Paul Kutler

Computation of Space Shuttle Flowfields Using Noncentered Finite-Difference Schemes

Second- and third-order, noncentered finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The advantages of noncentered methods over the more conventional centered schemes are: simpler programming logic, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. Second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability. These schemes are then used in a shock-capturing technique to determine the inviscid, supersonic flow field surrounding space shuttle vehicles (SSV). Resulting flow fields about typical pointed and blunted, delta-winged SSVs at angle of attack are presented and compared with experiment.

Second- and Third-Order Noncentered Difference Schemes for Nonlinear Hyperbolic Equations

Second- and third-order, explicit finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The schemes are uncentered in the sense that spatial derivatives are generally approximated by forward or backward difference quotients. The advantages of noncentered methods over the more conventional centered schemes are: programing logic is simpler, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. The von Neumann stability analysis for the proposed methods is reviewed and second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability.

A perspective of theoretical and applied computational fluid dynamics

O heighten his understanding of the fluid dynamics and aerodynamics pertinent to the early stages of the atmospheric flight-vehicle design process, the aerodynamicist has at his disposal three standard tools: analytical methods, computational procedures, and experimentation. Some of the advantages and disadvantages of each design tool are summarized in Fig. 1. Analytical methods provide quick, closed-form solutions, but they require unduly restrictive assumptions, can treat only simple configurations, and capture only the idealized aerodynamics. Through experimentation, representative or actual configurations can be tested and representative and complete aerodynamic data can be produced. Experimentation is costly, however, both in terms of the model and actual test time. In addition, the limited conditions that can be attained in wind tunnels restrict the scope of ex

Computation of three-dimensional, inviscid supersonic flows

The paper sets forth in detail a method for the finite-difference computation of three-dimensional supersonic fields in an Eulerian mesh. First-, second-, and third-order finite difference schemes are examined. Attention is given to proper treatment of the impermeable and permeable boundaries encompassing the computational plane. Numerical results are presented for certain specific configurations: a conical wing-body combination, internal corner flow, a two-dimensional blunt body, an interfering shock problem, and three-dimensional inviscid supersonic flow past a shuttle-orbiter type vehicle.

Two-Dimensional Unsteady Euler-Equation Solver for Arbitrarily Shaped Flow Regions

A new technique is described for solving supersonic fluid dynamics problems containing multiple regions of continuous flow, each bounded by a permeable or impermeable surface. Region boundaries are, in general, arbitrarily shaped and time dependent. Discretization of such a region for solution by conventional finite difference procedures is accomplished using an elliptic solver which alleviates the dependence on a particular base coordinate system. Multiple regions are coupled together through the boundary conditions. The technique has been applied to a variety of problems including a shock diffraction problem and supersonic flow over a pointed ogive.

Numerical solutions for supersonic corner flow

Abstract Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for swept-compressive and swept-expansive corner flows are obtained. The governing equations are written in strong conservation law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number (Re > 3 × 10 6 ) experimental data and show very good agreement. The results clearly show that supersonic corner flow at reasonably high Reynolds numbers including the effect of sweep is dominated by the inviscid field.

Diffraction of a Shock Wave by a Compression Corner: Part II - Single Mach Reflection

The two-dimensional time-dependent Euler equations which govern the flow field resulting from the interaction of a planar shock with a compression corner are solved for initial conditions which result in single Mach reflection of the incident planar shock. The Euler equations are first transformed to include the self-similarity of the flow field. A second transformation is employed to normalize the distances between the ramp and the reflected shock and between the wall and the Mach stem. The resulting equations in strong conservation-law form are solved using a second-order discontinuity-fitting finite-difference approach. The results are compared with experimental interferograms and existing first-order shock-capturing numerical solutions.

Three-dimensional, shock-on-shock interaction problem

The unsteady, three-dimensional flowfield resulting from the interaction of a plane shock with a cone-shaped vehicle traveling supersonically is determined, using a second-order, shock-capturing, finite-difference approach. The time-dependent, inviscid gasdynamic equations are transformed to include the self-similar property of the flow, to align various coordinate surfaces with known shock waves, and to cluster points in the vicinity of the intersection of the transmitted incident shock and the surface of the vehicle. The governing partial differential equations in conservation-law form are then solved iteratively using MacCormacks (1969) algorithm.

Status of computational fluid dynamics in the United States

CFD-related progress in U.S. aerospace industries and research institutions is evaluated with respect to methods employed, their applications, and the computer technologies employed in their implementation. Goals for subsonic CFD are primarily aimed at greater fuel efficiency; those of supersonic CFD involve the achievement of high sustained cruise efficiency. Transatmospheric/hypersonic vehicles are noted to have recently become important concerns for CFD efforts. Attention is given to aspects of discretization, Euler and Navier-Stokes general purpose codes, zonal equation methods, internal and external flows, and the impact of supercomputers and their networks in advancing the state-of-the-art.

The computation of supersonic flow fields about wing-body combinations by “shock-capturing” finite difference techniques

Supersonic flow field computation for wing-body combinations by shock-capturing finite difference techniques, discussing improvement based on Runge-Kutta method