John V. Rakich

Numerical Computation of Space Shuttle Laminar Heating and Surface Streamlines

Exact inviscid flowfield codes are used, together with a quasi-three-dimensional boundary-layer analysis, to provide estimates of the windward surface heating and streamline patterns of the shuttle orbiter vehicle under laminar flow conditions. The accuracy and limitations of the methods are established by comparison with available wind-tunnel experiments and with more exact numerical solutions for simple flows. Flight predictions are presented showing the effects of finite-rate (nonequilibrium) chemical reactions, and the effects of varying boundary-layer edge conditions due to the growth of the boundary layer into the inviscid flow (entropy-layer swallowing). Differences between flowfield predictions at wind-tunnel and nominal flight conditions are discussed.

Comparison of a two-dimensional shock impingement computation with experiment

Results of computations of two-dimensional viscous blunt-body flowfields with an impinging shock wave, with a time-dependent finite-difference method employed to solve the complete set of Navier-Stokes equations, are compared with experimental results. The experimental results were obtained in a 20-inch hypersonic tunnel with a planar shock impinging on the cylindrical leading edge of a fin, hence with the shock parallel to the centerline of the leading edge, so that type III and type IV interference patterns were generated. Close agreement is found. The overall effects of smoothing and grid size on the calculations are determined. A 31 x 51 mesh is adequate for wall pressure values (except in peaked regions).

Theoretical and Experimental Study of Supersonic Steady Flow around Inclined Bodies of Revolution

A three-dimensional method of characteristics is described and numerical results are critically assessed by comparison with the results of hypersonic wind-tunnel experiments. Calculations for a 15° half-angle sphere-cone have been performed for angles of attack up to a = 20°, and have been carried downstream 44 nose radii for a = 10°. Comparisons with pointed-cone calculations show that effects of bluntness persist at this distance. Pitot pressure distributions in the flowfield are in good agreement with experiment except on the leeward side of the body far from the nose, where low-energy, viscous fluid accumulates. The present calculations for 20° angle of attack indicate the formation of an embedded shock on the leeward side of the 15° sphere cone. Theoretical upwash angles around a Sears-Haack body are compared with classical slender body theory, indicating nonlinearities due to Mach number which may reduce the interference lift of wing-body combinations.

Three-dimensional flow calculation by the method of characteristics.

Characteristic method computer program for calculating three-dimensional supersonic flow around blunt and pointed bodies of revolution in reasonable time

Numerical solution of Space Shuttle Orbiter flowfield

The supersonic viscous laminar flow around the Space Shuttle Orbiter forebody has been computed with a parabolized Navier-Stokes code using a generalized coordinate transformation. The initial solution for the nose part of the Orbiter was obtained with a three-dimensional time-dependent Navier-Stokes solver. It was necessary to employ a wind-axis oriented coordinate system to obtain the initial solution with the time-dependent code. The generalized PNS technique was then used to march the solution downstream from the given initial data surface. An algebraic grid generation scheme was employed which accurately describes the body shape by clustering points at the wing tip and at the wing-body juncture. The computed heat-transfer coefficients, pressure coefficients, and shock shapes are compared with the available experimental data for 0 and 30 deg angle of attack.

Supersonic Laminar Viscous Flow Past a Cone at Angle of Attack in Spinning and Coning Motion

Computational results obtained with a parabolic Navier-Stokes marching code are presented for supersonic viscous flow past a pointed cone at angle of attack undergoing a combined spinning and coning motion. The code takes into account the asymmetries in the flowfield resulting from the motion and computes the asymmetric shock shape, crossflow and streamwise shear, heat transfer, crossflow separation and vortex structure. The side force and moment are also computed. Reasonably good agreement is obtained with the side force measurements of Schiff and Tobak. Comparison is also made with the only available numerical inviscid analysis. It is found that the asymmetric pressure loads due lo coning motion are much larger than all other viscous forces due lo spin and coning, making viscous forces negligible in the combined motion.

Numerical solution of Space Shuttle Orbiter flow field

The supersonic, viscous laminar flow around the Space Shuttle Orbiter forebody has been computed with a parabolized Navier-Stokes code using a generalized coordinate transformation. The initial solution for the nose part of the Orbiter geometry was obtained with a three-dimensional time-dependent Navier-Stokes solver. It was necessary to employ a wind axis oriented coordinate system to obtain the initial solution with the time-dependent code. The generalized PNS technique used in this study allows the solution to be marched from the given initial data surface to any desired surface downstream. A grid point clustering scheme was employed to accurately describe the body shape by clustering points at the wing tip and at the wing body juncture. The computed heat transfer coefficients, pressure coefficients, and shock shapes are compared with the available experimental data for 0 degrees and 30 degrees angle of attack.

Navier-Stokes calculations for laminar and turbulent hypersonic flow over indented nosetips

A time-accurate finite-difference Navier-Stokes code has been used to calculate the viscous flow over a severely indented blunt body in a supersonic stream. An algebraic turbulence model is used and the results are compared with experimental data from wind-tunnel tests. Qualitative agreement is obtained for the surface pressure distribution and flow-field structure, including the separated bubble in the indented region. However, uncertainties still exist in the heating calculations, which are attributed to the turbulence model. For both laminar and turbulent calculations, the flow exhibits a fundamental unsteady character at a frequency of about 50 kHz.