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NASA NTRS1986

Wake shape and its effects on aerodynamic characteristics

The wake shape under symmetrical flight conditions and its effects on aerodynamic characteristics are examined. In addition, the effect of wake shape in sideslip and discrete vortices such as strake or forebody vortex on lateral characteristics is presented. The present numerical method for airplane configurations, which is based on discretization of the vortex sheet into vortex segments, verified the symmetrical and asymmetrical roll-up process of the trailing vortices. Also, the effect of wing wake on tail planes is calculated. It is concluded that at high lift the assumption of flat wake for longitudinal and lateral-directional characteristics should be reexamined.

Emdad, H.↗

NASA NTRS1986

Report on the feasibility of hypercube concurrent processing systems in computational fluid dynamics

The feasibility of using hypercube-connected concurrent processor systems for problems in computational fluid dynamics is studied. Both explicit and implicit numerical methods are considered and several alternative implementations of these methods are evaluated on concurrent processor systems. A Lax-Wendroff explicit method was designed and implemented for the Navier-Stokes equations. The code runs on the Intel iPSC concurrent processor system. Tests of this code show that it is reasonably efficient. The Beam and Warming implicit factored method was designed and implemented for Berger's equation. Preliminary tests show that the efficiency of code is poor.

Bruno, J.↗

NASA NTRS1986

Numerical simulation of the flowfield over ice accretion shapes

The primary goals are directed toward the development of a numerical method for computing flow about ice accretion shapes and determining the influence of these shapes on flow degradation. It is expedient to investigate various aspects of icing independently in order to assess their contribution to the overall icing phenomena. The specific aspects to be examined include the water droplet trajectories with collection efficiencies and phase change on the surface, the flowfield about specified shapes including lift, drag, and heat transfer distribution, and surface roughness effects. The configurations computed were models of ice accretion shapes formed on a circular cylinder in the NASA Lewis Icing Research Tunnel. An existing Navier-Stokes program was modified to compute the flowfield over four shapes (2, 5, and 15 minute models of glaze ice, and a 15 minute accumulation of rime ice).

Scott, J. N.↗

NASA NTRS1986

Studies of the aurorally-induced ultraviolet emissions on the nightside of Venus

The effect of a monoenergetic flux of electrons on a model atmosphere of the nightside thermosphere of Venus was examined. The neutral model chosen is that of Hedin for high solar activity and l65 degrees solar zenith angle. The model is based on measurements made by the Pioneer Venus Orbiter Neutral Mass Spectrometer. Four species were included in the calculation: CO2, O, CO, and N2. The numerical method that was chosen for energy deposition of the primary electrons is the continuous slowing down approximation. The secondary electron distribution was computed using the empirically determined shape of the differential cross section.

Fox, J. L.↗

NASA NTRS1984

On the solution of problems involving impact type loading

The response of beam and plate members to pulse and impact loading is investigated, and numerical methods are analyzed and compared. The equations of motion, the finite difference and finite element methods, the time integration/Runge-Kutta techniques, and material modeling are discussed in detail. It is found that both the finite difference and the finite element methods could be accurately employed to discretize the spatial variation in the displacements. Central differences or a fourth order Runge-Kutta algorithm could be used for the time integration. The total energy of the system would give the stability and accuracy of the solution. Results showed that the finite element method provided better efficiency in obtaining accurate solution than the finite difference method when a scalar processor is used. However, the finite difference method was more efficient on the vector processor. Therefore, the most efficient method of solution depends on the type of computer present for the analysis.

Moyer, E. T., Jr.↗

NASA NTRS1985

Propagation of quasifracture in viscoelastic media under low-cycle repeated stressing

The propagation of a craze as quasifracture under repeated cyclic stressing in polymeric systems has been under intensive investigation recently. Based upon a time-dependent crazing theory, the governing differential equation describing the propagation of a single craze as quasifracture in an infinite viscoelastic plate has been solved for sinusoidal stresses. Numerical methods have been employed to obtain the normalized craze length as a function of time. The computed results indicate that the length of a quasifracture may decelerate and decrease indicating that its velocity can reverse. This behavior may be consistent with the observed and much discussed craze healing and the enclosure model in fatigue and fracture of solids.

Liu, X. P.↗

NASA NTRS1985

On an algorithm for analysis of the radiation patterns of dual reflector and segmented reflector antennas

An algorithm has been developed to calculate the radiation patterns of a large reflector antenna for space applications. The algorithm treats each panel in the reflector array as an analytic surface having n-sided polygonal boundaries. The radiation fields for individual panels are computed and stored separately, and then added to yield a uniform radiation pattern for the entire reflector. Numerical methods developed to reduce the overlap of the aperture fields of adjacent panels are described in detail. Calculations of the tangential field components of the aperture plane are carried out based on the principles of geometric optics (GO). Some radiation patterns calculated with the algorithm are compared with patterns produced by other methods, together with measured data for a classical Cassegrain antenna and the calculated patterns are illustrated.

Christodoulou, C. G.↗

NASA NTRS1985

Delta wings with shock-free cross flow

In order to have a high level of maneuverability, supersonic delta wings should have a cross flow that is free of embedded shock waves. The conical cross flow sonic surface differs from that of plane transonic flow in many aspects. Well-known properties such as the monotone law are not true for conical cross flow sonic surfaces. By using a local analysis of the cross flow sonic line, relevant conditions for smooth cross flow are obtained. A technique to artificially construct a smooth sonic surface and an efficient numerical method to calculate the flow field are used to obtain cones with smooth cross flow.

Sritharan, S. S.↗

NASA NTRS1985

Finite-amplitude steady waves in plane viscous shear flows

Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Milinazzo, F. A.↗

NASA NTRS1984

Finite difference simulation of unsteady interactive flows

The development of time-dependent numerical simulations of unsteady interactive flows of an aerodynamic nature is reviewed with emphasis on compressible flows at flight Reynolds numbers and noniterative schemes based on Navier-Stokes equations. The importance of writing the equations in strong conservation-law form for a generalized body-oriented coordinate system is pointed out. The discussion covers time and length scales and numerical methods currently in use. Some computed results are presented and compared with experimental data.

Deiwert, G. S.↗

NASA NTRS1985

MHD modelling of the earth's magnetosphere

Attention is given to the shock capturing technique, nonuniform grid system, and multiple time scale problem aspects of a global MHD model of the earth's magnetosphere that uses numerical methods. Because of the fast Alfven waves near the earth, the model is more difficult to solve than problems of hydrodynamic flow past bodies. The Rusanov (1962) scheme, which is a variant of the Lax (1954) method that maintains viscosity at a minimum value except where a large one is required, is used. The magnetosphere shape obtained by these means is noted.

Wu, C. C.↗

NASA NTRS1985

Numerically-simulated formation and propagation of interplanetary shocks

The present numerical method for simulating the formation and propagation of interplanetary shocks is based on the shock-capturing finite difference scheme of Lax (1950) and Lax and Wendroff (1960), as well as the recent method of NEAR characteristics of Nakagawa (1980, 1981). Attention is given to examples which strongly suggest that all the shocked solar wind plasma parameters due to given physical perturbations, such as flare-generated shocks, can be predicted through the use of this method; the method is, however, limited to the supersonic and super-Alfvenic flow.

Wu, S. T.↗

NASA NTRS1985

Particle behavior in the magnetosphere

The Rice Convection Model deals with large-scale processes in the earth's inner and middle magnetosphere, including coupling to the ionosphere. Starting from appropriate initial and boundary conditions, the model computes the following physical parameters: ionospheric electric fields and currents; magnetospheric particle distributions, electric fields, and electric currents; and magnetic-field-aligned (Birkeland) currents connecting the two regions. This paper evaluates work on the model, with emphasis on the assumptions made, the basic equations, and the numerical methods. The theoretical basis of the model is compared and contrasted with standard magnetohydrodynamics. The limitations imposed by the major assumptions are discussed. Model inputs and boundary conditions are listed, and the methods of specifying them discussed. Some physical conclusions and insights that have been gained from the model are listed and described very briefly. References are given to published discussions of the major points of physics.

Wolf, R. A.↗

NASA NTRS1985

Hybrid simulation techniques applied to the earth's bow shock

The application of a hybrid simulation model, in which the ions are treated as discrete particles and the electrons as a massless charge-neutralizing fluid, to the study of the earth's bow shock is discussed. The essentials of the numerical methods are described in detail; movement of the ions, solution of the electromagnetic fields and electron fluid equations, and imposition of appropriate boundary and initial conditions. Examples of results of calculations for perpendicular shocks are presented which demonstrate the need for a kinetic treatment of the ions to reproduce the correct ion dynamics and the corresponding shock structure. Results for oblique shocks are also presented to show how the magnetic field and ion motion differ from the perpendicular case.

Winske, D.↗

NASA NTRS1985

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 0.1 - 1000 from constant viscosity up to viscosity variations of 100,000. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10 to the 22nd sq cm/s in order for a 10 km diapir to penetrate a distance of several radii.

Daly, S. F.↗

NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗

NASA NTRS1986

Polynomial elimination theory and non-linear stability analysis for the Euler equations

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Kennon, S. R.↗

NASA NTRS1985

Evolution of a vortical structure associated with the bursting event in a channel flow

The temporal evolution of a horseshoe vortex structure in a channel is investigated by a numerical simulation. A spectral numerical method is employed to integrate the time-dependent, three-dimensional Navier-Stokes equations. The initial vortical structure is obtained by applying a conditional sampling technique to a data base generated from a direct simulation of a turbulent channel flow. The evolution of this vortical structure under the influence of the self-induced motion and the mean shear is presented. It is shown that the initial sheet-like vortical structure rolls up into a vortex tube as it is convected downstream. Turbulence structures associated with the vortex stretching are investigated. Production of vorticity stretching is high inside the vortex legs, although it is also substantial in the tip region and above the legs. High Reynolds shear stress is produced near the tip of the vortex.

Kim, J.↗