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The case of isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory and direct numerical simulation. An exact solution to the rapid distortion problem is given, and results are compared to those of direct numerical simulation. Implications for modelling turbulent flows are discussed.
A calculation of periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, a calculation is conducted of the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modeled but the subgrid-scale Reynolds stresses are only moderately well modeled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.
Direct numerical simulations and large eddy simulations of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed time scales are compared with the spectral times scales that are frequently used in Eddy Damped Quasi-Normal Markovian calculations of the spectrum. The time scale models are rather good at high wavenumber and the results point to directions for improvement of the time scales at low wavenumber.
This report describes the research performed during the second year of this three-year project. The ultimate objective of the project is extend the applicability of probability density function (pdf) methods from incompressible to compressible turbulent reactive flows. As described in subsequent sections, progress has been made on: (1) formulation and modelling of pdf equations for compressible turbulence, in both homogeneous and inhomogeneous inert flows; and (2) implementation of the compressible model in various flow configurations, namely decaying isotropic turbulence, homogeneous shear flow and plane mixing layer.
Two grids have been developed for the Virginia Tech 6 ft x 6 ft Stability wind tunnel for the purpose of generating homogeneous isotropic turbulent flows for the study of unsteady airfoil response. The first, a square bi-planar grid with a 12" mesh size and an open area ratio of 69.4%, was mounted in the wind tunnel contraction. The second grid, a metal weave with a 1.2 in. mesh size and an open area ratio of 68.2% was mounted in the tunnel test section. Detailed statistical and spectral measurements of the turbulence generated by the two grids are presented for wind tunnel free stream speeds of 10, 20, 30 and 40 m/s. These measurements show the flows to be closely homogeneous and isotropic. Both grids produce flows with a turbulence intensity of about 4% at the location planned for the airfoil leading edge. Turbulence produced by the large grid has an integral scale of some 3.2 inches here. Turbulence produced by the small grid is an order of magnitude smaller. For wavenumbers below the upper limit of the inertial subrange, the spectra and correlations measured with both grids at all speeds can be represented using the von Karman interpolation formula with a single velocity and length scale. The spectra maybe accurately represented over the entire wavenumber range by a modification of the von Karman interpolation formula that includes the effects of dissipation. These models are most accurate at the higher speeds (30 and 40 m/s).
A theoretical analysis of the acoustic wave field radiated by a time-harmonic point source in a homogeneous, isotropic turbulent medium is presented. The smoothing method is used to study the incoherent, or randomly fluctuating, component of the wave field. The analysis considers the effect on the wave of the velocity fluctuations, as well as the index-of-refraction fluctuations, of the medium. An approximate expression for the second moment of the incoherent wave is obtained for the case in which the wavelenght is much less than the minimum correlation length of the medium. This expression shows that the fluctuations of the wave increase initially in proportion to the propagation distance, but that at larger distances they tend to a limiting, or saturation, value. These results agree with observations of waves propagating in real media. It is also found that the mean square of the total (i.e., coherent plus incoherent) acoustic pressure is unaffected by the randomness of the medium.
The objective of the present research was to extend the Direct Numerical Simulation (DNS) approach to particle-laden turbulent flows using a simple model of particle/flow interaction. The program addressed the simplest type of flow, homogeneous, isotropic turbulence, and examined interactions between the particles and gas phase turbulence. The specific range of problems examined include those in which the particle is much smaller than the smallest length scales of the turbulence yet heavy enough to slip relative to the flow. The particle mass loading is large enough to have a significant impact on the turbulence, while the volume loading was small enough such that particle-particle interactions could be neglected. Therefore, these simulations are relevant to practical problems involving small, dense particles conveyed by turbulent gas flows at moderate loadings. A sample of the results illustrating modifications of the particle concentration field caused by the turbulence structure is presented and attenuation of turbulence by the particle cloud is also illustrated.
The dependence of subgrid-scale stresses on variables of the resolved field is studied using direct numerical simulations of isotropic turbulence, homogeneous shear flow, and channel flow. The projection pursuit algorithm, a promising new regression tool for high-dimensional data, is used to systematically search through a large collection of resolved variables, such as components of the strain rate, vorticity, velocity gradients at neighboring grid points, etc. For the case of isotropic turbulence, the search algorithm recovers the linear dependence on the rate of strain (which is necessary to transfer energy to subgrid scales) but is unable to determine any other more complex relationship. For shear flows, however, new systematic relations beyond eddy viscosity are found. For the homogeneous shear flow, the results suggest that products of the mean rotation rate tensor with both the fluctuating strain rate and fluctuating rotation rate tensors are important quantities in parameterizing the subgrid-scale stresses. A model incorporating these terms is proposed. When evaluated with direct numerical simulation data, this model significantly increases the correlation between the modeled and exact stresses, as compared with the Smagorinsky model. In the case of channel flow, the stresses are found to correlate with products of the fluctuating strain and rotation rate tensors. The mean rates of rotation or strain do not appear to be important in this case, and the model determined for homogeneous shear flow does not perform well when tested with channel flow data. Many questions remain about the physical mechanisms underlying these findings, about possible Reynolds number dependence, and, given the low level of correlations, about their impact on modeling. Nevertheless, demonstration of the existence of causal relations between sgs stresses and large-scale characteristics of turbulent shear flows, in addition to those necessary for energy transfer, provides important insight into the relation between scales in turbulent flows.
A Chebyshev-Fourier discretization with shock fitting is used to solve the unsteady Euler equations. The method is applied to shock interactions with plane waves and with a simple model of homogeneous isotropic turbulence. The plane wave solutions are compared to linear theory.
A Chebyshev-Fourier discretization with shock fitting is used to solve the unsteady Euler equations. The method is applied to shock interactions with plane waves and with a simple model of homogeneous isotropic turbulence. The plane wave solutions are compared to linear theory. Previously announced in STAR as N83-27952
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.
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.
The Langmuir probe technique for measurement of electron concentration in the mesosphere is capable of excellent altitude resolution, of order 1 m. Measurements from nine daytime rocket flights carrying an electron density fine structure experiment frequently show small scale ionization structures in the altitude region 70 to 90 km. The irregularities are believed to be the result of turbulent advection of ions and electrons. The fine structure experiment flown by the University of Illinois is described and methods of analyzing the collected data is presented. Theories of homogeneous, isotropic turbulence are reviewed. Power spectra of the measured irregularities are calculated and compared to spectra predicted by turbulence theories.
Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.
It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.
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.
We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.
Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.