Simulation Of Complex Turbulent Flows Research Articles

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

Non-equilibrium wall functions for large Eddy simulations of complex turbulent flows and heat transfer

In this paper novel unified wall function formulations for large eddy simulation of complex turbulent flows and heat transfer are presented. In contrast to existing wall functions, the proposed analytical expressions for velocity and temperature are: (1) valid over the whole range of dimensionless wall distance y+, (2) applicable to complex flow situations that include local non-equilibrium effects, (3) suitable for a wide range of molecular Prandtl numbers, (4) thermodynamically consistent with the second law of thermodynamics, and (5) easily extendable to account for contributions of additional source term e.g. gravity, radiation, chemical reactions. Such an universal and consistent wall function formulation is particularly useful for computational fluid dynamics applications in providing appropriate wall boundary conditions for complex high Reynolds number flows. The accuracy and thermodynamic consistency of the proposed wall treatment is first testified by comparison with experimental and direct numerical simulation data. Second, in order to highlight the applicability and performance of the proposed wall functions for computational fluid dynamics, results of large eddy simulations of various complex turbulent flows including heat transfer relevant to internal combustion engine applications are presented and evaluated. It turns out that the suggested wall function approach features a superior physics modeling accuracy in terms of well-known key parameters in near-wall bounded flows in comparison to state-of-the-art wall functions.

Wavelet-based adaptive delayed detached eddy simulations for wall-bounded compressible turbulent flows

A novel wavelet-based adaptive delayed detached eddy simulation (W-DDES) approach for simulations of wall-bounded compressible turbulent flows is proposed. The new approach utilizes anisotropic wavelet-based mesh refinement and its effectiveness is demonstrated for flow simulations using the Spalart–Allmaras DDES model. A variable wavelet thresholding strategy blending two distinct thresholds for the Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) regimes is used. A novel mesh adaptation on mean and fluctuating quantities with different wavelet threshold levels is proposed. The new strategy is more accurate and efficient compared to the adaptation on instantaneous quantities using a priori defined uniform thresholds. The effectiveness of the W-DDES method is demonstrated by comparing the results of the W-DDES simulations with results already available in the literature. Supersonic plane channel flow for two different configurations is tested as benchmark wall-bounded flows. Both the accuracy indicated by the threshold and efficiency in terms of degrees of freedom for the novel adaptation strategy are successfully gained compared with the wavelet-based adaptive LES method. Moreover, the newly proposed W-DDES resolves the typical log-layer match issue encountered in the conventional non-adaptive DDES method mainly due to the use of wavelet-based adaptive mesh refinement. The W-DDES capability for simulations of complex turbulent flows is validated by two other flow configurations – a subsonic channel flow with periodic hill constrictions and a supersonic flow over a compression ramp inducing the shock wave–turbulent boundary layer interaction. The current study serves as a crucial step towards construction of a unified wavelet-based adaptive hierarchical RANS/LES modelling framework, capable of performing simulations of varying fidelities from no-modelling direct numerical simulations to full-modelling RANS simulations.

Investigation of Rotor Tip Vortex in Hover Based on IDDES Methods

A calculation and analysis program of high-precision numerical simulation for rotor blade tip vortex in hovering state was developed. The fifth order Roe-WENO scheme was carried out in order to reduce the numerical dissipation of the rotor wake region. The rotary motion of the rotor was realized by using the dynamic patched technology of structured grids. And at the same time, the technology also helped to avoid the tremendous increase of grid number of the far-field due to the refined grids of the flow region where emphasis was placed on. Hybrid RANS/LES approach was investigated based on the issues about inadequate capabilities of simulations of complex turbulent flows, and IDDES approach was developed. The numerical simulation of the tandem cylinder was carried out firstly to verify the reliability of the IDDES method and the patched grid technology. Then the RANS and IDDES approaches were used to simulate the flow field of the rotor in hover performance, respectively. The analysis of the vortex magnitude, vortex core position and diameter as well as the velocity profiles of the rotor tip vortex were made comparatively in detail. The numerical results showed that the resolutions obtained through IDDEES approach agreed with the experimental results much better than that of the RANS approach with the same gird scales. Meanwhile, the IDDES results can capture the tiny worm vortex structures and vortex paring phenomena in accordance with the practical status, which contributes to study the flow mechanism of rotor and related problems.

A scalable solution strategy for high-order stabilized finite-element solvers using an implicit line preconditioner

This paper presents a robust, efficient, and strongly scalable solution methodology for simulation of complex turbulent flows on unstructured grids. The compressible Reynolds averaged Navier–Stokes (RANS) equations and the negative Spalart–Allmaras (SA) turbulence model are discretized, in coupled form, using a Streamline Upwind Petrov–Galerkin (SUPG) scheme. The time integration is fully implicit, and the discretized equations are advanced towards a steady-state solution using a pseudo-transient continuation (PTC). For solution of the linearized systems, a preconditioned Krylov solver is used. Seeking robustness, Krylov solvers are commonly preconditioned using incomplete factorization methods such as ILU(k). However, these methods are neither memory efficient, nor strongly scalable. To provide a better alternative, the implicit line solution method, which has been traditionally used in finite-volume methods, is revised and enhanced to solve stiffer linear systems. In the developed method, the lines are generated using a matrix-based approach, which connects the strongly-coupled unknowns. In addition, to improve the robustness of the line solver for high-CFL systems, a dual-CFL strategy, with a lower CFL number in the preconditioner matrix, is developed. Also, it is shown that for high-order continuous finite-element discretizations, the interconnections of the degrees of freedom on a line form a banded matrix which is wider than tridiagonal, but still can be factorized completely without generating any fill-ins. The developed line preconditioner is strongly scalable and, in contrast to the ILU factorization, its convergence behavior does not depend on the number of partitions. Two three-dimensional numerical examples are presented in which the performance of the line preconditioner is compared with that of the ILU(k) preconditioner. This comparison shows that, in addition to robustness improvements, the line preconditioner offers significant benefits in terms of memory efficiency.

Direct and large-eddy simulation of turbulent flows on composite multi-resolution grids by the lattice Boltzmann method

In order to properly address the simulation of complex (weakly compressible) turbulent flows, the lattice Boltzmann method, originally designed for uniform structured grids, needs to be extended to composite multi-domain grids displaying various levels of spatial resolution. Therefore, physical conditions must be specified to determine the mapping of statistical information (about the populations of moving particles) at the interface between two domains of different resolutions. quite simply in terms of the probability distributions of the underlying discrete-velocity Boltzmann equation. Namely, the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions, whereas the discontinuity of the rate-of-strain tensor is ensured by applying a “spatial transformation” to the collision term of the discrete-velocity Boltzmann equation. The latter condition allows us to explicitly account for the subgrid-scale modeling in the treatment of resolution changes.Test computations of a turbulent plane-channel flow have been carried out. The lattice Boltzmann scheme relies on the standard D3Q19 lattice in a cell-vertex representation, and uses the BGK approximation for the collision term. A shear-improved variant of the Smagorinsky viscosity is used to account for possible subgrid-scale dynamics. In a quasi-direct numerical simulation at Reτ=180 with two levels of grid resolution, the results are found in excellent agreement with reference data obtained by a high-resolution pseudo-spectral simulation. In a Large-Eddy Simulation (LES) at Reτ=395 with three levels of grid resolution, the results compare reasonably well with high-resolution reference data. The accuracy is improved in comparison with a standard finite-volume LES performed with the same subgrid-scale viscosity and comparable grid resolution.By combining the simplicity and physical relevance of the shear-improved Smagorinsky model and the computational efficiency of the lattice Boltzmann scheme, here extended to composite multi-resolution grids, we believe that our proposal offers a high potential for the simulation of complex turbulent flows.

Smoothing algorithms for mean-flow extraction in large-eddy simulation of complex turbulent flows

Based on physical arguments, the importance of separating the mean-flow from turbulence in the modeling of the subgrid-scale eddy-viscosity is emphasized. Therefore, two distinct time-domain smoothing algorithms are proposed to estimate the mean-flow as the simulation progresses, namely, an exponentially weighted moving average (or exponential smoothing) and an adaptive low-pass Kalman filter. These algorithms highlight the longer-term evolution or cycles of the flow but erase short-term fluctuations. Indeed, it is our assumption that the mean-flow (in the statistical sense) may be approximated as the low-frequency component of the velocity field and that the turbulent part of the flow adds itself to this “unsteady mean.” The cutoff frequency separating these two components is fixed according to some characteristic time-scale of the flow in the exponential smoothing, but inferred dynamically from the recent history of the flow in the Kalman filter. In practice, these two algorithms are implemented in large-eddy simulations that rely on a shear-improved Smagorinsky’s model. In this model, the magnitude of mean-flow rate of strain is subtracted from the magnitude of the instantaneous rate of strain in the subgrid-scale eddy-viscosity. Two test-cases have been investigated: a turbulent plane-channel flow (Rew=395) and the flow past a circular cylinder in the subcritical turbulent regime (ReD=4.7×104). Comparisons with direct numerical simulation and experimental data demonstrate the good efficiency of the whole modeling. This allows us to address nonhomogeneous unsteady configurations without adding significant complication and computational cost to the standard Smagorinsky’s model. From a computational viewpoint, this modeling deserves interest since it is entirely local in space. It is therefore adapted for parallelization and convenient for boundary conditions.

Turbulence Modeling Applied to Flow Through a Staggered Tube Bundle

Both two-dimensional and three-dimensional numerical simulations of the turbulent flow through a staggered tube bundle are presented. The primary aim of the present study is to search for a turbulent model that could serve as an engineering design tool at a relatively low computational cost. In the present study, the performances of the Spalart-Allmaras model, the k-e model, and large eddy simulation are evaluated by comparing their simulation results against experimental measurements. The turbulence models are assessed mainly based on their ability to resolve time-dependent features of the flow related to vortex shedding. Simulations are performed at a Reynolds number of 9300. Overall, the predicted streamwise mean velocity and transverse mean velocity in the present study are in good agreement with measurements, and the results show that the simple one-equation Spalart-Allmaras model could be a very promising tool for numerical simulation of complex turbulent flows, since the Strouhal number obtained by it agrees well with measurements available in the literature for similar tube geometries.

Direct numerical simulation of separated flow in a three-dimensional diffuser

A direct numerical simulation (DNS) of turbulent flow in a three-dimensional diffuser at Re = 10000 (based on bulk velocity and inflow-duct height) was performed with a massively parallel high-order spectral element method running on up to 32768 processors. Accurate inflow condition is ensured through unsteady trip forcing and a long development section. Mean flow results are in good agreement with experimental data by Cherry et al. (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811), in particular the separated region starting from one corner and gradually spreading to the top expanding diffuser wall. It is found that the corner vortices induced by the secondary flow in the duct persist into the diffuser, where they give rise to a dominant low-speed streak, due to a similar mechanism as the ‘lift-up effect’ in transitional shear flows, thus governing the separation behaviour. Well-resolved simulations of complex turbulent flows are thus possible even at realistic Reynolds numbers, providing accurate and detailed information about the flow physics. The available Reynolds stress budgets provide valuable references for future development of turbulence models.

A numerical strategy to combine high-order schemes, complex geometry and parallel computing for high resolution DNS of fractal generated turbulence

Impressive advances in parallel platform architectures over the past decade have made Direct Numerical Simulation (DNS) a powerful tool which can provide full access to the spatial structure of turbulent flows with complex geometries. An innovative approach which combines high-order schemes and a dual domain decomposition method is presented in this paper and is applied to DNS of multiscale-generated turbulent flows by a fractal grid. These DNS illustrate the applicability of our approach to the simulation of complex turbulent flows and provide results which are compared with recent laboratory experiments thus providing new insights for the interpretation of the experimental measurements.

Modeling of Internal Reacting Flows and External Static Stall Flows Using RANS and PRNS

The reacting flow in a research lean direct injection (LDI) hydrogen combustor and the static stall of NACA0012 airfoil were simulated using both Reynolds averaged Navier–Stokes (RANS) and partially resolved numerical simulation (PRNS) approaches. The concept and the main features of the PRNS approach are briefly described. The PRNS basic equations are grid independent or grid invariant; the subscale models are a dynamic equation system. We consider PRNS as an engineering tool for the very large eddy simulation of complex turbulent flows. Two CFD codes, NCC and Wind-US, with two different subscale models (i.e. two- and one-transport equation models, respectively) are used in the presented PRNS simulations. Based on the comparisons with available experimental data, the numerical results indicate that the PRNS subscale models seem to be able to capture important large scale turbulent structures and to improve the quality of numerical simulations while keeping a relatively low cost comparable to the unsteady RANS simulations.

High Accurate Finite Volume Method for Large Eddy Simulation of Complex Turbulent Flows

High Accurate Finite Volume Method for Large Eddy Simulation of Complex Turbulent Flows

A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows

A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations (LES) of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs (such as when the filter scale approaches the limits of the inertial range), the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the Smagorinsky–Lilly model with wall-damping (which is overdissipative) or the scale-invariant dynamic model (which is underdissipative), the scale-dependent Lagrangian dynamic model is shown to have good dissipation characteristics. The model is also tested against detailed atmospheric boundary layer data that include measurements of the response of the flow to abrupt transitions in wall roughness. For such flows over variable surfaces, the plane-averaged version of the dynamic model is not appropriate and the Lagrangian averaging is desirable. The simulated wall stress overshoot and relaxation after a jump in surface roughness and the velocity profiles at several downstream distances from the jump are compared to the experimental data. Results show that the dynamic Smagorinsky coefficient close to the wall is very sensitive to the underlying local surface roughness, thus justifying the use of the Lagrangian formulation. In addition, the Lagrangian formulation reproduces experimental data more accurately than the planar-averaged formulation in simulations over heterogeneous rough walls.

Dynamic wall modeling for large-eddy simulation of complex turbulent flows

The efficacy of large-eddy simulation (LES) with wall modeling for complex turbulent flows is assessed by considering turbulent boundary-layer flows past an asymmetric trailing-edge. Wall models based on turbulent boundary-layer equations and their simpler variants are employed to compute the instantaneous wall shear stress, which is used as approximate boundary conditions for the LES. It is demonstrated that, as first noted by Cabot and Moin [Flow Turb. Combust. 63, 269 (2000)], when a Reynolds-averaged Navier–Stokes type eddy viscosity is used in the wall-layer equations with nonlinear convective terms, its value must be reduced to account for only the unresolved part of the Reynolds stress. A dynamically adjusted mixing-length eddy viscosity is used in the turbulent boundary-layer equation model, which is shown to be considerably more accurate than the simpler wall models based on the instantaneous log law. This method predicts low-order velocity statistics in good agreement with those from the full LES with resolved wall-layers, at a small fraction of the original computational cost. In particular, the unsteady separation near the trailing-edge is captured correctly, and the prediction of surface pressure fluctuations also shows promise.

Numerical Simulation of Isotropic Turbulence Using a Collocated Approach and a Nonorthogonal Grid System

We studied the effect of using a nonorthogonal grid coordinate system and a finite-volume approach in the simulation of decaying isotropic turbulence. Calculations were performed in distorted periodic cubic boxes and with a turbulent Reynolds number, based on the Taylor microscale and on a root mean square turbulent velocity, of approximately 40. A preliminary study showed that in the nonorthogonal grids some Fourier modes of the discretized derivatives can have greater amplitude or the phase inverted relatively to the modes of the exact derivative, contrary to what occurs with a Cartesian grid system. However, in the simulations, the statistical distributions of velocity, pressure, and longitudinal and lateral velocity derivatives were always identical, regardless of the grid distortion. The temporal evolution of the energy was also similar and the differences at the end of the simulations (after about two eddy turnover times) did not exceed 1%. Furthermore, the grid nonorthogonality affected neither the isotropy of the fields nor the correlation between the vorticity and the principal rates of strain. We concluded that the finite-volume approach in nonorthogonal grid systems may be used in the numerical simulation of complex turbulent flows with either the direct numerical simulation or large-eddy simulation methodologies.

Large eddy simulation of complex turbulent flows: Physical aspects and research trends

In the current paper, we have primarily addressed one powerful simulation tool developed during the last decades-Large Eddy Simulation (LES), which is most suitable for unsteady three-dimensional complex turbulent flows in industry and natural environment. The main point in LES is that the large-scale motion is resolved while the small-scale motion is modeled or, in geophysical terminology, parameterized. With a view to devising a subgrid-scale(SGS) model of high quality, we have highlighted analyzing physical aspects in scale interaction and-energy transfer such as dissipation, backscatter, local and non-local interaction, anisotropy and resolution requirement. They are the factors responsible for where the advantages and disadvantages in existing SGS models come from. A case study on LES of turbulence in vegetative canopy is presented to illustrate that LES model is more based on physical arguments. Then, varieties of challenging complex turbulent flows in both industry and geophysical fields in the near future-are presented. In conclusion; we may say with confidence that new century shall see the flourish in the research of turbulence with the aid of LES combined with other approaches.

B-Spline Method and Zonal Grids for Simulations of Complex Turbulent Flows

A numerical technique for computations of turbulent flows is described. The technique is based on B-splines and allows grid embedding in physically significant flow regions. Numerical tests, which include solutions of nonlinear advection-diffusion equations and computations of flow over a circular cylinder at Reynolds numbers up to 300, indicate that the method is accurate and efficient. In computations of flow over a cylinder, the lift, drag, and base suction coefficients agree well with existing experimental data and previous numerical simulations.

Simulation of complex turbulent flows: recent advances and prospects in wind engineering

Simulation of complex turbulent flows: recent advances and prospects in wind engineering

Simulation of complex turbulent flows: recent advances and prospects in wind engineering

Publisher Summary Turbulent flows are found everywhere and are of interest to engineers and scientists working in many fields. There is a great variation in the physics of the flows and the required predictive capability among the fields. This might lead to difficulties. Researchers in one field might believe that their field is so unique that they need not borrow from others or they might adopt methods and concepts from other fields without sufficient critical thought. Either approach might lead to difficulties. Accuracy requirements vary greatly among the fields. Turbulence is strongly affected by “extra strains” including stratification, buoyancy, rotation, chemical reaction, and compression. To some, these are essential issues; to others, they are of no interest. In some fields, temporal fluctuations are of great importance; others are satisfied with time-averaged quantities. The accuracy demanded in some high technology areas is a few percent; other fields, including the geophysical and astrophysical sciences, might be satisfied with the order of magnitude results.

Towards large eddy and direct simulation of complex turbulent flows

Recent advances in the methodology for direct numerical simulation of turbulent flows and some of the current applications are reviewed. It is argued that high-order finite difference schemes yield solutions with comparable accuracy to the spectral methods with the same number of degrees of freedom. The effects of random inflow conditions on-the downstream evolution of turbulence are discussed.