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At least 181 records · Page 10

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗

Simple numerical method for predicting steady compressible flows

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

Vonlavante, Ernst↗

Two-dimensional subsonic compressible flow past elliptic cylinders

The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.

Kaplan, Carl↗

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Roberts, Thomas W.↗

Extension to an analysis of turbulent swirling compressible flow for application to axisymmetric small gas turbine ducts

An existing computer program, the Axisymmetric Diffuser Duct Code (ADD code), which calculates compressible turbulent swirling flow through axisymmetric ducts was modified to permit calculation of flows through small gas turbine ducts with struts, guide vanes and large degrees of turning. The improvements include a coordinate generator, an end-wall loss model, and a generalized geometry capability to describe struts and guide vanes in ducts which turn more than 90 degrees. An improved output format was developed to provide the solution on any arbitrary plane in the duct and an extensive literature survey of calculation procedures used in gas turbine technology was completed which suggests improvements in the computer code. Calculations are presented for the flow through the AGT101 small gas turbine inlet duct and turbine exhaust diffuser which demonstrate the ADD code modifications implemented in the investigation. The computed results compare favorably with experimental results.

Anderson, O. L.↗

Slow plastic strain rate compressive flow in binary CoAl intermetallics

Constant-velocity elevated temperature compression tests have been conducted on a series of binary CoAl intermetallics produced by hot extrusion of blended prealloyed powders. The as-extruded materials were polycrystalline, and they retained their nominal 10-micron grain size after being tested between 1100 and 1400 K at strain rates ranging from 2 x 10 to the -4th to 2 x 10 to the -7th per sec. Significant plastic flow was obtained in all cases; while cracking was observed, much of this could be due to failure at matrix-oxide interfaces along extrusion stringers rather than to solely intergranular fracture. A maximum in flow strength occurs at an aluminum-to-cobalt ratio of 0.975, and the stress exponent appears to be constant for aluminum-to-cobalt ratios of 0.85 or more. It is likely that very aluminum-deficient materials deform by a different mechanism than do other compositions.

Whittenberger, J. D.↗

Simple numerical method for predicting steady compressible flows

The present numerical method for the solution of the isenthalpic form of the governing equations for compressible viscous and inviscid flows has its basis in the concept of flux vector splitting in its implicit form, and has been tested in the cases of several difficult viscous and inviscid configurations. An acceleration of time-marching to steady state is accomplished by implementing a multigrid procedure which effectively increases the convergence rate. The steady state results obtained are largely of good quality, and required only short computational times.

Von Lavante, E.↗

Calculation of the recirculating compressible flow downstream a sudden axisymmetric expansion

Significant progress has been made during the last five years to adapt conventional Navier-Stokes solver for handling nonconservative equations. A primary type of application is to use transport equation turbulence models, but the extension is also possible for describing the transport of nonpassive scalars, such as in reactive media. Among others, combustion and gas dissociation phenomena are topics needing a considerable research effort. An implicit two step scheme based on the well-known MacCormack scheme has been modified to treat compressible turbulent flows on complex geometries. Implicit treatment of nonconservative equations (in the present case a two-equation turbulence model) opens the way to the coupled solution of thermochemical transport equations.

Vandromme, D.↗

Enabling Metric-Based Mesh Adaptation for Advanced Compressible Flow Simulations Using US3D

This work presents a metric-based mesh adaptation capability added to the flow solver US3D that is used to improve the accuracy of atmospheric entry simulations. Flow past an entry vehicle in free-flight is usually unsteady and characterized by anisotropic flow features like a strong bow shock and small-scale isotropic flow features like turbulent eddies in the wake. The results presented in this paper demonstrate that we are currently able to iteratively apply metric-based mesh adaptation to improve the solution accuracy by simultaneously targeting isotropic and anisotropic flow features. A simplified workflow of running CFD simulations for entry vehicles is presented where we start off with a coarse initial mesh to compute a first approximation of the flow. This coarse mesh is then iteratively refined using the newly developed metric to improve the resolution of the CFD computation. Furthermore, we demonstrate that we are able to adapt large mesh sizes in a timely fashion which allows us to start thinking about applying this adaptive framework to unsteady atmospheric entry CFD simulations.

Mesh adaptation↗

On the effect of boundary layer growth on the stability of compressible flows

The method of multiple scales is used to describe a formally correct method based on the nonparallel linear stability theory, that examines the two and three dimensional stability of compressible boundary layer flows. The method is applied to the supersonic flat plate layer at Mach number 4.5. The theoretical growth rates are in good agreement with experimental results. The method is also applied to the infinite-span swept wing transonic boundary layer with suction to evaluate the effect of the nonparallel flow on the development of crossflow disturbances.

El-Hady, N. M.↗

Experimental investigation of a Mach 6 fixed-geometry inlet featuring a swept external-internal compression flow field

An investigation of a fixed-geometry, swept external-internal compression inlet was conducted at a Mach number of 6.0 and a test-section Reynolds number of 1.55 x 10 to the 7th power per meter. The test conditions was constant for all runs with stagnation pressure and temperature at 20 atmospheres and 500 K, respectively. Tests were made at angles of attack of -5 deg, 0 deg, 3 deg, and 5 deg. Measurements consisted of pitot- and static-pressure surveys in inlet throat, wall static pressures, and surface temperatures. Boundary-layer bleed was provided on the centerbody and on the cowl internal surface. The inlet performance was consistently high over the range of the angle of attack tested, with an overall average total pressure recovery of 78 percent and corresponding adiabatic kinetic-energy efficiency of 99 percent. The inlet throat flow distribution was uniform and the Mach number and pressure level were of the correct magnitude for efficient combustor design. The utilization of a swept compression field to meet the starting requirements of a fixed-geometry inlet produced neither flow instability nor a tendency to unstart.

Torrence, M. G.↗

A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

42 ENGINEERING↗

A two-equation turbulence model for compressible flows

A k-epsilon model of turbulence that accounts for pressure gradients and compressibility effects is presented. To correct the degradation of k-epsilon model performance when pressure gradients are introduced, an extra term is added to the dissipation equation. By including this term and by adding terms to account for compressibility effects, a new k-epsilon model is developed for shear flows. The results show that the new model performs better than the existing k-epsilon models.

Abid, Ridha↗