Decay Of Homogeneous Isotropic Turbulence Research Articles

GPU-accelerated DNS of compressible turbulent flows

This paper explores strategies to transform an existing CPU-based high-performance computational fluid dynamics solver, HyPar, for compressible flow simulations on emerging exascale heterogeneous (CPU+GPU) computing platforms. The scientific motivation for developing a GPU-enhanced version of HyPar is to simulate canonical turbulent flows at the highest resolution possible on such platforms. We show that optimizing memory operations and thread blocks results in 200x speedup of computationally intensive kernels compared with a CPU core. Using multiple GPUs and CUDA-aware MPI communication, we demonstrate both strong and weak scaling of our GPU-based HyPar implementation on the NVIDIA Volta V100 GPUs. We simulate the decay of homogeneous isotropic turbulence in a triply periodic box on grids with up to 10243 points (5.3 billion degrees of freedom) and on up to 1,024 GPUs. We compare the wall times for CPU-only and CPU+GPU simulations. The results presented in the paper are obtained on the Summit and Lassen supercomputers at Oak Ridge and Lawrence Livermore National Laboratories, respectively.

An efficient discrete unified gas-kinetic scheme for compressible turbulence

In this paper, we develop an efficient Boltzmann-equation-based mesoscopic approach to simulate three-dimensional (3D) compressible turbulence, using reduced Gauss–Hermite quadrature (GHQ) orders by redefining the second distribution in terms of the total energy in the double distribution function approach. This allows the use of two sets of 3D off-lattice discrete particle velocity models, namely, a 27 discrete velocity model of the seventh-order GHQ accuracy (D3V27A7) combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5), to achieve full consistency with the Navier–Stokes–Fourier system. The source terms in the Boltzmann–Bhatnagar–Gross–Krook system are designed to adjust both the Prandtl number and bulk-to-shear viscosity ratio. Compressible decaying homogeneous isotropic turbulence (DHIT) is simulated at low and moderate turbulent Mach numbers to validate our code. It is observed that the simulation results are in good agreement with those in the existing literatures. Furthermore, the terms in the transport equation of turbulent kinetic energy are analyzed in detail, to illustrate four different transient stages from the initial random flow field to the developed DHIT. It is shown that the transient pressure-dilatation transfer happens rapidly, while the small-scale vortical structures take a longer time to establish physically. Compared to the existing literatures, our approach represents the most efficient mesoscopic scheme for compressible turbulence under the double distribution function formulation.

Analysis of the Influence of Incoming Flow Turbulence on the Flow in a Supersonic Air Intake by the RANS/ILES Method. Estimation of Dissipative Properties of the Difference Scheme by an Example of Modeling the Decay of Homogeneous Isotropic Turbulence in the ILES

Analysis of the Influence of Incoming Flow Turbulence on the Flow in a Supersonic Air Intake by the RANS/ILES Method. Estimation of Dissipative Properties of the Difference Scheme by an Example of Modeling the Decay of Homogeneous Isotropic Turbulence in the ILES

Geometry and dynamics of passive scalar structures in compressible turbulent mixing

We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Reλ=40 and turbulence Mach number Mt=0.2, and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.

Extended Lattice Boltzmann Model.

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

Direct numerical simulation of decaying homogeneous isotropic turbulence — numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods

Stability, consistency and accuracy of various lattice Boltzmann schemes are investigated by means of numerical experiments on decaying homogeneous isotropic turbulence (DHIT). Therefore, the Bhatnagar–Gross–Krook (BGK), the entropic lattice Boltzmann (ELB), the two-relaxation-time (TRT), the regularized lattice Boltzann (RLB) and the multiple-relaxation-time (MRT) collision schemes are applied to the three-dimensional Taylor–Green vortex, which represents a benchmark case for DHIT. The obtained turbulent kinetic energy, the energy dissipation rate and the energy spectrum are compared to reference data. Acoustic and diffusive scaling is taken into account to determine the impact of the lattice Mach number. Furthermore, three different Reynolds numbers [Formula: see text], [Formula: see text] and [Formula: see text] are considered. BGK shows instabilities, when the mesh is highly underresolved. The diverging simulations for MRT are ascribed to a strong lattice Mach number dependency. Despite the fact that the ELB modifies the bulk viscosity, it does not mimic a turbulence model. Therefore, no significant increase of stability in comparison to BGK is observed. The TRT “magic parameter” for DHIT at moderate Reynolds numbers is estimated with respect to the energy contribution. Stability and accuracy of the TRT scheme is found to be similar to BGK. For small lattice Mach numbers, the RLB scheme exhibits lowered energy contribution in the dissipation range compared to an analytical model spectrum. Overall, to enhance stability and accuracy, the lattice Mach number should be chosen with respect to the applied collision scheme.

One-point and two-point statistics of homogeneous isotropic decaying turbulence with variable viscosity

The decay of homogeneous isotropic turbulence in a variable viscosity fluid with a viscosity ratio up to 15 is analyzed by means of highly resolved direct numerical simulations (DNS) at low Reynolds numbers. The question addressed by the present work is how quantities such as the kinetic energy and the associated dissipation rate, as well as the inter-scale transport mechanism of turbulence are changed by local fluctuations of the viscosity. The comparison is performed with respect to the decaying homogeneous isotropic turbulence with constant viscosity (CV), equal to the mean value of the variable viscosity (VV). From the one-point budget equation of the turbulent kinetic energy, it is shown that the mean dissipation rate is nearly unchanged by variable viscosity effects. This result is explained by a negative correlation between the local viscosity and the local velocity gradients. However, the dissipation is a highly fluctuating quantity with a strong level of intermittency. From a statistical analysis it is shown that turbulent flows with variable viscosity are characterized by an enhanced level of small-scale intermittency with respect to CV flow, which results in the presence of smaller length scales. The effect of variable viscosity on the turbulent cascade is analyzed by a budget equation for the velocity structure function. From DNS it is shown that viscosity gradients contribute to the inter-scale transport mechanism in the form of an inverse transport, where information propagates from the small scales to the large scales.

Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening

Direct Numerical Simulation of turbulent flows is a computationally demanding problem that requires efficient parallel algorithms. We investigate the applicability of the time-parallel Parareal algorithm to an instructional case study related to the simulation of the decay of homogeneous isotropic turbulence in three dimensions. We combine a Parareal variant based on explicit time integrators and spatial coarsening with the space-parallel Hybrid Navier–Stokes solver. We analyse the performance of this space–time parallel solver with respect to speedup and quality of the solution. The results are compared with reference data obtained with a classical explicit integration, using an error analysis which relies on the energetic content of the solution. We show that a single Parareal iteration is able to reproduce with high fidelity the main statistical quantities characterizing the turbulent flow field.

Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence

ABSTRACTThe emergence of anomalous fast decay regimes in homogeneous isotropic turbulence (HIT) decay is investigated via both theoretical analysis and eddy-damped quasi-normal Markovian simulations. The work provides new insight about a fundamental issue playing a role in HIT decay, namely the influence of non-standard shapes of the energy spectrum, in particular in the large energetic scale region. A detailed analysis of the kinetic energy spectrum E(k) and the non-linear energy transfer T(k) shows that anomalous decay regimes are associated with the relaxation of initial energy spectra which exhibit a bump at energetic scales. This feature induces an increase in the energy cascade rate, toward solutions with a smooth shape at the spectrum peak. Present results match observations reported in wind-tunnel experiments dealing with turbulence decay in the wake of grids and bluff bodies, including scaling laws for the dissipation parameter Cϵ. They also indicate that the ratio between the initial eddy turnover time and the advection time determines of how fast anomalous regimes relax toward classical turbulence free-decay. This parameter should be used for consistent data comparison and it opens perspectives for the control of multiscale effects in industrial applications.

Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay

The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.

The signature of initial production mechanisms in isotropic turbulence decay

In the present work the quantification of the time-lasting effects of production mechanisms in homogeneous isotropic turbulence decay is addressed. The analysis is developed through the use of theoretical tools as well as numerical calculations based on the eddy damped quasinormal Markovian (EDQNM) model. In both cases a modified Lin equation is used, which accounts for production mechanisms as proposed by Meldi, Lejemble, and Sagaut [“On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence,” J. Fluid Mech. 756, 816–843 (2014)]. The approaches used show that an exponential decay law can be observed if the intensity of the forcing is strong enough to drive the turbulence dynamics, before a power-law decay is eventually attained. The EDQNM numerical results indicate that the exponential regime can persist for long evolution times, longer than the observation time in grid turbulence experiments. A rigorous investigation of the self-similar behavior of the pressure spectrum has been performed by a comprehensive comparison of EDQNM data with direct numerical simulation (DNS)/experiments in the literature. While DNS and free decay EDQNM simulations suggest the need of a very high Reλ threshold in order to observe a clear −7/3 slope of the pressure inertial range, experimental data and forced EDQNM calculations indicate a significantly lower value. This observation suggests that the time-lasting effects of production mechanisms, which cannot be excluded in experiments, play a role in the lack of general agreement with classical numerical approaches. These results reinforce the urge to evolve the numerical simulation state of the art towards the prediction of realistic physical states.

The evaluation of a detached eddy simulation based on the k–ω–[formula omitted]–f model with three flow configurations

Detached Eddy Simulation (DES) based on the k–ω–υ2¯–f model, termed DES–k-ω–υ2¯-f, is developed and evaluated in the present study. In this model, the RANS–LES switching is achieved by an adaptation of the turbulent length scale between the LES and RANS regions. The SGS model coefficient is calibrated by the decaying homogeneous isotropic turbulence (DHIT). The capabilities of the proposed model are evaluated on various geometries, i.e. the plane channel flow, wavy channel flow and two side by side square cylinders. The DES results are compared with the URANS and LES results obtained in the present study and the available results obtained in other references. A good agreement is found between the results of the proposed DES model and the LES for three flow configurations employed. For the cases with flow separation, the DES model demonstrates accurate predictions in reproducing the resolved flow and turbulence quantities in comparison with full-resolved LES.

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting, and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor–Green vortex problem and the turbulent flow in a channel. We compare the results obtained using different VMS models, paying special attention to the effect of using orthogonal subscale spaces. The VMS results are also compared against classical LES scheme based on filtering and the dynamic Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these experiments, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.

The effects of variable viscosity on the decay of homogeneous isotropic turbulence

In this paper, we investigate the decay of incompressible homogeneous isotropic turbulence in a variable viscosity fluid. The viscosity coefficient is assumed to depend linearly on a scalar, representing either a temperature or a concentration, and obeying a simple advection-diffusion equation. At high Reynolds numbers, Direct Numerical Simulations (DNS) allow us to confirm the validity of Taylor's postulate that the dissipation is independent from the viscosity and its fluctuations. At low Reynolds numbers, we report the presence of extra energy at small scales due to these variable viscosity effects. This implies that the turbulent kinetic energy decreases less rapidly as a function of time in variable viscosity fluids. In order to explain this phenomenon and quantify its importance on the turbulent flow, we propose a statistical approach based on an eddy-damped quasi-normal Markovian (EDQNM) spectral closure which takes into account the nonlinearity introduced by variable viscosity. It is shown that this latter additional term is of constant sign in the energy spectrum equation and reduces the dissipation of the flow as observed. Also, by assuming the dominance of distant interactions between wave numbers, we can propose a simple formula expressing that variable viscosity effects lead to an effective reduction of the mean viscosity proportional to the variance of viscosity fluctuations.

Computational technologies for simulation of complex near-wall turbulent flows using unstructured meshes

The work is devoted to the peculiarities of the implementation of hybrid Reynolds’ Averaged Navier-Stokes equations-Large Eddy Simulation (RANS-LES) approaches of the Detached Eddy Simulation (DES) family for simulation of complex near-wall turbulent flows using unstructured meshes. The problems of determining required geometric characteristics in the mesh nodes and adaptation of hybrid approaches to the used accurate numerical approximation scheme in space are considered. The classic benchmark problem of the decay of homogeneous isotropic turbulence and the results of the computation of a complex turbulent flow near the wall with the presence of flow separation and reattachment are considered to verify the implemented technique and to demonstrate its efficiency.

The Polymer Effect on Nonlinear Processes in Decaying Homogeneous Isotropic Turbulence

In order to study the polymer effect on the behavior of nonlinearities in decaying homogeneous isotropic turbulence (DHIT), direct numerical simulations were carried out for DHIT with and without polymers. We investigate the nonlinear processes, such as enstrophy production, strain production, polymer effect, the curvature of vortex line, and many others. The analysis results show that the nonlinear processes like enstrophy production (and many others) are strongly depressed in regions dominated by enstrophy as compared to those dominated by strain either in the Newtonian fluid case or in polymer solution case. Polymers only decrease the values of these parameters in the strongest enstrophy and strain regions. In addition, polymer additive has a negative effect on enstrophy and strain production, that is, depression of nonlinearity in DHIT with polymers.

A new look at the final period decay of homogeneous isotropic turbulence

Final-period decay law in homogeneous and isotropic turbulence is reexamined here from the concept of a simple point-merging technique.

On non-self-similar regimes in homogeneous isotropic turbulence decay

AbstractBoth theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\ensuremath{\rightarrow} 0)$ or the velocity correlation function $f(r\ensuremath{\rightarrow} + \infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence (DHIT) of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase “strain generation resistance" and “vorticity generation resistance", i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.

Langevin equation of big structure dynamics in turbulence: Landau’s invariant in the decay of homogeneous isotropic turbulence

As empirically observed over some fifty years, the steepness of the “infrared” spectrum of velocity fluctuations in a turbulent flow— E ( κ ) ∝ κ μ at scales D ∼ 1 / κ ≫ ℓ larger than energy-containing eddies—constrains the decay of turbulent kinetic energy. However, the theoretical understanding of the physical process controlling decay is still patchy, even in the simplest case of homogeneous isotropic turbulence (HIT). Here, HIT decay laws are derived from angular momentum invariance at big scales D —an approach first mentioned by Landau in 1944, but unduly dismissed later. It is restated in terms of a stochastic equation similar to a Langevin equation, to which usual investigation techniques can be adapted. By deriving two forms of closed equations for the variance of angular momentum fluctuations, various new results on HIT are established: (i) the clear physical difference of the present approach with respect to previous investigations based on the Kármán–Howarth equation—or its various integrated forms such as Loitsyanskii’s integral—due to the separation of fast (noise) and slow (friction) components of the fluctuating fields; (ii) under the appropriate closure assumptions and necessary conditions, a proof of the so-far conjectured “permanence of big structures”; (iii) novel relationships relating μ and the velocity correlation function f ( s ) , obtained from the higher order terms of the expansion in D ; (iv) the relationship between the exponent of the infrared spectrum κ μ and the decay invariant in self-similar regimes, both for μ ≤ 3 and 3 < μ ≤ 4 which display different behavior; (v) the stringent conditions required to reach Kolmogorov’s decay exponent n = 10 / 7 in ideal HIT; (vi) a closed relationship between the velocity correlation function f ( s ) at big scales and the “turbulent viscosity” coefficient C μ . Beyond an improved theoretical understanding and the present results, this framework will lead to new predictions on turbulence decay and dissipation in numerous other types of flows with practical impact.