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At least 289 records · Page 16

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NASA NTRS1989

Totally parallel multilevel algorithms for sparse elliptic systems

The fastest known algorithms for the solution of a large elliptic boundary value problem on a massively parallel hypercube all require O(log(n)) floating point operations and O(log(n)) distance-1 communications, if massively parallel is defined to mean a number of processors proportional to the size n of the problem. The Totally Parallel Multilevel Algorithm (TPMA) that has, as special cases, four of these fast algorithms is described. These four algorithms are Parallel Superconvergent Multigrid (PSMG), Robust Multigrid, the Fast Fourier Transformation (FFT) based Spectral Algorithm, and Parallel Cyclic Reduction. The algorithm TPMA, when described recursively, has four steps: (1) project to a collection of interlaced, coarser problems at the next lower level; (2) apply TPMA, recursively, to each of these lower level problems, solving directly at the lowest level; (3) interpolate these approximate solutions to the finer grid, and to verage them to form an approximate solution on this grid; and (4) refine this approximate solution with a defect-correction step, using a local approximate inverse. Choice of the projection operator (P), the interpolation operator (Q), and the smoother (S) determines the class of problems on which TPMA is most effective. There are special cases in which the first three steps produce an exact solution, and the smoother is not needed (e.g., constant coefficient operators).

Frederickson, Paul O.↗

NASA NTRS1991

Unsteady-flow-field predictions for oscillating cascades

The unsteady flow field around an oscillating cascade of flat plates with zero stagger was studied by using a time marching Euler code. This case had an exact solution based on linear theory and served as a model problem for studying pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step size was shown for a moderate reduced frequency. Results show that an approximate nonreflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer to the airfoils than when reflective boundaries are used. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates captures the unsteady flow field better than when uniform grids are used as long as the 'Courant Friedrichs Levy' (CFL) number is less than 1 for a sufficient portion of the grid. Finally, a solution based on an optimization of grid, CFL number, and boundary conditions shows good agreement with linear theory.

Huff, Dennis L.↗

NASA NTRS2019

A Correction Method for Unsteady Transonic Aerodynamics

This paper presents a new method for transonic pitching airfoils based on a RANS CFD study and the Theodorsen model of an oscillating pitching flat plate. This study quantifies the deviation of the lift coefficient predictions using CFD from that obtained using the Theodorsen model, which is based on the incompressible potential flow assumption. The present method corrects this theoretical model by modulating the Theodorsen functions by coefficient functions that depend on the reduced frequency and the Mach number. It is demonstrated that the modified theoretical model predicts lift coefficient in good agreement with the CFD results in the Mach number range from incompressible (M =0.2) to transonic (M =0.755) flow for a range of reduced frequencies typical of transonic flutter. The simulations are first validated by comparing pitching NACA0012 airfoil results with experimental results at transonic flight conditions, which establishes the requirements for a grid converged unsteady transonic solution. The hysteresis loop, Cl versus α, attains a grid independent solution that compares well with experiment. The present correction method will guide the development of a new state space model for the Variable Camber Continuous Trailing Edge Flap (VCCTEF) system and eventually a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the future aircraft systems in development under the NASA Advanced Air Transportation Technologies (AATT) project.

Kaul, Upender K.↗

NASA NTRS1984

A practical adaptive-grid method for complex fluid-flow problems

A practical solution, adaptive-grid method utilizing a tension and torsion spring analogy is proposed for multidimensional fluid flow problems. The tension spring, which connects adjacent grid points to each other, controls grid spacings. The torsion spring, which is attached to each grid node, controls inclinations of coordinate lines and grid skewness. A marching procedure was used that results in a simple tridiagonal system of equations at each coordinate line to determine grid-point distribution. Multidirectional adaptation is achieved by successive applications of one-dimensional adaptation. Examples of applications for axisymmetric afterbody flow fields and two dimensional transonic airfoil flow fields are shown.

Nakahashi, K.↗

NASA NTRS1988

Prediction of the oscillating incompressible aerodynamics of a loaded airfoil cascade by a locally analytical method

A complete first order model is developed to predict the oscillating incompressible aerodynamics of an airfoil cascade, including the effects of steady loading. The cascade steady and unsteady flow fields are analyzed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components each of which is described by a Laplace equation. An analytical solution in individual grid elements of a body fitted computational grid is then determined, with the complete solution obtained by assembling these local solutions. The capabilities and validity of this model and solution technique are demonstrated by considering the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Chiang, Hsiao-Wei D.↗

NASA NTRS1990

Cascade aerodynamic gust response including steady loading effects

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first-order model is formulated. The flow is analyzed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body-fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analyzing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Chiang, Hsiao-Wei D.↗

NASA NTRS2000

DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed

Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.

Liou, Meng-Sing↗

NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testing on a Blunt Mars Entry Vehicle Concept

Supersonic retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle was simulated using the Overflow Computational Fluid Dynamics (CFD) solver. Two nozzle configurations were tested (1E and 1F) as a subset of the seven total configurations in the Descent System Study (DSS) testing campaign. A generalized, Adaptive Mesh Refinement (AMR) shock capturing and plume refinement technique was developed and calibrated for producing automatic and unique grid systems optimized for any given testing condition. Solution independence from grid resolution was determined by successively increasing grid refinement until asymptotic convergence of the mean aerodynamic loads was observed. Overflow Reynolds-averaged Navier-Stokes (RANS) solutions produced realistic SRP flow phenomena, including Mach disk normal shocks contained in high-thrust plumes and bow shock triple-points. Solutions for the 1E nozzle configuration were steady. Conversely, a subset of the 1F test conditions were unsteady and exhibited periodic, non-sinusoidal expansions and contractions of the streamwise-oriented plume, resulting in unsteady aerodynamic loads on the vehicle. Initial investigations into the effect of turbulence modeling fidelity demonstrated significant differences between the aerodynamic loads simulated with RANS and Detached Eddy Simulation (DES). Multiple flow mechanisms were identified as root causes of these differences, including bow shock shape augmentation and reduced entrainment due to reduced turbulence in the DES simulations. Initial comparisons of pitching moment control authority and aerodynamic drag performance between the tested nozzle configurations demonstrated that the 1E configuration may be more advantageous for the Mars Entry, Descent, and Landing (EDL) task.

Supersonic Retropropulsion↗

NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testing on a Blunt Mars Entry Vehicle Concept

Supersonic Retropropulsion↗

NASA NTRS1991

Navier-Stokes solutions for an oscillating double-delta wing

An upwind-biased implicit scheme is used to investigate steady-state and unsteady Navier-Stokes solutions of the vortical flow over a double-delta wing configuration. The governing equations are solved numerically with a fully upwind, implicit, iterative, and factorized numerical scheme. Steady-state solutions for fixed angles of attack and unsteady solutions for a sinusoidal oscillatory motion are obtained. The steady-state solutions on the baseline grid are in agreement with the experiment, and grid refinements show some improvements of the predictions. The higher-order accuracy of the present scheme yields equivalent solutions on smaller grid densities compared to solutions obtained with a second-order accurate method on larger grids. As the angle of attack increases, the grid resolution requirements for adequate resolution of the leeward-side vortical flowfield become very severe. The unsteady solutions are in general agreement with the measurements and show a qualitative correlation with the experiment.

Ekaterinaris, John A.↗

NASA NTRS1989

Computation of aircraft component flow fields at transonic Mach numbers using a three-dimensional Navier-Stokes algorithm

A computer analysis was developed for calculating steady (or unsteady) three-dimensional aircraft component flow fields. This algorithm, called ENS3D, can compute the flow field for the following configurations: diffuser duct/thrust nozzle, isolated wing, isolated fuselage, wing/fuselage with or without integrated inlet and exhaust, nacelle/inlet, nacelle (fuselage) afterbody/exhaust jet, complete transport engine installation, and multicomponent configurations using zonal grid generation technique. Solutions can be obtained for subsonic, transonic, or hypersonic freestream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin shear layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flow field solution is determined on a body-fitted computational grid. A fully-implicit alternating direction implicit method is employed for the solution of the finite difference equations. For viscous computations, either a two layer eddy-viscosity turbulence model or the k-epsilon two equation transport model can be used to achieve mathematical closure.

Shrewsbury, George D.↗

NASA NTRS1983

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Johnson, G. M.↗

NASA NTRS1983

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results is substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed. Previously announced in STAR as N83-21847

Johnson, G. M.↗

NASA NTRS1990

A time-accurate adaptive grid method and the numerical simulation of a shock-vortex interaction

A time accurate, general purpose, adaptive grid method is developed that is suitable for multidimensional steady and unsteady numerical simulations. The grid point movement is performed in a manner that generates smooth grids which resolve the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling of the adaptive grid and the PDE solver is performed with a grid prediction correction method that is simple to implement and ensures the time accuracy of the grid. Time accurate solutions of the 2-D Euler equations for an unsteady shock vortex interaction demonstrate the ability of the adaptive method to accurately adapt the grid to multiple solution features.

Bockelie, Michael J.↗

NASA NTRS1994

On the vortical-flow-prediction capability of an unstructured-grid Euler solver

The results from a concentrated computational effort are presented with the primary objective being directed at evaluating the vortical-flow-prediction capability of an unstructured-grid Euler solver. Both viscous and inviscid solutions, obtained from an established structured-grid method, along with experimental wind-tunnel data are used as benchmark measures to assess the validity of the unstructured-grid Euler results. Viscous effects on vortical flows are first identified by comparing the viscous and inviscid solutions obtained from the structured-grid method. Computational data analysis is then presented which reveals excellent correlations between the inviscid structured and unstructured-grid results in terms of off-surface flow structures, surface pressure distribution, and the predicted longitudinal aerodynamic characteristics. The sensitivity of the unstructured-grid inviscid solutions to grid refinement is also discussed along with an analysis of the convergence and performance characteristics for each method.

Unstructured grid↗

NASA NTRS1994

On the Vortical-Flow Prediction Capability of an Unstructured-Grid Euler Solver

The results from a concentrated computational effort are presented with the primary objective being directed at evaluating the vortical-flow-prediction capability of an unstructured-grid Euler solver. Both viscous and inviscid solutions, obtained from an established structured-grid method, along with an experimental wind-tunnel data are used as bench-mark measures to assess the validity of the unstructured-grid Euler results. Viscous effects on vortical flows are first identified by comparing the viscous and inviscid solutions obtained form the structured-grid method. Computational data analysis are then presented which reveal excellent correlations between the inviscid structured and unstructured-grid results in terms of off-surface flow structures, surface pressure distribution and the predicted longitudinal aerodynamic characteristics. The sensitivity of the unstructured-grid inviscid solutions to grid refinement is also discussed along with an analysis of the convergence and performance characteristics for each method.

Unstructured grid↗

NASA NTRS2004

Single Airfoil Gust Response Problem: Category 3, Problem 1

An unsteady aerodynamic code, called GUST3D (ref. 3), has been developed to solve equation (8) for flows with periodic vortical disturbances. The code uses a frequency-domain approach with second-order central differences and a pressure radiation condition in the far field. GUST3D requires as input certain mean flow quantities which are calculated separately by a potential flow solver. The solver calculates the mean ow using a Gothert's Rule approximation (ref. 3). On the airfoil surface, it uses the solution calculated by the potential code FLO36 (ref. 4). Figures 1-2 show the mean pressure along the airfoil surface for the two airfoil geometries. In Figures 3 - 8, we present the RMS pressure on the airfoil surface. Each figure shows three GUST3D solutions (calculated on grids with different far-field boundary locations). Three solutions are shown to provide some indication of the numerical uncertainty in the results. Figures 9 - 13 present the acoustic intensity. We again show three solutions per case. Note that no results are presented for the k1 = k2 = 2.0 loaded airfoil case, as an acceptable solution could not be obtained. A few comments need to be made about the results shown. First, since the last Workshop, the GUST3D code has been substantially upgraded. This includes implementing a more accurate far-field boundary condition (ref. 5) and developing improved gridding capabilities. This is the reason for any differences that may exist between the present results and results from the last Workshop. Second, the intensity results on the circle R = 4C were obtained using a Kirchoff method (ref. 6). The Kirchoff surface was the circle R = 2C. Finally, the GUST3D code is most accurate for low reduced frequencies. A new domain decomposition approach (ref. 7) has been developed to improve accuracy. Both the single domain and domain decomposition approaches were used in generating the present results.

Scott, James R.↗

NASA NTRS1988

Fast interpolation schemes for moving grids

Search algorithms are developed for efficiently locating interpolation points to facilitate transfer of data in moving grid and related problems. Applications in the construction of adaptive grids and in the solution of problems on composite grids are included.

Mastin, C. Wayne↗