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Results for “Homogeneous Isotropic Turbulence”

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NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗

NASA NTRS1979

Some observations of flow structure in multiple jet mixing

Results of hot wire measurements in an incompressible jet issuing from an array of rectangular lobes, equally spaced with their small dimensions in a line, both as a free jet, and as a confined jet, are presented. In the case of a multiple free jet, the flow field for downstream distance x greater than 60D (D = width of a lobe) resembles that of a jet exiting from a two-dimensional nozzle with its short dimension being the long dimension of the lobe. The field of turbulence is found to be nearly isotropic in the plane containing the small dimension of the lobes for x greater than 60D. In the case of a confined multiple jet, the flow field is observed to be nearly homogeneous and isotropic for x greater than 60D.

Krothapalli, A.↗

NASA NTRS1976

Effect of anisotropy and rotation on turbulence production

The dynamical equations for the Reynolds stresses in a form which is suitable for incompressible homogeneous flows are used as a starting point in the investigation. It is assumed that the mean flow is two-dimensional. The equation for the rate of change of the kinetic energy of turbulence is derived. If the turbulence is isotropic, there is no turbulence production. However, the isotropic condition is not stable. The production mechanism is found to be autocatalytic. Rotation always inhibits production because it reduces anisotropy.

Ferziger, J. H.↗

NASA NTRS1991

The use of direct numerical simulation data in turbulence modeling

Direct numerical simulations (DNS) of turbulent flows provide a complete data base to develop and to test turbulence models. In this article, the progress made in developing models for the dissipation rate equation is reviewed. New scaling arguments for the various terms in the dissipation rate equation were tested using data from DNS of homogeneous shear flows. Modifications to the epsilon-equation model that take into account near-wall effects were developed using DNS of turbulent channel flows. Testing of new models for flows under mean compression was carried out using data from DNS of isotropically compressed turbulence. In all of these studies the data from the simulations was essential in guiding the model development. The next generation of DNS will be at higher Reynolds numbers, and will undoubtedly lead to improved models for computations of flows of practical interest.

Mansour, N. N.↗

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 NTRS1987

Spectral multigrid methods for the solution of homogeneous turbulence problems

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Erlebacher, G.↗

NASA NTRS1988

Spectral multigrid methods for the solution of homogeneous turbulence problems

Erlebacher, G.↗

NASA NTRS1991

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.↗

NASA NTRS1995

Modeling the decay of energy containing eddies: A source of solar wind heating

To understand the solar wind heating and acceleration mechanisms one needs to understand the decay of energy containing eddies. With this goal in mind, attempts have been made to extend the fluid dynamic phenomenology of large scale quasi-equilibrium to the case of magnetohydrodynamics. Matthaeus et al. have proposed a model for the inhomogeneous transport and decay of five mean variables, namely, two mean square Elsasser variables z(exp 2) (sub +/-) their correlation lengths, and the difference between the kinetic and magnetic energies. We test the validity of this model in the simplified case of homogeneous turbulence simulated in a periodic box. We propose a class of models and show that they may fit the simulation satisfactorily. Analytic solutions of this class of model reveal their inherent properties and demonstrate the difficulties associated with finite cross helicity. It is noted that adjustments are required to make the simplest models, which are based upon isotropic turbulence, scale properly with respect to the strength of the mean magnetic field. This can be interpreted as due to anisotropic turbulence, which can be modelled by simple parameterization in the phenomenology.

Hossain, M.↗

DOE OSTI2026

Wake-Resolving Acoustic Tomography: Advances through Numerical Covariance Methods

Acoustic tomography offers path-integrated measurements of atmospheric velocity and temperature fluctuations with high spatial resolution. Classical implementations of time-dependent stochastic inversion rely on homogeneous, isotropic covariance models that are poorly suited to the anisotropic structure of wind turbine wakes. By directly estimating heterogeneous covariances from large-eddy simulations (LESs) into the time-dependent stochastic inversion operator, we relax implicit assumptions in the analytical models used historically. Retrievals using these LES-informed models improve agreement with true fields in variance, turbulent kinetic energy, and spectral content compared to analytical and precursor-based covariance models. The results indicate that LES-informed covariance models can enhance the accuracy of acoustic tomography retrievals in complex, anisotropic flows such as wind turbine wakes in some cases and highlight instances where analytical models still offer competitive performance, despite their simplifying assumptions.

17 WIND ENERGY↗

NASA NTRS1978

Evidence for two-dimensional inertial turbulence in a cosmic-scale low-beta plasma

Magnetospheric electric-field power spectral densities measured from high-altitude balloons and the Hawkeye 1 satellite are combined in wavenumber space and exhibit a power-law spectrum with index -1.6 + or -0.3 below a wavenumber of 0.05 reciprocal km and index -2.8 + or -0.3 above 2 reciprocal km. This spectrum agrees with that predicted for the inertial subrange of an isotropic homogeneous two-dimensional fluid and for a two-dimensional plasma when energy enters the system at the spectral knee and there exists a viscous dissipation mechanism at large wavenumbers. The wavelength of the spectral knee corresponds to that of folds and curls in the aurora and may be due to an instability of the auroral particle beams.

Kelley, M. C.↗

NASA NTRS1990

Generation of large-scale density fluctuations by buoyancy

The generation of fluid motion from a state of rest by buoyancy forces acting on a homogeneous isotropic small-scale density field is considered. Nonlinear interactions between the generated fluid motion and the initial isotropic small-scale density field are found to create an anisotropic large-scale density field with spectrum proportional to kappa(exp 4). This large-scale density field is observed to result in an increasing Reynolds number of the fluid turbulence in its final period of decay.

Chasnov, J. R.↗

NASA NTRS1992

Turbulence modeling and experiments

The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat flux equations for the buoyant plume.

Shabbir, Aamir↗

NASA NTRS1994

Evolution of energy-containing turbulent eddies in the solar wind

Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.

Matthaeus, William H.↗

NASA NTRS1998

Some Results Relevant to Statistical Closures for Compressible Turbulence

For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.

Ristorcelli, J. R.↗

DOE OSTI2022

Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

Here, in this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (P N ) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of P N and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of P N methods increases with its order, , but the gain in accuracy reduces with the increase in , i.e., improvement of P 7 over P 5 is less than that of P 3 over P 1 . This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM’s accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P 1 to P 7 approximations for P N , and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The P N solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.

42 ENGINEERING↗

NASA NTRS1991

Analysis of two-equation turbulence models for recirculating flows

The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.

Thangam, S.↗

NASA NTRS1992

Mixing and chemical reaction in sheared and nonsheared homogeneous turbulence

Direct numerical simulations were made to examine the local structure of the reaction zone for a moderately fast reaction between unmixed species in decaying, homogeneous turbulence and in a homogeneous turbulent shear flow. Pseudospectral techniques were used in domains of 64 exp 3 and higher wavenumbers. A finite-rate, single step reaction between non-premixed reactants was considered, and in one case temperature-dependent Arrhenius kinetics was assumed. Locally intense reaction rates that tend to persist throughout the simulations occur in locations where the reactant concentration gradients are large and are amplified by the local rate of strain. The reaction zones are more organized in the case of a uniform mean shear than in isotropic turbulence, and regions of intense reaction rate appear to be associated with vortex structures such as horseshoe vortices and fingers seen in mixing layers. Concentration gradients tend to align with the direction of the most compressive principal strain rate, more so in the isotropic case.

Leonard, Andy D.↗