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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 NTRS1974

The solution of three-variable duct-flow equations

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

Stuart, A. R.↗
NASA NTRS1979

Calculated global conditions for the unsteady Euler's flow equations

This paper considers the numerical solution of a fluid dynamical system with time-dependent oscillating boundaries. The problem detailed, a compressible and inviscid flow in a one-dimensional pipe with vibrating ends, is examined to develop techniques needed to solve the more complex unsteady flows in turbomachine cascades. The problem is shown to be mathematically ill-posed but by complementing the governing equations with energy conservation, a unique solution is obtained. An artificial damping term is introduced into the governing equations to improve the performance of the time-marching integration.

Kuzo, D. M.↗
NASA NTRS1993

Airfoil shape optimization using sensitivity analysis on viscous flow equations

An aerodynamic shape optimization method has previously been developed by the authors using the Euler equations and has been applied to supersonic-hypersonic nozzle designs. This method has also included a flowfield extrapolation (or flow prediction) method based on the Taylor series expansion of an existing CFD solution. The present paper reports on the extension of this method to the thin-layer Navier-Stokes equations in order to account for the viscous effects. Also, to test the method under highly nonlinear conditions, it has been applied to the transonic flows. Initially, the success of the flow prediction method is tested. Then, the overall method is demonstrated by optimizing the shapes of two supercritical transonic airfoils at zero angle of attack. The first one is shape optimized to achieve a minimum drag while obtaining a lift above a specified value. Whereas, the second one is shape optimized for a maximum lift while attaining a drag below a specified value. The results of these two cases indicate that the present method can produce successfully optimized aerodynamic shapes.

Eleshaky, Mohamed E.↗
NASA NTRS2000

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Roberts, Thomas W.↗
NASA NTRS1997

Some Approaches Towards Constructing Optimally Efficient Multigrid Solvers for the Inviscid Flow Equations

Some important advances took place during the last several years in the development of genuinely multidimensional upwind schemes for the compressible Euler equations. In particular, a robust, high-resolution genuinely multidimensional scheme which can be used for any of the flow regimes computations was constructed. This paper summarizes briefly these developments and outlines the fundamental advantages of this approach.

Sidilkover, David↗
NASA NTRS1993

Preconditioning and the limit to the incompressible flow equations

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Turkel, E.↗
NASA NTRS1993

Pseudo-compressibility methods for the incompressible flow equations

Preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamics equations are considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. The method is compared to other types of pseudo-compressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.

Turkel, Eli↗
NASA NTRS1992

Solution of nonlinear flow equations for complex aerodynamic shapes

Solution-adaptive CFD codes based on unstructured methods for 3-D complex geometries in subsonic to supersonic regimes were investigated, and the computed solution data were analyzed in conjunction with experimental data obtained from wind tunnel measurements in order to assess and validate the predictability of the code. Specifically, the FELISA code was assessed and improved in cooperation with NASA Langley and Imperial College, Swansea, U.K.

Djomehri, M. Jahed↗
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 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 NTRS1984

Surface-slip equations for low-Reynolds-number multicomponent gas flows

Equations have been obtained for jump (or slip) in the wall values of species concentration, pressure, velocity, and temperature for the low-Reynolds-number high-altitude flight regime of a space vehicle. The analysis, based on the Chapman-Enskog method as applied by Shidlovskiy for a single-species gas, includes multicomponent diffusion with finite-rate surface catalytic recombination. A consistent set of equations is provided for multicomponent, binary, and single species mixtures.

Gupta, R. N.↗
NASA NTRS1984

Surface-slip equations for low-Reynolds-number multicomponent gas flows

Equations have been obtained for jump (or slip) in the wall values of species concentration, pressure, velocity, and temperature for the low-Reynolds-number high-altitude flight regime of a space vehicle. The analysis, based on the Chapman-Enskog method as applied by Shidlovskiy for a single-species gas, includes multicomponent diffusion with finite-rate surface catalytic recombination. A consistent set of equations is provided for multicomponent, binary, and single species mixtures.

Gupta, R. N.↗
NASA NTRS1967

Equation relates flow at free jet to flow downstream

Nonlinear equation relates the flowrate at an orifice to that at a station downstream from the orifice. This equation should aid in understanding combustion instabilities and should not be subject to the substantial errors of prior analytical methods.

Fenwick, J. R.↗
NASA NTRS1989

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.↗
NASA NTRS1993

Variational approaches to CFD: Applications to potential Euler and Navier-Stokes equations

Flow simulations based on variational techniques are discussed. Variational techniques are applied for the problem formulation, for the construction of discrete schemes, and for the solution procedures. Inviscid transonic flows, as well as viscous incompressible and compressible flows, are analyzed by several methods. Variational techniques to solve the discrete systems of equations are well known. The most popular one is the conjugate gradient method. Extensions to nonsymmetric and nonpositive definite systems were under investigation for the last two decades. Variational techniques were used for convergence acceleration of iterative procedures. Some of these ideas based on recent work are examined. The lectures are organized in three parts including numerical simulation of inviscid as well as viscous incompressible and compressible flows.

Hafez, M.↗