Numerical simulation of a compressible homogeneous, turbulent shear flow

A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part

A three-dimensional simulation of transition and early turbulence in a time-developing mixing layer

The physics of the transition and early turbulence regimes in the time developing mixing layer was investigated. The sensitivity of the mixing layer to the disturbance field of the initial condition is considered. The growth of the momentum thickness, the mean velocity profile, the turbulence kinetic energy, the Reynolds stresses, the anisotropy tensor, and particle track pictures of computations are all examined in an effort to better understand the physics of these regimes. The amplitude, spectrum shape, and random phases of the initial disturbance field were varied. A scheme of generating discrete orthogonal function expansions on some nonuniform grids was developed. All cases address the early or near field of the mixing layer. The most significant result shows that the secondary instability of the mixing layer is produced by spanwise variations in the straining field of the primary vortex structures

Simulation and modeling of homogeneous, compressed turbulence

Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates

Evaluation of subgrid-scale turbulence models using a fully simulated turbulent flow

An exact turbulent flow field was calculated on a three-dimensional grid with 64 points on a side. The flow simulates grid-generated turbulence from wind tunnel experiments. In this simulation, the grid spacing is small enough to include essentially all of the viscous energy dissipation, and the box is large enough to contain the largest eddy in the flow. The method is limited to low-turbulence Reynolds numbers, in our case R sub lambda = 36.6. To complete the calculation using a reasonable amount of computer time with reasonable accuracy, a third-order time-integration scheme was developed which runs at about the same speed as a simple first-order scheme. It obtains this accuracy by saving the velocity field and its first-time derivative at each time step. Fourth-order accurate space-differencing is used

Large-eddy simulation of a turbulent mixing layer

The three dimensional, time dependent (incompressible) vorticity equations were used to simulate numerically the decay of isotropic box turbulence and time developing mixing layers. The vorticity equations were spatially filtered to define the large scale turbulence field, and the subgrid scale turbulence was modeled. A general method was developed to show numerical conservation of momentum, vorticity, and energy. The terms that arise from filtering the equations were treated (for both periodic boundary conditions and no stress boundary conditions) in a fast and accurate way by using fast Fourier transforms. Use of vorticity as the principal variable is shown to produce results equivalent to those obtained by use of the primitive variable equations

EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it

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

Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows

The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained

Hydrodynamic Character of the Non-equipartition of Kinetic Energy in Binary Granular Gases

The influence of the heating mechanism on the kinetic energy densities of the components of a vibrated granular mixture is investigated. Collisions of the particles with the vibrating wall are inelastic and characterized by two coefficients of normal restitution, one for each of the two species. By means of molecular dynamics simulations, it is shown that the non-equipartition of kinetic energy is not affected by the differential mechanism of energy injection, aside the usual boundary layer around the wall. The macroscopic state of the mixture in the bulk is defined by intensive variables that do not include the partial granular temperatures of the components