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At least 325 records · Page 18

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NASA NTRS1977

Numerical solutions of Navier-Stokes equations for the structure of a trailing vortex

The structure and decay of a trailing vortex were analyzed during the numerical solutions of the full Navier-Stokes equations. Unsteady forms of the governing equations were recast in terms of circulation, vorticity, and stream function as dependent variables, and a second upwind finite difference scheme was used to integrate them with prescribed initial and boundary conditions. The boundary conditions at the outer edge and at the outflow section of the trailing vortex were considered. Different models of the flow were postulated, and solutions were obtained describing the development of the flow as integration proceeds in time. A parametric study was undertaken with a view to understanding the various phenomena that may possibly occur in the trailing vortex. Using the Hoffman and Joubert law of circulation at the inflow section, the results of this investigation were compared with experimental data for a Convair 990 wind model and a rectangular wing. With an exponentially decaying law of circulation at the inflow section and an adverse pressure gradient at the outer edge of the trailing vortex, solutions depict vortex bursting through the sudden expansion of the core and/or through the stagnation and consequent reversal of the flow on the axis. It was found that this bursting takes place at lower values of the swirl ratio as the Reynolds number increases.

Jain, A. C.↗

NASA NTRS1982

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics with computed boundaries for real and perfect gases

Implicit methods developed by Beam and Warming (1978 and Briley and McDonald (1977) make it possible to overcome the hyperbolic stiffness of the conservative compressible Navier-Stokes equations in the fine wall region computational mesh for high Reynold's number flow. Certain difficulties related to the use of these methods could be overcome by employing an approach reported by Roe (1981). In the present investigation Roe's conceptual framework has been adopted for constructing globally conservative finite difference methods. A globally conservative upwind finite difference method (CSCM) consisting of both implicit interior point and boundary point equations is constructed from a new characteristics based flux difference splitting. It is found that the employed upwind eigenvector split scheme which combines fully coupled implicit interior point and boundary point approximations has the desired properties of robust stability and accuracy.

Lombard, C. K.↗

NASA NTRS1985

Numerical simulation of transient inviscid gas flows in a shock tube

Time-dependent upwind high resolution schemes for solving the Euler equations were developed and applied to simulate 1-D and 2-D transient inviscid gas flows in a shock tube. Using obstacles of different geometries, a series of calculations were carried out to investigate the transient complex shock-wave diffraction phenomena. Shock-wave and objects interactions with shock Mach-number Ms ranging from 2 to 20 were considered. Comparison with analytical and available experimental results indicate good agreement. Display of detailed flow structures including multiple Mach shocks, slip surfaces, and vortex are also given.

Yang, J. Y.↗

NASA NTRS1985

An efficient iteration strategy for the solution of the Euler equations

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Walters, R. W.↗

NASA NTRS1987

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Walters, Robert W.↗

NASA NTRS1985

Improved numerical methods for turbulent viscous recirculating flows

The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.

Turan, A.↗

NASA NTRS1988

Zonal techniques for flowfield simulation about aircraft

A technique for performing conservative flowfield calculations on zonal meshes is described. The underlying flow solver is an implicit, upwind finite volume scheme which can incorporate either a perfect gas or an equilibrium air equation of state. Two different approaches which yield identical results, in terms of performing a conservative flux calculation on a zonal interface, are described and compared in terms of numerical efficiency. The capability of the method to handle relatively complex geometries is demonstrated by considering the flowfield about a model SR71 aircraft.

Walters, Robert W.↗

NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux-difference splitting method has been extended to treat two-dimensional viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-stage Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗

NASA NTRS1989

A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry

The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.

Shuen, Jian-Shun↗

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 NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗

NASA NTRS1992

Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes

An algorithm which combines spatial and temporal adaption for the time integration of the two dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

Hooker, John R.↗

NASA NTRS1992

Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes

An algorithm which combines spatial and temporal adaption for the time integration of the two-dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four-stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

Hooker, John R.↗

NASA NTRS1992

A comparative study of advanced shock-capturing schemes applied to Burgers' equation

A systematic evaluation is conducted of all extant numerical schemes for nonlinear scalar transport problems, and several advanced shock-capturing schemes are used to solve the nonlinear Burgers' equation in order to characterize their ability to resolve the sharp discontinuity, expansion zone, and propagation and collision features of shocks. For discontinuous functions, the Warming-Beam scheme generates preshock wiggles, while the Lax-Wendroff scheme generates postshock ones. Such limiters as the MUSCL or the superbee are more compressive than minimod or monotonic limiters. The performance of such TVD schemes as the upwind, the symmetric, and the Roe-Sweby, resemble each other.

Yang, H. Q.↗

NASA NTRS1993

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

Eppard, W. M.↗

NASA NTRS1994

Installed F/A-18 inlet flow calculations at 30 degrees angle-of-attack: A comparative study

NASA Lewis is currently engaged in a research effort as a team member of the High Alpha Technology Program (HATP) within NASA. This program utilizes a specially equipped F/A-18, the High Alpha Research Vehicle (HARV), in an ambitious effort to improve the maneuverability of high-performance military aircraft at low subsonic speed, high angle of attack conditions. The overall objective of the Lewis effort is to develop inlet technology that will ensure efficient airflow delivery to the engine during these maneuvers. One part of the Lewis approach utilizes computational fluid dynamics codes to predict the installed performance of inlets for these highly maneuverable aircraft. Full Navier-Stokes (FNS) calculations on the installed F/A-18 inlet at 30 degrees angle of attack, 0 degrees yaw, and a freestream Mach number of 0.2 have been obtained in this study using an algebraic turbulence model with two grids (original and revised). Results obtained with the original grid were used to determine where further grid refinements and additional geometry were needed. In order to account properly for the external effects, the forebody, leading edge extension (LEX), ramp, and wing were included with inlet geometry. In the original grid, the diverter, LEX slot, and leading edge flap were not included due to insufficient geometry definition, but were included in a revised grid. In addition, a thin-layer Navier-Stokes (TLNS) code is used with the revised grid and the numerical results are compared to those obtained with the FNS code. The TLNS code was used to evaluate the effects on the solution using a code with more recent CFD developments such as upwinding with TVD schemes versus central differencing with artificial dissipation. The calculations are compared to a limited amount of available experimental data. The predicted forebody/fuselage surface static pressures compared well with data of all solutions. The predicted trajectory of the vortex generated under the LEX was different for each solution. These discrepancies are attributed to differences in the grid resolution and turbulence modeling. All solutions predict that this vortex is ingested by the inlet. The predicted inlet total pressure recoveries are lower than data and the distortions are higher than data. The results obtained with the revised grid were significantly improved from the original grid results. The original grid results indicated the ingested vortex migrated to the engine face and caused additional distortions to those already present due to secondary flow development. The revised grid results indicate that the ingested vortex is dissipated along the inlet duct inboard wall. The TLNS results indicate the flow at the engine face was much more distorted than the FNS results and is attributed to the pole boundary condition introducing numerical distortions into the flow field.

Smith, C. Frederic↗

NASA NTRS1994

Computation of oscillating airfoil flows with one- and two-equation turbulence models

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Ekaterinaris, J. A.↗

NASA NTRS1999

On Multi-Dimensional Unstructured Mesh Adaption

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Wood, William A.↗