The analysis and simulation of compressible turbulence

The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. I n this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. I n the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic vaue of about 0.2 for supersonic convective Mach numbers.

Journal of Fluid Mechanics, 1991

Modern Physics Letters B, 2016

Acta Mechanica Sinica, 2010

Direct numerical simulation of turbulent channel flows between isothermal walls have been carried out using discontinuous Galerkin method. Three Mach numbers are considered (0.2, 0.7, and 1.5) at a fixed Reynolds number %2800, based on the bulk velocity, bulk density, half channel width, and dynamic viscosity at the wall. Power law and log-law with the scaling of the mean streamwise velocity are considered to study their performance on compressible flows and their dependence on Mach numbers. It indicates that power law seems slightly better and less dependent on Mach number than the log-law in the overlap region. Mach number effects on the second-order (velocity, pressure, density, temperature, shear stress, and vorticity fluctuations) and higher-order (skewness and flatness of velocity, pressure, density, and temperature fluctuations) statistics are explored and discussed. Both inner (that is wall variables) and outer (that is global) scalings (with Mach number) are considered. It is found that for some second-order statistics (i.e. velocity, density, and temperature), the outer scaling collapses better than the inner scaling. It is also found that near-wall large-scale motions are affected by Mach number. The near-wall spanwise streak spacing increases with increasing Mach number. Iso-surfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Mach number increases, which is similar to the distribution of near-wall low speed streaks.

2003

Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using p...

Physical Review E, 2010

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence ͑DHIT͒ in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, Z R , and the initial ratio of the rotational and translational temperatures, T R0 / T L0 , on the dynamics of various turbulence statistics including the kinetic energy K͑t͒, the dissipation rate ͑t͒, the energy spectrum E͑k , t͒, the root mean square of the velocity divergence Ј͑t͒, the skewness S u ͑t͒ and the flatness F u ͑t͒ of the velocity derivatives, and the probability distribution functions of the local Mach number Ma and the shocklet strength . The larger the Z R is, the faster the compressibility decays after an initial time. Similarly, with a fixed T L0 , the higher the initial energy ratio T R0 / T L0 , the weaker is the compressibility in the flow. It is also observed that the effect of T R0 / T L0 is strong in all times in the decay, while the effect of Z R is severe only in the later times passing through the stage with strong nonlinearity. We also observe that the multitemperature model does not affect the self-similarities obeyed by the probability distribution functions of Ma and , which appear to be a robust feature of the compressible DHIT.

Thermal Science

In this work, the ability of a Reynolds stress model to compute turbulent homogeneous shear flow with significant compressibility effects is discussed. Several studies of compressible turbulent flows carried out in the past years have shown that the pressure strain correlation is mainly responsible for the strong changes in the magnitude of the Reynolds stress anisotropies. Two recent compressible models of this term are considered in conjunction with the standard model of the dissipation rate of the turbulent kinetic energy to predict compressible homogeneous flow highly sheared are tested. It is found that deficiencies appear in the calculations even if the pressure strain model is improved by compressibility corrections. Consistent with earlier studies, this deficiency is attributed to the use of the incompressible model for turbulent dissipation. However, a compressibility correction of this equation model uncovers the main focus of the present study. This correction makes the s...

Numerical Mathematics and Advanced Applications

Unsteady Reynolds-averaged Navier-Stokes (RANS) computations are presented for subsonic and transonic flow past a plunging NACA 64A010 aerofoil. The Implicit RANS solver used for obtaining the time-accurate solution is based on finite volume nodal point spatial discretization scheme with dual time stepping. Results for the subsonic and transonic cases compare well with the experimental data, thus demonstrating the capability of the solver to provide useful unsteady pressure data for aeroelastic analysis.

Five round jets at Mach number 0.9 and diameter-based Reynolds number 10 5 originating from a pipe nozzle are computed by Large-Eddy Simulations using grids of 252 million points. In the pipe, the boundary layers are tripped, in order to obtain, at the exit section, laminar mean velocity profiles of momentum thickness equal to 1.8% of the jet radius, and peak turbulence intensities of 0, 3, 6, 9 and 12% of the jet velocity. The influence of initial turbulence on flow development is thus investigated. As the nozzle-exit turbulence level increases, the coherent structures typically found in initially laminar jets gradually disappear, which leads to shear layers spreading at lower rate with strongly reduced rms fluctuating velocities. The jets also develop farther downstream, resulting in longer potential cores.