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NASA NTRS1993

Numerical simulation of free shear flows: Towards a predictive computational aeroacoustics capability

Implicit and explicit spatial differencing techniques with fourth order accuracy have been developed. The implicit technique is based on the Pade compact scheme. A Dispersion Relation Preserving concept has been incorporated into both of the numerical schemes. Two dimensional Euler computation of a spatially-developing free shear flow, with and without external excitation, has been performed to demonstrate the capability of numerical schemes developed. Results are in good agreement with theory and experimental observation regarding the growth rate of fluctuating velocity, the convective velocity, and the vortex-pairing process.

Soh, W. Y.↗
NASA NTRS1993

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

The first section is on 3-D numerical modeling of terrain-induced circulations and covers the following: (1) additional insights into gravity wave generation mechanisms based on the control simulation; (2) ongoing nested-grid numerical simulations; (3) work to be completed during the remainder of FY-93; and (4) work objectives for FY-94. The second section is on linear theory and theoretical modeling and covers the following: (1) the free response of a uniform barotropic flow to an initially stationary unbalanced (ageostrophic) zonal wind anomaly; and (2) the free response of a uniform barotropic flow to an initially stationary balanced zonal wind anomaly.

Lin, Yuh-Lang↗
NASA NTRS1992

Numerical modeling of runback water on ice protected aircraft surfaces

A numerical simulation for 'running wet' aircraft anti-icing systems is developed. The model includes breakup of the water film, which exists in regions of direct impingement, into individual rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted in the numerical solution procedure. The solid wall is modeled as a multilayer structure and the anti-icing system used is of the thermal type utilizing hot air and/or electrical heating elements embedded with the layers. Details of the calculation procedure and the methods used are presented.

Al-Khalil, Kamel M.↗
NASA NTRS1993

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↗
NASA NTRS1992

Testing and numerical modeling of hypervelocity impact damaged Space Station multilayer insulation

Results are presented of experiments measuring the degradation of the insulating capabilities of the multilayer insulation (MLI) of the Space Station Freedom, when subjected to hypervelocity impact damage. A simple numerical model was developed for use in an engineering design environment for quick assessment of thermal effect of the impact. The model was validated using results from thermal vacuum tests on MLI with simulated damage. The numerical model results agreed with experimental data.

Rule, William K.↗
NASA NTRS1992

Numerical simulation of a low-emission gas turbine combustor using KIVA-II

A modified version of the KIVA-II code was used to obtain a multidimensional numerical solution for the turbulent two-phase chemically reacting flows inside a staged turbine combustor (STC). The STC under consideration is equipped with an advanced airblast fuel nozzle and encompasses a fuel nozzle (FN), a rich-burn (RB) zone, a converging connecting pipe, a quick-quench (QQ) zone, a diverging connecting pipe, and a lean-combustion (LC) zone. The STC was divided into two subsystems, namely, FN/RB zone and QQ/LC zones, and the numerical solutions were obtained separately for each subsystem. Preliminary data characterize the major features of the flow and temperature fields inside the STC. Information on velocity, temperature, and some critical species in the FN/RB zone is presented. In the QQ/LC zones, formation of the co- and counter-rotating bulk flow and the sandwiched-ring-shaped temperature field can be clearly seen. The calculations of the mass-weighted standard deviation and the pattern factor of temperature indicated that the mixing performance of the STC is very promising.

Yang, S. L.↗
NASA NTRS1992

Numerical simulations of inductive-heated float-zone growth

The present work provides an improved fluid flow and heat-transfer modeling of float-zone growth by introducing a RF heating model so that an ad hoc heating temperature profile is not necessary. Numerical simulations were carried out to study the high-temperature float-zone growth of titanium carbide single crystal. The numerical results showed that the thermocapillary convection occurring inside the molten zone tends to increase the convexity of the melt-crystal interface and decrease the maximum temperature of the molten zone, while the natural convection tends to reduce the stability of the molten zone by increasing its height. It was found that the increase of induced heating due to the increase of applied RF voltage is reduced by the decrease of zone diameter. Surface tension plays an important role in controlling the amount of induced heating. Finally, a comparison of the computed shape of the free surface with a digital image obtained during a growth run showed adequate agreement.

Chan, Y. T.↗
NASA NTRS1992

Numerical simulation of shock-induced combustion/detonation

A numerical study is conducted to simulate the shock-induced combustion in premixed H2-air mixtures. Two types of bodies, blunt (spherical projectile) and sharp (wedge), are considered in the study. A nine-species, 18-step finite-rate H2-air chemical reaction mechanism coupled with the Navier-Stokes equations is solved. The flow field over the blunt body is found to be unsteady, when the projectile velocity is same as the Chapman-Jouget velocity of the mixture. The unsteadiness is caused by the periodic instabilities originating in the stagnation zone. Numerical results show good qualitative agreement with the ballistic range shadowgraph. In addition, the frequency of oscillations, determined by using the Fourier power spectrum, is found to be in good agreement with the experiment. The flow field over the wedge is found to be stable for the conditions considered in this study. The oblique detonation wave structure is investigated and the important flow features are discussed.

Singh, D. J.↗
NASA NTRS1993

Fourier analysis of numerical algorithms for the Maxwell equations

The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.

Liu, Yen↗
NASA NTRS1993

Numerical quasi-linear study of the critical ionization velocity phenomenon

The critical ionization velocity (CIV) for a neutral barium (Ba) gas cloud moving across the static magnetic field is studied numerically using quasi-linear equations and a parameter range which is typical for the shaped-charge Ba gas release experiments in space. For consistency the charge exchange between the background oxygen ions and neutral atoms and its reverse process, as well as the excitation of the neutral Ba atoms, are included. The numerical results indicate that when the ionization rate due to CIV becomes comparable to the charge exchange rate the energy lost to the ionization and excitation collisions by the superthermal electrons exceeds the energy gain from the waves that are excited by the ion beam. This results in a CIV yield less than the yield by the charge exchange process.

Moghaddam-Taaheri, E.↗
NASA NTRS1993

Comparison of Numerical Model Results with Diffusion Flames in Microgravity

The effects of gravity on methane diffusion flames were studied using a finite difference numerical model. Variables under consideration included velocity, pressure, temperature, enthalpy, reactive species, and inert carrier gas. Results obtained showed that flames in zero gravity were wider and taller than those in normal gravity. The use of a six reaction scheme produced similar predictions of flame width and height compared to those of the single reaction case. The numerical models predicted a considerable difference in the flame base region between normal gravity and low gravity. This region is considered to be beyond the boundaries of current analytical models.

Hyer, Paul V.↗
NASA NTRS1993

Three-dimensional magnetotail equilibria by numerical relaxation techniques

Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.

Hesse, Michael↗
NASA NTRS1993

Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗
NASA NTRS1993

A fast method of numerical quadrature for p-version finite element matrices

A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.

Hinnant, Howard E.↗
NASA NTRS1991

Numerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pts. 1 & 2

Consideration is given to the impulse response of a laminar boundary layer and receptivity; numerical transition to turbulence in plane Poiseuille flow; large eddy simulation of turbulent wake flow; a viscous model and loss calculation of a multisplitter cascade; vortex initiation during dynamic stall of an airfoil; a numerical analysis of isothermal flow in a combustion chamber; and compressible flow calculations with a two-equation turbulence model and unstructured grids. Attention is also given to a 2D calculation of a buoyant flow around a burning sphere, a fast multigrid method for 3D turbulent incompressible flows, a streaming flow induced by an oscillating cascade of circular cylinders, an algebraic multigrid scheme for solving the Navier-Stokes equations on unstructured meshes; and nonlinear coupled multigrid solutions to thermal problems employing different nodal grid arrangements and convective transport approximations.

Taylor, C.↗
NASA NTRS1991

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.

Hwang, Chyi↗
NASA NTRS1993

Numerical solution of wave equations for the stability of the inner cometo-sheath

Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.

Srivastava, Krishna M.↗
NASA NTRS1993

Experimental and numerical study of a turbulent boundary layer with pressure gradients

Results are presented of an experimental and numerical study of a turbulent boundary layer with pressure gradients conducted using the recent 'fringe method' with its numerical advantages and good inflow quality. After an inflow transient good agreement is observed; the differences, of up to 13 percent, are discussed. Moderate deviations from the law of the wall are found in the velocity profiles of the simulation. They are fully correlated with the pressure gradient, are in fair quantitative agreement with the experimental results of Nagano et al. (1992), and are roughly the opposite of uncorrected mixing-length-model predictions. Large deviations from the wall scaling are observed for other quantities, notably for the turbulence dissipation rate. The a(1) structure parameter drops mildly in the upper layer with adverse pressure gradient.

Spalart, Philippe R.↗