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NASA NTRS1985

Analytical-numerical methods of calculations of energy and three-dimensional particle distributions in electromagnetic cascades

Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.

Ivanenko, I. P.↗

NASA NTRS1984

Numerical experiments on galaxy clustering in open universes

Numerical studies were performed on the dynamical effects on the evolution of clumps, filaments, voids, and galaxy clusters by various final Omega values. The final Omega values examined ranged from 0.03-1, and attention was given to defining observations of superclusters which would aid in determining an actual value for Omega. The numerical trials consisted of n-body integration programs governed by the total expansion and final Omega value and included comparisons between results for open and closed universes. All runs started from the same initial conditions. The dispersion trajectories of particles and the final galactic cluster forms were found to be equivalent, regardless of the final Omega value. The possibility of deriving a value for Omega from velocity data on galaxies which have not yet joined clusters is discussed.

Miller, R. H.↗

NASA NTRS1984

Numerical viscosity and the entropy condition for conservative difference schemes

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Tadmor, E.↗

NASA NTRS1984

Development of numerical procedures for analysis of complex structures

The paper is concerned with the development of novel numerical procedures for the solution of static, stability, free vibration and dynamic response analysis of large, complex practical structures. Thus, details of numerical algorithms evolved for dynamic analysis of usual non-rotating and also rotating structures as well as finite dynamic elements are presented in the paper. Furthermore, the article provides some description of a general-purpose computer program STARS specifically developed for efficient analysis of complex practical structures.

Gupta, K. K.↗

NASA NTRS1984

Numerical simulation of reconnection in an emerging magnetic flux region

Numerical solutions in two dimensions are presented for the resistive MHD equations of an initial boundary value problem, simulating reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. This numerical model displays four main phases, which are interpreted in terms of (1) a slowly evolving quasi-steady phase during which most of the magnetic flux emerges, with approximate equilibrium between magnetic and pressure forces; (2) an impulsive phase in which either the reconnection or continuing emergence of the first phase comes to disrupt the equilibrium, and extensive acceleration occurs as the high pressure region within the emerging region drives the fluid upwards and outwards; (3) a second quasi-steady phase; and (4) a potential-static phase in which continuing reconnection, ohmic dissipation, and fluid transport through boundaries depletes the system of all currents and flows.

Forbes, T. G.↗

NASA NTRS1983

A numerical investigation of the effects of cloudiness on mesoscale atmospheric circulation

The development of a comprehensive scheme for computing radiative transfer in a cloudy, stratified atmosphere is described, and the interactions of radiation, clouds, surface heating, and frictional processes are investigated utilizing a three-dimensional numerical weather prediction model. This model is described along with the design of a reliable radiative transfer scheme which allows any vertical moisture and temperature stratifications occurring within a numerical weather prediction model to be taken into account. Some preliminary results of sensitivity tests for three 24-hour simulations are depicted in order to identify the forecast fields which respond to change in atmospheric radiation induced by cloudiness.

Wong, V. C.↗

NASA NTRS1985

An efficient numerical algorithm for transverse impact problems

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Sankar, B. V.↗

NASA NTRS1985

Numerical simulation and comparison with experiment for self-excited oscillations in a diffuser flow

This paper describes numerical simulations of self-excited oscillations in a two-dimensional transonic diffuser flow obtained by solving the Navier-Stokes equations with a two-equation turbulence model. Comparisons were made between the computational results and experimental data. For the mean flowfields, the agreement between computation and experiment is good for the wall pressures, shock location, and the separation and reattachment points. However, the thickness of the computed recirculation zone is about 50 percent of the measured thickness. For the fluctuating flowfields, a great deal of qualitative similarity exists between the computation and experiment; however, the predicted oscillation frequency is about 50 percent higher than the measured value. The formation of a succession of downstream-traveling counter-rotating vortices, as seen experimentally, is also vividly displayed in the numerical results.

Hsieh, T.↗

NASA NTRS1985

Refined numerical solution of the transonic flow past a wedge

A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

Liang, S.-M.↗

NASA NTRS1985

Experimental and numerical investigation of supersonic flow through a square duct

Steady, developing, adiabatic supersonic flow in a square duct is investigated for an inlet Mach number of 3.91 and a unit Reynolds number of 1.8 x 10 to the 6th/m. The numerical results for laminar flow show that two secondary flow cells develop in the near vicinity of the corner which are centered about the corner bisector and distort the primary flow in this region. For turbulent flow, the experimental results indicate that two secondary flow cells also develop about the corner bisector, but are directed in an opposite sense to that observed for the laminar case. Numerical results based on the Baldwin-Lomax model show that this model is incapable of predicting turbulence-generated secondary flow cells. For a suitable choice of constants, the Gessner-Emery model is able to predict the strength of these cells, but is deficient with respect to predicting their positions in the flow and their distorting influence on the primary flow. These observations are based on comparisons made in this paper between predicted and measured total pressure contours, cross flow velocity profiles, and local wall shear stress distributions.

Davis, D. O.↗

NASA NTRS1985

Numerical simulation of flow through scramjet inlets using a three-dimensional Navier-Stokes code

A three-dimensional Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either the fully explicit or explicit-implicit method due to MacCormack. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects which are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flow field. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, A.↗

NASA NTRS1985

Numerical simulation of compressible, turbulent, two-phase flow

A computer program for numerically simulating compressible, turbulent, two-phase flows is described and applied. Special attention is given to flows in which dust is ingested into the turbulent boundary layer behind shock waves moving over the earth's surface. it is assumed that the two phases are interpenetrating continua which are coupled by drag forces and heat transfer. The particle phase is assumed to be dilute, and turbulent effects are modeled by zero- and two-equation eddy viscosity models. An important feature of the turbulence modeling is the treatment of surface boundary conditions which control the ingestion of particles into the boundary layer by turbulent friction and diffusion. The numerical method uses second-order implicit upwind differencing of the inviscid terms of the equations and second-order central differencing of the viscous terms. A diagonal form of the implicit algorithm is used to improve efficiency, and the transformation to a curvilinear coordinate system is accomplished by the finite volume techniques. Applications to a series of representative flows include a two-phase nozzle flow, the steady flow of air over a sand bed, and the air flow behind a normal shock wave in uniform motion over a sand bed. Results of the latter two applications are compared with experimental results.

Coakley, t. J.↗

NASA NTRS1985

A numerical study of the effects of a large sandbar upon sea breeze development

Two-dimensional numerical simulations of sea breeze development over a large sandbar on the North Sea coast of Germany are reported. The numerical model used in these experiments contains a detailed treatment of soil moisture, which allows evaluation of the effects of differential surface characteristics on the airflow pattern. Results of the simulations indicate that the contrast between the moist sandbar and adjacent dry land, the tidal inundation of the sandbar, and the westward penetration of the Baltic sea breeze play important roles in the development of mesoscale airflow patterns in the sandbar region.

Kessler, R. C.↗

NASA NTRS1985

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.

Kerr, R. M.↗

NASA NTRS1985

Numerical Techniques in Acoustics

This is the compilation of abstracts of the Numerical Techniques in Acoustics Forum held at the ASME's Winter Annual Meeting. This forum was for informal presentation and information exchange of ongoing acoustic work in finite elements, finite difference, boundary elements and other numerical approaches. As part of this forum, it was intended to allow the participants time to raise questions on unresolved problems and to generate discussions on possible approaches and methods of solution.

Baumeister, K. J.↗

NASA NTRS1985

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Korkan, K. D.↗

NASA NTRS1986

A numerical simulation of the inviscid flow through a counter-rotating propeller

The results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration are presented. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown.

Celestina, M. L.↗

NASA NTRS1986

Analytical and numerical studies of the thermocapillary flow in a uniformly floating zone

The microgravity environment of an orbiting vehicle permits crystal growth experiments in the presence of greatly reduced buoyant convection in the liquid melt. Crystals grown in ground-based laboratories do not achieve their potential properties because of dopant variations caused by flow in the melt. The floating zone crystal growing system is widely used to produce crystals of silicon and other materials. However, in this system the temperature gradient on the free sidewall surface of the melt is the source of a thermocapillary flow which does not disappear in the low-gravity environment. The idea of using a uniform rotation of the floating zone system to confine the thermocapillary flow to the melt sidewall leaving the interior of the melt passive is examined. A cylinder of fluid with an axial temperature gradient imposed on the cylindrical sidewall is considered. A half zone and the linearized, axisymmetric flow in the absence of crystal growth is examined. Rotation is found to confine the linear thermocapillary flow. A simplified model is extended to a full zone and both linear and nonlinear thermocapillary flows are studied theoretically. Analytical and numerical methods are used for the linear flows and numerical methods for the nonlinear flows. It was found that the linear flows in the full zone have more complicated and thicker boundary layer structures than in the half zone, and that these flows are also confined by the rotation. However, for the simplified model considered and for realistic values for silicon, the thermocapillary flow is not linear. The fully nonlinear flow is strong and unsteady (a weak oscillation is present) and it penetrates the interior. Some non-rotating flow results are also presented. Since silicon as a large value of thermal conductivity, one would expect the temperature fields to be determined by conduction alone. This is true for the linear and weakly nonlinear flows, but for the stronger nonlinear flow the results show that temperature advection is also important. Uniform rotation may still be a means of confining the flow and the results obtained define the procedure to be used to examine this hypothesis.

Fowlis, W. W.↗