Euler and Navier-Stokes solutions for flow over a conical delta wing
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Newsome, R. W.↗
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Euler analysis of forebody-strake vortex flows at supersonic speeds
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Rose, O. J.↗
Subsonic Analysis of 0.04-Scale F-16XL Models Using an Unstructured Euler Code
The subsonic flow field about an F-16XL airplane model configuration was investigated with an inviscid unstructured grid technique. The computed surface pressures were compared to wind-tunnel test results at Mach 0.148 for a range of angles of attack from 0 deg to 20 deg. To evaluate the effect of grid dependency on the solution, a grid study was performed in which fine, medium, and coarse grid meshes were generated. The off-surface vortical flow field was locally adapted and showed improved correlation to the wind-tunnel data when compared to the nonadapted flow field. Computational results are also compared to experimental five-hole pressure probe data. A detailed analysis of the off-body computed pressure contours, velocity vectors, and particle traces are presented and discussed.
Lessard, Wendy B.↗
A finite element formulation of Euler equations for the solution of steady transonic flows
The main objective of the considered investigation is related to the development of a relaxation scheme for the analysis of inviscid, rotational, transonic flow problems. To formulate the equations of motion for inviscid flows in a fixed coordinate system, an Eulerian type variational principle is required. The derivation of an Eulerian variational principle which is employed in the finite element formulation is discussed. The presented numerical method describes the mathematical formulation and the application of a numerical process for the direct solution of steady Euler equations. The development of the procedure as an extension of existing potential flow formulations provides the applicability of previous procedures, e.g., proper application of the artificial viscosity for supersonic elements, and the accurate modeling of the shock.
Ecer, A.↗
Aerodynamic properties of turbulent combustion fields
Flow fields involving turbulent flames in premixed gases under a variety of conditions are modeled by the use of a numerical technique based on the random vortex method to solve the Navier-Stokes equations and a flame propagation algorithm to trace the motion of the front and implement the Huygens principle, both due to Chorin. A successive over-relaxation hybrid method is applied to solve the Euler equation for flows in an arbitrarily shaped domain. The method of images, conformal transformation, and the integral-equation technique are also used to treat flows in special cases, according to their particular requirements. Salient features of turbulent flame propagation in premixed gases are interpreted by relating them to the aerodynamic properties of the flow field. Included among them is the well-known cellular structure of flames stabilized by bluff bodies, as well as the formation of the characteristic tulip shape of flames propagating in ducts. In its rudimentary form, the mechanism of propagation of a turbulent flame is shown to consist of: (1) rotary motion of eddies at the flame front, (2) self-advancement of the front at an appropriate normal burning speed, and (3) dynamic effects of expansion due to exothermicity of the combustion reaction. An idealized model is used to illustrate these fundamental mechanisms and to investigate basic aerodynamic features of flames in premixed gases. The case of a confined flame stabilized behind a rearward-facing step is given particular care and attention. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and reattachment length.
Hsiao, C. C.↗
Supersonic wing and wing-body shape optimization using an adjoint formulation
This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used to~eviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.
Reuther, James↗
A comparison of high resolution upwind solvers on 3-D inviscid hypersonic flows
A detailed comparison of numerical results obtained by solving the Euler equations for the inviscid flow over delta wings in reentry configurations is presented. The investigation involves a side-by-side comparison between independently developed upwind Euler solvers at VKI (M3D) and NASA Johnson Space Center (E3D) using identical grids. In both solvers the governing equations are integrated by means of time marching finite volume shock capturing methods, based on a cell centered upwind evaluation of the cell face fluxes and nonlinear limiters. High resolution schemes are obtained via MUSCL characteristic variable extrapolation to ensure total variation diminishing (TVD) properties and therefore monotonic discontinuity capturing. Further comparisons are made with several published results by other authors based on both upwind and central discretizations. The present results contribute in asserting the high resolution upwind TVD schemes as the most reliable numerical technique to handle the strong discontinuities typical of high speed flows. The performances of the two upwind solvers are satisfactory and the numerical results in good agreement. However, the important issue of reaching a grid converged solution for the present complex three-dimensional inviscid flow problems was not achieved.
Manna, M.↗
A New Paradigm for Flow Analyses and a Novel Technique to Enhance the Thrust from Scarfed Nozzles
A new flow analysis paradigm and a novel technique to enhance scarfed nozzle thrust are presented. The new paradigm, the space-time Conservation Element and Solution Element (CESE) method, a truly unsteady and genuinely multi-dimensional flow solver that provides accurate solutions for Euler and Navier-Stokes flows, is well suited for next generation flow analyses.In this study, the space-time CESE method was applied to solve scarfed nozzles flow-fields. Nozzle scarfing is frequently used for vectoring control of a space propulsion sub-system; it reduces nozzle weight and length and lowers nozzle thrust. A novel technique to enhance scarfed nozzles' thrust is discussed and investigated. Results of 2D and 3D flow analyses are presented.
Chang, I-Shih↗
A comparison of Euler and Navier-Stokes solutions for supersonic flow over a conical delta wing
The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.
Newsome, R. W.↗
Scalar formulation of ideal charged gas flow.
Scalar formulation of ideal charged adiabatic gas flow in presence of gravitational and electromagnetic fields
IDEAL GAS↗
Time-dependent hydrodynamic phenomena in the envelopes of the Be stars
Temporal and angular variations in the motion and distribution of circumstellar material about Be stars are studied by means of a simple hydrodynamical approach. The flow variables are each written as the sum of a known, steady-state axisymmetric term and a smaller component which contains both temporal and angular dependence. Substitution of these dichotomous expressions for the flow variables into Euler's equation and the continuity equation leads to a set of linearized equations for the terms which depend on time and angle. Solutions can be found to a somewhat approximated version of the linearized equations, and these solutions explain the qualitative features of the observed short-time variations.
Morgan, T. H.↗
Upwind relaxation algorithms for Euler/Navier-Stokes equations
A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.
Thomas, J. L.↗
A computational challenge - Euler solution for ellipses
The Euler equations for flow past an ellipse are solved numerically. A computationally complex problem involving inviscid flow past an elliptical two-dimensional surface at subcritical Mach number and angle of attack is introduced. A lifting solution for any combination of grid and/or angle of attack which is nonsymmetric is obtained.
Pulliam, Thomas H.↗
Viscous shock profiles and primitive formulations
Weak solutions of hyperbolic systems in primitive (non-conservation) form for which a consistent conservation form exists are considered. It is shown that primitive formulations, shock relations are not uniquely defined by the states to either side of the shock but also depend on the viscous path connecting the two. Scheme-dependent high order correction terms are derived that enforce consistent viscous shock profiles. The resulting primitive algorithm is conservative to the order of approximation. One dimensional Euler calculations of flows containing strong shocks clearly show that conservation errors in primitive flow calculations are of comparable quality.
Karni, S.↗
Calculation Of Aeroelastic Transients Using Euler Equations
Method for calculation of transient aeroelastic effects on airplane wings based on Euler equations of flow. Conforming grids facilitate calculations of flows about changing shapes. Capability to compute aeroelastic effects reduces cost of developing aircraft.
Guruswamy, Guru P.↗
Performance of a parallel code for the Euler equations on hypercube computers
The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.
Barszcz, Eric↗
Euler/experiment correlations of sonic boom pressure signatures
The ability of inviscid computational fluid dynamics (CFD) codes to compute sonic boom pressure signatures is examined using three different codes that solve the Euler equations of fluid flow on structured hexahedral and unstructured tetrahedral grids. The results of these Euler codes were evaluated by comparing the computed pressure signatures with near-field experimental data. The computational pressure signatures were determined at distances of one body length or less below the configuration in the plane of symmetry and extrapolated to experimental distances. The extrapolated CFD pressure signatures gave acceptable correlations with experimental data, provided that fine grids were used near the surface and downstream of the configuration.
Cliff, Susan E.↗
Some recent applications of Navier-Stokes codes to rotorcraft
Many operational limitations of helicopters and other rotary-wing aircraft are due to nonlinear aerodynamic phenomena incuding unsteady, three-dimensional transonic and separated flow near the surfaces and highly vortical flow in the wakes of rotating blades. Modern computational fluid dynamics (CFD) technology offers new tools to study and simulate these complex flows. However, existing Euler and Navier-Stokes codes have to be modified significantly for rotorcraft applications, and the enormous computational requirements presently limit their use in routine design applications. Nevertheless, the Euler/Navier-Stokes technology is progressing in anticipation of future supercomputers that will enable meaningful calculations to be made for complete rotorcraft configurations.
Mccroskey, W. J.↗