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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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At least 181 records · Page 10
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NASA NTRS1984

Turbulent heat transfer in a channel with two right-angled bends

A numerical study is reported on the flow and heat transfer in a channel with two right-angled bends. The k-epsilon turbulence model with a refined near-wall model is adopted for the computation of the flow field for step ratios ranging H/W = 1-4 and for Reynolds numbers Re = 3,000-10,000. The solution method of the governing transport equations is based on the modified hybrid scheme which produces very small truncation error. As a result of extensive computations, the complex flow patterns in the channel with two bends are clarified and the mechanisms of heat transfer are explained relating to the flow behaviors of separation, deflection, recirculation, and reattachment.

Amano, R. S.↗
NASA NTRS1984

Three-dimensional Navier-Stokes calculations of multiple interacting vortex rings

Results from a finite-difference Navier-Stokes code for three-dimensional, unsteady, vortical flows in unbounded domains are presented and analyzed in this paper. The vortical flows presented are representative of vortex rings and other closed vortical tubes or structures in fluid mechanics. Such structures are important elements in fluid flows such as jets, atmospheric turbulence, and the far-field wakes of aircraft, and studies of their interaction may aid in an understanding of complex fluid flows. The paper demonstrates that computational methods can be used as a viable alternative or supplement to experimental techniques for studying the physics of vortex flows. The separate visualization of vortex stretching, convection, and diffusion is presented in this paper for a single elliptical vortex ring.The calculations employ a truncated series expansion technique to simulate the unbounded nature of the fluid flow with a finite computational domain, which is a more accurate technique than the conventional freestream boundary specification. The numerical divergence of the three-dimensional vorticity field is considered as a useful estimate of truncation error, and the use of a kinetic energy decay law as a calculation check is demonstrated. Results from the Navier-Stokes code are presented for the unsteady motion of two and four vortex rings along parallel axes, and the results agree qualitatively with experimental flow visualization.

Chamberlain, J. P.↗
NASA NTRS1985

Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Harten, A.↗
NASA NTRS1985

Parameterization in Grid Generation

The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.

Mastin, C. W.↗
NASA NTRS1985

Numerical and experimental evaluation for single-axis control of an LSS laboratory model

One of the major problems of LSS attitude control design stems from the modeling uncertainties due to modal truncation errors and modal parameter estimation errors. This modeling problem is investigated by evaluating poles and zeros of the frequency response functions, described in terms of constrained or unconstrained modes. The frequency domain approach is utilized to evaluated the results of modal analyses and direct output feedback controller experiments using a simple flexible spacecraft model consisting of a rigid primary body and flexible aluminum beam(s) with a control moment gyro as an actuator. The modal data are compared under the conditions that the model is constrained as the canti-lever and it is rotationally free on a single-axis air bearing table. In addition, the open-loop responses are experimentally examined under the impulsive disturbance to the appendage. The results of the control experiments show that the first vibration mode of the appendage and the interacted rotational motion of the primary body are damped in a short time as predicted by the numerical analysis, to produce damping ratio of 10-20%.

Ohkami, Y.↗
NASA NTRS1985

Solution method for a hovering helicopter rotor using the Euler equations

A method for the calculation of the flow field of a helicopter rotor blade in hover is presented. The approach uses a finite volume solution of the three dimensional Euler equations for the blade near field. In the Euler solver the velocity field is decomposed into two parts. One is the induced velocity of the vortex wake extending below the blade, found from a free wake calculation procedure. The other part is the unknown additional velocity field of the rotor blade. This approach eliminates numerical diffusion of the rolled up wake vorticity due to truncation error and artificial viscosity. Also, the effects of the far wake are included in the limited computational domain. Solutions are presented for an isolated wing and a model helicopter rotor and compared to experiment.

Roberts, T. W.↗
NASA NTRS1984

Recent advances in methods for numerical solution of O.D.E. initial value problems

In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.

Bui, T. D.↗
NASA NTRS1985

A new class of high accuracy TVD schemes for hyperbolic conservation laws

A new family of high accuracy Total Variation Diminishing (TVD) schemes has been developed. Members of the family include the conventional second-order TVD upwind scheme, various other second-order accurate TVD schemes with lower truncation error, and even a third-order accurate TVD approximation. All the schemes are defined with a five-point grid bandwidth. In this paper, the new algorithms are described for scalar equations, systems, and arbitrary coordinates. Selected numerical results are provided to illustrate the new algorithms and their properties.

Chakravarthy, S. R.↗
NASA NTRS1985

Effects of upstream-biased third-order space correction terms on multidimensional Crowley advection schemes

The impact of upstream-biased corrections for third-order spatial truncation error on the stability and phase error of the two-dimensional Crowley combined advective scheme with the cross-space term included is analyzed, putting primary emphasis on phase error reduction. The various versions of the Crowley scheme are formally defined, and their stability and phase error characteristics are intercompared using a linear Fourier component analysis patterned after Fromm (1968, 1969). The performances of the schemes under prototype simulation conditions are tested using time-dependent numerical experiments which advect an initially cone-shaped passive scalar distribution in each of three steady nondivergent flows. One such flow is solid rotation, while the other two are diagonal uniform flow and a strongly deformational vortex.

Schlesinger, R. E.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1986

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Caughey, D. A.↗
NASA NTRS1986

Euler solutions for the flow around a hovering helicopter rotor

A method for computing the flow around a hovering helicopter rotor is presented. The solution procedure is divided into two parts. The first part is a finite volume solution of the Euler equations for the near field flow around a rotor blade. The second part is a free wake approach for determining the wake geometry and induced velocities. These two parts are solved in a coupled fashion. The rolled-up vortex wake of the rotor is included in the Euler computational domain through a nonlinear perturbation technique. This eliminates the numerical diffusion of the wake vorticity due to truncation error and artificial viscosity without the need for excessive grid resolution near the vortex core. The method is used to compute both hovering rotor and wing/vortex interaction flows, and the results are compared to experiment.

Roberts, T. W.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1986

Wing/body interference flow investigation

The concept of using parametric bicubic patch surface definitions with bilinear vorticity or biquadratic doublet distributions was tested by modeling the vortex sheet and predicting its shape numerically in the vicinity of the wing. For the purpose of computing induced velocities, it was shown that higher order of vorticity would not improve the truncation error. The bilinear distribution, used to model the tip vorticity, was satisfactory but gave rise to some difficulty. The bicubic geometric surface representation proved very suitable for curved surfaces such as the rolled-up vortex sheet, with the surface fit scheme failing only for complex wings, far downstream beyond the region of concern.

Vogel, J. M.↗
NASA NTRS1985

Numerical solution of the unsteady Navier-Stokes equation

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Osher, Stanley J.↗
NASA NTRS1987

Leading-edge vortex solutions with large total pressure losses

Computations are presented for a Lambda = 75 deg delta wing in a supersonic freestream under two conditions which lead to leading-edge vortices. For one condition, analysis of the computed vortical flow reveals a closed streamline in the core. From varying computational parameters, it appears that this is due to truncation error of the convective derivatives. For the other condition, comparisons are made with wind-tunnel data, and good agreement is noted for pitot pressure distributions, flow angles on the symmetry plane, and the position of an embedded shock. Many of the aerodynamic parameters are shown to be insensitive to grid spacing.

Murman, Earll M.↗
NASA NTRS1988

Total Variation Diminishing (TVD) schemes of uniform accuracy

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

Hartwich, PETER-M.↗
NASA NTRS1987

Modeling and control of beam-like structures

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for beam-like continua. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗