Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “total variation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Numerical study of shock-wave/boundary layer interactions in premixed hydrogen-air hypersonic flows

A computational study of shock wave/boundary layer interactions involving premixed combustible gases, and the resulting combustion processes is presented. The analysis is carried out using a new fully implicit, total variation diminishing (TVD) code developed for solving the fully coupled Reynolds-averaged Navier-Stokes equations and species continuity equations in an efficient manner. To accelerate the convergence of the basic iterative procedure, this code is combined with vector extrapolation methods. The chemical nonequilibrium processes are simulated by means of a finite-rate chemistry model for hydrogen-air combustion. Several validation test cases are presented and the results compared with experimental data or with other computational results. The code is then applied to study shock wave/boundary layer interactions in a ram accelerator configuration. Results indicate a new combustion mechanism in which a shock wave induces combustion in the boundary layer, which then propagates outwards and downstream. At higher Mach numbers, spontaneous ignition in part of the boundary layer is observed, which eventually extends along the entire boundary layer at still higher values of the Mach number.

Yungster, Shaye↗
NASA NTRS1990

A numerical study of hypersonic stagnation heat transfer predictions at a coordinate singularity

The problem of grid induced errors associated with a coordinate singularity on heating predictions in the stagnation region of a three-dimensional body in hypersonic flow is examined. The test problem is for Mach 10 flow over an Aeroassist Flight Experiment configuration. This configuration is composed of an elliptic nose, a raked elliptic cone, and a circular shoulder. Irregularities in the heating predictions in the vicinity of the coordinate singularity, located at the axis of the elliptic nose near the stagnation point, are examined with respect to grid refinement and grid restructuring. The algorithm is derived using a finite-volume formulation. An upwind-biased total-variation diminishing scheme is employed for the inviscid flux contribution, and central differences are used for the viscous terms.

Grasso, Francesco↗
NASA NTRS1991

Efficient real gas upwinded Navier-Stokes computations of high speed flows

An efficient method to account for the chemically frozen thermodynamic and transport properties of air in three-dimensional Navier-Stokes calculations has been demonstrated. This approach uses an explicitly specified equation of state (EOS) so that the fluid pressure, temperature, and transport properties are directly related to the flow variables. The method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code. The flexibility of the EOS approach is shown by its implementation into a high-order total variation diminishing upwinding scheme as well as a standard central-differencing scheme. The EOS approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central-differencing schemes.

Coirier, William J.↗
NASA NTRS1990

A user guide for the EMTAC-MZ CFD code

The computer code (EMTAC-MZ) was applied to investigate the flow field over a variety of very complex three-dimensional (3-D) configurations across the Mach number range (subsonic, transonic, supersonic, and hypersonic flow). In the code, a finite volume, multizone implementation of high accuracy, total variation diminishing (TVD) formulation (based on Roe's scheme) is used to solve the unsteady Euler equations. In the supersonic regions of the flow, an infinitely large time step and a space-marching scheme is employed. A finite time step and a relaxation or 3-D approximate factorization method is used in subsonic flow regions. The multizone technique allows very complicated configurations to be modeled without geometry modifications, and can easily handle combined internal and external flow problems. An elliptic grid generation package is built into the EMTAC-MZ code. To generate the computational grid, only the surface geometry data are required. Results obtained for a variety of configurations, such as fighter-like configurations (F-14, AVSTOL), flow through inlet, multi-bodies (shuttle with external tank and SRBs), are reported and shown to be in good agreement with available experimental data.

Szema, Kuo-Yen↗
NASA NTRS1992

Nonlinearly stable compact schemes for shock calculations

The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. These ideas can also be applied to other implicit schemes such as the continuous Galerkin finite element methods.

Cockburn, Bernardo↗
NASA NTRS1992

Triangle based adaptive stencils for the solution of hyperbolic conservation laws

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Durlofsky, Louis J.↗
NASA NTRS1991

Time accurate Navier-Stokes computations of solid rocket motor internal field joint cavity flows

The low-speed flow of combustion gases in the Space Shuttle Solid Rocket Motor (SRM) following ignition are investigated with a time-accurate CFD technique. The flow of the combustion gases is examined in the forward joint section of the SRM at 80 s after ignition with attention given to the amplification of existing 'organ-pipe' modes of 15, 30, and 45 Hz resulting from frequency lock-in with vortex-shedding modes. The CFD code employed is a multizone compressible Navier-Stokes flow solver using a finite-volume, upwind-biased, total-variation-diminishing scheme. The vortex-generated oscillations generated by the inhibitor and the cavity at the forward field joint are described in terms of amplitude and frequency and related to the flow dynamics in the SRM. Oscillations are shown to occur spontaneously when the trailing edge of the cavity at the joint is sharp and can be amplified if the unburned portion of the inhibitor protrudes into the flow.

Farr, Rebecca A.↗
NASA NTRS1992

On central-difference and upwind schemes

A class of numerical dissipation models for central-difference schemes constructed with second- and fourth-difference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a Total Variation Diminishing (TVD) scheme. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a central-difference scheme are demonstrated by computing both inviscid and viscous transonic airfoil flows.

Swanson, R. C.↗
NASA NTRS1992

Numerical analysis of bipropellant combustion in liquid thrust chambers by an Eulerian-Eulerian approach

The liquid thrust chambers performance (LTCP) code is used for parametric studies of flow and combustion in liquid rocket engines. Multiphase flow equations are solved in an Eulerian-Eulerian framework, and multistep finite rate chemistry is incorporated. The discretization scheme is fully implicit and is based on the total variation diminishing (TVD) scheme, which is accurate, robust, very efficient and capable of handling steep gradients and stiff chemistry. Effects of injection velocity and chamber size have been considered, and the effect of group combustion on the evaporation rate has been studied for a dense spray.

Dang, A. L.↗
NASA NTRS1992

Calculating Shocks In Chemically Reacting Flows

Total-variation-diminishing dissipation operator results in crisp shocks. Report discusses method for numerical simulation of shocks in hypersonic, chemically reacting flows. Introduces mathematical model of gas of as many as three species for which species-conservation equations coupled with gas-dynamic equations.

Eberhardt, Scott↗
NASA NTRS1993

Development of computational methods for heavy lift launch vehicles

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Yoon, Seokkwan↗
NASA NTRS1992

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Kim, Hyun Dae↗
NASA NTRS1992

A comparison of upwind schemes for computation of three-dimensional hypersonic real-gas flows

The method of Suresh and Liou (1992) is extended, and the resulting explicit noniterative upwind finite-volume algorithm is applied to the integration of 3D parabolized Navier-Stokes equations to model 3D hypersonic real-gas flowfields. The solver is second-order accurate in the marching direction and employs flux-limiters to make the algorithm second-order accurate, with total variation diminishing in the cross-flow direction. The algorithm is used to compute hypersonic flow over a yawed cone and over the Ames All-Body Hypersonic Vehicle. The solutions obtained agree well with other computational results and with experimental data.

Gerbsch, R. A.↗
NASA NTRS1993

Investigation of three-dimensional separation at wing/body junctions in supersonic flows using TVD MacCormack's scheme

A Total Variation Diminishing (TVD) MacCormack scheme is used to study the three-dimensional separation at wing/body junctions in supersonic flows. The new scheme is robust, resolves discontinuities well with-out any numerical oscillations present in the flow field. Moreover, this new scheme does not contain any problem dependent parameters to be adjusted and many production codes employing MacCormack algorithm can be easily updated to good effect. Numerical simulation carried out in laminar supersonic junction flows using the new scheme yields improved prediction for the separation location and the axial velocity profiles in the separated flow region.

Lakshmanan, B.↗
NASA NTRS1991

Application of program LAURA to thermochemical nonequilibrium flow through a nozzle

Program LAURA (Langley Aerothermodynamic Upwind Relaxation Algorithm) is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D viscous hypersonic flows in chemical and thermal nonequilibrium. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The code has been applied to Problem 8.2 of this workshop for the case of thermochemical nonequilibrium flow through a nozzle. Chemical reaction rates are defined with the model of Park (1987). Thermal nonequilibrium is modeled using a two-temperature approximation in which the vibrational energies of all molecules are assumed to be in equilibrium at a single temperature which is generally different from the translational-rotational temperature. Two grids were used to define the flow for the original problem, with a stagnation temperature of 6500 K. A third case with a stagnation temperature of 10,000 K is also presented. The solution domain includes the converging nozzle, subsonic flow domain in which the gas is substantially in thermochemical equilibrium and the diverging nozzle, hypersonic flow domain in which the gas is substantially in thermochemical nonequilibrium.

Gnoffo, Peter A.↗
NASA NTRS1993

Conservative high-order-accurate finite-difference methods for curvilinear grids

Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

Rai, Man M.↗
NASA NTRS1992

Point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Gnoffo, P. A.↗
NASA NTRS1993

An adaptive grid/Navier-Stokes methodology for the calculation of nozzle afterbody base flows with a supersonic freestream

This paper describes an adaptive grid method for base flows in a supersonic freestream. The method is based on the direct finite-difference statement of the equidistribution principle. The weighting factor is a combination of the Mach number, density, and velocity first-derivative gradients in the radial direction. Two key ideas of the method are to smooth the weighting factor by using a type of implicit smoothing and to allow boundary points to move in the grid adaptation process. An AGARD nozzle afterbody base flow configuration is used to demonstrate the performance of the adaptive grid methodology. Computed base pressures are compared to experimental data. The adapted grid solutions offer a dramatic improvement in base pressure prediction compared to solutions computed on a nonadapted grid. A total-variation-diminishing (TVD) Navier-Stokes scheme is used to solve the governing flow equations.

Williams, Morgan↗