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At least 631 records · Page 35
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NASA NTRS1990

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

Gnoffo, Peter A.↗
NASA NTRS1990

Effects of turbulence mixing, variable properties, and vaporization on spray droplet combustion

Combustion of liquid fuels in the form of spray droplets is simulated numerically. Various vaporization models are examined as to their performance in finite element calculations involving a turbulent flow field. The Eulerian coordinate for the gas and Lagrangian coordinate for the liquid spray droplets are coupled through source terms being updated in the equations of continuity, momentum, and energy. The k-epsilon and modified eddy breakup models are used for simulating turbulent spray combustion flow field. Numerical results for the droplet trajectories, droplet heating, recirculation characteristics, and effects of evaporation models are evaluated. It is also shown that the finite element method is advantageous in dealing with complex geometries, complex boundary conditions, adaptive unstructured grids.

Kim, Y. M.↗
NASA NTRS1989

Euler and Navier-Stokes solutions for hypersonic flows

An upwind finite-element technique that uses cell-centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured grids in two and three dimensions. A perfect gas model as well as an equilibrium air model is implemented for solving high-speed flows. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been used to predict 'Type III and IV' shock interactions on a cylinder in two dimensions and a swept cylinder in three dimensions, with a view to determine the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively-generated grids. Three-dimensional corner flow, typically encountered in engine inlets due to compression of the flow by ramps in the walls, is also modeled. This procedure is the first step in developing an integrated fluid, thermal, structural analysis capability for hypersonic flight vehicles like the National Aero-Space Plane.

Thareja, Rajiv R.↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1990

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the three-dimensional time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multi-stage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1990

Conical Euler simulation and active suppression of delta wing rocking motion

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

Lee, Elizabeth M.↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1990

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the 3-D time dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time integration scheme using a multistage Runge-Kutta procedure or an implicit time integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1990

CFD code evaluation for internal flow modeling

Research on the computational fluid dynamics (CFD) code evaluation with emphasis on supercomputing in reacting flows is discussed. Advantages of unstructured grids, multigrids, adaptive methods, improved flow solvers, vector processing, parallel processing, and reduction of memory requirements are discussed. As examples, researchers include applications of supercomputing to reacting flow Navier-Stokes equations including shock waves and turbulence and combustion instability problems associated with solid and liquid propellants. Evaluation of codes developed by other organizations are not included. Instead, the basic criteria for accuracy and efficiency have been established, and some applications on rocket combustion have been made. Research toward an ultimate goal, the most accurate and efficient CFD code, is in progress and will continue for years to come.

Chung, T. J.↗
NASA NTRS1991

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in a high gradient region or the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational costs. A detailed description is given of the enrichment and coarsening procedures and comparisons with alternative results and experimental data are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Rausch, Russ D.↗
NASA NTRS1991

Conical Euler methodology for unsteady vortical flows about rolling delta wings

A conical Euler methodology was developed to study unsteady vortex-dominated flows about rolling highly swept delta wings undergoing either forced or free-to-roll motions. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization of the Euler equations on an unstructured grid of triangles. Results are presented for a 75-deg swept sharp-leading-edge delta wing at a freestream Mach number of 1.2 and at alpha = 10, 20, and 30 deg. At the 10 and 20 deg, forced harmonic analyses indicate that the rolling moment coefficients provide a positive damping which is verified by free-to-roll calculations. In contrast, at 30 deg, a forced harmonic analysis indicates that the rolling moment coefficient provides a negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation.

Lee, Elizabeth M.↗
NASA NTRS1991

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper gives a detailed description of the enrichment and coarsening procedures and presents comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Rausch, Russ D.↗
NASA NTRS1991

Multi-Dimensional ENO Schemes for General Geometries

A class of ENO schemes is presented for the numerical solution of multidimensional hyperbolic systems of conservation laws in structured and unstructured grids. This is a class of shock-capturing schemes which are designed to compute cell-averages to high order accuracy. The ENO scheme is composed of a piecewise-polynomial reconstruction of the solution form its given cell-averages, approximate evolution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is based on an adaptive selection of stencil for each cell so as to avoid spurious oscillations near discontinuities while achieving high order of accuracy away from them.

Harten, Ami↗
NASA NTRS1991

Multi-resolution analysis for ENO schemes

Given an function, u(x), which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. This multi-resolution analysis was applied to essentially non-oscillatory (ENO) schemes in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. An efficient algorithm for implementing this program in the 1-D case is presented; this algorithm can be extended to the multi-dimensional case with Cartesian grids.

Harten, Ami↗
NASA NTRS1991

Multidisciplinary modeling and simulation of a generic hypersonic vehicle

The modeling and simulation of hypersonic vehicles which involve the interaction of a number of major technical disciplines including aerodynamics, structures, heat transfer, propulsion, and control engineering are described. Finite element numerical formulations of individual disciplines including their appropriate integration for multidisciplinary simulation are presented. An efficient unstructured grid generation strategy, evolved by modifying an existing code, is developed.

Gupta, K. K.↗
NASA NTRS1992

A nearly-monotone genuinely multidimensional scheme for the Euler equations

Recent progress made in the development of a genuinely multidimensional finite-volume method for the Euler equations is reported. In this method, wave information is derived from a reconstruction procedure applied to the data on a triangle. The algorithm is therefore best suited to application on an unstructured grid. A flux formula which provides nearly-monotone solutions is also presented. The new method is tested on three simple 2D flows, and the results show that dominant-wave resolution is high, and that strong-wave transitions are nearly monotone.

Parpia, Ijaz H.↗
NASA NTRS1993

Advancing-Front Algorithm For Delaunay Triangulation

Efficient algorithm performs Delaunay triangulation to generate unstructured grids for use in computing two-dimensional flows. Once grid generated, one can optionally call upon additional subalgorithm that removes diagonal lines from quadrilateral cells nearly rectangular. Resulting approximately rectangular grid reduces cost per iteration of flow-computing algorithm.

Merriam, Marshal L.↗
NASA NTRS1993

Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. A detailed description of the enrichment and coarsening procedures are presented and comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply.

Rausch, Russ D.↗