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At least 163 records · Page 9

The Proteus Navier-Stokes code

An effort is currently underway at NASA Lewis to develop two and three dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. Proteus solves the Reynolds-averaged, unsteady, compressible Navier-Stokes equations in strong conservation law form. Turbulence is modeled using a Baldwin-Lomax based algebraic eddy viscosity model. In addition, options are available to solve thin layer or Euler equations, and to eliminate the energy equation by assuming constant stagnation enthalpy. An extensive series of validation cases have been run, primarily using the two dimensional planar/axisymmetric version of the code. Several flows were computed that have exact solution such as: fully developed channel and pipe flow; Couette flow with and without pressure gradients; unsteady Couette flow formation; flow near a suddenly accelerated flat plate; flow between concentric rotating cylinders; and flow near a rotating disk. The two dimensional version of the Proteus code has been released, and the three dimensional code is scheduled for release in late 1991.

Towne, Charles E.↗

Single-grid spectral collocation for the Navier-Stokes equations

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Bernardi, Christine↗

Calculation of a simulated 3-D high speed inlet using the Navier-Stokes equations

A hybrid numerical algorithm, developed to solve the full three-dimensional Navier-Stokes equations, is applied to the computation of the flowfield in a simulated three-dimensional high speed aircraft inlet at a Mach number of 2.5 and Reynolds number of 1.4 x 10 to the 7th based on inlet length. The numerical algorithm incorporates a coordinate transformation in order to handle general flow geometries, and utilizes the algebraic turbulent eddy viscosity model of Baldwin and Lomax. The hybrid algorithm has been vectorized on the CDC CYBER 203 computer using the SL/1 vector programming language developed at NASA Langley. The computed results are compared with experimental measurements of the ramp and cowl static pressures, and boundary layer pitot profiles. The results are also compared with a previous two-dimensional Navier-Stokes computation of the same configuration. The agreement with the experimental data is generally good; however, additional improvements in turbulence modeling are needed.

Knight, D. D.↗

Baseline Validation of Unstructured Grid Reynolds-Averaged Navier-Stokes Toward Flow Control

The value of the use of the Reynolds-averaged Navier-Stokes methodology for active flow control applications is assessed. An experimental flow control database exists for a NACA0015 airfoil modified at the leading edge to implement a fluidic actuator; hence, this configuration is used. Computational results are documented for the baseline wing configuration (no control) with the experimental results and assumes two-dimensional flow. The baseline wing configuration has discontinuities at the leading edge, trailing edge, and aft of midchord on the upper surface. A limited number of active flow control applications have been tested in the laboratory and in flight. These applications include dynamic stall control using a deformable leading edge, separation control for takeoff and landing flight conditions using piezoelectric devices, pulsed vortex generators, zero-net-mass oscillations, and thrust vectoring with zero-net-mass piezoelectric-driven oscillatory actuation. As yet, there is no definitive comparison with experimental data that indicates current computational capabilities can quantitatively predict the large aerodynamic performance gains achieved with active flow control in the laboratory. However, one study using the Reynolds-averaged Navier-Stokes (RANS) methodology has shown good quantitative agreement with experimental results for an isolated zero-net-mass actuator. In addition, some recent studies have used RANS to demonstrate qualitative performance gains compared with the experimental data for separation control on an airfoil. Those quantitative comparisons for both baseline and flow control cases indicated that computational results were in poor quantitative agreement with the experiments. The current research thrust will investigate the potential use of an unstructured grid RANS approach to predict aerodynamic performance for active flow control applications building on the early studies. First the computational results must quantitatively match experiments for the no-control case before proceeding to the time-dependent flow control case. This paper documents the baseline (no-control) case using an unswept airfoil configuration. The next section describes the configurations used for the computations and the experimentals. The computational approach is then described followed by results and concluding remarks.

Joslin, Ronald D.↗

Navier-Stokes calculations of scramjet-nozzle-afterbody flowfields

A comprehensive computational fluid dynamics effort was conducted from 1987 to 1990 to properly design a nozzle and lower aft end of a generic hypersonic vehicle powered by a scramjet engine. The interference of the exhaust on the control surfaces of the vehicle can have adverse effects on its stability. Two-dimensional Navier-Stokes computations were performed, where the exhaust gas was assumed to be air behaving as a perfect gas. Then the exhaust was simulated by a mixture of Freon-12 and argon, which required solving the Navier-Stokes equations for four species: (nitrogen, oxygen, Freon-12, and argon). This allowed gamma to be a field variable during the mixing of the multispecies gases. Two different mixing models were used and comparisons between them as well as the perfect gas air calculations were made to assess their relative merits. Finally, the three dimensional Navier-Stokes computations were made for the full-span scramjet nozzle afterbody module.

Baysal, Oktay↗

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

Compton, William B., III↗

An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry

High-order (p-type) finite element methods combine the geometric flexibility of standard low-order finite element (or finite volume) techniques with the rapid convergence properties of spectral methods. Various p-type schemes have been proposed for elliptic problems. However, an application of p-type methods to more complex equations, in particular the passive scalar or Navier-Stokes equations, is complicated by the nature of the equations and by efficiency considerations as regards the solution procedure. Patera (1984) has proposed a p-type method for the Navier-Stokes equations, taking into account the arising additional complications. The present study is concerned with an isoparametric spectral element discretization for the solution of flow problems in fully general, curvy geometries. Attention is given to the isoparametric formulation for elliptic equations and a time-splitting scheme for the Navier-Stokes equations.

Korczak, K. Z.↗

Analysis of turbulent flow about an isolated airfoil using a time dependent Navier-Stokes procedure

The procedure solves the Navier-Stokes equations by the consistently split linearized block implicit method of Briley and McDonald in a body fitted coordinate system. The procedure is described and results are presented for flow about an airfoil whose incidence changes from 6 degrees to 19 degrees at a Reynolds number of one million and Mach number of 0.2. In addition, the unsteady flow about an airfoil held at a constant 19 degree incidence is examined and compared to data.

Shamroth, S. J.↗

Study of hypersonic inlet flow fields with a three-dimensional Navier-Stokes code

A three-dimensional Navier-Stokes code is used to study the flow through an inlet with a rectangular capture area, but with circular or essentially circular internal cross-sections. The inlet may have a center body extending partially or fully over the length of the inlet. Calculations are made under a variety of geometrical constraints imposed on the inlet cross-sections to study the flow quality in the inlet. It is observed that for this class of inlets, the boundary layer has a tendency to thicken and separate readily due to the adverse pressure gradient caused by the continuous compression in the inlet. Since no experimental results are yet available, this paper has presented only the numerical results from the present analysis.

Kumar, A.↗

Propulsive-jet flow field analysis using the three-dimensional Navier-Stokes equations

A three-dimensional Navier-Stokes code has been applied to the analysis of flow fields containing propulsive jets. Specifically, the application was made to a flow field containing a supersonic jet injected at an angle of 90 degrees to a subsonic free stream. Although wind tunnel data were available, the computational results were not readily comparable to the experimental data because of significant differences between the two plume trajectories. Reasons for the differences are suggested in the report and include: (1) incomplete convergence, (2) inadequate grid resolution in the high gradient regions, and (3) use of a low-order turbulence closure model.

Reed, C. L.↗

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, Dimitri J.↗

An upwind-differencing scheme for the incompressible Navier-Stokes equations

The steady state incompressible Navier-Stokes equations in 2-D are solved numerically using the artificial compressibility formulation. The convective terms are upwind-differenced using a flux difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. Although the current study is limited to steady state problems, it is shown that this entire formulation can be used for solving unsteady problems. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudotime steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square-driven cavity, flow over a backward facing step, and flow around a 2-D circular cylinder.

Rogers, Stuart E.↗

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗

Recent advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations

A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.

Vatsa, Veer N.↗

Jet noise predictions from unsteady Navier-Stokes simulations

Numerical solutions of the Navier-Stokes equations are employed to predict the characteristics of round jets at supersonic speeds. The simulations are performed with a finite volume method which is fourth order accurate in space and second order in time. The overall sound pressure level (OASPL) in the near field of a round free jet is over-predicted by roughly 8 dB relative to an experimental correlation. In an impinging jet, shock motion and vortex stretching are identified as noise generation mechanisms in the impingement zone.

Childs, Robert E.↗

Implicit methods for the Navier-Stokes equations

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Yoon, S.↗

Prediction of airfoil stall using Navier-Stokes equations in streamline coordinates

A Navier-Stokes procedure to calculate the flow about an airfoil at incidence was developed. The parabolized equations are solved in the streamline coordinates generated for an arbitrary airfoil shape using conformal mapping. A modified k-epsilon turbulence model is applied in the entire domain, but the eddy viscosity in the laminar region is suppressed artificially to simulate the region correctly. The procedure was applied to airfoils at various angles of attack, and the results are quite satisfactory for both laminar and turbulent flows. It is shown that the present choice of the coordinate system reduces the error due to numerical diffusion, and that the lift is accurately predicted for a wide range of incidence.

Choi, D. H.↗

Analysis of a High-Lift Multi-Element Airfoil using a Navier-Stokes Code

A thin-layer Navier-Stokes code, CFL3D, was utilized to compute the flow over a high-lift multi-element airfoil. This study was conducted to improve the prediction of high-lift flowfields using various turbulence models and improved glidding techniques. An overset Chimera grid system is used to model the three element airfoil geometry. The effects of wind tunnel wall modeling, changes to the grid density and distribution, and embedded grids are discussed. Computed pressure and lift coefficients using Spalart-Allmaras, Baldwin-Barth, and Menter's kappa-omega - Shear Stress Transport (SST) turbulence models are compared with experimental data. The ability of CFL3D to predict the effects on lift coefficient due to changes in Reynolds number changes is also discussed.

Whitlock, Mark E.↗