Flow-thermodynamics interactions in decaying anisotropic compressible turbulence with imposed temperature fluctuations

The fundamental nature of the non-linear flow-thermodynamics interactions in a compressible turbulent flow with imposed temperature fluctuations is investigated. Direct numerical simulations (DNS) of decaying anisotropic compressible turbulence (turbulent Mach number 0.06–0.6) with imposed temperature fluctuations are performed to examine: (i) interactions between solenoidal and dilatational kinetic energy; (ii) partition between dilatational kinetic energy and thermodynamic potential energy; and (iii) redistribution of solenoidal and dilatational kinetic energy among the various Reynolds stress components. It is found that solenoidal kinetic energy levels and return-to-isotropy are weakly dependent on Mach number but independent of imposed temperature fluctuations in the parameter range studied. The dilatational kinetic energy generated is proportional to the square of the pressure fluctuations associated with the initial solenoidal and temperature fluctuations and thus a strong function of Mach number and heat release intensity. The energy exchange between dilatational kinetic and potential energy is driven by a strong proclivity toward equipartition. Consequently, the dynamics of pressure-dilatation ( ${\overline{pd}}$ ), which is the mechanism of this energy exchange between dilatational and potential energies, is dictated entirely by the requirement to impose energy equipartition. Based on the results, we provide a physical picture of the solenoidal–dilatational–potential energy interactions and the action of pressure-dilatation. The identification of the fundamental precepts underlying the various interactions is of great utility for turbulence closure model development.     

Recent progress in compressible turbulence

In this paper, we review some recent studies on compressible turbulence conducted by the authors' group,which include fundamental studies on compressible isotropic turbulence(CIT) and applied studies on developing a constrained large eddy simulation(CLES) for wall-bounded turbulence. In the first part, we begin with a newly proposed hybrid compact–weighted essentially nonoscillatory(WENO) scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet–turbulence interaction, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and formulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.     

Grid turbulence in compressible flow

 This paper describes an experimental investigation of the effects of mean compressibility on the structure and the decay characteristics of grid turbulence. The experiments comprise laser Doppler velocimetry measurements of an approximately homogeneous, isotropic turbulence field in subsonic compressible flow, with the Mach number ranging from 0.15 to 0.7. The results reveal that the turbulence intensity and decay characteristics are influenced by mean compressibility. Experience with the high subsonic and supersonic regimes is also reported. Received: 27 February 1996/Accepted: 13 February 1997     

Scaling laws of compressible turbulence

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the –5/3 and –2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.     

Generation of compressible modes in MHD turbulence

Astrophysical turbulence is magnetohydrodynamic (MHD) in nature. We discuss fundamental properties of MHD turbulence and in particular the generation of compressible MHD waves by Alfvénic turbulence and show that this process is inefficient. This allows us to study the evolution of different types of MHD perturbations separately. We describe how to separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that the degree of suppression of slow and fast modes production by Alfvénic turbulence depends on the strength of the mean field. We review the scaling relations of the modes in strong MHD turbulence. We show that Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes exhibit isotropy and a scaling similar to that of acoustic turbulence both in high and low plasmas. We show that our findings entail important consequences for star formation theories, cosmic ray propagation, dust dynamics, and gamma ray bursts. We anticipate many more applications of the new insight to MHD turbulence and expect more revisions of the existing paradigms of astrophysical processes as the field matures. PACS 47.65.+a; 52.30.Cv; 52.35.Ra; 95.30.Qd     

Scaling of energy spectra in weakly compressible turbulence

We find an asymptotic expression for the char-acteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit ?7/3 scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as ?3. Meanwhile, the energy spectra of incompressible components display the same scaling of ?5/3 as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

Numerical simulation on compressible turbulence by spectral method

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.     

A simple hybrid finite volume solver for compressible turbulence

A simple, explicit, hybrid finite volume method for simulating compressible turbulence is developed by combining a fourth‐order central scheme and a shock‐capturing simple low‐dissipation advection upstream splitting method. The total flux on each of the cell faces is computed as a weighted average of central/nondissipative and upwind/dissipative fluxes. The weights are determined using an unphysical oscillation sensor in addition to a more traditional discontinuity sensor used in earlier studies. Shocks are well captured, but overshoots in density are predicted around contact discontinuities that are normal to the flow. The use of the latter sensor effectively prevents these overshoots from generating spurious oscillations that travel away from the contact lines. The efficacy of the proposed method for direct or large‐eddy simulations of supersonic turbulence is established using several canonical test problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Deconvolutional artificial-neural-network framework for subfilter-scale models of compressible turbulence

Acta Mechanica Sinica - We establish a deconvolutional artificial-neural-network (D-ANN) approach in large-eddy simulation (LES) of compressible turbulent flow. Filtered variables in the...     

Nonlinear gravity-wave interactions in stratified turbulence

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called “fast”) gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 ≤ Fr ≤ 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach ?2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.     

Optical technique for direct measurement of power spectra in compressible turbulence

We present exploratory tests of a new optical method which measures directly two components of the 3-D power spectrum of the refractive-index fluctuation. The method was applied to a Mach 2 turbulent shear layer. Length scales of 0.1 mm to 1.0 mm were resolved within a shear-layer thickness ranging from 5 mm to 10 mm. At low-to-moderate wavenumbers, the spectral behavior is roughlyκ ⁻³, while at higher wavenumbers it isκ ^−3.7. These spectral slopes are in agreement with prevailing theoretical predictions for anisotropic (low-wavenumber) and isotropic (high-wavenumber) turbulence. ]This study was funded by a grant from Lawrence Livermore National Laboratory and by a grant from the California Space Institute. DP is indebted to HFR and Dr. Alfred C. Buckingham of LLNL for their support.     

A shock tube research facility for high-resolution measurements of compressible turbulence

A new shock tube facility with a 30.5 cm (1 ft) inside diameter is currently in operation that allows for high-spatial-resolution measurements of compressible turbulence. Small scales of turbulence behave very differently from large scales when they interact with shock or expansion waves. Highly resolved measurements can provide new information on the interaction at small scales. Another notable characteristic of the present facility is the ability to control the flow velocity behind the reflected shock through the porosity of the reflecting wall. Tests showed good flow quality with sufficiently long observation times. Measurements of piecewise average skin friction over short segments of the tube indicated strong viscous effects very close to the diaphragm where the shock is developing. The skin friction and the shock propagation speed virtually remained constant inside the working section of the shock tube in all investigated flow cases, even in low Mach number cases where viscous effects are stronger. The experimental results are compared with numerical simulations, including the effects of the reflecting porous wall and viscous effects.     

Hybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence

Acta Mechanica Sinica - Bogies are responsible for a significant amount of aerodynamic resistance and noise, both of which negatively affect high-speed train performance and passenger comfort. In...     

Implicit unfactored implementation of two-equation turbulence models in compressible Navier–Stokes methods

An implicit unfactored method for the coupled solution of the compressible Navier–Stokes equations with two-equation turbulence models is presented. Both fluid-flow and turbulence transport equations are discretized by a characteristics-based scheme. The implicit unfactored method combines Newton subiterations and point-by-point Gauss–Seidel subrelaxation. Implicit-coupled and -decoupled strategies are compared for their efficiency in the solution of the Navier–Stokes equations in conjunction with low-Re two-equation turbulence models. Computations have been carried out for the flow over an axisymmetric bump using the k–ϵ and k–ω models. Comparisons have been obtained with experimental data and other numerical solutions. The present study reveals that the implicit unfactored implementation of the two-equation turbulence models reduces the computing time and improves the robustness of the CFD code in turbulent compressible flows. © 1998 John Wiley & Sons, Ltd.     

Experimental validation of a two equation RANS transitional turbulence model for compressible microflows

Laminar-to-turbulent flow transition in microchannels can be useful to enhance mixing and heat transfer in microsystems. Typically, the small characteristic dimensions of these devices hinder in attaining higher Reynolds numbers to limit the total pressure drop. This is true especially in the presence of a liquid as a working medium. On the contrary, due to lower density, Reynolds number larger than 2000 can be easily reached for gas microflows with an acceptable pressure drop. Since microchannels are used as elementary building blocks of micro heat exchangers and micro heat-sinks, it is essential to predict under which conditions, the laminar-to-turbulent flow transition inside such geometries can be expected. In this paper, experimental validation of a two equations transitional turbulence model, capable of predicting the laminar-to-turbulent flow transition for internal flows as proposed by Abraham etal. (2008), is presented for the first time for microchannels. This is done by employing microchannels in which Nitrogen gas is used as a working fluid. Two different cross-sections namely circular and rectangular are utilized for numerical and experimental investigations. The inlet mass flow rate of the gas is varied to cover all the flow regimes from laminar to fully turbulent flow. Pressure loss experiments are performed for both cross-sectional geometries and friction factor results from experiments and numerical simulations are compared. From the analysis of the friction factor as a function of the Reynolds number, the critical value of the Reynolds number linked to the laminar-to-turbulent transition has been determined. The experimental and numerical critical Reynolds number for all the tested microchannels showed a maximum deviation of less than 12%. These results demonstrate that the transitional turbulence model proposed by Abraham etal. (2008) for internal flows can be extended to microchannels and proficiently employed for the design of micro heat exchangers in presence of gas flows.