Time-dependent inverse solution of three-dimensional, compressible, turbulent, integral boundary-layer equations in nonorthogonal curvilinear coordinates
A method for computing three-dimensional, turbulent, compressible boundary layers in a time-dependent inverse mode has been developed and results compared with measurements. The three-dimensional inverse formulation is well suited for incorporation into an inviscid solver for viscous/inviscid interaction calculations.
It can be concluded that although the inverse formulation appears to yield more accurate solutions compared to solutions obtained from the direct formulation, the present inverse form of the equations has coefficient matrices which yield complex eigenvalues for some flow conditions. For the van den Berg infinite swept wing case, this appears to result in instabilities when solving the equations using a four-stage Runge-Kutta scheme, whereas the MacCormack scheme enabled a converged solution to be obtained. However, the latter solution magnifies the inherent inadequacies of integral methods which must rely upon empirical correlations being accurate over a very wide range of flow conditions. Accuracy of the present integral method will therefore be limited until more general correlations, particularly the crossflow velocity profile model, are incorporated into the code.
KeywordsTurbulent Boundary Layer AIAA Paper Flow Angle Compressible Boundary Layer Edge Velocity
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- 1.Swafford, T. W., “Three-Dimensional, Time-Dependent, Compressible, Turbulent, Integral Boundary-Layer Equations in General Curvilinear Coordinates and Their Numerical Solution,” Ph.D Dissertation, Mississippi State University, Mississippi State, MS, August 1983 (Also AEDC-TR-83-37, Arnold Air Force Station, TN, September 1983).Google Scholar
- 2.Swafford, T. W. and Whitfield, D. L., “Numerical Solutions of Three-Dimensional Time-Dependent Compressible Turbulent Integral Boundary-Layer Equations in General Curvilinear Coordinates,” AIAA Paper No. 83-1674, July 1983.Google Scholar
- 3.Whitfield, D. L., “Analytical Description of the Complete Two-Dimensional Turbulent Boundary-Layer Velocity Profile,” AEDC-TR-77-79, Arnold Air Force Station, TN, September 1977 (also AIAA Paper No. 78-1158, July 1978).Google Scholar
- 4.Johnston, J. P., “Three-Dimensional Turbulent Boundary Layers,” M.I.T. Gas Turbine Lab, Report 39, 1957.Google Scholar
- 5.Smith, P. D., “An Integral Prediction Method for Three-Dimensional Compressible Turbulent Boundary Layers,” RAE R&M No. 3739, December 1972.Google Scholar
- 6.Wigton, L. B. and Yoshihara, H., “Viscous-Inviscid Interactions with a Three-Dimensional Inverse Boundary Layer Code,” Paper presented at the 2nd Symposium on Numerical and Physical Aspects of Aerodynamic Flows, January 17–20, 1983, Long Beach, CA.Google Scholar
- 7.Samant, Satish S. and Wigton, Laurence B., “Coupled Euler/Integral Boundary Layer Analysis in Transonic Flow,” AIAA Paper No. 83-1806, July 1983.Google Scholar
- 8.Carter, J. E., “A New Boundary-Layer Inviscid Iteration Technique for Separated Flow,” AIAA Paper No. 79-1450, July 1979.Google Scholar
- 9.Donegan, Tracy, “Unsteady Viscous-Inviscid Interaction Procedures for Transonic Airfoil Flows,” M.S. Thesis, The University of Tennessee, Knoxville, TN, December 1983.Google Scholar
- 10.van den Berg, B. and Elsenaar, A., “Measurements in a Three-Dimensional Incompressible Turbulent Boundary Layer in an Adverse Pressure Gradient Under Infinite Swept Wing Conditions,” NLR TR 72092 U, 1972.Google Scholar
- 11.MacCormack, R. W., “The Effect of Viscosity in Hypervelocity Impact Cratering,” AIAA Paper No. 69-354, May 1969.Google Scholar
- 12.Jacocks, J. L. and Kneile, K. R., “Computation of Three-Dimensional Time-Dependent Flow Using the Euler Equations,” AEDC-TR-80-49, Arnold Air Force Station, TN, October 1980.Google Scholar