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At least 973 records · Page 54

K-distribution and polarimetric terrain radar clutter

A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

Yueh, S. H.↗

High speed turbulent reacting flows: DNS and LES

Work on understanding the mechanisms of mixing and reaction in high speed turbulent reacting flows was continued. Efforts, in particular, were concentrated on taking advantage of modern computational methods to simulate high speed turbulent flows. In doing so, two methodologies were used: large eddy simulations (LES) and direct numerical simulations (DNS). In the work related with LES the objective is to study the behavior of the probability density functions (pdfs) of scalar properties within the subgrid in reacting turbulent flows. The data base obtained by DNS for a detailed study of the pdf characteristics within the subgrid was used. Simulations are performed for flows under various initializations to include the effects of compressibility on mixing and chemical reactions. In the work related with DNS, a two-dimensional temporally developing high speed mixing layer under the influence of a second-order non-equilibrium chemical reaction of the type A + B yields products + heat was considered. Simulations were performed with different magnitudes of the convective Mach numbers and with different chemical kinetic parameters for the purpose of examining the isolated effects of the compressibility and the heat released by the chemical reactions on the structure of the layer. A full compressible code was developed and utilized, so that the coupling between mixing and chemical reactions is captured in a realistic manner.

Givi, Peyman↗

Nonlinear phase-space diffusion approach to turbulent organized structures

The study deals with the approximation of the effect of all velocity-increment moments on the spatial evolution of the pdf for maximally correlated structures by the effect of the second moment alone by assuming independence of separated length scales. The dependence of the two-point velocity statistics on length-scale or separation is found to be governed by the gradients of the stress, rather than of the velocity. This may provide a new approach for predicting the domain patterns observed in turbulent flows and a new means of characterizing or classifying different structures, namely, by their nonlinear diffusion coefficient.

Shen, Hubert H.↗

Scalar dissipation and mixing in turbulent reacting flows

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 64-cubed Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence-dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions were compared to predictions of D/D models that make use of parameters evaluated from the nonreacting or inert system.

Leonard, Andy D.↗

Asymptotic behavior of curvature of surface elements in isotropic turbulence

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.

Girimaji, S. S.↗

Evaluation of an efficient statistical transport model for turbulent droplet dispersion in dilute combusting sprays

Evaluation of an efficient statistical transport model for turbulent droplet dispersion is made for a dilute spray of methanol droplets injected into a turbulent, axisymmnetric methane-fuelled diffusion flame burning in stagnant air. In the dispersion model, a computational parcel representing a group of physical particles (droplets) is considered to have a normal probability density function (pdf) in space. The mean is determined by Lagrangian tracking through a sequence of stochastically generated turbulent eddies and the variance is evaluated from a statistical formulation based on the linearized particle equations of motion. The basic validity of this model is established through comparison with available experimental data and with theoretical predictions using a conventional stochastic direct modeling approach. The conclusion of the evaluation is that the proposed dispersion model compares favorably with experimental data and provides a valid technique for simulating turbulent combusting sprays with significant computational savings over conventional methods.

Litchford, Ron J.↗

Going through a quantum phase

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Shapiro, Jeffrey H.↗

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Madnia, C. K.↗

Modeling of the reactant conversion rate in a turbulent shear flow

Results are presented of direct numerical simulations (DNS) of spatially developing shear flows under the influence of infinitely fast chemical reactions of the type A + B yields Products. The simulation results are used to construct the compositional structure of the scalar field in a statistical manner. The results of this statistical analysis indicate that the use of a Beta density for the probability density function (PDF) of an appropriate Shvab-Zeldovich mixture fraction provides a very good estimate of the limiting bounds of the reactant conversion rate within the shear layer. This provides a strong justification for the implementation of this density in practical modeling of non-homogeneous turbulent reacting flows. However, the validity of the model cannot be generalized for predictions of higher order statistical quantities. A closed form analytical expression is presented for predicting the maximum rate of reactant conversion in non-homogeneous reacting turbulence.

Frankel, S. H.↗

Pre-mixed flame simulations for non-unity Lewis numbers

A principal effect of turbulence on premixed flames in the flamelet region is to wrinkle the flame fronts. For non-unity Lewis numbers (Le), the local flame structure is altered in curved regions. This effect is examined using direct numerical simulations of the three dimensional, constant density, decaying isotropic turbulence with a single step, finite rate chemical reaction. Simulations of Lewis numbers 0.8, 1.0, and 1.2 are compared. The turbulent flame speed, S(sub T), increases as Le decreases. The correlation between S(sub T) and u prime found in previous Le = 1 simulations has a strong Lewis number dependency. The variance of the pdf of the flame curvature increases as Le decreases, indicating that the flames become more wrinkled. A strong correlation between local flame speed and curvature was found. For Le greater than 1, the flame speed increases in regions concave towards the products and decreases in convex regions. The opposite correlation was found for Le less than 1. The mean temperature of the products was also found to vary with Lewis number. For Le = 0.8, it is less than the adiabatic flame temperature and for Le = 1.2 it is greater.

Rutland, C. J.↗

A subgrid mixing model for LES of nonpremixed turbulent combustion

A new sub-grid mixing model for use in large eddy simulations of turbulent combustion is presented and applied to a hydrogen-air diffusion flame. The sub-grid model is based on Kerstein's Linear Eddy Model (1988). The model is first used to predict the mixing of a conserved scalar in a turbulent shear flow. The model correctly predicts the behavior of the pdf of the scalar field and displays a nonmarching peak at the preferred mixture fraction as the shear layer is traversed. It is then illustrated how a reduced chemical mechanism can be implemented within the linear eddy subgrid model formulation. The model is used to predict NO formation in hydrogen-air diffusion flame using a reduced chemical mechanism involving nine reactive scalars.

Mcmurtry, P. A.↗

Turbulent reacting flow computations including turbulence-chemistry interactions

A two-equation (k-epsilon) turbulence model has been extended to be applicable for compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. A turbulence-chemistry interaction model is outlined. In this model, the effects of temperature and species mass concentrations fluctuations on the species mass production rates are decoupled. The effect of temperature fluctuations is modeled via a moment model, and the effect of concentration fluctuations is included using an assumed beta-pdf model. Preliminary results obtained using this model are presented. A two-dimensional reacting mixing layer has been used as a test case. Computations are carried out using the Navier-Stokes solver SPARK using a finite rate chemistry model for hydrogen-air combustion.

Narayan, J. R.↗

Conceptual aspects of a statistical-dynamical approach to represent landscape subgrid-scale heterogeneities in atmospheric models

A parameterization of land surfaces based on a statistical-dynamical approach is presented. With this approach, the most important characteristics of the soil-plant-atmosphere system that affect the partition of energy (e.g., plant stomatal conductance, soil humidity, and surface roughness) are represented by a pdf rather than by a single 'representative' value. A primary simplified version of this parameterization is used to estimate the land-surface energy fluxes that are produced at the grid scale by various distributions of stomatal conductance under a broad range of environmental conditions. To demonstrate the approach's potential, results are compared with the same fluxes calculated with a big leaf model using the mean stomatal conductance that corresponds to the distributions. Large absolute and relative differences are obtained between the two schemes for many combinations of stomatal conductance pdfs and environmental conditions.

Avissar, Roni↗

Comparison of laser transit anemometry data analysis techniques

Two techniques for the extraction of two-dimensional flow information from laser transit anemometry (LTA) data sets are presented and compared via a simulation study and experimental investigation. The methods are a probability density function (PDF) estimation technique and a marginal distribution analysis technique. The simulation study builds on the results of previous work and provides a quantification of the accuracy of both techniques for various LTA data acquisition scenarios. The experimental comparison consists of using an LTA system to survey the flow downstream of a turbulence generator in a small low-speed wind tunnel. The collected data sets are analyzed and compared.

Humphreys, William M., Jr.↗

Simulated meteorite impacts and volcanic explosions: Ejecta analyses and planetary implications

Past cratering studies have focused primarily on crater morphology. However, important questions remain about the nature of crater deposits. Phenomena that need to be studied include the distribution of shock effects in crater deposits and crater walls; the origin of mono- and polymict breccia; differences between local and distal ejecta; deformation induced by explosive volcanism; and the production of unshocked, high-speed ejecta that could form the lunar and martian meteorites found on the Earth. To study these phenomena, one must characterize ejecta and crater wall materials from impacts produced under controlled conditions. New efforts at LLNL simulate impacts and volcanism and study resultant deformation. All experiments use the two-stage light-gas gun facility at LLNL to accelerate projectiles to velocities of 0.2 to 4.3 km/s, including shock pressures of 0.9 to 50 GPa. We use granite targets and novel experimental geometries to unravel cratering processes in crystalline rocks. We have thus far conducted three types of simulations: soft recovery of ejecta, 'frozen crater' experiments, and an 'artificial volcano. Our ejecta recovery experiments produced a useful separation of impactites. Material originally below the projectile remained trapped there, embedded in the soft metal of the flyer plate. In contrast, material directly adjacent to the projectile was jetted away from the impact, producing an ejecta cone that was trapped in the foam recovery fixture. We find that a significant component of crater ejecta shows no signs of strong shock; this material comes from the near-surface 'interference zone' surrounding the impact site. This phenomenon explains the existence of unshocked meteorites on the Earth of lunar and martian origin. Impact of a large bolide on neighboring planets will produce high-speed, weakly shocked ejecta, which may be trapped by the Earth's gravitational field. 'Frozen crater' experiments show that the interference zone is highly localized; indeed, disaggregation does not extend beyond approx. 1.5 crater radii. A cone-shaped region extending downward from the impact site is completely disaggregated, including powdered rock that escaped into the projectile tube. Petrographic analysis of crater ejecta and wall material will be presented. Finally, study of ejecta from 0.9- and 1.3-GPa simulations of volcanic explosions reveal a complete lack of shock metamorphism. The ejecta shows no evidence of PDF's, amorphization, high-pressure phases, or mosaicism. Instead, all deformation was brittle, with fractures irregular (not planar) and most intergranular. The extent of fracturing was remarkable, with the entire sample reduced to fragments of gravel size and smaller.

Gratz, A. J.↗

Where's the Beaverhead beef?

Only rare quartz grains with single-set planar (1013) deformation features (PDF's) are present in breccia dikes found in association with uniformly oriented shatter cones that occur over an area 8 x 25 km. This suggests that the Beaverhead shocked rocks come from only the outer part of the central uplift of what must have been a large (greater than 100 km diameter) complex impact structure. An impact event of this magnitude on continental crust (thought to have occurred in late Precambrian or ealy Paleozoic time) could be expected to punctuate local geologic history. Furthermore, although it may now be covered, its scar should remain despite all the considerable subsequent erosion/deposition and tectonism since the impact. The following are three large-scale singularities or anomalies that may reflect the event and mark its source. (1) The Lemhi Arch is a major structural uplift that occurred in late Proterozoic-early Paleozoic time in East Central Idaho and caused the erosion of at least 4 km of sedimentary cover. This may be directly related to the impact. (2) Of the many thrust sheets comprising the Cordilleran belt, the Cabin plate that carries the shocked rocks is unique in that it alone intersected the crystalline basement. It also now marks the apex of the Southwest Montana Recess in the Sevier front. The basement uplift remaining from the impact may have constituted a mechanical obstacle to the advancing thrust sheets in Cretaceous time, causing the recess. (3) What could be interpreted as a roughly circular aeromagnetic anomaly approx. 70 km in diameter can be discerned in the state aeromagnetic map centered about 20 km southeast of Challis, Idaho, in the Lost River range. It is in approximately the right place, and ignoring the possibility that the anomalies have diverse causes and the circular pattern is coincidental, it may mark what remains of the buried central uplift structure.

Hargraves, R. B.↗

Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992

The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Liou, William W.↗