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NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗

NASA NTRS1986

Application of a computational model for vortex generators in subsonic internal flows

A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vorticity source term is used in a modified form of the Parabolized Navier-Stokes equations to model the shed vortex. Computed results are compared with idealized flow vortex paths, and with experimental data for vortex generators embedded in a thick turbulent boundary layer. The analysis is also compared with experimental data for a separated diffusing S-duct and for a diffusing S-duct with vortex generators. Quantitative comparisons are shown for the latter three cases. Emphasis is placed on verifying the ability of the model to predict global distortions in the flow field.

Kunik, W. G.↗

NASA NTRS1986

Application of a computational model for vortex generators in subsonic internal flows

Kunik, W. G.↗

NASA NTRS1987

Numerical experiments on transition control in wall-bounded shear flows

Results are presented from a numerical simulation of transition control in plane channel and boundary layer flows. The analysis is based on a pseudo-spectral/finite difference semi-implicit solution procedure employed to numerically integrate the time-dependent, three-dimensional, incompressible Navier-Stokes equations in a doubly periodic domain. In the channel flow, it was found that the active periodic suction/blowing method was effective in controlling strongly three-dimensional disturbances. In the boundary layer, the preliminary analysis indicated that in the early stages, passive control by suction is as effective as active control to suppress instabilities. The current work is focused on a detailed comparison of active and passive control by suction/blowing in the boundary layer.

Biringen, S.↗

NASA NTRS1989

Modeling of high speed chemically reacting flow-fields

The SPARK3D and SPARK3D-PNS computer programs were developed to model 3-D supersonic, chemically reacting flow-fields. The SPARK3D code is a full Navier-Stokes solver, and is suitable for use in scramjet combustors and other regions where recirculation may be present. The SPARK3D-PNS is a parabolized Navier-Stokes solver and provides an efficient means of calculating steady-state combustor far-fields and nozzles. Each code has a generalized chemistry package, making modeling of any chemically reacting flow possible. Research activities by the Langley group range from addressing fundamental theoretical issues to simulating problems of practical importance. Algorithmic development includes work on higher order and upwind spatial difference schemes. Direct numerical simulations employ these algorithms to address the fundamental issues of flow stability and transition, and the chemical reaction of supersonic mixing layers and jets. It is believed that this work will lend greater insight into phenomenological model development for simulating supersonic chemically reacting flows in practical combustors. Currently, the SPARK3D and SPARK3D-PNS codes are used to study problems of engineering interest, including various injector designs and 3-D combustor-nozzle configurations. Examples, which demonstrate the capabilities of each code are presented.

Drummond, J. P.↗

NASA NTRS1992

Streamwise Upwind, Moving-Grid Flow Algorithm

Extension to moving grids enables computation of transonic flows about moving bodies. Algorithm computes unsteady transonic flow on basis of nondimensionalized thin-layer Navier-Stokes equations in conservation-law form. Solves equations by use of computational grid based on curvilinear coordinates conforming to, and moving with, surface(s) of solid body or bodies in flow field. Simulates such complicated phenomena as transonic flow (including shock waves) about oscillating wing. Algorithm developed by extending prior streamwise upwind algorithm solving equations on fixed curvilinear grid described in "Streamwise Algorithm for Simulation of Flow" (ARC-12718).

Goorjian, Peter M.↗

NASA NTRS1961

Applicability of Mixing Length Theory to a Turbulent Vortex System

The ability of mixing length theory to correlate vortex data is evaluated. Expressions are derived for eddy diffusivity by applying the techniques of von Karman and Prandtl which have been established for pipe flow. Total and static pressures were measured from the outer radius to the exhaust-nozzle radius of a vortex generator for a range of mass flows. These data are combined with Navier-Stokes solutions for this region of a compressible vortex to determine turbulent Reynolds numbers. The Reynolds number is related to Prandtl and Karman functions for various assumed boundary conditions, and the experimental data are used to determine the usefulness of these expressions. The following conclusions were reached: (1) Mixing length functions developed by applying von Karman's similarity hypothesis to vortex motion correlate the data better than do Prandtl functions obtained with the assumption that mixing length is proportional to radius. (2) Some of the expressions developed do not adequately represent the experimental data. (3) The data are correlated with acceptable scatter by evaluating the fluid radial inertia at the outer boundary and the shear stress at the inner boundary. The universal constant K was found to be 0.04 to 0.08, rather than the value of 0.4 which is accepted for rectilinear flow. (4) The data are best correlated by a modified Karman expression which includes an effect of radial inertia, as well as shear stress, on eddy diffusivity.

Ragsdale, Robert G.↗

NASA NTRS2013

Analysis of Low-Speed Stall Aerodynamics of a Swept Wing with Laminar-Flow Glove

This is the presentation related to the paper of the same name describing Reynolds Averaged Navier Stokes (RANS) computational Fluid Dynamics (CFD) analysis of low speed stall aerodynamics of a swept wing with a laminar flow wing glove.

Bui, Trong↗

NASA NTRS1995

Design, construction and testing of annular diffusers for high speed civil transportation combustor applications

A theoretical and an experimental design study of subsonic flow through curved-wall annular diffusers is being carried out in order to establish the most pertinent design parameters for such devices and the implications of their application in the design of engine components in the aerospace industries. This investigation consists of solving numerically the full Navier Stokes and Continuity equations for the time-mean flow. Various models of turbulence are being evaluated for adoption throughout the study and comparisons would be made with experimental data where they exist. Assessment of diffuser performance based on the dissipated mechanical energy would also be made. The experimental work involves the application of Computer Aided Design software tool to the development of a suitable annular diffuser geometry and the subsequent downloading of such data to a CNC machine at Central State University. The results of the investigations are expected to indicate that more cost effective component design of such devices as effective component design of such devices as diffusers which normally contain complex flows can still be achieved. In this regard a review paper was accepted and presented at the First International Conference on High Speed Civil Transportation Research held at North Carolina A&T in December of 1994.

Okhio, Cyril B.↗

NASA NTRS1996

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗

NASA NTRS1992

Optimum design of ninety degree bends

An algorithm for the optimum design of an internal flow component to obtain the maximum pressure rise is presented. Maximum pressure rise in a duct with simultaneous turning and diffusion is shown to be related to the control of flow separation on the passage walls. Such a flow is usually associated with downstream conditions that are desirable in turbomachinery and propulsion applications to ensure low loss and stable performance. The algorithm requires the solution of an 'adjoint' problem in addition to the 'direct' equations governing the flow in a body, which in the present analysis are assumed to be the laminar Navier-Stokes equations. The theoretical framework and computational algorithms presented in this study are for the steady Navier-Stokes equations. A procedure is developed for the numerical solution of the adjoint equations. This procedure is coupled with a direct solver in a design iteration loop, that provides a new shape with a higher pressure rise. This procedure is first validated for the design of optimum plane diffusers in two-dimensional flow. The direct Navier-Stokes and the 'adjoint' equations are solved using a finite volume formulation for spatial discretization in an artificial compressibility framework. A simplified version of the above approach is then utilized to design ninety degree diffusing bends. Calculations were carried out for a mean radius ratio at inlet of 2.5 and Reynolds numbers varying from 100 to 500. While at this stage laminar flows is assumed, it is shown that a similar approach can be conceived for turbulent flows.

Modi, Vijay↗

NASA NTRS1985

Surface-slip equations for multicomponent, nonequilibrium air flow

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

Gupta, Roop N.↗

NASA NTRS1991

Flight test and numerical simulation of transonic flow around YAV-8B Harrier II wing

A computational fluid dynamics (CFD) method is used to study the aerodynamics of the YAV-8B Harrier II wing in the transonic region. A numerical procedure is developed to compute the flow field around the complicated wing-pylon-fairing geometry. The surface definition of the wing and pylons were obtained from direct measurement using theodolite triangulation. A thin-layer Navier-Stokes code with the Chimera technique is used to compute flow solutions. The computed pressure distributions at several span stations are compared with flight test data and show good agreement. Computed results are correlated with flight test data that show the flow is severely separated in the vicinity of the wing-pylon junction. Analysis shows that shock waves are induced by pylon swaybrace fairings, that the flow separation is much stronger at the outboard pylon and that the separation is caused mainly by the crossflow passing the geometry of wing-pylon junction.

Gea, Lie-Mine↗

NASA NTRS1985

Surface-slip equations for multicomponent nonequilibrium air flow

Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip.

Gupta, R. N.↗

NASA NTRS1995

Progress in Navier-Stokes Simulation of Delta Wing Maneuver Aerodynamics

This paper will summarize recent progress in the numerical simulation of high incidence vortical flow about a generic 65 degree sweep delta wing using the three dimensional, time-dependent, Reynolds averaged, Navier-Stokes (RANS) equations. Computations have been carried out at 15 and 30 degrees angle of attack under subsonic turbulent flow conditions, and compared with experimental data provided by Hanff, Jenkins, and their colleagues. This work has already been published elsewhere and widely disseminated. Computations carried out at 15 degrees angle of attack included static roll angles ranging up to 65 degrees, and a large-amplitude (40 degree), high rate (7 Hz), forced roll motion. There was very good agreement between computed and experimental forces and moments, and static surface pressures. There was a significant hysteresis of the dynamic rolling moment due to the high rate of roll motion. At this angle of attack, no vortex breakdown was observed in the computations or experiment. Computations were also carried out at 30 degrees angle of attack, where vortex breakdown was present in both the computations and experiment. There was overall good agreement in the computed and experimental forces and moments. The static rolling moment varied with roll angle in a highly nonlinear manner, and exhibited three stable trim points and two unstable trim points. This behavior was attributed to the presence of vortex breakdown. Two large-amplitude (30 degrees), high-rate (10 Hz) forced roll motions were computed. The dynamics of the vortex breakdown motion was dramatically visualized by tracking the time-dependent motion of particles released near the delta wing apex. This numerical visualization is analogous to experimental smoke flow techniques. In one of the dynamic cases the breakdown was found to move off the wing, convected downwind of the trailing edge, and later reformed near the trailing edge through an instability of the vortex core. A damped free-to-roll motion was also computed by releasing the wing from rest at 40 degrees of roll. The wing went to the same trim point as in the experiment.

Chaderjian, Neal M.↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

A rapid technique is used for calculating inviscid and viscous flows in turbomachinery cascades. The Euler and thin-layer Navier-Stokes equations are solved using the original explicit MacCormack algorithm. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. Convergence to a steady state is accelerated by use of a variable time-step and a multiple-grid scheme. Computer time is reduced through vectorization. Details of the numerical method are presented along with computed results for two low-speed wind tunnel turning vanes, a space shuttle fuel pump turbine rotor, and a supersonic inflow compressor rotor. The method can predict subtle viscous flow phenomena in cascades and is fast enough to be used as a design tool.

Chima, R. V.↗

NASA NTRS1984

Computation of viscous flow in planar and axisymmetric ducts by an implicit marching procedure

A streamwise marching procedure, approximately 200 times faster than a full Navier-Stokes procedure with comparable accuracy, is presented for solving problems of compressible viscous subsonic flow. Results are presented and compared with experimental data for the cases of developing turbulent flow in a circular pipe; turbulent flow in a two-dimensional S-duct; and turbulent flow in a typical subsonic diffuser. Prior to each main marching step, a preliminary marching step is taken in which the integral continuity equation and an uncoupled form of the streamwise momentum equation are solved simultaneously to obtain the viscous pressure correction. During the main marching step the equations for continuity, streamwise momentum, cross-flow momentum, and energy are solved simultaneously as a coupled system using an implicit finite-difference method, with the viscous pressure correction treated as a source term. The analysis may be used for flows with both favorable and adverse pressure gradients and to predict the location of flow separation.

Towne, C. E.↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

Chima, R. V.↗

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