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Finite difference method for calculating inviscid flow field around supersonic/hypersonic space shuttle
Computer program for determining radiating nonadiabatic inviscid flow over blunt body by integral equations
The results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration are presented. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown.
A three-dimensional potential analysis has been formulated and applied to the inviscid flow over a turbofan forced mixer. The method uses a unique small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a symmetric mixer in a planar duct. In addition calculations showing pressure distributions and induced secondary vorticity fields are presented for practical turbofan mixer configurations, and where possible, comparison has been made with available experimental data.
A small disturbance formulation for the three-dimensional potential analysis of the inviscid flow over a turbofan forced mixer configuration in which the governing equations are reduced by means of a flux volume formulation along a Cartesian grid is presently extended to include the effects of power addition within the potential formulation. Calculations are presented for practical turbofan mixer designs, and comparison calculations are also given with measured surface pressure distributions and measured axial velocity profiles.
Recent advances in computational techniques and computer hardware have made it possible to attack the problem of computing steady-state inviscid flowfields over complex three-dimensional bodies such as the Space Shuttle Orbiter. Certain problems have arisen in connection with cases involving high angles of attack. Weilmuenster et al. (1981, 1982) have, therefore, presented a time asymptotic computational method, HALIS, designed to handle the high angle-of-attack problem for the inviscid flow over the Space Shuttle vehicle. The code was modified to include all of the Shuttle vehicle forward of the wing root. Body surface pressures generated by the HALIS code were shown to be in excellent agreement with flight pressures measured on the Shuttle vehicle. In the present investigation, results from the HALIS code, which has been extended to cover the first 1212 inches of the Shuttle vehicle, are compared with flight surface pressures. Shock shapes at several angles of attack are also presented.
Package of three programs accurately and efficiently computes inviscid super/hypersonic flow field about complex vehicle geometries.
In the setting of the conservation element-solution element (CE/SE) method, a new and unified wall boundary treatment for the Navier-Stokes and Euler Equations is proposed. In essence, the shear stress exerted on the fluid by a wall is modeled as a source term as a part of local spacetime flux conservation in the vicinity of a wall boundary. When the fluid is inviscid, the source term vanishes and the boundary condition reduces to the usual 'slip' condition. On the other hand, when the fluid is viscous, the source-term effect is consistent with the traditional no-slip condition. Numerical results show that the new treatment is robust, efficient, and accurate for viscous and inviscid flows.
Procedures and methods for predicting aerothermodynamic heating to delta orbiter shuttle vehicles were reviewed. A number of approximate methods were found to be adequate for large scale parameter studies, but are considered inadequate for final design calculations. It is recommended that final design calculations be based on a computer code which accounts for nonequilibrium chemistry, streamline spreading, entropy swallowing, and turbulence. It is further recommended that this code be developed with the intent that it can be directly coupled with an exact inviscid flow field calculation when the latter becomes available. A nonsimilar, equilibrium chemistry computer code (BLIMP) was used to evaluate the effects of entropy swallowing, turbulence, and various three dimensional approximations. These solutions were compared with available wind tunnel data. It was found study that, for wind tunnel conditions, the effect of entropy swallowing and three dimensionality are small for laminar boundary layers but entropy swallowing causes a significant increase in turbulent heat transfer. However, it is noted that even small effects (say, 10-20%) may be important for the shuttle reusability concept.
The applicability of a multigrid technique to block-structured, body-fitted meshes is examined focusing on three different strategies. In the first strategy data are exchanged between blocks in each stage of a five-stage Runge-Kutta time-stepping scheme which keeps a possible time lag between blocks to a minimum, but requires a large amount of I/O operations and storage. The second strategy is based on performing a complete Runge-Kutta cycle within a block before switching to the next. In the third strategy both a complete Runge-Kutta cycle and the residual evaluation for the restriction operator are done within a block, allowing a minimum of I/O and storage. The inviscid flow around a wing-body/engine-pylon configuration was computed on a mesh consisting of 11 computational blocks. It was found that both the first and the second strategies delivered converged results, but the third failed due to larger time lag between blocks.
A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects for equilibrium air are included using curve fits of Mollier charts. This report deals only with modifications to these procedures in four specific areas: inlet mass ingestion, subsonic axial Mach number, improved conformal mappings, and vehicles flying at yaw. In each area both the modifications to the computational procedures and computer code are discussed.
Finite difference method for unified solutions to inviscid supersonic flow distribution about blunt bodies
In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.
A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
Application of a general method for calculation of inviscid hypersonic flow fields is discussed. General considerations are analyzed along with the sonic corner and the stagnation region. It is concluded that the complications caused by the requirement for sonic flow at the rear corner and particularly by the uncertain position of the stagnation streamline lead to sufficient difficulties with convergence of iterations that a practical procedure is not likely to be found.
Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.
Recent progress in the development of finite element methodology for the prediction of aerothermal loads is described. Two dimensional, inviscid computations are presented, but emphasis is placed on development of an approach extendable to three dimensional viscous flows. Research progress is described for: (1) utilization of a commerically available program to construct flow solution domains and display computational results, (2) development of an explicit Taylor-Galerkin solution algorithm, (3) closed form evaluation of finite element matrices, (4) vector computer programming strategies, and (5) validation of solutions. Two test problems of interest to NASA Langley aerothermal research are studied. Comparisons of finite element solutions for Mach 6 flow with other solution methods and experimental data validate fundamental capabilities of the approach for analyzing high speed inviscid compressible flows.