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At least 1,063 records · Page 59

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NASA NTRS1985

Computational aspects of zonal algorithms for solving the compressible Navier-Stokes equations in three dimensions

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.

Holst, T. L.↗

NASA NTRS1985

Shock modelling in transonic and supersonic flow

Numerical simulation studies of problems in transonic flow are conducted in connection with the design of aircraft flying near the speed of sound, while recently there has also been a great deal of interest in supersonic and hypersonic flow calculations. Three important models for inviscid compressible gasdynamics are utilized in the study of these flow problems, taking into account the transonic small disturbance equation (TSD), the transonic full potential equation (FP), and the full Euler equations for compressible gasdynamics (EU). The present paper has the objective to provide a description of shock capturing methods recently developed for each model. The design principles behind the algorithms are also examined, giving attention to consistency, conservative form, monotone and sharp discrete shocks, and a bound on the variation, which prevents spurious oscillations.

Osher, S.↗

NASA NTRS1989

A package for unstructured grid generation and finite element flow solvers

A set of programs for unstructured mesh construction, fluid flow calculation and flow field visualization in two and three dimensions is described. The grid generators are based on the advancing front concept. The flow solvers use the finite element methods with Flux Corrected Transport techniques to solve several sets of equations including the Euler and Burger's equations. Several examples show the flexibility and accuracy of the methods.

Gumbert, Clyde↗

NASA NTRS1991

Blade design and analysis using a modified Euler solver

An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.

Leonard, O.↗

NASA NTRS1992

LEWICE/E: An Euler based ice accretion code

A new version of the LEWICE ice accretion computer code was developed which calculates the ice growth on two dimensional surfaces, incorporating the effects of compressibility through the solution of the Euler equations. The code is modular and contains separate stand-alone program elements that create a grid, calculate the flow field parameters, calculate the droplet trajectory paths, determine the amount of ice growth, and plot results. This code increases the applicability of ice accretion predictions by allowing calculations at higher Mach numbers. The new elements of the code are described. Calculated results are compared to experiment for several cases, including a LEWICE example case and a thin airfoil section at a Mach number of 0.58.

Potapczuk, Mark G.↗

NASA NTRS1992

LEWICE/E - An Euler based ice accretion code

Potapczuk, Mark G.↗

NASA NTRS2001

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

Zhang, Zeng-Chan↗

NASA NTRS2012

Design of Rail Instrumentation for Wind Tunnel Sonic Boom Measurements and Computational-Experimental Comparisons

An innovative pressure rail concept for wind tunnel sonic boom testing of modern aircraft configurations with very low overpressures was designed with an adjoint-based solution-adapted Cartesian grid method. The computational method requires accurate free-air calculations of a test article as well as solutions modeling the influence of rail and tunnel walls. Specialized grids for accurate Euler and Navier-Stokes sonic boom computations were used on several test articles including complete aircraft models with flow-through nacelles. The computed pressure signatures are compared with recent results from the NASA 9- x 7-foot Supersonic Wind Tunnel using the advanced rail design.

Cliff, Susan E.↗

DOE OSTI2020

Instability of an electron-plasma shear layer in an externally imposed strain flow

The E x B shear instability of a two-dimensional (2D) filament (i.e., a thin, rectangular strip perpendicular to the magnetic field) of magnetized pure electron plasma is investigated experimentally in the presence of an externally imposed strain flow. Data are acquired using a specialized Penning–Malmberg trap in which strain flows can be applied in 2D by biasing segmented electrodes surrounding the plasma. The E x B drift dynamics are well-described by the Drift-Poisson equations, which are isomorphic to the 2D Euler equations describing ideal fluids. Thus, the experimental results correspond to the Rayleigh instability of a shear layer in a 2D ideal fluid, where the electron density is analogous to the fluid vorticity. Shear layers are prepared by stretching initially axisymmetric electron vortices using a strong, applied strain flow. The data at early times are in quantitative agreement with a linear model which extends Rayleigh’s work to account for the influence of an external strain flow. In the presence of weak strain, the system approximately maintains a phase relationship that corresponds to an instantaneous Rayleigh eigenmode. The instability develops into the nonlinear regime later in time and at smaller spatial scales as the strain rate is increased. A secondary vortex pairing instability is observed, but it is suppressed when the strain-to-vorticity ratio exceeds roughly 0.025. In this way, vorticity transport perpendicular to the filament is diminished due to the applied strain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1984

Adaptive grid refinement for the Euler and compressible Navier-Stokes equations

The incorporation of a simple a posteriori adaptive mesh method into an explicit finite element based procedure for the solution of compressible flow problems is described. The re-interpolation problem is discussed and results are presented that indicate the improvement in solution quality which can be obtained via such an adaptive mesh approach. The method may lead to the appearance of some badly deformed elements which are removed from the domain of computation.

Lohner, R.↗

NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

NASA NTRS1992

Long time behavior of unsteady flow computations

This paper addresses a specific issue of time accuracy in the calculation of external aerodynamic problems. The class of problems discussed consists of inviscid compressible subsonic flows. These problems are governed by a convective equation. A key issue that is not understood is the long time behavior of the solution. This is important if one desires transient calculations of problems governed by the Euler equations or its derivatives such as the small disturbance equations or the potential formulations for the gust problem. Difficulties arise for two dimensional problems where the time rate decay solutions of the wave equation is slow. In concert with the above mentioned problem, exterior flows require proper modeling of the boundary conditions. In particular, this requires the truncation of infinite regions into finite regions with the aid of artificial boundaries. These boundary conditions must be consistent with the physics of the unbounded problem as well as consistent in time and space. Our treatment of the problem is discussed in detail and examples are given to verify the results.

Hariharan, S. I.↗

NASA NTRS1985

Finite element algorithms for compressible flow computation on a supercomputer

Methods of applying computational fluid dynamics techniques to engineering problems are discussed. The linking factors between theoretical and applied research are the shape and weight functions which produce the Galerkin finite element schemes. The flow is unsteady, viscous, heat conducting and compressible, and steady-state flows are the asymptotic limit of unsteady flows. All flows are described by the time-averaged Navier-Stokes equations (NSE) with mass and energy conservation. Local curvilinear intrinsic coordinates are applied to discretize the NSE in arbitrary geometric domains. A modified weighted residuals approach defines the discrete analogs of the physical systems modeled and a general interpolants method is used to derive families of numerical models, both implicit and explicit, finite difference and finite elemnt, from a single point of departure. Time-dependent element approximations are achieved with a progressive assembly of generalized elements method. Hyperbolic steady-state Euler algorithms and quasi-parabolic are spatial marching algorithms for solving the discretized equations. Application of the techniques is illustrated through calculation of the compressible flow around a hypersonic flight vehicle at 100,000 ft at zero angle of attack at speeds of Mach 4-10.

Spradley, L. W.↗

NASA NTRS1992

Progress in unstructured-grid methods development for unsteady aerodynamic applications

The development of unstructured-grid methods for the solution of the equations of fluid flow and what was learned over the course of the research are summarized. The focus of the discussion is on the solution of the time-dependent Euler equations including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an implicit upwind method using a CFL number of infinity is presented for the Boeing 747 aircraft. The results were obtained in less than one hour CPU time on a Cray-2 computer, thus, demonstrating the speed and robustness of the capability. Additional calculations for the ONERA M6 wing demonstrate the accuracy of the method through the good agreement between calculated results and experimental data for a standard transonic flow case.

Batina, John T.↗

NASA NTRS1983

Streamwise computation of three-dimensional parabolic flows

A new approach to calculate three-dimensional parabolic flows is presented. The flow field is computed by calculating velocity along a set of streamlines. The dependent variables commonly used in the computation of three-dimensional flows are the three velocity components. In contrast, the dependent variables in the present approach are the streamwise velocity and the two coordinates, in the cross-stream plane, of the chosen streamlines. The streamwise velocity is calculated from the finite difference equations obtained by applying Euler's momentum theorem to streamtubes constructed around the chosen streamlines; the streamline coordinates are calculated from the conservation of mass. Results of the calculations, based on the present approach, are compared with the experimental data for flow through rectangular ducts; the agreement is satisfactory.

Greywall, M. S.↗

DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part II: linesweep ALE rezoning for nonconformal block-structured AMR meshes

The simulation of flows presenting contact discontinuities, vorticity, and large variations in spatial scales can be performed in a framework coupling Arbitrary Lagrangian Eulerian (ALE) algorithms and Adaptive Mesh Refinement (AMR). This coupling requires adaptation of ALE rezoning techniques to meshes containing nonconformal nodes arising from both the AMR topology and the junction of mesh blocks. Here, in this paper, we present an ALE rezoning strategy that is compatible with such meshes, and that can also act as a disentangling algorithm. Emphasis is put on an algorithm that respects intrinsic Lagrangian mesh properties in order to preserve accuracy around discontinuities. To that end, we adapt the weighted linesweep algorithm to nonconformal block-structured AMR meshes. Then, we present control parameters introduced in the method for it to be applicable in practical situations. Notably, the method is coupled to a specific metric optimization in order to palliate some shortcomings of the linesweep method. Finally, numerical test cases are presented that feature the capabilities of the ALE-AMR algorithm for flows that present discontinuities, vorticity, and a variety of scales. Notably, we show that our ALE-AMR algorithm gives results at least similar to Euler-AMR, but provides better accuracy in cases where discontinuities are involved, thanks to a method that respects the Lagrangian features of the mesh. Additionally, it enables Euler-AMR-like computations on domains with temporally varying domain boundaries.

Adaptive mesh refinement↗

NASA NTRS1983

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

Hussaini, M. Y.↗

NASA NTRS1985

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods - their history and especially their implementation - is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

Hussaini, M. Y.↗