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NASA NTRS1996

Evaluation of Subgrid-Scale Models for Large Eddy Simulation of Compressible Flows

The objective of this project was to evaluate and develop subgrid-scale (SGS) turbulence models for large eddy simulations (LES) of compressible flows. During the first phase of the project results from LES using the dynamic SGS model were compared to those of direct numerical simulations (DNS) of compressible homogeneous turbulence. The second phase of the project involved implementing the dynamic SGS model in a NASA code for simulating supersonic flow over a flat-plate. The model has been successfully coded and a series of simulations has been completed. One of the major findings of the work is that numerical errors associated with the finite differencing scheme used in the code can overwhelm the SGS model and adversely affect the LES results. Attached to this overview are three submitted papers: 'Evaluation of the Dynamic Model for Simulations of Compressible Decaying Isotropic Turbulence'; 'The effect of the formulation of nonlinear terms on aliasing errors in spectral methods'; and 'Large-Eddy Simulation of a Spatially Evolving Compressible Boundary Layer Flow'.

Blaisdell, Gregory A.↗

NASA NTRS1979

Wave tilt sounding of a linearly inhomogeneous layered half-space

The wave tilt of a transverse electric (TE) electromagnetic wave over a linearly inhomogeneous lossy layer overlying a homogeneous half-space is studied. Two approaches are used: an exact formulation using solutions of Airy's equation and an approximate numerical solution using a large number of homogeneous layers with a linearly increasing dielectric constant. The numerical results of both solutions are practically identical as long as the thickness of the layers in the approximate model are somewhat smaller than a quarter-wave length.

Warne, L.↗

NASA NTRS1999

Data Structure and Parallel Decomposition Considerations on a Fibonacci Grid

The Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.

Michalakes, John↗

NASA NTRS1992

Reynolds stress calculations of homogeneous turbulent shear flow with bounded energy states

Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for non-equilibrium vortex stretching in the dissipation rate transport equation, as recently proposed by Bernard and Speziale. As with the earlier reported k-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is not achieved until the dimensionless time greater than 60, an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this non-equilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.

Speziale, Charles G.↗

NASA NTRS1993

Reynolds stress calculations of homogeneous turbulent shear flow with bounded energy states

Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for nonequilibrium vortex stretching in the dissipation rate transport equation as recently proposed by Bernard and Speziale (1992). As with the earlier reported K-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is now not achieved until the dimensionless time St greater than 60 - an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this nonequilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.

Speziale, Charles G.↗

NASA NTRS1978

Numerical solutions and laser-Doppler measurements of spin-up

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. A series of laser-Doppler measurements was made of the zonal flow over a range of Ekman numbers and Rossby numbers at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Warn-Varnas, A.↗

NASA NTRS1972

Some spatially homogeneous gas motions

A functional equation is derived for a spatially homogeneous distribution function and examples of spatially homogeneous gas motions are considered. Numerical calculation was conducted for one such motion with the use of a model equation.

Rykov, V. A.↗

NASA NTRS1984

Electromagnetic ion beam instabilities

The linear theory of electromagnetic instabilities driven by an energetic ion beam streaming parallel to a magnetic field in a homogeneous Vlasov plasma is considered. Numerical solutions of the full dispersion equation are presented. At propagation parallel to the magnetic field, there are four distinct instabilities. A sufficiently energetic beam gives rise to two unstable modes with right-hand polarization, one resonant with the beam, the other nonresonant. A beam with sufficiently large T (perpendicular to B)/T (parallel to B) gives rise to the left-hand ion cyclotron anisotropy instability at relatively small beam velocities, and a sufficiently hot beam drives unstable a left-hand beam resonant mode. The parametric dependences of the growth rates for the three high beam velocity instabilities are presented here. In addition, some properties at oblique propagation are examined. It is demonstrated that, as the beam drift velocity is increased, relative maxima in growth rates can arise at harmonics of the ion cyclotron resonance for both right and left elliptically polarized modes.

Gary, S. P.↗

NASA NTRS1985

Morphological Stability and Fluid Dynamics of Vapor Crystal Growth

A fundamental understanding of the conditions under which crystals can retain morphological stability, i.e., shape stability of the advancing interface, during growth from vapors was studied. Morphological stability (MS) is a necessary condition for the growth of homogeneous single crystals required for numerous device applications. For crystallization from melts, the MS concepts are well developed and are essentially based on heat and mass transfer conditions about the advancing interface. For crystallization from vapors, the MS requirements are more complex and not well understood. The added complexity arises from the fact that anisotropies in interfacial kinetics are typically stronger in crystallization from vapors than from melts. These pronounced anisotropies root in the distinctly lower atomic roughness of most vapor-solid interfaces.

Rosenberger, F.↗

NASA NTRS1989

The analysis and modeling of dilatational terms in compressible turbulence

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Sarkar, S.↗

NASA NTRS1991

The analysis and modelling of dilatational terms in compressible turbulence

Sarkar, S.↗

NASA NTRS1990

Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence

The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.

Aupoix, B.↗

NASA NTRS1992

The mirror and ion cyclotron anisotropy instabilities

The linear dispersion equation for fully electromagnetic waves and instabilities at arbitrary directions of propagation relative to a background magnetic field B(0) in a homogeneous Vlasov plasma is solved numerically for bi-Maxwellian particle distributions. For isotropic plasmas the dispersion and damping of the three modes below the proton cyclotron frequency are studied as functions of Beta(i) and T(e)/T(i). The transport ratios of helicity, cross-helicity, Alfven ratio, compressibility, and parallel compressibility are defined. Under the condition that the proton temperature perpendicular to B(0) is greater than the parallel temperature, the growth rates and transport ratios of the mirror instability and the ion cyclotron anisotropy instability are examined and compared. Both the proton parallel compressibility and the proton Alfven ratio are significantly different for the two growing modes.

Gary, S. P.↗

NASA NTRS1995

A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow

Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

Blaisdell, Gregory A.↗

NASA NTRS1998

FU Orionis Outbursts and the Solar Nebula

Protostellar systems are variable on many timescales. The FU Orionis outburst is one of the most drastic forms of variability known to occur in low mass stellar systems. During a typical outburst lasting several decades, system luminosities may be a hundred times what is normal of the quiescent state. FU Orionis outburst events are believed to have significant impacts on the thermal structure of the protosolar nebula. Their existence has been utilized to explain features in the meteoritic record from thermally induced homogenization to chondrule formation. Recent numerical models have shown the viability of the hypothesis that the radiation observed during outburst is emitted by a luminous circumstellar disk transporting mass at a thousand times the quiescent rate. We will begin by describing what is known about the FU Orionis outburst phenomenon from recent observations and theory. We will discuss evidence that suggests that outburst radiation is emitted by a circumstellar disk rather than by the star and will briefly describe the thermal instability as a mechanism for outburst. Additional information is contained in the original extended abstract.

Bell, Robbins↗

NASA NTRS1981

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.

Shirani, E.↗

NASA NTRS2000

CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets

This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.

Farge, Marie↗

NASA NTRS1979

Electrostatic and electromagnetic gyroharmonic emissions due to energetic electrons in magnetospheric plasma

The paper derives the growth rates and growth lengths of the electrostatic emission for spatially homogeneous and inhomogeneous energetic electrons, and numerically evaluates the growth rate and growth length spectra for several parameter sets representative of magnetospheric plasmas. In addition, the growth rates are derived for the case of electromagnetic emission modeled by the ordinary mode. The numerical results of the electromagnetic and electrostatic cases are compared with observations made by satellites in the earth's magnetosphere. It is concluded that the electrostatic gyroharmonic excitation is possible without the cold composition of plasma which is often postulated in the existing literature.

Curtis, S. A.↗