Compressible Navier-Stokes Solutions over Low Reynolds Number Airfoils

Unsteady, laminar and turbulent, compressible and incompressible flow at low Reynolds numbers over a Wortmann FX63–137 airfoil is numerically modeled by solving the time-averaged two-dimensional compressible Navier-Stokes equations by means of the implicit central difference scheme of Beam-Warming. Recent improvements in efficiency, accuracy and convergence for the approximate factorization scheme are employed, including nonlinear artificial dissipation and refined body and farfield boundary conditions. C-type grids are generated by the hyperbolic grid generation technique. Turbulence is modeled by the modified algebraic turbulence model of Baldwin-Lomax and various transition criteria are tested. Results cover a range of test cases with Re ∞ =60,000 to 700,000 and M ∞ =0.01 to 0.5 for which experimental and computational results exist.

[1]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[2]  Thomas J. Mueller,et al.  Boundary layer characteristics of the Miley airfoil at low Reynolds numbers , 1983 .

[3]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[4]  R. F. Warming,et al.  An Implicit Factored Scheme for the Compressible Navier-Stokes Equations , 1977 .

[5]  Paul S. Granville Baldwin-Lomax factors for turbulent boundary layers in pressure gradients , 1987 .

[6]  J. Steger Implicit Finite-Difference Simulation of Flow about Arbitrary Two-Dimensional Geometries , 1978 .

[7]  M. D. Salas,et al.  Far-field boundary conditions for transonic lifting solutions to the Euler equations , 1986 .

[8]  P. D. Thomas Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory , 1979 .

[9]  T. Mueller,et al.  Laminar Separation, Transition, and Turbulent Reattachment near the Leading Edge of Airfoils , 1980 .

[10]  Tuncer Cebeci,et al.  Calculation of compressible turbulent boundary layers with heat and mass transfer , 1970 .

[11]  B. Mueller Navier-Stokes solution for hypersonic flow over an indented nosetip , 1985 .

[12]  Two dimensional hyperbolic grid generation , 1987 .

[13]  H. C. Yee,et al.  High-Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows , 1990 .

[14]  H. C. Yee,et al.  Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations , 1986 .

[15]  Henri Viviand,et al.  Computation of Viscous Compressible Flows based on the Navier-Stokes Equations, , 1975 .

[16]  S. M. Batill,et al.  Experimental studies of the laminar separation bubble on a two-dimensional airfoil at low Reynolds numbers , 1980 .

[17]  W. Hankey,et al.  Numerical solution of the Navier Stokes equations for supersonic turbulent flow over a compression ramp , 1975 .

[18]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[19]  H. Schlichting Boundary Layer Theory , 1955 .