Results for “Homogenization” — Page 16

NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗

NASA NTRS1989

Optical propagation through a homogeneous turbulent shear flow

Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow have been studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that rms phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.

Truman, C. Randall↗

NASA NTRS1989

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri = -2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Speziale, Charles G.↗

NASA NTRS1988

On the prediction of equilibrium states in homogeneous turbulence

A comparison of several commonly used turbulence models (including the Kappa-epsilon and two second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for a variety of models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to accurately predict equilibrium states for a range of the parameter Omega/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler Kappa-epsilon model for the turbulent flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the Kappa-epsilon model erroneously yields equilibrium states that are independent of Omega/S while the Launder, Reece, and Rodi model predicts a flow relaminarization when Omega/S is greater than 0.39 - a result which is contrary to numerical simulations and linear spectral analysis which indicate flow instability for at least the range 0 less than or = Omega/S less than or = 0.5. The physical implications of the results obtained from the various turbulence models considered here are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Speziale, C. G.↗

NASA NTRS1989

Distortion of homogeneous turbulence by axisymmetric strain and dilatation

Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: the axisymmetric contraction (AC, nozzle-type flow), and the axisymmetric expansion (AE, diffuser-type flow). The paper explores the differences in effects of the two axisymmetric strain modes on the anisotropy of correlations and structures of turbulence; examines the effect of dilatation on the distortion of turbulence; and provides a theoretical background for turbulence model development. It is found that velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; contraction produces much higher anisotropy in velocity and vorticity than expansion; root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. A simple model that reflects the dependence of turbulence evolution on structural parameters such as the Reynolds-stress anisotropy and total strain is proposed, and is shown to outperform all other models for all cases examined, regardless of the mean strain rate.

Lee, Moon Joo↗

NASA NTRS1989

A Doppler centroid estimation algorithm for SAR systems optimized for the quasi-homogeneous source

Radar signal processing applications frequently require an estimate of the Doppler centroid of a received signal. The Doppler centroid estimate is required for synthetic aperture radar (SAR) processing. It is also required for some applications involving target motion estimation and antenna pointing direction estimation. In some cases, the Doppler centroid can be accurately estimated based on available information regarding the terrain topography, the relative motion between the sensor and the terrain, and the antenna pointing direction. Often, the accuracy of the Doppler centroid estimate can be improved by analyzing the characteristics of the received SAR signal. This kind of signal processing is also referred to as clutterlock processing. A Doppler centroid estimation (DCE) algorithm is described which contains a linear estimator optimized for the type of terrain surface that can be modeled by a quasi-homogeneous source (QHS). Information on the following topics is presented: (1) an introduction to the theory of Doppler centroid estimation; (2) analysis of the performance characteristics of previously reported DCE algorithms; (3) comparison of these analysis results with experimental results; (4) a description and performance analysis of a Doppler centroid estimator which is optimized for a QHS; and (5) comparison of the performance of the optimal QHS Doppler centroid estimator with that of previously reported methods.

Jin, Michael Y.↗

NASA NTRS1989

Correlation of optical phase distortion with turbulent structure in a homogeneous shear flow

The relative importance of small-scale and large-scale turbulent structure to phase distortion in propagation through the homogeneous shear flow is the focus of this study. The importance of large-scale vortical structure and the associated scalar distribution to optical distortion induced by propagation through a turbulent shear flow has been established (Truman and Lee 1989). Phase errors induced in a coherent optical beam by these turbulent fluctuations are computed. This scalar field shows elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. Long-term plans include an examination of the effects of inhomogeneity through consideration of direct numerical simulations of the channel flow, boundary layer or mixing layer.

Truman, C. Randall↗

NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of thier predictions.

Speziale, Charles G.↗

NASA NTRS1990

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗

NASA NTRS1991

Estimating SAR Doppler Shifts From Homogeneous Targets

Algorithm that processes some of information in synthetic-aperture-radar (SAR) echoes from homogeneous targets yields optimal estimates of Doppler frequency shifts. Helps in further processing to extract as much information as possible about targets. Used to improve radiometric calibrations, to estimate direction of radar antenna, and to determine speeds of moving targets more accurately. Also helpful in measurements of speeds of ocean currents and of wind shears at airports.

Jin, Michael Y.↗

NASA NTRS1991

An analysis of RNG based turbulence models for homogeneous shear flow

In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG based calculation of C(sub epsilon1). It is shown that with the new value of C(sub epsilon1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.

Speziale, Charles G.↗

NASA NTRS1991

Fourier transform infrared and Raman spectroscopic characterization of homogeneous solution concentration gradients near a container wall at different temperatures

Fourier transform infrared (FTIR) and Raman spectroscopic techniques were used to study the solution concentration gradient in succino nitrile-rich and water-rich homogeneous solutions. The spectroscopic data shows significant concentration dependency. Although FTIR-attenuated total reflectance could not yield surface spectra since the evanescent infrared wave penetrated deep into the bulk solution, it showed that water-rich clusters were decreased at higher temperatures. This result is consistent with the calorimetric results reported earlier.

Loo, B. H.↗

NASA NTRS1991

Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

Squires, Kyle D.↗

NASA NTRS1991

The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow

The effect of an arbitrarily oriented mean passive scalar gradient on one-point passive scalar statistics is studied in homogeneous turbulent shear flow in the limit of rapid shearing. By neglecting the nonlinear inertial transfer to small scales an analytical solution for individual Fourier modes is obtained for the case of unity Prandtl number. This solution is used to compute the development of one-point statistics for the velocity and scalar fields in the inviscid limit. Comparisons to direct numerical simulations of the full nonlinear equations for the same flow show that, in addition to describing the early time response to the imposed shear, the linear solution gives reasonable estimates of several correlation coefficients for the developed shear flow.

Rogers, Michael M.↗

NASA NTRS1991

Polarimetric signatures of a layer of random nonspherical discrete scatterers overlying a homogeneous half-space based on first- and second-order vector radiative transfer theory

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. Some of the salient features of the numerical results are as follows: (1) the inclusion of the nondiagonal extinction matrix in the vector radiative transfer theory accounts for an appreciable phase difference between vv and hh polarizations, particularly for aligned scatterers; (2) the ensemble-averaged scattered Stokes vector is generally partially polarized, with the degree of polarization less than unity; (3) there generally exists a pedestal in the copolarization return when plotted as a function of ellipticity and orientation angles, which may be due to heterogeneity of scattering objects and/or multiple scattering effects; and (4) multiple scattering effects generally enhance the pedestal in copolarization return, decrease the degree of polarization, affect phase difference, and also enhance the depolarization return.

Tsang, Leung↗

NASA NTRS1991

Homogeneity of spatial correlation statistics of tropical oceanic rainfall

The possibility of uniform horizontal correlation scales for tropical oceanic rainfall has been examined by a study of satellite-observed microwave data as a proxy measure of rain rates. From the brightness temperatures from the electrically scanning microwave radiometer on Nimbus 5 near nadir during the year 1974, the mean spatial autocorrelation function as a function of simultaneous pixel separation was calculated in each 5 by 5 deg grid box over the tropical Pacific and Atlantic for each season. The equal-time spatially lagged correlations were compared for geographical dependence to investigate the hypothesis of homogeneity. A simple model of the spatial statistics of the microwave brightness temperatures was used, consisting of a mixture of uncorrelated spatial white noise incoherently superimposed on a spatially correlated field (spatial red noise). The red noise signals are presumed to be generated by convective activity in the tropical atmosphere. The parameters of the red noise are consistent with this scheme over the tropical oceans, yielding a uniform spatial scale of about 50 km throughout.

Shin, Kyung-Sup↗

NASA NTRS1991

Estimation of homogeneous nucleation flux via a kinetic model

The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.

Wilcox, C. F.↗

NASA NTRS1989

Effects of rotation on homogeneous turbulence

Turbulence models are known to have difficulty in flows with strong rotation. This paper examines the effect of rotation, using rapid distortion theory for homogeneous turbulence as a guide. It is shown that rotation significantly modifies the turbulent stress anisotropy in a way not predicted by current turbulence models. The reasons for this failure of models is argued to be a lack of information about the turbulence structure. A new tensor quantity, the structure tensor, is defined and shown to be of critical importance in the rotation problem. The physical reasons for the effects of rotation are explained, and a simple model that does display the effects is proposed.

Reynolds, W. C.↗