Numerical computation of viscous flow around bodies and wings moving at supersonic speeds

Research in aerodynamics is discussed. The development of equilibrium air curve fits; computation of hypersonic rarefield leading edge flows; computation of 2-D and 3-D blunt body laminar flows with an impinging shock; development of a two-dimensional or axisymmetric real gas blunt body code; a study of an over-relaxation procedure forthe MacCormack finite-difference scheme; computation of 2-D blunt body turbulent flows with an impinging shock; computation of supersonic viscous flow over delta wings at high angles of attack; and computation of the Space Shuttle Orbiter flowfield are discussed

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results

Simplified curve fits for the transport properties of equilibrium air

New, improved curve fits for the transport properties of equilibruim air have been developed. The curve fits are for viscosity and Prandtl number as functions of temperature and density, and viscosity and thermal conductivity as functions of internal energy and density. The curve fits were constructed using grabau-type transition functions to model the tranport properties of Peng and Pindroh. The resulting curve fits are sufficiently accurate and self-contained so that they can be readily incorporated into new or existing computational fluid dynamics codes. The range of validity of the new curve fits are temperatures up to 15,000 K densities from 10 to the -5 to 10 amagats (rho/rho sub o)

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures were developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data

Improved curve fits for the thermodynamic properties of equilibrium air suitable for numerical computation using time-dependent or shock-capturing methods, part 1

Simplified curve fits for the thermodynamic properties of equilibrium air were devised for use in either the time-dependent or shock-capturing computational methods. For the time-dependent method, curve fits were developed for p = p(e, rho), a = a(e, rho), and T = T(e, rho). For the shock-capturing method, curve fits were developed for h = h(p, rho) and T = T(p, rho). The ranges of validity for these curves fits were for temperatures up to 25,000 K and densities from 10 to the minus 7th power to 10 to the 3d power amagats. These approximate curve fits are considered particularly useful when employed on advanced computers such as the Burroughs ILLIAC 4 or the CDC STAR

Simplified curve fits for the thermodynamic properties of equilibrium air

New, improved curve fits for the thermodynamic properties of equilibrium air have been developed. The curve fits are for pressure, speed of sound, temperature, entropy, enthalpy, density, and internal energy. These curve fits can be readily incorporated into new or existing computational fluid dynamics codes if real gas effects are desired. The curve fits are constructed from Grabau-type transition functions to model the thermodynamic surfaces in a piecewise manner. The accuracies and continuity of these curve fits are substantially improved over those of previous curve fits. These improvements are due to the incorporation of a small number of additional terms in the approximating polynomials and careful choices of the transition functions. The ranges of validity of the new curve fits are temperatures up to 25 000 K and densities from 10 to the -7 to 10 to the 3d power amagats

Numerical computation of space shuttle orbiter flow field

The complete inviscid viscous real gas flow around the Space Shuttle Orbiter was computed. Real gas effects are important in predicting the reentry environment around the Orbiter because the high temperatures within the shock layer cause the air to dissociate and ionize, thus invalidating the perfect gas assumption. It is shown that real gas effects has a significant influence on the Orbiter aerodynamics. The approach utilizes a time dependent Navier-Stokes code to compute the subsonic nose portion of the flow field. This nose solution provides the initial conditions for the parabolized Navier-Stokes (PNS) code

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed

Simplified curve fits for the thermodynamic properties of equilibrium air

New improved curve fits for the thermodynamic properties of equilibrium air were developed. The curve fits are for p = p(e,rho), a = a(e,rho), T = T(e,rho), s = s(e,rho), T = T(p,rho), h = h(p,rho), rho = rho(p,s), e = e(p,s) and a = a(p,s). These curve fits can be readily incorporated into new or existing Computational Fluid Dynamics (CFD) codes if real-gas effects are desired. The curve fits were constructed using Grabau-type transition functions to model the thermodynamic surfaces in a piecewise manner. The accuracies and continuity of these curve fits are substantially improved over those of previous curve fits appearing in NASA CR-2470. These improvements were due to the incorporation of a small number of additional terms in the approximating polynomials and careful choices of the transition functions. The ranges of validity of the new curve fits are temperatures up to 25,000 K and densities from 10 to the minus 7th to 100 amagats (rho/rho sub 0)

Numerical computation of two-dimensional viscous blunt body flows with an impinging shock

A time dependent finite difference method used to calculate blunt body flows with impinging shock is reported. The use of the method to predict maximum heat rates and pressure is discussed