Solution-adaptive grid procedure for high-speed parabolic flow solvers
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Harvey, Albert D., III↗
Engineering topics
Lawrence, Scott L.
Publications and source records attributed to Lawrence, Scott L..
Numerical performance estimates for a generic hypersonic forebody
The computation of a hypersonic flow past the forebody of a hypersonic vehicle is analyzed for two sets of flow conditions: the first represents flow conditions of an experimental test of the model in the Calspan 96-inch shock tunnel, and the second set is chosen to represent actual flight conditions. Solutions are derived for sharp- and blunt-nose versions of the geometry in order to understand the effects of the entropy layer on the forebody pressure and heat transfer rates. Some sensitivity of predicted heating rates to grid refinement is observed, but it is found to be small compared to the effects of bluntness. Real-gas effects are studied for the blunt-nose version at flight-like conditions, and these effects are found to have a significant effect on inlet-face performance measures such as mass capture and kinetic energy efficiency.
Lawrence, Scott L.↗
Parabolized Navier-Stokes methods for hypersonic flows
A representative sampling of the techniques used in the integration of the Parabolized Navier-Stokes (PNS) equations is presented. Special atention is given to recent algorithms developed specifically for application to high speed flows, characterized by the presence of strong embedded shock waves and real gas effects. It is shown that PNS solvers are being used in the analysis of sonic boom signatures. Methods for modeling physical effects are discussed, including an overview of commonly used turbulence models and a more detailed discussion of techniques for including equilibrium and finite rate real gas effects.
Lawrence, Scott L.↗
A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations
A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations is developed on the basis of the two-dimensional line-by-line solution-adaptive technique of Harvey et al. (1990). It is shown that the new adaptive grid algorithm provides improved shock resolving characteristics over the conventional flow algorithm. The adaptation process has the ability of aligning grid lines with the existing flow-field structure, yielding increasing resolution of high gradient regions.
Harvey, Albert D., III↗
Hypersonic cone flow predictions using an implicit upwind space-marching code
Solutions have been computed and results are presented for Problem 1, the case of Mach 9 transitional flow past a 7 deg half-angle cone at zero incidence. The solutions were computed using a code developed for the integration of the parabolized Navier-Stokes equations. The algorithm employed in the code is based on a Roe-type flux-difference-splitting scheme applied following a finite-volume approach. The basic algorithm has been modified to make it implicit and second-order accurate in the crossflow directions. Results are presented in terms of surface pressure and heat transfer as well as boundary layer profiles of pitot pressure, Mach number, and tangential velocity. The case was recalculated several times in an effort to determine sensitivities to such parameters as grid density, wall temperature, turbulence model parameters, as well as freestream expansion. Comparisons with the experimental data are presented and discussed.
Lawrence, Scott L.↗
Application of CFD to sonic boom near and mid flow-field prediction
A three-dimensional parabolized Navier-Stokes (PNS) code has been used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind-tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown in this paper. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind-tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.
Cheung, Samson H.↗
Application of CFD to sonic boom near and mid flow-field prediction
A 3-D parabolized Navier-Stokes (PNS) code was used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.
Cheung, Samson H.↗
Development of a three-dimensional upwind parabolized Navier-Stokes code
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Lawrence, Scott L.↗
A solution adaptive grid procedure for an upwind parabolized flow solver
A solution adaptive grid procedure based on an error equi-distribution scheme is developed and applied to a Parabolized Navier-Stokes solver. An improved method for selecting weighting functions is introduced which involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme re-distributes grid points line-by-line, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum. Results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure.
Harvey, Albert D.↗
Upwind Algorithm For Parabolized Navier-Stokes Equations
Supersonic flow about cone calculated accurately. Report presents theoretical basis of computer code solving parabolized Navier-Stokes equations of supersonic and hypersonic flow. For increased accuracy in resolution of details of strong aerodynamic shocks, code incorporates implicit, finite-volume, upwind numerical-integration scheme. Performs well in numerical simulations of flows around simple bodies.
Lawrence, Scott L.↗
Three-dimensional upwind parabolized Navier-Stokes code for real gas flows
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Tannehill, John C.↗
Upwind parabolized Navier-Stokes code for chemically reacting flows
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Tannehill, John C.↗
A three-dimensional upwind parabolized Navier-Stokes code for chemically reacting flows
A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional flow of chemically reacting air around hypersonic vehicles. The code is a modification of the perfect gas, three-dimensional UPS code of Lawrence et al. (1986) which has been extended in the present study to permit the calculation of hypersonic, viscous flows in chemical nonequilibrium. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for real gas effects. The present code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Results are presented for the hypersonic laminar flow over a cone at 0- and 10-deg angles of attack and for a generic hypersonic vehicle. Calculations are performed assuming either perfect gas, equilibrium air, or finite-rate chemistry.
Buelow, Philip E.↗
Experimental and computational surface and flow-field results for an all-body hypersonic aircraft
The objective of the present investigation is to establish a benchmark experimental data base for a generic hypersonic vehicle shape for validation and/or calibration of advanced computational fluid dynamics computer codes. This paper includes results from the comprehensive test program conducted in the NASA/Ames 3.5-foot Hypersonic Wind Tunnel for a generic all-body hypersonic aircraft model. Experimental and computational results on flow visualization, surface pressures, surface convective heat transfer, and pitot-pressure flow-field surveys are presented. Comparisons of the experimental results with computational results from an upwind parabolized Navier-Stokes code developed at Ames demonstrate the capabilities of this code.
Lockman, William K.↗
Experimental and computational surface and flow-field results for an all-body hypersonic aircraft
Personnel from NASA Ames Research Center presented a paper on establishing a benchmark experimental data base for generic hypersonic vehicle shape for validation and/or calibration of advanced computational fluid dynamics computer codes. The need for this capability is based on a requirement for extensive hypersonic data to fully validate CFD codes to be used for NASP and other hypersonic vehicles. The use of wind tunnel models in the Ames 3.5-ft Hypersonic Wind Tunnel to obtain pertinent surface and flow-field data over a broad range of test conditions is described.
Lockman, William K.↗
Upwind algorithm for the parabolized Navier-Stokes equations
A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.
Lawrence, Scott L.↗
Calculation of winged-body-like flow fields using an implicit upwind space-marching code
The Mach-8 flow past a 60-deg swept fin mounted on a 12-degree ramp has been simulated using a parabolized Navier-Stokes solver employing an upwind algorithm in order to investigate the interference patterns that develop when a bow shock impinges on a wing shock. Good agreement with experimental data is found downstream of the interaction for each of three meshes of varying grid point density and computed surface pressure and heat transfer. In the wedge flow region, some disagreement with experimental data is noted for both pressure and heat transfer.
Lawrence, Scott L.↗
A three-dimensional upwind parabolized Navier-Stokes code for real gas flows
A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's (1981) flux-difference splitting scheme which has been modified to account for real gas effects using the nearly exact approach of Vinokur and Liu (1988). Simplified curve fits are employed to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the M-infinity = 25 laminar flow of air over cones at various angles of attack. The results of these computations are compared with the results from a conventional centrally-differenced, real gas PNS code and the previous axisymmetric, upwind, real gas code. The agreement is excellent in all cases.
Tannehill, John C.↗