS INTEGER. FILE# NREC CONTAINS FORMAT COMMENTS 1 - TEXT FILE - CONTAINS ITEMS 1 TO 11 OF THIS WRITE-UP 2 31 (X/DH)/REB,CP, 5E13.6/ RECORDS 1&2 - (X/DH)/REB,CP, 5E13.6 MAXIMUM VALUES (X/DH)/REB,CP, FOR REB = (X/DH)/REB,CP, 0.651*10**5, (X/DH)/REB,CP 0.735*10**5, 1.222*10**5, 1.564*10**5, AND 1.858*10**5, RESPECTIVELY. (X/DH)/REB,CP, 5E13.6/ RECORDS 3&4 - (X/DH)/REB,CP, 5E13.6 MINIMUM VALUES (X/DH)/REB,CP, FOR REB = (X/DH)/REB,CP, 0.651*10**5, (X/DH)/REB,CP 0.735*10**5, 1.222*10**5, 1.564*10**5, AND 1.858*10**5, RESPECTIVELY. (X/DH)/REB,CP, 10I6 RECORDS 5 - 31 (X/DH)/REB,CP, NORMALIZED VALUES (X/DH)/REB,CP, FOR REB = (X/DH)/REB,CP, 0.651*10**5, (X/DH)/REB,CP 0.735*10**5, 1.222*10**5, 1.564*10**5, AND 1.858*10**5, RESPECTIVELY. 3 15 (X/DH)/REB,U0/UB, 5E13.6/ RECORDS 1&2 - (X/DH)/REB,U0/UB, 5E13.6 MAXIMUM VALUES (X/DH)/REB,U0/UB, FOR RUNS 1, 2, (X/DH)/REB,U0/UB, 3, 4, AND 5 (X/DH)/REB,U0/UB RESPECTIVELY. (X/DH)/REB,U0/UB, 5E13.6/ RECORDS 3&4 - (X/DH)/REB,U0/UB, 5E13.6 MINIMUM VALUES (X/DH)/REB,U0/UB, FOR RUNS 1, 2, (X/DH)/REB,U0/UB, 3, 4, AND 5 (X/DH)/REB,U0/UB RESPECTIVELY. (X/DH)/REB,U0/UB, 10I6 RECORDS 5 - 15 (X/DH)/REB,U0/UB, NORMALIZED VALUES (X/DH)/REB,U0/UB, FOR RUNS 1, 2, (X/DH)/REB,U0/UB, 3, 4, AND 5 (X/DH)/REB,U0/UB RESPECTIVELY. 4 14 Y/A,U/UB(H1),U/UB(VERT1), 5E13.6/ RECORDS 1&2 - Y/A,U/UB(H1), 4E13.6 MAXIMUM VALUES Y/A,U/UB(H1R), NOTE: (X/DH)/REB = Y/A,U/UB(H2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMNS 4 - 9 RESPECTIVELY. Y/A,U/UB(H1),U/UB(VERT1), 5E13.6/ RECORDS 3&4 - Y/A,U/UB(H1), 4E13.6 MINIMUM VALUES Y/A,U/UB(HIR), NOTE: (X/DH)/REB = Y/A,U/UB(H2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMNS 4 - 9 RESPECTIVELY. Y/A,U/UB(H1),U/UB(VERT1), 9I6 RECORDS 5 - 14 Y/A,U/UB(H1), NORMALIZED VALUES Y/A,U/UB(HIR), NOTE: (X/DH)/REB = Y/A,U/UB(H2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMNS 4 - 9 RESPECTIVELY. 5 13 Y/A,U/UB(H1), 5E13.6/ RECORDS 1&2 - Y/A,U/UB(H1R), 5E13.6 MAXIMUM VALUES Y/A,U/UB(H2), NOTE: (X/DH)/REB = Y/A,U/UB(VERT1), 0.1500 FOR ALL Y/A,U/UB(VERT2) COLUMNS. Y/A,U/UB(H1), 5E13.6/ RECORDS 3&4 - Y/A,U/UB(H1R), 5E13.6 MINIMUM VALUES Y/A,U/UB(H2), NOTE: (X/DH)/REB = Y/A,U/UB(VERT1), 0.1500 FOR ALL Y/A,U/UB(VERT2) COLUMNS. Y/A,U/UB(H1), 10I6 RECORDS 5 - 13 Y/A,U/UB(H1R), NORMALIZED VALUES Y/A,U/UB(H2), NOTE: (X/DH)/REB = Y/A,U/UB(VERT1), 0.1500 FOR ALL Y/A,U/UB(VERT2) COLUMNS. 6 13 YPRIME/APRIME,U/UB(D1), 4E13.6/ RECORDS 1&2 - U/UB(D1R),U/UB(D1), 4E13.6 MAXIMUM VALUES YPRIME/APRIME,U/UB(D1), NOTE: (X/DH)/REB = U/UB(D1R),U/UB(D2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMN 4 AND 0.1500 FOR COLUMNS 5 - 8 RESPECTIVELY. YPRIME/APRIME,U/UB(D1), 4E13.6/ RECORDS 3&4 - U/UB(D1R),U/UB(D1), 4E13.6 MINIMUM VALUES YPRIME/APRIME,U/UB(D1), NOTE: (X/DH)/REB = U/UB(D1R),U/UB(D2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMN 4 AND 0.1500 FOR COLUMNS 5 - 8 RESPECTIVELY. YPRIME/APRIME,U/UB(D1), 8I6 RECORDS 5 - 13 U/UB(D1R),U/UB(D1), NORMALIZED VALUES YPRIME/APRIME,U/UB(D1), NOTE: (X/DH)/REB = U/UB(D1R),U/UB(D2) 0.0075 FOR COLUMNS 1 - 3, AND 0.0200 FOR COLUMN 4 AND 0.1500 FOR COLUMNS 5 - 8 RESPECTIVELY. 7 36 X/DH,CPWA,CPWB 3E13.6 RECORD 1 - MAXIMUM VALUES X/DH,CPWA,CPWB 3E13.6 RECORD 2 - MINIMUM VALUES X/DH,CPWA,CPWB 3I6 RECORD 3 - 36 NORMALIZED VALUES 8 21 X/DH,U/UB,U/UB,U/UB, 5E13.6 RECORDS 1&2 - U/UB,U/UB,U/UB,U/UB,U/UB 4E13.6 MAXIMUM VALUES FOR Y/A = 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 RESPECTIVELY. X/DH,U/UB,U/UB,U/UB, 5E13.6 RECORDS 3&4 - U/UB,U/UB,U/UB,U/UB,U/UB 4E13.6 MINIMUM VALUES FOR Y/A = 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 RESPECTIVELY. X/DH,U/UB,U/UB,U/UB, 9I6 RECORDS 5 - 21 U/UB,U/UB,U/UB,U/UB,U/UB NORMALIZED VALUES FOR Y/A = 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 RESPECTIVELY. 9 21 X/DH,U/UB,U/UB,U/UB, 5E13.6 RECORDS 1&2 - U/UB,U/UB,U/UB,U/UB,U/UB 4E13.6 MAXIMUM VALUES FOR YPRIME/APRIME= 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 . RESPECTIVELY. X/DH,U/UB,U/UB,U/UB, 5E13.6 RECORDS 3&4 - U/UB,U/UB,U/UB,U/UB,U/UB 4E13.6 MINIMUM VALUES FOR YPRIME/APRIME= 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 . RESPECTIVELY. X/DH,U/UB,U/UB,U/UB, 9I6 RECORDS 5 - 21 U/UB,U/UB,U/UB,U/UB,U/UB NORMALIZED VALUES. FOR YPRIME/APRIME= 0.02, 0.04, 0.06, 0.10, 0.20, 0.40, 0.60, 1.00 . RESPECTIVELY. 10 20 Y/A,V/UB,V/UB, 5E13.6 RECORD 1 - V/UB,V/UB MAXIMUM VALUES FOR X/DH = 40 AND RUNS: 1, 2, 3, AND 4 RESPECTIVELY. Y/A,V/UB,V/UB, 5E13.6 RECORD 2 - V/UB,V/UB MINIMUM VALUES FOR X/DH = 40 AND RUNS: 1, 2, 3, AND 4 RESPECTIVELY. Y/A,V/UB,V/UB, 5I6 RECORDS 3 - 20 V/UB,V/UB NORMALIZED VALUES FOR X/DH = 40 AND RUNS: 1, 2, 3, AND 4 RESPECTIVELY. 11 21 YPRIME/APRIME, 3E13.6 RECORD 1 - VPRIME/UB,VPRIME/UB MAXIMUM VALUES FOR X/DH = 40 AND RUNS: 1, AND 2 RESPECTIVELY. YPRIME/APRIME, 3E13.6 RECORD 2 - VPRIME/UB,VPRIME/UB MINIMUM VALUES FOR X/DH = 40 AND RUNS: 1, AND 2 RESPECTIVELY. YPRIME/APRIME, 3I6 RECORDS 3 - 21 VPRIME/UB,VPRIME/UB NORMALIZED VALUES FOR X/DH = 40 AND RUNS: 1, AND 2 RESPECTIVELY. 12 17 Y/A,V/UB,V/UB, 6E13.6 RECORD 1 - YPRIME/APRIME, MAXIMUM VALUES VPRIME/UB,VPRIME/UB FOR X/DH = 84 AND RUNS: 1, AND 2 RESPECTIVELY. Y/A,V/UB,V/UB, 6E13.6 RECORD 2 - YPRIME/APRIME, MINIMUM VALUES VPRIME/UB,VPRIME/UB FOR X/DH = 84 AND RUNS: 1, AND 2 RESPECTIVELY. Y/A,V/UB,V/UB, 6I6 RECORDS 3 - 17 YPRIME/APRIME, NORMALIZED VALUES VPRIME/UB,VPRIME/UB FOR X/DH = 84 AND RUNS: 1, AND 2 RESPECTIVELY. 13 27 Y/A,TAUW/TAUWBAR 2E13.6 RECORD 1 - MAXIMUM VALUES FOR X/DH = 84 Y/A,TAUW/TAUWBAR 2E13.6 RECORD 2 - MINIMUM VALUES FOR X/DH = 84 Y/A,TAUW/TAUWBAR 2I6 RECORDS 3 - 27 NORMALIZED VALUES FOR X/DH = 84 14 32 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 8, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 8, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 32 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 8, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. 15 35 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 16, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 16, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 35 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 16, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. 16 27 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 24, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 24, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 27 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 24, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. 17 24 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 40, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 40, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 24 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 40, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. 18 24 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 84, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 84, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 24 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 84, AND U/UC = 0.70, 0.80, 0.85, 0.90, AND 0.95 RESPECTIVELY. 19 15 Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MAXIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND -U*V/UB2*10**4 = 2, 4, 6, 8, 12, AND 16 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 3&4 Y/A,Z/A,Y/A,Z/A, 6E13.6 MINIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND -U*V/UB2*10**4 = 2, 4, 6, 8, 12, AND 16 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 12I6 RECORDS 5 - 15 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND -U*V/UB2*10**4 = 2, 4, 6, 8, 12, AND 16 RESPECTIVELY. 20 26 Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MAXIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND K/UB2*10**4 = 10, 20, 30, 40, 50, AND 60 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MINIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND K/UB2*10**4 = 10, 20, 30, 40, 50, AND 60 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 12I6 RECORDS 5 - 26 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 24, AND K/UB2*10**4 = 10, 20, 30, 40, 50, AND 60 RESPECTIVELY. 21 8 Y/A,Z/A 2E13.6 RECORD 1 - MAXIMUM VALUES FOR X/DH = 24, AND K/UB2*10**4 = 70 Y/A,Z/A 2E13.6 RECORD 2 - MINIMUM VALUES FOR X/DH = 24, AND K/UB2*10**4 = 70 Y/A,Z/A 2I6 RECORDS 3 - 8 NORMALIZED VALUES FOR X/DH = 24, AND K/UB2*10**4 = 70 22 18 Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MAXIMUM VALUES Y/A,Z/A FOR X/DH = 40, AND -U*V/UB2*10**4 = 2, 4, 6, 8, AND 12 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 5E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 5E13.6 MINIMUM VALUES Y/A,Z/A FOR X/DH = 40, AND -U*V/UB2*10**4 = 2, 4, 6, 8, AND 12 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 10I6 RECORDS 5 - 18 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A FOR X/DH = 40, AND -U*V/UB2*10**4 = 2, 4, 6, 8, AND 12 RESPECTIVELY. 23 12 Y/A,Z/A,Y/A,Z/A 4E13.6 RECORD 1 - MAXIMUM VALUES FOR X/DH = 40, AND -U*V/UB2*10**4 = 16, AND 20 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A 4E13.6 RECORD 2 - MINIMUM VALUES FOR X/DH = 40, AND -U*V/UB2*10**4 = 16, AND 20 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A 4I6 RECORDS 3 - 12 NORMALIZED VALUES FOR X/DH = 40, AND -U*V/UB2*10**4 = 16, AND 20 RESPECTIVELY. 24 24 Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MAXIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 40, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MINIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 40, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 12I6 RECORDS 5 - 24 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 40, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. 25 12 Y/A,Z/A 2E13.6 RECORD 1 - MAXIMUM VALUES FOR X/DH = 40, AND K/UB2*10**4 = 80 Y/A,Z/A 2E13.6 RECORD 2 - MINIMUM VALUES FOR X/DH = 40, AND K/UB2*10**4 = 80 Y/A,Z/A 2I6 RECORDS 3 - 12 NORMALIZED VALUES FOR X/DH = 40, AND K/UB2*10**4 = 80 26 16 Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MAXIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND -U*V/UB2*10**4 = -3, -2, -1, 0, 2, AND 4 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MINIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND -U*V/UB2*10**4 = -3, -2, -1, 0, 2, AND 4 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 12I6 RECORDS 5 - 16 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND -U*V/UB2*10**4 = -3, -2, -1, 0, 2, AND 4 RESPECTIVELY. 27 15 Y/A,Z/A,Y/A,Z/A, 4E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 4E13.6 MAXIMUM VALUES FOR X/DH = 84, AND -U*V/UB2*10**4 = 6, 8, 12, AND 16 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 4E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 4E13.6 MINIMUM VALUES FOR X/DH = 84, AND -U*V/UB2*10**4 = 6, 8, 12, AND 16 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 8I6 RECORDS 5 - 15 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES FOR X/DH = 84, AND -U*V/UB2*10**4 = 6, 8, 12, AND 16 RESPECTIVELY. 28 24 Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 1&2 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MAXIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 6E13.6 RECORDS 3&4 - Y/A,Z/A,Y/A,Z/A, 6E13.6 MINIMUM VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. Y/A,Z/A,Y/A,Z/A, 12I6 RECORDS 5 - 24 Y/A,Z/A,Y/A,Z/A, NORMALIZED VALUES Y/A,Z/A,Y/A,Z/A FOR X/DH = 84, AND K/UB2*10**4 = 20, 30, 40, 50, 60, AND 70 RESPECTIVELY. A SAMPLE PROGRAM FOR READING FILE 7 AND PRINTING, IS SHOWN BELOW. THE JCL SHOWN IS FOR THE STANFORD CIT FACILITY. CHECK WITH YOUR OWN COMPUTER INSTALLATION FOR THE EXACT JCL NEEDED. //TAPE JOB BZC$NJ /*SETUP TAPE=1,INPUT=(LIBRARY NUMBER ASSIGNED TO TAPE) // EXEC FORTCG //FORT.SYSIN DD * C TO READ FILE 7 OFF TAPE C PRINT MAXIMAS AND MINIMAS OF ALL THE VARIABLES C PRINT NORMALIZED INTEGERIZED VALUES OF ALL THE VARIABLES. INTEGER XDH(40),CPWA(40),CPWB(40) READ (23,30) XDHMX,CPWAMX,CPWBMX READ (23,30) XDHMN,CPWAMN,CPWBMN DO 10 I = 1, 34 10 READ (23,40) XDH(I),CPWA(I),CPWB(I) WRITE (6,50) XDHMX,CPWAMX,CPWBMX WRITE (6,50) XDHMN,CPWAMN,CPWBMN DO 20 I = 1, 34 20 WRITE (6,60) XDH(I),CPWA(I),CPWB(I) 30 FORMAT(3E13.6) 40 FORMAT(3I6) 50 FORMAT(1X,3E13.6) 60 FORMAT(1X,3I6) STOP END //GO.FT23F001 DD UNIT=T1600,VOL=SER=(TAPE LIBRARY NUMBER), // DISP=(OLD,KEEP),DCB=(RECFM=FB,LRECL=80,BLKSIZE=8000,DEN=3), // LABEL=(7,NL) // -------------- END OF FILE NUMBER 2------------- ----------------- FILE NUMBER 3----------------- 0.747000E-01 0.660000E 01 0.715000E-01 0.644000E 01 0.740000E-01 0.661000E 01 0.767000E-01 0.667000E 01 0.649000E-01 0.600000E 01 0.130000E-02 0.155000E 01 0.280000E-01 0.383000E 01 0.900000E-03 0.145000E 01 0.400000E-03 0.136000E 01 0.325000E-01 0.409000E 01 0 0 0 0 0 0 0 0 0 0 95 297 1241 1340 136 426 91 320 3302 3455 217 495 2528 2643 273 678 301 772 5000 5078 313 712 6275 6321 424 988 406 960 6635 6753 422 891 7517 7432 560 1182 1048 1902 8302 8429 517 1049 8758 8735 697 1453 1245 2128 10000 10000 626 1188 10000 10000 834 1608 1454 2391 20000 20000 722 1366 20000 20000 971 1763 1651 2617 20000 20000 831 1504 20000 20000 1381 2286 1874 2862 20000 20000 1035 1801 20000 20000 1682 2616 2096 3088 20000 20000 1253 2039 20000 20000 1983 2906 2293 3295 20000 20000 1457 2297 20000 20000 2243 3100 2503 3521 20000 20000 1662 2534 20000 20000 2489 3430 2896 3917 20000 20000 1866 2831 20000 20000 2790 3740 3342 4312 20000 20000 2084 2990 20000 20000 3091 4011 4141 5065 20000 20000 2288 3207 20000 20000 3351 4282 4980 5838 20000 20000 2520 3425 20000 20000 3912 4806 5819 6553 20000 20000 2929 3841 20000 20000 4487 5329 6657 7269 20000 20000 3337 4257 20000 20000 5540 6298 7483 7966 20000 20000 4128 4990 20000 20000 6662 7228 8335 8662 20000 20000 4986 5762 20000 20000 7783 8139 9174 9340 20000 20000 5817 6495 20000 20000 8891 9108 10000 10000 20000 20000 6648 7227 20000 20000 10000 10000 20000 20000 20000 20000 7493 7920 20000 20000 20000 20000 20000 20000 20000 20000 8324 8613 20000 20000 20000 20000 20000 20000 20000 20000 9155 9326 20000 20000 20000 20000 20000 20000 20000 20000 10000 10000 20000 20000 20000 20000 20000 20000 20000 20000 -------------- END OF FILE NUMBER 3------------- ----------------- FILE NUMBER 4----------------- 0.160900E 00 0.208600E 01 0.175000E 00 0.208300E 01 0.890000E-01 0.206800E 01 0.324000E-01 0.193400E 01 0.181000E-01 0.179100E 01 0.170000E-01 0.172900E 01 0.637000E-01 0.204000E 01 0.381000E-01 0.194600E 01 0.130000E-01 0.167000E 01 0.510000E-02 0.141100E 01 0 0 0 0 0 0 0 0 0 0 583 3949 1141 3953 2495 4508 3350 4507 2769 3342 1181 5854 2300 6279 4263 7704 6649 7575 2999 3526 1765 7254 4007 10000 7485 8770 10000 10000 4615 4842 2355 8123 4582 10000 10000 10000 20000 20000 6461 6263 3530 9103 5732 10000 20000 20000 20000 20000 10000 10000 4718 9411 6945 7441 20000 20000 20000 20000 20000 20000 5899 9579 7753 7441 20000 20000 20000 20000 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01 0.124800E 01 0.439000E 00 0.196000E 00 0.314000E 00 0.381000E 00 0.389000E 00 0 20000 20000 0 0 0 0 0 1243 20000 20000 2507 1243 2061 1829 1617 2487 0 0 4992 2487 3735 3465 3440 3756 5364 6360 6592 3756 5436 5365 5240 5000 8124 9118 8169 5000 7064 6797 6840 6243 9791 9118 9084 6243 8309 8229 8206 7487 10000 9846 9709 7487 9388 9222 9232 8756 10000 10000 9985 8756 9977 9824 9771 10000 9531 9655 10000 10000 10000 10000 10000 -------------- END OF FILE NUMBER 7------------- ----------------- FILE NUMBER 8----------------- 0.840000E 02 0.121600E 01 0.123800E 01 0.100000E 01 0.140000E-01 0.320000E-01 0 0 0 120 266 116 240 415 215 361 565 447 481 815 464 602 915 729 722 865 878 843 1098 1061 963 1297 1144 1084 1397 1210 1325 1730 1542 1566 1963 1824 1807 2196 2056 2048 2479 2288 2289 2595 2537 2530 2945 2570 2771 3211 2852 3012 3444 3233 3253 3510 3482 3493 3860 3615 3734 4109 3980 4216 4276 4245 4698 4941 4859 5180 5091 5091 5662 5806 5638 6144 6272 6102 6626 6755 6500 7108 7304 7014 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1097 1060 1082 674 3061 6496 7232 8553 1909 1219 959 1082 898 3265 6624 7053 10000 2272 1280 1161 1210 898 3877 6751 7142 -------------- END OF FILE NUMBER 9------------- ----------------- FILE NUMBER 10----------------- 0.840000E 02 0.592000E 00 0.707000E 00 0.785000E 00 0.954000E 00 0.103600E 01 0.109800E 01 0.115800E 01 0.123500E 01 0.100000E 01 0.560000E 00 0.660000E 00 0.736000E 00 0.826000E 00 0.934000E 00 0.101300E 01 0.101300E 01 0.101100E 01 0 0 0 1020 10000 7745 0 0 0 120 2812 3404 5306 6796 8529 941 551 446 361 8437 5744 7551 5546 10000 2823 1655 1160 843 10000 10000 10000 3671 6176 7411 4344 2901 1325 4374 4255 3061 1484 1764 10000 6068 4017 1807 4999 4255 2040 546 784 9529 7862 5178 2289 3437 1914 0 0 0 7058 9448 6294 2771 3437 1914 0 0 686 6117 10000 7366 3253 3437 2127 408 156 1568 5411 9793 8482 3734 2812 1914 1020 468 1960 4941 9172 9375 4216 5312 3404 1632 625 2058 4823 8344 9910 4698 6875 4680 3061 1250 2450 5411 8137 10000 5180 8125 5531 3061 1484 3235 5529 7724 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