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Abstract
This paper describes some studies on flow separation and on the extended Cebeci-Smith turbulence and transition models, carried out using a three-dimensional turbulent boundary layer code developed at the Vikram Sarabhai Space Center (VSSC), Thiruvananthapuram, India. This code uses an orthogonal curvilinear surface fitted co-ordinate system. The governing equations are solved, by an implicit space marching numerical method called the Keller Box Scheme with suitable modifications for reverse crossflows. Initial data on two intersecting planes for starting the solution procedure, are obtained by solving the appropriate limiting form of the governing equations. Three transition models available in the Literature are studied. A few sample results are presented and compared with experimental measurements.
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References
- Blottner, F. G. and Ellis, M. A., "Finite Difference Solution of the Incompressible Three Dimensional Boundary Layer Equations for a Biunt Body", Computers and Fluids, Vol.1,1973.
- Cebeci, T., Kaups, K., Mosinskis, C. J. and Rehn, J. A., "Some Problems of the Calculation of Three Dimensional Boundary Layer Flows on General Configurations", NASA -CR- 2285,1973.
- Couesteix. J.. "Calculation Methods of Three Dimensional Boundary Layers", Computational Methods in Viscous Aerodynamics Ed. T.K.S.Murthy and C.A. Brebbia, Elsevier, 1990. pp-43-74.
- Bradshaw, P., Cebeci, T. and Whitelaw, J .H., "Engineering Calculation Methods for Turbulent Flow", Academic Press, 1981.
- Dwyer, H.A., "Solutions of Three Dimensional Boundary Layer Flow with Separation", AIAA Journal, Vol.6, 1968, pp 1336-1342.
- Chang, K.C. and Patel, V. C., "Calculation of Three Dimensional Boundary Layers on Ship Forms",IIHR Report No. 178, Univ. of Iowa, 1975.
- Johnston, L. J., " An Upwind Scheme for the Three Dimensional Boundary Layer Equations ", Int. Journal of Numerical Methods in Fluids. Vol.11, Dec, 1990. pp.1043-1073.
- Grundmann. R. . " Introduction to Three Dimensional Boundary Layers ", Computational Methods in Viscous Aerodynamics, Ed. T.K.S. Murthy and C.A. Brebbia, Elsevier, 1990. pp.1-41.
- Iyer, V. and Hanis, J ," Three Dimensional Compressible Boundary Layer Calculations to Fourth Otder Accuracy on Wings and Fuselages", AIAA Paper 89-0130,1989.
- Swaminathan, R. and Balu, R.," Computation of Three Dimensional Turbulent Boundary Layer Flows over arbitrary Blunt Bodies ", VSSC: TR:292:92, Trivandrum, India, 1992.
- Swaminathan, R. and Balu, R., " Some Studies on 3-D Boundary Layer Flows ", VSSC : TR : 373 : 95, Dec.1995.
- Der. J.and Raetz. " Solution of General Three Dimensional Laminar Boundary Layer Problems by an Exact Numerical Method", Instt. of Aerospace Science, Paper No: 62-70.1962.
- Krause, E., Hirschel, W.W. and Th.Bothmann, "Numerical Stability of Three Dimensional Boundary Layer Solutions, ZAMM, Vol.48, 1968.
- Cebeci,T., Khattab A.K. and Stewartson K , " On Nose Separation ", J. Fluid Mechanics, Vol .97, 1980. pp.435-454.
- Cebeci, T., Khattab, A.K. and Stewartson, K, " Three Dimensional Laminar Boundary Layers and the O.K. of Accessibility ", J. Fluid Mechanics, Vol.107, 1981 pp.57-87.
- Balu, R. and Swaminathan, R.," Solution of General Non -Linear Two Point Boundary Value Problems by Keller's Box Method with Application [o Boundary Layer Flows ", ISRO-VSSC:TR:77:78, March, 1978, India.
- Ramesh, O.N., Dey, J and Prabhu, A : " Transition Zone in a Constant Pressure Laterally Diverging Flow", The Seventh Asian Congress of Fluid Mechanics, Dec.8-12, 1997, Chennai.
- Dey, J. and Narasimha, R. ," Integral Method for the Calculation of Incompressible Two Dimensional Boundary Layers ", J. Aircraft, Vol.30, 1990.
- Arnal, D , "Three Dimensional Boundary Layels: Laminar - Turbulent - Transitional", AGRAD Report No.741, 1986.
- Chen, K.K. and Thyson, N.A. , " Extension of Emmon's Spot Theory to Flows on Blunt Bodies", AIAA Journal. Vol.9. 1971.
- Wang, K.C., "Separation Patterns of Boundary Layer over an Inclined Body of Revolution", AIAA Journal, Vol. 10, 1972, pp.1044-1050.
- Van den Berg, B. and Elsenaar, A., "Measurement in Three Dimensional Incompressible Turbulent Boundary Layer in an Adverse Pressure Gradient under Infinite Swept Wing Conditions", NLR -TR 7 209, 1972. Netherlands.
- Fannelop, T. K. and Humphreys, D.A., " A Simple Finite Difference Method for Solving the Three Dimensional Turbulent Boundary Layer Equations ", AIAA Paper 74-13,1974.
- Abid, R., "Extension of the Johnson-King Turbulence Model to 3-D Flows", AIAA Paper 880223.1988.
- Bettelini, M.S.G., " Numerical Study of Some Engineering Turbulence Models for Three Dimensional Boundary Layers ', Ph.D Thesis, Federal Instt. of Technology, Zwich, Switzerland, 1990.
- Prahlad, T .S. ,"Modelling Considerations for Eddy Viscosity for 3-D Turbulent Boundary Layers ", EPFL Report T-83-9, 1983, Lausanne, Switzerland.
- . Cumpsty, N.A. and Head, M.R., "The Calculation of Three Dimensional Turbulent Boundary Layers- Part 3 - Comparison of Attachment Line Calculation with Experiment", The Aeronautical Quarterly, Vol.
- ,1969. pp.94-113.
- Cham, T.S. and Head, M.R., "Turbulent Boundary Layer Flow on a Rotating Disk", J. Fluid Mech, Vol37. 1969, pp.129-147 .
- Cebeci, T, "Boundary Layers on a Rotating Disk", AIAA Journal, Vo. 13, 1975, pp. 829-831.
- Meier, M.U. and Kreplin, H.P., " Experimental Investigation of the Transition and Separation Phenomena on a Body of Revolution", Z. Flug. Welt. Forschung, Vol.4, 1980.
- Cebeci, T., " Problems and Opportunities with Three Dimensional Boundary Layers", AGARD Report 719,1984.
- Cousteix, J., " Three Dimensional Boundary Layers -Introduction to Calculation Methods", VKIAGARD Lecture Series on "Computation of Three Dimensional Boundary Layers including Separation", AGARD Report No. 741, 1986
- Singer, B.A., Dinavahi, S.P.G. and Iyer, V, " Testing of Transition Region Model-Test Cases and Data ", NASA CR-4371,1991
- Srinivasa, P. and Raveendran, P .G., "Heat Transfer Measurements on PSLV Heat Shield at M = 5.75 and Angles of Incidence 0 to 17", ATTF:03 :8g, VSSC, Trivandrum, India, 1988.
References
Blottner, F. G. and Ellis, M. A., "Finite Difference Solution of the Incompressible Three Dimensional Boundary Layer Equations for a Biunt Body", Computers and Fluids, Vol.1,1973.
Cebeci, T., Kaups, K., Mosinskis, C. J. and Rehn, J. A., "Some Problems of the Calculation of Three Dimensional Boundary Layer Flows on General Configurations", NASA -CR- 2285,1973.
Couesteix. J.. "Calculation Methods of Three Dimensional Boundary Layers", Computational Methods in Viscous Aerodynamics Ed. T.K.S.Murthy and C.A. Brebbia, Elsevier, 1990. pp-43-74.
Bradshaw, P., Cebeci, T. and Whitelaw, J .H., "Engineering Calculation Methods for Turbulent Flow", Academic Press, 1981.
Dwyer, H.A., "Solutions of Three Dimensional Boundary Layer Flow with Separation", AIAA Journal, Vol.6, 1968, pp 1336-1342.
Chang, K.C. and Patel, V. C., "Calculation of Three Dimensional Boundary Layers on Ship Forms",IIHR Report No. 178, Univ. of Iowa, 1975.
Johnston, L. J., " An Upwind Scheme for the Three Dimensional Boundary Layer Equations ", Int. Journal of Numerical Methods in Fluids. Vol.11, Dec, 1990. pp.1043-1073.
Grundmann. R. . " Introduction to Three Dimensional Boundary Layers ", Computational Methods in Viscous Aerodynamics, Ed. T.K.S. Murthy and C.A. Brebbia, Elsevier, 1990. pp.1-41.
Iyer, V. and Hanis, J ," Three Dimensional Compressible Boundary Layer Calculations to Fourth Otder Accuracy on Wings and Fuselages", AIAA Paper 89-0130,1989.
Swaminathan, R. and Balu, R.," Computation of Three Dimensional Turbulent Boundary Layer Flows over arbitrary Blunt Bodies ", VSSC: TR:292:92, Trivandrum, India, 1992.
Swaminathan, R. and Balu, R., " Some Studies on 3-D Boundary Layer Flows ", VSSC : TR : 373 : 95, Dec.1995.
Der. J.and Raetz. " Solution of General Three Dimensional Laminar Boundary Layer Problems by an Exact Numerical Method", Instt. of Aerospace Science, Paper No: 62-70.1962.
Krause, E., Hirschel, W.W. and Th.Bothmann, "Numerical Stability of Three Dimensional Boundary Layer Solutions, ZAMM, Vol.48, 1968.
Cebeci,T., Khattab A.K. and Stewartson K , " On Nose Separation ", J. Fluid Mechanics, Vol .97, 1980. pp.435-454.
Cebeci, T., Khattab, A.K. and Stewartson, K, " Three Dimensional Laminar Boundary Layers and the O.K. of Accessibility ", J. Fluid Mechanics, Vol.107, 1981 pp.57-87.
Balu, R. and Swaminathan, R.," Solution of General Non -Linear Two Point Boundary Value Problems by Keller's Box Method with Application [o Boundary Layer Flows ", ISRO-VSSC:TR:77:78, March, 1978, India.
Ramesh, O.N., Dey, J and Prabhu, A : " Transition Zone in a Constant Pressure Laterally Diverging Flow", The Seventh Asian Congress of Fluid Mechanics, Dec.8-12, 1997, Chennai.
Dey, J. and Narasimha, R. ," Integral Method for the Calculation of Incompressible Two Dimensional Boundary Layers ", J. Aircraft, Vol.30, 1990.
Arnal, D , "Three Dimensional Boundary Layels: Laminar - Turbulent - Transitional", AGRAD Report No.741, 1986.
Chen, K.K. and Thyson, N.A. , " Extension of Emmon's Spot Theory to Flows on Blunt Bodies", AIAA Journal. Vol.9. 1971.
Wang, K.C., "Separation Patterns of Boundary Layer over an Inclined Body of Revolution", AIAA Journal, Vol. 10, 1972, pp.1044-1050.
Van den Berg, B. and Elsenaar, A., "Measurement in Three Dimensional Incompressible Turbulent Boundary Layer in an Adverse Pressure Gradient under Infinite Swept Wing Conditions", NLR -TR 7 209, 1972. Netherlands.
Fannelop, T. K. and Humphreys, D.A., " A Simple Finite Difference Method for Solving the Three Dimensional Turbulent Boundary Layer Equations ", AIAA Paper 74-13,1974.
Abid, R., "Extension of the Johnson-King Turbulence Model to 3-D Flows", AIAA Paper 880223.1988.
Bettelini, M.S.G., " Numerical Study of Some Engineering Turbulence Models for Three Dimensional Boundary Layers ', Ph.D Thesis, Federal Instt. of Technology, Zwich, Switzerland, 1990.
Prahlad, T .S. ,"Modelling Considerations for Eddy Viscosity for 3-D Turbulent Boundary Layers ", EPFL Report T-83-9, 1983, Lausanne, Switzerland.
. Cumpsty, N.A. and Head, M.R., "The Calculation of Three Dimensional Turbulent Boundary Layers- Part 3 - Comparison of Attachment Line Calculation with Experiment", The Aeronautical Quarterly, Vol.
,1969. pp.94-113.
Cham, T.S. and Head, M.R., "Turbulent Boundary Layer Flow on a Rotating Disk", J. Fluid Mech, Vol37. 1969, pp.129-147 .
Cebeci, T, "Boundary Layers on a Rotating Disk", AIAA Journal, Vo. 13, 1975, pp. 829-831.
Meier, M.U. and Kreplin, H.P., " Experimental Investigation of the Transition and Separation Phenomena on a Body of Revolution", Z. Flug. Welt. Forschung, Vol.4, 1980.
Cebeci, T., " Problems and Opportunities with Three Dimensional Boundary Layers", AGARD Report 719,1984.
Cousteix, J., " Three Dimensional Boundary Layers -Introduction to Calculation Methods", VKIAGARD Lecture Series on "Computation of Three Dimensional Boundary Layers including Separation", AGARD Report No. 741, 1986
Singer, B.A., Dinavahi, S.P.G. and Iyer, V, " Testing of Transition Region Model-Test Cases and Data ", NASA CR-4371,1991
Srinivasa, P. and Raveendran, P .G., "Heat Transfer Measurements on PSLV Heat Shield at M = 5.75 and Angles of Incidence 0 to 17", ATTF:03 :8g, VSSC, Trivandrum, India, 1988.