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At least 145 records · Page 8

Multigrid method with weighted mean scheme

Multigrid algorithms based on the weighted mean scheme are developed for the solution of the two dimensional incompressible Navier-Stokes equations. They are applied to two typical problems encountered in engineering applications, namely, the convection diffusion problem of the Benard convection cell, and the driven cavity problem. An analysis of the smoothing rates and stability is given. The efficiency of the multigrid method is investigated.

Lustman, L. R.↗

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Shih, T. I.-P.↗

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗

Improved solar models constructed with a formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations

We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.

Lydon, Thomas J.↗

Solar flare particle propagation: Comparision of a new analytic solution with spacecraft measurements

An analytic solution was obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion. It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events were observed with solar and galactic cosmic ray experiment aboard OGO 6. Detailed comparisons of the predictions of the solution with observations of 1 to 70 MeV protons show that the model adequately describes both the rise and decay times. The solution also yields a time evolution for the vector anisotropy which agrees well with reported observations.

Lupton, J. E.↗

A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

Luhmann, J. G.↗

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗

Mixing and mixing enhancement in supersonic reacting flowfields

Propulsion systems planned for use late in this century and beyond will require appropriate physical models for describing supersonic combustion and numerical techniques for solving the model governing equations. A computer program to study these flows is reported which considers the multicomponent diffusion and convection of important chemical species, the finite-rate reaction of these species, and the resulting interaction of the field mechanics and the chemistry. The application of the program to a spatially developing and reacting mixing layer, which serves an an excellent physical model for the mixing and reaction processes that take place in a scramjet combustor, is reported. Several techniques to enhance the fuel-air mixing and growth of that layer and improve its overall combustion efficiency are considered.

Drummond, J. P.↗

A turbulence module for the NPARC code

A turbulence module is developed for the 2D version of the NPARC code which is currently restricted to planar or axisymmetric flows without swirling. Four turbulence models have been built into the module: Baldwin-Lomax, Chien, Shih-Lumley and CMOTT models. The first is a mixing-length eddy-viscosity model which is mainly used for initialization of computational fields and the last three are the low Reynolds number two-equation models. Unlike chien's model, both the Shih-Lumley and CMOTT models do not involve the dimensionless wall distance y(sup +), an advantage for separated flow calculations. Contrary to the NPARC and most other compressible codes, the non-delta form of transport equations is used which leads to a simpler linearization and is more effective than using the delta form in ensuring the positiveness of the turbulent kinetic energy and its dissipation rate. To reduce numerical diffusion while maintaining necessary stability, a second-order accurate and bounded scheme is used for the convective terms of the turbulent transport equations. This scheme is implemented in a deferred correction manner so that the main coefficients of the resulting difference equations are always positive, thus making the numerical solutions process unconditionally stable. The system of equations is solved via a decoupled method and by the alternating direction TDMA of Thomas. The module can be easily linked to the NPARC code for turbulent flow calculations.

Zhu, J.↗

A two-dimensional numerical simulation of a supersonic, chemically reacting mixing layer

Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy.

Drummond, J. Philip↗

Solution techniques for incompressible flow problems

A three-step Petrov-Galerkin (PG)/operator spliting scheme for the time-dependent incompressible Navier-Stokes equations is proposed. Each time step is split into two Stokes problems and one nonlinear convection-diffusion problem. Using a PG technique on the two outer Stokes problems ensures a stable scheme despite equal-order interpolation, while using a streamline upwind PG scheme on the inner convection-diffusion problem ensures a numerically stable solution at high Reynolds numbers. Numerical tests of this method have been carried out.

Tezduyar, T. E.↗

Two-Dimensional Transport Studies for the Composition and Structure of the Io Plasma Torus

The overall objective of this project is to investigate the roles of local and spatially extended plasma sources created by Io, plasma torus chemistry, and plasma convective and diffusive transport in producing the long-lived S(+), S(++) and O(+) radial ribbon structures of the plasma torus, their System III longitude and local-time asymmetries, their energy sources and their possible time variability. To accomplish this objective, two-dimensional [radial (L) and System III longitude] plasma transport equations for the flux-tube plasma content and energy content will be solved that include the convective motions for both the east-west electric field and co-rotational velocity-lag profile near Io s orbit, radial diffusion, and the spacetime dependent flux-tube production and loss created by both neutral-plasma and plasma-ion reaction chemistry in the plasma torus. For neutral-plasma chemistry, the project will for the first time undertake the calculation of realistic three-dimensional, spatially-extended, and time-varying contributions to the flux-tube ion-production and loss that are produced by Io's corona and extended neutral clouds. The unknown two-dimensional spatial nature of diffusion in the plasma transport will be isolated and better defined in the investigation by the collective consideration of the foregoing different physical processes. For energy transport, the energy flow from hot pickup ions (and a new electron source) to thermal ions and electrons will be included in investigating the System III longitude and local-time temperature asymmetries in the plasma torus. The research is central to the scope of the NASA Sun-Earth Connection Roadmap in Quest II Campaign 4 "Comparative Planetary Space Environments" by addressing key questions for understanding the magnetosphere of planets with high rotation rates and large internal plasma sources and, in addition, is of considerable importance to the NASA Solar System Exploration Science Theme. In this regard, Jupiter is the most extreme example with its rapid rotation and with its inner Galilean satellite Io providing the dominant plasma source for the magnetosphere.

Smyth, William H.↗

Evolution of a magnetic flux tube in two-dimensional penetrative convection

Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field B sub tor is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that the absolute value of B sub tor/rho is approximately constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle.

Jennings, R. L.↗

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Steinthorsson, Erlendur↗

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗

Use of the Burton-prim-slichter Equation at High Growth Rates

The following must be assumed in order to derive the classic Burton-Prim-Slichter equation for segregation during crystal growth: isobaric, isothermal, isopotential or uncharged species, binary, planar interface, steady state, constant diffusion coefficient in fluid, no diffusion in crystal, no lateral convection within fluid film at interface with complete mixing beyond (stagnant film model), and either density, total concentration or partial molar volumes constant in the fluid phase. In addition, the effective distribution coefficient and the interfacial distribution coefficient must be defined properly. The velocity in the equation is the growth rate times a factor correcting for the difference in volumetric properties between crystal and fluid. The stagnant film thickness is found to be a function of freezing rate, with the precise functionality depending on the type of stirring occurring in the growth fluid.

Wilcox, W. R.↗