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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.

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NASA NTRS1987

Multiscale turbulence effects in underexpanded supersonic jets

A modified version of the multiscale turbulence model of Hanjalic has been applied to the problem of underexpanded supersonic jets. In particular, the shock-cell decay resulting from shock-mixing layer interactions has been studied for both mildly interacting and strongly resonant jet conditions. A version of the Hanjalic model which accounts for nonequilibrium energy transfer between two spectral scales of turbulence was incorporated into an existing shock-capturing, parabolized Navier-Stokes computational model in order to perform numerical experiments. Results are presented for nominal initial jet Mach numbers of 2.0, 1.4, and 1.0 and are compared to experiments and to predictions made using single-scale models. The results show significant effects of multi-spectral turbulent energy transfer on the predicted shock-cell decay particularly for the lower jet Mach numbers.

Abdol-Hamid, Khaled S.↗
NASA NTRS1987

Full potential integral solution for transonic flows with and without embedded Euler domains

Two methods are presented to solve for the transonic airfoil flow problems. The first method is based on the integral equation solution of the full-potential equation in terms of the velocity field, and a Shock Capturing-Shock Fitting (SCSF) scheme has been developed. The SCSF-scheme consists of a shock-capturing part and a shock-fitting part in which shock panels are introduced at the shock location. The sock panels are fitted and crossed by using the Rankine-Hugoniot relations. The second method is based on coupling the integral equation of the full-potential equation with the pseudo time integration of Euler equations in a small embedded region around the shock. The integral solution provides the initial and boundary conditions for the Euler domain. This scheme is named as the Integral Equation-Embedded Euler (IEEE) scheme. The two methods are applied to NACA 0012 and NACA 64A010A over a wide range of Mach numbers, and the reults are in good agreement with the experimental data and other computational results. The schemes converge within a number of iterations which is one-order of magnitude less than the finite-difference schemes.

Kandil, Osama A.↗
NASA NTRS1987

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Palmer, Grant↗
NASA NTRS1987

Uniformly high order accurate essentially non-oscillatory schemes. III

In the present continuation of development and analysis efforts towards essentially nonoscillatory shock-capturing approximations of hyperbolic conservation laws, the Godunov (1959) scheme and its MUSCL second-order-accurate extension are generalized to an arbitrary order of accuracy by means of a hierarchy of uniformly high-order-accurate schemes. The design method, which involves the solution's essentially nonoscillatory piecewise polynomial reconstruction on the basis of its cell averages, followed by time-evolution through an approximate solution of the resulting initial value problem and its averaging over each cell, employs an adaptive stencil of grid points to yield schemes that are highly nonlinear.

Harten, Ami↗
NASA NTRS1988

Numerical study of unsteady viscous hypersonic blunt body flows with an impinging shock

A complex two-dimensional, unsteady, viscous hypersonic shock wave interaction is numerically simulated by a high-resolution, second-order fully implicit shock-capturing scheme. The physical model consists of a nonstationary oblique shock impinging on the bow shock of a blunt body. Studies indicated that the unsteady flow patterns are slightly different from their steady counterparts. However, for the sample cases investigated the peak surface pressures for the unsteady flows seem to occur at very different impingement locations than for the steady flow cases.

Klopfer, G. H.↗
NASA NTRS1987

Modification of the Osher upwind scheme for use in three dimensions

The Osher upwind scheme, a shock-capturing algorithm based on an approximate Riemann solver, which has been developed for the solution of hyperbolic conservation laws, is briefly described, and the need for modification of the scheme for use in three dimensions is demonstrated. Two forms of a scheme modification for use on a three-dimensional arbitrary grid are then presented.

Hessenius, Kristin A.↗
NASA NTRS1988

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Palmer, Grant↗
NASA NTRS1988

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Grossman, B.↗
NASA NTRS1989

Algorithm For Hypersonic Flow In Chemical Equilibrium

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Palmer, Grant↗
NASA NTRS1988

Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

Leonard, B. P.↗
NASA NTRS1988

Integral equation solution for transonic and subsonic aerodynamics

Two methods are presented to solve for the subsonic and transonic flows around airfoils. The first method is based on the integral solution of the full-potential equation with a shock-capturing technique only or with shock capturing-shock fitting technique. In the second method, the integral soluton of the full potential equation is coupled with an embedded region of Euler equations around the shock location. The second method is a computationally efficient technique for flows with strong shocks where the entropy increase and vorticity production across the shock are not small. Several numerical examples are presented and compared with the experimental data and other computational results.

Kandil, Osama A.↗
NASA NTRS1988

Unsteady transonic airfoil computation using the integral solution of full-potential equation

The shock-capturing integral-equation scheme developed by Kandil and Hu (1987) for the analysis of steady transonic flow over airfoils is extended to the unsteady case. The full potential formulation of the governing equations is reviewed; the solution method is outlined; and results for a NACA 0012 airfoil in forced pitching oscillation at Mach 0.755 are presented in extensive graphs and briefly characterized. The present technique is shown to require significantly less computation time than finite-difference or finite-volume methods, and to give shock-motion predictions in good agreement with those of an implicit finite-volume Euler solver; the surface-pressure peaks are slightly underpredicted.

Kandil, O. A.↗
NASA NTRS1989

Comparisons of TVD schemes applied to the Navier-Stokes equations

In this study, the following total variation diminishing (TVD) schemes for solving the Navier-Stokes equations have been tested: the Chakravarthy and Szema (1985) upwind biased TVD scheme, the Harten's upwind TVD scheme described by Yee et al. (1983), and the Yee's (1985) symmetric TVD scheme. The schemes have been compared using three test cases. The first case was the one-dimensional shock tube problem which tested the shock-capturing abilities of the schemes. Chakravarthy's and Harten's schemes gave similar results which were found to be more accurate than the results from Yee's scheme. The second case was a compressible boundary layer which tested the schemes's abilities to solve fiscous flows. In this case, the three schemes yielded almost identical results. Finally, the shock/boundary-layer interaction case studied experimentally by Hakkinen et al. (1959) was computed. Here, Chakravarthy's and Yee's schemes compared most favorably with the published data, with Yee's scheme giving slightly better results.

Buelow, Philip E.↗
NASA NTRS1988

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Mostrel, M. M.↗
NASA NTRS1989

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

Palmer, Grant↗
NASA NTRS1989

Numerical study of unsteady viscous hypersonic blunt body flows with an impinging shock

A complex two-dimensional, unsteady, viscous hypersonic shock wave interaction is numerically simulated by a high-resolution, second-order fully implicit shock-capturing scheme. The physical model consists of a nonstationary oblique shock impinging on the bow shock of a blunt body. Studies indicate that the unsteady flow patterns are slightly different from their steady counterparts. However, for the sample cases investigated the peak surface pressures for the unsteady flows seem to occur at very different impingement locations than for the steady flow cases.

Klopfer, G. H.↗
NASA NTRS1989

Hypersonic blunt body computations including real gas effects

Various second-order explicit and implicit TVD shock-capturing methods, a generalization of Roe's approximate Riemann solver, and a generalized flux-vector splitting scheme are used to study two-dimensional hypersonic real-gas flows. Special attention is given to the identification of some of the elements and parameters which can affect the convergence rate for high Mach numbers or real gases, but have negligible effect for low Mach numbers, for cases involving steady-state inviscid blunt flows. Blunt body calculations at Mach numbers of greater than 15 are performed to treat real-gas effects, and impinging shock results are obtained to test the treatment of slip surfaces and complex structures. Even with the addition of improvements, the convergence rate of algorithms in the hypersonic flow regime is found to be generally slower for a real gas than for a perfect gas.

Montagne, J.-L.↗
NASA NTRS1990

Integral solution of unsteady full-potential equation for a transonic pitching airfoil

The unsteady full-potential equation formulation in a moving frame of reference has been has been developed and used to solve unsteady transonic flow problems. An unsteady integral-equation shock-capturing (IE-SC) scheme has been developed. The resulting unsteady IE-SC scheme is applied to a NACA 0012 airfoil undergoing a pitching oscillation. The numerical results are compared with those of an implicit, approximately factored, finite-volume Euler scheme. The present scheme is efficient in terms of the number of iterations as compared to the other existing schemes, which use finite-difference or finite-volume methods.

Kandil, Osama A.↗