Compressible Turbulent Flows Research Articles

Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness

In the approximation of one-fluid hydrodynamics, a closed system of Favre-averaged magneto-hydrodynamic equations is formulated, intended for the numerical simulation of compressible turbulent flows of electrically conductive media in the presence of a magnetic field. Special emphasis is paid to the method of obtaining, within the framework of irreversible thermodynamics, the constitutive relations for the turbulent flux heat and the total (kinetic plus magnetic) tensor of turbulent stresses. A new approach to modeling the coefficient of turbulent kinematic viscosity for an astrophysical disk is proposed, which takes into account the influence of an external and generated magnetic field, as well as the processes of convective heat transfer on turbulence in a stratified layer of finite thickness, and thereby modifies the Shakura–Sunyaev alpha formalism developed by for a thin disk and widely used in the astrophysical literature.

Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Kinetic-energy-flux-constrained model using an artificial neural network for large-eddy simulation of compressible wall-bounded turbulence

Kinetic energy flux (KEF) is an important physical quantity that characterizes cascades of kinetic energy in turbulent flows. In large-eddy simulation (LES), it is crucial for the subgrid-scale (SGS) model to accurately predict the KEF in turbulence. In this paper, we propose a new eddy-viscosity SGS model constrained by the properly modelled KEF for LES of compressible wall-bounded turbulence. The new methodology has the advantages of both accurate prediction of the KEF and strong numerical stability in LES. We can obtain an approximate KEF by the tensor-diffusivity model, which has a high correlation with the real value. Then, using the artificial neural network method, the local ratios between the real KEF and the approximate KEF are accurately modelled. Consequently, the SGS model can be improved by the product of that ratio and the approximate KEF. In LES of compressible turbulent channel flow, the new model can accurately predict mean velocity profile, turbulence intensities, Reynolds stress, temperature–velocity correlation, etc. Additionally, for the case of a compressible flat-plate boundary layer, the new model can accurately predict some key quantities, including the onset of transitions and transition peaks, the skin-friction coefficient, the mean velocity in the turbulence region, etc., and it can also predict the energy backscatters in turbulence. Furthermore, the proposed model also shows more advantages for coarser grids.

Heterogeneous CPU+GPU parallelization for high-accuracy scale-resolving simulations of compressible turbulent flows on hybrid supercomputers

A heterogeneous parallel algorithm for simulation of compressible turbulent flows and its portable software implementation are presented. The underlying numerical method is based on a family of higher accuracy edge-based reconstruction schemes on unstructured mixed-element meshes. The proposed parallel solution can engage a large number of computing devices of most of the existing computing architectures used in modern supercomputers, including manycore CPUs and GPUs. It is capable of co-execution on both CPUs and accelerators simultaneously. The multilevel parallel algorithm combines: MPI for distributing workload among hybrid cluster nodes and between devices inside nodes; OpenMP for manycore CPUs and other supporting devices, such as Intel Xeon Phi; OpenCL for massively-parallel accelerators, such as GPUs of various vendors, including NVIDIA, AMD, Intel. The main focus is on the adaptation of the numerical method and its computational algorithm to the stream processing parallel paradigm. The very limited device memory inherent in GPU computing is also taken into account. A detailed description of the parallel algorithm is presented, as well as the techniques used for its efficient parallel implementation. Special attention is paid to implicit time integration with its linear solver and calculation of convective fluxes and viscous terms. The use of mixed floating-point precision and overlapping communications and computations is also discussed. Parallel performance is demonstrated in practical applications on different kinds of supercomputers using up to 10 thousand cores and multiple GPUs of comparable overall performance.

Computational fluid dynamic modelling of supersonic ejectors: comparison between 2D and 3D modelling

It is known that the global performances of ejector-based systems (viz., at the “global-scale”) depend on the local flow properties within the ejector (viz., at the “local-scale”). For this reason, reliable computational fluid-dynamics (CFD) approaches, to obtain a precise and an a-priori knowledge of the local flow phenomena, are of fundamental importance to support the deployment of innovative ejector-based systems. This communication contributes to the existing discussion by presenting a numerical study of the turbulent compressible flow in a supersonic ejector. In particular, this communication focuses on a precise knowledge gap: the comparison between 2D and 3D modelling approaches as well as density-based and pressure-based solvers. The different approaches have been compared and validated against literature data consisting in entrainment ratio and wall static pressure measurements. In conclusion, this paper is intended to provide guidelines for researchers dealing with the numerical simulation of ejectors.

Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.

Unsteady flow simulation of compressible turbulent flow in dual-bell nozzle with movement of extendible section from its initial to working position

The use of extendible nozzles in propulsion systems is one of the ways to increase the geometric degree of expansion of the nozzle and the thrust. Numerical simulation of a supersonic turbulent flow of a viscous compressible gas in an extendible nozzle is considered. The simulations performed take into account the movement of the extendible part of the nozzle from the its initial to the working position. The Reynolds-averaged Navier–Stokes equations and the equations of the SST turbulence model discretized on moving meshes are used for numerical calculations. The unsteady flowfield formed when the nozzle is brought to the working position is studied, and the topological features of the flow (separation, mixing, reattachment, secondary flow), and the spatial and temporal distributions of flow quantities are investigated. The distributions of pressure at different times and the axial force applied to the inner walls of the nozzle during the outflow of a supersonic underexpanded jet from the nozzle are discussed. The distributions of flow quantities computed with unsteady and quasi-state formulations of the problem are compared.

Unsteady turbulent flow simulations on moving Cartesian grids using immersed boundary method and high-order scheme

To simulate the unsteady compressible turbulent flow around moving bodies, a new moving grid method that uses the immersed boundary method on Cartesian grids is proposed. Here, the immersed boundary method is combined with the wall function to impose the wall boundary conditions for turbulent flow simulation around moving bodies. In addition, the high-order scheme for stationary Cartesian grids is extended to that for moving Cartesian grids. The proposed method is validated through two- and three-dimensional flow simulations on moving grids. First, steady flow simulations around NACA0012 airfoil on stationary and moving grids are conducted, with identical results obtained using the proposed method when the relative velocity of the airflow to the grid is the same. Second, flow simulations around the pitching airfoil are conducted. The conservation laws are not strictly satisfied when immersed boundary methods are used. Therefore, the results are compared with the simulation on a body-fitted grid that satisfies the conservation laws as well as with the experimental results. When the proposed method is used, the hysteresis loop of the aerodynamic coefficients is consistent with that on the body-fitted grid. Finally, flow simulations of specific rotor blades in the hover condition are conducted to explore the capacity of the proposed method to predict the aerodynamic coefficients and unsteady flow phenomena. The surface pressure coefficient distributions and the vortex trajectories of the simulations show good agreement with the experimental data. Moreover, fine vortex structures are observed when the high-order scheme is used.

High-order gas-kinetic scheme with parallel computation for direct numerical simulation of turbulent flows

The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime [9]. Due to the multi-scale nature and coupled temporal-spatial evolution process, HGKS provides a valid tool for the numerical simulation of compressible turbulent flow. Based on the domain decomposition and message passing interface (MPI), a parallel HGKS code is developed for large-scale computation in this paper. The standard tests from the nearly incompressible flow to the supersonic one, including Taylor-Green vortex problem, turbulent channel flow and isotropic compressible turbulence, are presented to validate the parallel scalability, efficiency, accuracy and robustness of parallel implementation. The performance of HGKS for the nearly incompressible turbulence is comparable with the high-order finite difference scheme, including the resolution of flow structure and efficiency of computation. Based on the accuracy of the numerical solution, the numerical dissipation of the scheme in the turbulence simulation is quantitatively evaluated. Meanwhile, based on the kinetic formulation HGKS shows advantage for supersonic turbulent flow simulation with its accuracy and robustness. The current work demonstrates the capability of HGKS as a powerful DNS tool from the low speed to supersonic turbulence study, which is less reported under the framework of finite volume scheme.

FlameFoam: An open source CFD solver for turbulent premixed combustion

Severe accidents in nuclear power plants may cause significant and long-lasting harm to the environment in the case of containment integrity loss. Numerical simulation of phenomena threatening containment integrity, e.g., hydrogen combustion and explosion, is essential for the effective severe accident management.International research projects and benchmarks are organized in order to promote improvement of simulation codes adequacy and accuracy in the severe accident relevant conditions. Results of the most recent benchmarks show that current state-of-the-art simulations were able to mostly reproduce the observable flame speed at the considered conditions, but there are still inadequacies in estimating velocity and its maximum value.Addressing a need for an accessible open source turbulent premixed combustion simulation tool, a new solver is being developed. An OpenFOAM version 7 based combustion solver called flameFoam has been built by implementing a progress variable approach and turbulent flame closure model for premixed combustion simulation. Turbulent flame speed is defined as a function of laminar flame speed and turbulence parameters, and is evaluated using one of three different correlations. Laminar flame speed can be set as a constant or calculated using a laminar flame speed correlation. The basis for the solver are standard compressible OpenFOAM solvers rhoPimpleFoam, buoyantPimpleFoam and chtMultiRegionFoam.The article presents initial public flameFoam version 0.8 and provides examples of its validation. Initial validation and verification of general solver features are represented by the simulations of shock tube and backward facing step cases. Solver capabilities in relation to the current turbulent premixed combustion modeling state-of-the-art are demonstrated with the simulations of ETSON-MITHYGENE benchmark experiments.It is shown that flameFoam version 0.8 is capable of adequate simulation of general flow features, turbulent compressible flow phenomena and turbulent premixed combustion of lean hydrogen-air mixtures at the considered conditions. Solver code is publicly hosted and being developed further.

Wavelet-Based Adaptive Eddy-Resolving Methods for Modeling and Simulation of Complex Wall-Bounded Compressible Turbulent Flows

This article represents the second part of a review by De Stefano and Vasilyev (2021) on wavelet-based adaptive methods for modeling and simulation of turbulent flows. Unlike the hierarchical adaptive eddy-capturing approach, described in the first part and devoted to high-fidelity modeling of incompressible flows, this companion paper focuses on the adaptive eddy-resolving framework for compressible flows in complex geometries, which also includes model-form adaptation from low to high fidelity models. A hierarchy of wavelet-based eddy-resolving methods of different fidelity has been developed for different speed regimes, various boundary conditions, and Reynolds numbers. Solutions of various fidelity are achieved using a range of modeling approaches from unsteady Reynolds-averaged Navier–Stokes simulation to delayed detached eddy simulation, wall-modeled and wall-resolved large eddy simulations. These novel methodologies open the door to construct a hierarchical approach for simulation of compressible flows covering the whole range of possibilities, from only resolving the average or dominant frequency, to capturing the intermittency of turbulence eddies, and to directly simulating the full turbulence spectrum. The generalized hierarchical wavelet-based adaptive eddy-resolving approach, once fully integrated into a single inherently interconnected simulation, results in being a very competitive and predictive tool for complicated flows in industrial design and analysis with high efficiency and accuracy.

Wavelet-based adaptive wall-modeled large eddy simulation method for compressible turbulent flows

We develop a wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method to overcome the stringent restriction on step size for time integration, caused by mesh resolution requirement to resolve inner viscous sublayer, which becomes computationally expensive as the Reynolds number increases. This approach uses a wavelet-based adaptive large eddy simulation, incorporated into the anisotropic-adaptive wavelet collocation framework, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the wall-shear-stress model, and extends the application of the wavelet-based adaptive methods to a realistic wall-bounded turbulent flow configuration at a relatively high (order of a million) Reynolds number.

Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer.

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Derivation of unifying formulae for convective heat transfer in compressible flow fields

Although many theoretical and experimental studies on convective heat transfer exist, the consistent analytical expression of advection heat flux vector in convection as well as its reference temperature in the thermal driving force remains unclear. Here we show theoretically and experimentally the unifying formulae for three-dimensional (3D) heat flux vector of forced and natural convections for compressible laminar flows based on the first law of thermodynamics. It is indicated for a single-phase compressible fluid that advection is no other than heat transfer owing to mass flow in the forms of enthalpy and mechanical energy by gross fluid movement, driven by the temperature difference between the fluid temperature and the potential temperature associated with the relevant adiabatic work done. A simple formula for the total convective heat flux vector of natural convection is also suggested and reformulated in terms of logarithmic density difference as the thermal driving force. The theoretical calculations agree well with the laminar flow experiment results. Our discovery of advection heat transfer for compressible flows caused by the temperature differential in which the potential temperature is regarded as the unifying reference temperature represents a previously unknown thermal driving mechanism. This work would bring fundamental insights into the physical mechanism of convective heat transfer, and opens up new avenue for the design, calculation and thermal management of the 3D convection heat flux problems using the novel thermal driving force for compressible laminar and turbulent flows.

High-order semi-Lagrangian kinetic scheme for compressible turbulence.

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

A Low Dissipative and Stable Cell-Centered Finite Volume Method with the Simultaneous Approximation Term for Compressible Turbulent Flows

A simultaneous-approximation term is a non-reflecting boundary condition that is usually accompanied by summation-by-parts schemes for provable time stability. While a high-order convective flux based on reconstruction is often employed in a finite-volume method for compressible turbulent flow, finite-volume methods with the summation-by-parts property involve either equally weighted averaging or the second-order central flux for convective fluxes. In the present study, a cell-centered finite-volume method for compressible Naiver–Stokes equations was developed by combining a simultaneous-approximation term based on extrapolation and a low-dissipative discretization method without the summation-by-parts property. Direct numerical simulations and a large eddy simulation show that the resultant combination leads to comparable non-reflecting performance to that of the summation-by-parts scheme combined with the simultaneous-approximation term reported in the literature. Furthermore, a characteristic boundary condition was implemented for the present method, and its performance was compared with that of the simultaneous-approximation term for a direct numerical simulation and a large eddy simulation to show that the simultaneous-approximation term better maintained the average target pressure at the compressible flow outlet, which is useful for turbomachinery and aerodynamic applications, while the characteristic boundary condition better preserved the flow field near the outlet.

Multi-beam interferometric Rayleigh scattering technique for simultaneous 2-D quantitative measurement of multi-parameters in high speed flow field

In order to diagnose the high-speed compressible turbulent flow field, a two-dimensional (2-D) multi-parameters measurement method based on multi-beam interferometric Rayleigh scattering (IRS) technique was proposed. Under the beam splitting of etalon, the Rayleigh scattering signals generated by the interaction between multi-beam laser probes and the flow field gas molecules formed 2-D interference measurement lattice. Each measurement point contained the thermodynamic and velocity information of the flow field corresponding to a specific spatial location. By calibrating the effective finesse and transmittance of the etalon at different incident angles, the measurement accuracy of temperature and density of high-order interferometric points was improved. A 2-D IRS measurement system was established by combining multi-beam laser probes, amplification imaging system and solid quartz etalon. A high speed jet was used to verify the technology. The distributions of temperature, density and velocity at different positions along the radial direction and axial direction of the nozzle were obtained. The results shown that the technique could be used to simultaneously measure the 2-D multi-parameter information of the flow field.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids

In this paper, we present recent improvements of an Immersed Boundary Method (IBM) for the simulation of turbulent compressible flows on Cartesian grids. The proposed approach enables to remove spurious oscillations at the wall on skin pressure and friction coefficients. Results are compared to a body-fitted approach using the same wall function, showing that the stair-step immersed boundary provides a smooth solution compared to the body-fitted one.The immersed boundary method has been modified to adapt the location of forced and forcing points involved in the immersed boundary reconstruction to the Reynolds number. This method has been validated either for subsonic and transonic flow regimes, through the simulation of the subsonic turbulent flow around a NACA0012 profile and the transonic flow around a RAE2822 profile and the three-dimensional ONERA M6 wing.

STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows

We present STREAmS, an in-house high-fidelity solver for direct numerical simulations (DNS) of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interaction. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated with the solution of high-speed turbulent flows and can be used across a wide range of Mach numbers, extending from the low subsonic up to the hypersonic regime. From the computational viewpoint, STREAmS is oriented to modern HPC platforms thanks to MPI parallelization and the ability to run on multi-GPU architectures. This paper discusses the main implementation strategies, with particular reference to the CUDA paradigm, the management of a single code for traditional and multi-GPU architectures, and the optimization process to take advantage of the latest generation of NVIDIA GPUs. Performance measurements show that single-GPU optimization more than halves the computing time as compared to the baseline version. At the same time, the asynchronous patterns implemented in STREAmS for MPI communications guarantee very good parallel performance especially in the weak scaling spirit, with efficiency exceeding 97% on 1024 GPUs. For overall evaluation of STREAmS with respect to other compressible solvers, comparison with a recent GPU-enabled community solver is presented. It turns out that, although STREAmS is much more limited in terms of flow configurations that can be addressed, the advantage in terms of accuracy, computing time and memory occupation is substantial, which makes it an ideal candidate for large-scale simulations of high-Reynolds number, compressible wall-bounded turbulent flows. The solver is released open source under GPLv3 license. Program summaryProgram Title: STREAmSCPC Library link to program files:https://doi.org/10.17632/hdcgjpzr3y.1Developer’s repository link:https://github.com/matteobernardini/STREAmSCode Ocean capsule:https://codeocean.com/capsule/8931507/tree/v2Licensing provisions: GPLv3Programming language: Fortran 90, CUDA Fortran, MPINature of problem: Solving the three-dimensional compressible Navier–Stokes equations for low and high Mach regimes in a Cartesian domain configured for channel, boundary layer or shock-boundary layer interaction flows.Solution method: The convective terms are discretized using a hybrid energy-conservative shock-capturing scheme in locally conservative form. Shock-capturing capabilities rely on the use of Lax–Friedrichs flux vector splitting and weighted essentially non-oscillatory (WENO) reconstruction. The system is advanced in time using a three-stage, third-order RK scheme. Two-dimensional pencil distributed MPI parallelization is implemented alongside different patterns of GPU (CUDA Fortran) accelerated routines.

Large-scale coherent structures in compressible turbulent boundary layers

Abstract