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NASA NTRS1999

Characterization of Sound Radiation by Unresolved Scales of Motion in Computational Aeroacoustics

Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future: although current large eddy simulation methods can resolve the largest scales of motion accurately the, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution of these unresolved scales is simply neglected. In this paper, the problem of evaluating the sound radiation properties of the unresolved, subgrid-scale motions is approached in the spirit of the simplest subgrid stress models: the unresolved velocity field is treated as isotropic turbulence with statistical descriptors, evaluated from the resolved field. The theory of isotropic turbulence is applied to derive formulas for the total power and the power spectral density of the sound radiated by a filtered velocity field. These quantities are compared with the corresponding quantities for the unfiltered field for a range of filter widths and Reynolds numbers.

Rubinstein, Robert↗

NASA NTRS1989

Second-Order Modeling of Low-Reynolds-Number Turbulence Near Walls

This paper presents a set of second-order closure models for low-Reynolds-number turbulence near the wall. Existing closure models for the Reynolds-stress equations were modified to show proper near-wall behavior. A dissipation-rate equation for the turbulent kinetic energy is also reformulated. The proposed models satisfy realizability and will not produce unphysical behavior. Fully developed channel flows are used for model testing. The equations are solved for the mean velocity, the Reynolds stresses, and the dissipation rate of the turbulent kinetic energy. The calculations are compared with both direct numerical simulations and with measurements. It is shown that the present models perform well in predicting the behavior of the turbulence near a wall. Significant improvements over previous models in predicting the components of the Reynolds stress tensor are obtained in the present models.

Shih, T.-H.↗

NASA NTRS1993

Compressibility Effects on the Growth and Structure of Homogeneous Turbulent Shear Flow

Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure-dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Blaisdell, G. A.↗

NASA NTRS1999

A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a Direct Numerical Simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. The Large Eddy Simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by computing the terms using the DNS database. Since LES of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the Subgrid Scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the Gradient model and the Scale-Similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the Gradient and Scale-Similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗

NASA NTRS2000

A Priori Subgrid Scale Modeling for a Droplet Laden Temporal Mixing Layer

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using a direct numerical simulation (DNS) database. The DNS is for a Reynolds number (based on initial vorticity thickness) of 600, with droplet mass loading of 0.2. The gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. Since Large Eddy Simulation (LES) of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be given by the filtered variables plus a correction based on the filtered standard deviation, which can be computed from the sub-grid scale (SGS) standard deviation. This model predicts unfiltered variables at droplet locations better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: Smagorinsky, gradient and scale-similarity. When properly calibrated, the gradient and scale-similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗

NASA NTRS1999

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work is limited to very simple models. In this project, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. The proposed work is based on previously funded NASA work that allowed us to develop a two-dimensional numerical method for boiling flows and to demonstrate the ability of the method to simulate film boiling. While numerical simulations of multi-fluid flows have been advanced in a major way during the last five years, or so, similar capability for flows with phase change are still in their infancy. Although the feasibility of the proposed approach has been demonstrated, it has yet to be extended and applied to fully three-dimensional simulations. Here, a fully three-dimensional, parallel, grid adaptive code will be developed. The numerical method will be used to study nucleate boiling in microgravity, with particular emphasis on two aspects of the problem: 1) Examination of the growth of bubbles at a wall nucleation site and the instabilities of rapidly growing bubbles. Particular emphasis will be put on accurately capturing the thin wall layer left behind as a bubble expands along a wall, on computing instabilities on bubble surfaces as bubbles grow, and on quantifying the effects of both these phenomena on heat transfer; and 2) Examination of the effect of shear flow on bubble growth and heat transfer.

Tryggvason, Gretar↗

NASA NTRS1999

Effects of Gravity on Sheared Turbulence Laden with Bubbles or Droplets

The objective of this numerical/experimental study is to improve the understanding of the effects of gravity on the two-way interaction between dispersed particles (bubbles or liquid droplets) and the carrier turbulent flow. The first phase of the project considers isotropic turbulence. Turbulent homogeneous shear flows laden with droplets/bubbles will be studied in the next phase. The experiments reported here are concerned with the dispersion of liquid droplets by homogeneous turbulence under various gravitational conditions and the effect of these droplets on the evolution of the turbulence of the carrier fluid (air). Direct numerical simulations (DNS) of bubble - laden isotropic decaying turbulence are performed using the two-fluid approach (TF) instead of the Eulerian-Lagrangian approach (EL). The motivation for using the TF formulation is that EL requires considerable computational resources especially for the case of two-way coupling where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum (without molecular diffusivity) characterized by the bubble phase velocity field and concentration (volume fraction). The bubble concentration, C, is assumed small enough to neglect the bubble-bubble interactions.

Elghobashi, Said↗

NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗

NASA NTRS2001

Turbulence Modeling Workshop

Advances in turbulence modeling are needed in order to calculate high Reynolds number flows near the onset of separation and beyond. To this end, the participants in this workshop made the following recommendations. (1) A national/international database and standards for turbulence modeling assessment should be established. Existing experimental data sets should be reviewed and categorized. Advantage should be taken of other efforts already under-way, such as that of the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) consortium. Carefully selected "unit" experiments will be needed, as well as advances in instrumentation, to fill the gaps in existing datasets. A high priority should be given to document existing turbulence model capabilities in a standard form, including numerical implementation issues such as grid quality and resolution. (2) NASA should support long-term research on Algebraic Stress Models and Reynolds Stress Models. The emphasis should be placed on improving the length-scale equation, since it is the least understood and is a key component of two-equation and higher models. Second priority should be given to the development of improved near-wall models. Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) would provide valuable guidance in developing and validating new Reynolds-averaged Navier-Stokes (RANS) models. Although not the focus of this workshop, DNS, LES, and hybrid methods currently represent viable approaches for analysis on a limited basis. Therefore, although computer limitations require the use of RANS methods for realistic configurations at high Reynolds number in the foreseeable future, a balanced effort in turbulence modeling development, validation, and implementation should include these approaches as well.

Rubinstein, R.↗

NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗

NASA NTRS1994

Compressible Turbulent Channel Flows: DNS Results and Modeling

The present paper addresses some topical issues in modeling compressible turbulent shear flows. The work is based on direct numerical simulation of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional time-and Favre-averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that the compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation is so successful in correlating compressible boundary layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

Huang, P. G.↗

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 NTRS1995

Energy Transfer in Rotating Turbulence

The influence or rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime tackled in an RDT (Rapid Distortion Theory) fashion, cannot Affect st homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (Direct Numerical Simulation) results are gathered here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on tile turbulence. The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping due to rotation of the energy transfer. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro(sup omega) = omega'/(2(OMEGA))-ratio of rms vorticity and background vorticity as the relevant rotation parameter, in accordance with DNS and EDQNM results fit addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (Ro(omega) = (omega)' and Ro(omega)w greater than 1), which is characterized by a marco-Rossby number Ro(sup L) less than 1 and Ro(omega) greater than 1 which is characterized by a macro-Rossby number based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in tile wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In Addition, a polarization of the energy distribution in this slow 2D manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally is demonstrated the ability of a generalized EDQNM (Eddy Damped Quasi-Normal Markovian) model to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space, when compared to recent LES results. Even if the applications mainly concern developed strong turbulence, a particular emphasis is given to the strong formal analogy of this EDQNM2 model with recent weakly nonlinear approaches to wave-turbulence.

Cambon, Claude↗

NASA NTRS1997

The Use of DNS in Turbulence Modeling

The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.

Mansour, Nagi N.↗

NASA NTRS2001

Adaptive Numerical Dissipation Controls for High Order Methods

A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

Yee, Helen C.↗

NASA NTRS1997

On the Numerical Prediction of Flow Transition

Knowledge from dynamical systems theory is used to study numerical uncertainties in direct numerical simulation of transition from laminar to turbulent flows. Spurious behavior due to underresolved grids and temporal discretizations is illustrated with 2-D CFD simulations.

Yee, H. C.↗

NASA NTRS2001

A New Look at Self-Similarity in Strained Plane Wakes

In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.

Rogers, Michael M.↗

NASA NTRS2002

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.

He, Guowei↗