A noniterative, implicit, space-marching, finite-difference algorithm is developed for the steady thin-layer Navier-Stokes equations in conservation-law-form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Numerical Simulation of Steady Supersonic Viscous Flow

2 Kreith, F. and Sonju, O. K., "The Decay of a Turbulent Swirl in a Pipe," Journal of Fluid Mechanics, Vol. 22, No. 2, 1965, pp.257-271. 3 Menis, M., "Effect of Vortex Decay on Pipe Flow," Rept. 61, Nov. 1960, Gas Turbine Lab., MIT, Cambridge', Mass. 4 Youssef, T. E. A., "Some Investigations on Rotating Flow with a Recirculation Core in Straight Pipes," Paper 66-WA-FE-36, Nov. 27, 1966, American Society of Mechanical Engineers, New York. 5 Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960, pp. 53-54. 6 Thompson, J. R., Jr., "The Structure of Free and Confined Turbulent Vortices," Research Note 44, May 1963, Aero Physics Dept, Mississippi State University, State College, Miss. 7 Yeh, H., "Boundary Layer Along Annular Walls in a Swirling Flow," and "Discussion," Transactions of the ASME, May 1958, pp. 767-776. 8 Kinney, R. B., "Universal Velocity Similarity in Fully Turbulent Rotating Flows," ASME Paper 67-APM-23, June 1967, Applied Mechanic Conference, Pasadena, Calif. 9 Baker, D. W., "Decay of Swirling, Turbulent Flow of Incompressible Fluids in Long Pipes," Ph.D. thesis, 1967, Univ. of Maryland, College Park, Md. 10 Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960, pp. 441-144. 11 Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960, p. 503. 12 Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960, pp. 502-508.

Calculation of the Flow on a Cone at High Angle of Attack

The effects of equilibrium- and nonequilihrium-air chemical reactions on the linear stability of a Mach 25, 10-deg half-angle sharp-cone shock layer are investigated. First, the basic state is computed using the parabolized Navier-Stokes equations with a shock-fitting scheme. This eliminates spurious numerical oscillations that could adversely affect the stability analysis. Spatial stability analyses are then described for three different approximations of the physics: perfect gas, air in local chemical equilibrium, and air in chemical nonequilibrium. It is shown in both the equilibrium- and nonequilibrium-air calculations that the second mode of Mack is shifted to lower frequencies

Linear disturbances in hypersonic, chemically reacting shock layers

: The hypersonic viscous pressure interaction is treated by the development of a set of equations valid throughout the boundary layer, shock-wave structure and inviscid core. Primary interest is concerned with the nature of the leading edge continuum merged layer in which the shock wave and boundary layer are indistinguishable. Due to the parabolic nature of the equations, finite-difference solutions are attainable. The flow over a flat plate at zero incidence, as well as angle of attack, was considered. Velocity and state variable distributions across the viscous layer depict the formation of an outer shock wave and inner constant pressure boundary layer. The calculated values of surface pressure, heat transfer and shock jump conditions were at first significantly below the values predicted by strong interaction theory. Agreement was quite good downstream of the merged layer where Rankine-Hugoniot jump conditions were satisfied to within 8%. (Author)

Hypersonic viscous flow over slender bodies with sharp leading edges.

Viscous flow over a cone at moderate incidence—I

: Numerical solutions of a set of parabolic equations, uniformly valid throughout the entire continuum flow domain, were obtained for the axi-symmetric flow over slender sharp nose cones at zero angle of attack, the hypersonic interference flow between two finite length flat plates and the flow over a sharp flat plate of finite span. The regions of interest are the leading edge merged layer and the initial portion of the strong interaction flow. The analysis represents an extension of the theory first used successfully for the flow over two-dimensional sharp flat plates. Merged layer interference, the merging of streams at different pressures in the wake of the channel geometry, the three-dimensional flow and shock structure, as well as the significant differences between two-dimensional, and axi-symmetric or three-dimensional flow fields are discussed. Comparisons with available experimental data are good, as evidenced by surface pressure and heat transfer results, for the flow over cones. (Author)

M. Pierucci

Papers

Hypersonic interactions near sharp leading edges.