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At least 541 records · Page 30

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NASA NTRS1989

Convergence acceleration of viscous and inviscid hypersonic flow calculations

The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presented for various cases; and a 50 percent savings in computer time is usually achieved. An analytical formula for the overrelaxation factor is derived, and the performance of this scheme is confirmed numerically. Moreover, application of this overrelaxation scheme produces a favorable preconditioning for Wynn's epsilon-algorithm. Both techniques have been extended to viscous three-dimensional flows and applied to accelerate the convergence of the compressible Navier-Stokes code. A savings of 40 percent in computer time is achieved in this case.

Cheer, A.↗

NASA NTRS1990

Prediction of vortical flows on wings using incompressible Navier-Stokes equations

Grid-density and Reynolds-number effects on integral values and static pressure distributions are presently studied in the steady-state Navier-Stokes solutions obtained for the flow around a round-edged double delta wing using an upwind-relaxation finite-difference algorithm. It is found that while the computed longitudinal aerodynamic coefficients are in good agreement with extant experimental data, the magnitudes of suction-pressure peaks are underpredicted in the vicinity of the trailing edge. It is judged that additional computations employing finer-grid solutions in the vortical flow region are required.

Hsu, C.-H.↗

NASA NTRS1987

A computational study of the flowfield surrounding the Aeroassist Flight Experiment vehicle

A symmetric total variation diminishing (STVD) algorithm has been applied to the solution of the three-dimensional hypersonic flowfield surrounding the Aeroassist Flight Experiment (AFE) vehicle. Both perfect-gas and chemical nonequilibrium models have been used. The perfect-gas flows were computed at two different Reynolds numbers, including a flight trajectory point at maximum dynamic pressure, and on two different grids. Procedures for coupling the solution of the species continuity equations with the Navier-Stokes equations in the presence of chemical nonequilibrium are reviewed and tested on the forebody of the AFE and on the complete flowfield assuming noncatalytic wall and no species diffusion. Problems with the STVD algorithm unique to flows with variable thermodynamic properties (real gas) are identified and algorithm modifications are suggested. A potential heating problem caused by strong flow impingement on the nozzle lip in the near wake at 0-deg angle of attack has been identified.

Gnoffo, Peter A.↗

NASA NTRS1989

Multigrid calculations of 3-D turbulent viscous flows

Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.

Yokota, Jeffrey W.↗

NASA NTRS1989

Multigrid calculations of 3-D turbulent viscous flows

Yokota, Jeffrey W.↗

NASA NTRS1991

Navier-Stokes Simulation Of Wind-Tunnel Flow

Report describes three-dimensional Navier-Stokes simulation of transonic flow past model wing in wind tunnel and in free air. Numerical integration performed by LU-ADI factorization algorithm. Simulation shows effects of walls of tunnel.

Obayashi, S.↗

NASA NTRS1989

Computational fluid dynamics on a massively parallel computer

A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.

Jespersen, Dennis C.↗

NASA NTRS1992

An analysis of the flow field in the region of the ASRM field joints

The flow field in the region of a solid rocket motor field joint is very important since fluid dynamic and mechanical propellant stresses can couple to cause a motor failure at a joint. Presented here is an examination of the flow field in the region of the Advanced Solid Rocket Motor (ASRM) field joints. The analyses were performed as a first step in assessing the design of the ASRM forward and aft field joints in order to assure the proper operation of the motor prior to further development of test firing. The analyses presented here were performed by employing a two-dimensional axisymmetric assumption. Fluent/BFC, a three dimensional full Navier-Stokes flow field code, was used to make the numerical calculations. This code utilizes a staggered grid formulation along with the SIMPLER numerical algorithm. Wall functions are used to determine the character of the laminar sublayer, and a standard kappa-epsilon turbulence model is used to close the fluid dynamic equations. The analyses performed to this date verify that the ASRM field joint design operates properly. The fluid dynamic stresses at the field joints are small due to the inherent design of the field joints. A problem observed in some other solid rocket motors is that large fluid dynamic stresses are generated at the motor joint on the downstream propellant grain due to forward facing step geometries. The design of the ASRM field joints are such that this is not a problem as shown by the analyses. Also, the analyses of the inhibitor stub left protruding into the port flow from normal propellant burn back show that more information is necessary to complete these analyses. These analyses were performed as parametric analyses in relation to the height of the inhibitor stub left protruding into the motor port. A better estimate of the amount of the inhibitor stub remaining at later burn times must be determined since the height which the inhibitor stub protrudes into the port flow drastically affects the fluid dynamics induced stresses on the propellant grain at the field joints.

Dill, Richard A.↗

NASA NTRS1992

Propulsion-related flowfields using the preconditioned Navier-Stokes equations

A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.

Venkateswaran, S.↗

DOE OSTI2021

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Feasibility of a special-purpose computer to solve the Navier-Stokes equations

Orders-of-magnitude improvements in computer performance can be realized with a parallel array of thousands of fast microprocessors. In this architecture, wiring congestion is minimized by limiting processor communication to nearest neighbors. When certain standard algorithms are applied to a viscous flow problem and existing LSI technology is used, performance estimates of this conceptual design show a dramatic decrease in computational time when compared to the CDC 7600.

Gritton, E. C.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1986

Efficient solution methods for the Navier-Stokes equations

Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed. The methods are demonstrated in fully vectorized codes for a Cray type architecture. The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used. The methods are either time accurate or accelerated non-time accurate steady state schemes. Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented. Two dimensional inviscid and viscous calculations (e.g., airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed.

Pulliam, T. H.↗

NASA NTRS1989

A numerical study of the contrarotating vortex pair associated with a jet in a crossflow

An implicit two-factor partially flux split solver for the thin-layer Navier-Stokes equations is used to solve the aerodynamic/propulsive interaction between a subsonic jet exhausting perpendicularly through a flat plat plate into a crossflow. The algorithm is applied to flows with a range of jet to crossflow velocity ratios between 4 and 8. The computed velocity field is analyzed and comparisons are made with experimentally determined properties of the contrarotating vortex pair.

Roth, Karlin R.↗

NASA NTRS1989

Solution of the incompressible Navier-Stokes equations using artificial compressibility methods

A modified artificial compressibility formulation is derived from a preconditioned low Mach number compressible formulation, and these two methods are compared on a two-dimensional laminar leading edge flow using a LBI/ADI solution algorithm. The two methods are essentially equivalent with appropriate preconditioning parameters and have the same convergence rates and efficiency, giving 4 orders of residual reduction in about 75 iterations with a vectorized CRAY-XMP run time of 20 seconds for 3000 grid points.

Briley, W. R.↗

NASA NTRS1990

Enhanced thermochemical nonequilibrium computations of flow around the aeroassist flight experiment vehicle

A three-dimensional explicit, finite-rate, shock-capturing numerical algorithm is used to calculate thermochemical nonequilibrium flowfields about the Aeroassist Flight Experiment vehicle at one of its flight trajectory points. The full Navier-Stokes equations and an eleven species chemical model with the latest reaction rates are incorporated into the code. Results are compared against experimental data and other numerical solutions. The effects of changes to the physical model on the stagnation line and base region flow and surface quantities on the forebody are investigated.

Palmer, Grant↗

NASA NTRS1995

High-order essentially non-oscillatory methods for computational aeroacoustics

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. In addition, it is desirable to highly resolve discontinuities that can develop in the solutions of the Euler or Navier-Stokes equations. The class of essentially non-oscillatory (ENO) shock-capturing schemes has been designed to have both of these properties. The dual capacity of ENO schemes for high-order accuracy and non-oscillatory shock-capturing is achieved through the use of adaptive stenciling, which makes these schemes highly nonlinear. These schemes are briefly described and referenced herein. A fourth-order algorithm is then applied to the solution of an acoustic wave in a quasi-one-dimensional converging-diverging nozzle.

Casper, Jay↗

NASA NTRS1994

Navier-Stokes Solutions of Rotor and Rotor-Body Flows

This paper will review the advances made recently in the Navier-Stokes CFD methods to simulate aerodynamics and aeroacoustics of helicopter rotors and rotor-body flows. Although a complete flowfield simulation of full helicopter is currently not feasible with these methods, impressive gains have been made in analyzing individual components of this complex problem in a very detailed manner. The use of the state-of-the-art numerical algorithms in solution methods, in conjunction with powerful supercomputers, like the Cray-2, have enabled noticeable progress to be made in modeling viscous-inviscid interactions, blade-vortex interactions, tip-vortex: simulation and wake effects, as well as high speed impulsive noise in hover and forward flight for isolated rotor blades. This paper will critically evaluate the presently available Euler and Navier-Stokes methods, both finite-difference and finite volume methods using structured and unstructured grids for helicopter applications for accuracy, suitability, and computational efficiency. The review will also include the recent progress made using overset grids to model rotor-body flows. All the material for this review will be drawn from the published material shown below.

Srinivasan, G. R.↗