Simulations Of Wall-bounded Turbulent Flows Research Articles

Data-driven wall modeling for turbulent separated flows

The large-eddy simulation of wall-bounded turbulent flows at high Reynolds numbers is made more efficient by the use of wall models that predict the wall shear stress, allowing coarser cell sizes at the wall. In this paper, a data-driven approach for the modeling of the wall shear stress is examined using filtered high-fidelity numerical data from two fully developed turbulent channel flows and two turbulent flows with separated regions: a three-dimensional diffuser and a backward-facing step. The model is a multilayer perceptron based on the flow information in the vicinity, given by the distance to the wall and the velocity components at a given number of grid points above the wall. The model is Mach number equivariant at the quasi-incompressible limit, Galilean invariant, statistically rotational invariant and can extrapolate to flow conditions unseen in the training dataset. The relevance of the machine-learning procedure is verified a priori using the filtered numerical data and a posteriori by performing wall-modeled large-eddy simulations implementing the model. The results show that the model is able to leverage the local spatial information to discriminate developed wall turbulence and separated regions in flow configurations not included in the training dataset.

Explicit wall models for large eddy simulation

Algebraic explicit wall models covering the entire inner region of the turbulent boundary layer are proposed to reduce the computational effort for large eddy simulation of wall-bounded turbulent flows. The proposed formulas are given in closed forms with either logarithmic- or power-function-based laws of the wall, allowing straightforward evaluation of the friction velocity on near wall grids independent of their locations in the turbulent boundary layer. The performance of the proposed models is demonstrated by the wall modeled large eddy simulation of a turbulent plane channel flow.

Mixed modeling for large-eddy simulation: The single-layer and two-layer minimum-dissipation-Bardina models

Predicting the behavior of turbulent flows using large-eddy simulation requires a modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD–Bardina model. In order to also obtain a physics-conforming model for wall-bounded flows, we further develop this mixed model into a two-layer approach: the near-wall region is parameterized with the AMD–Bardina model, whereas the outer region is computed with the Bardina model. The single-layer and two-layer AMD–Bardina models are tested in turbulent channel flows at various Reynolds numbers, and improved predictions are obtained when the mixed models are applied in comparison to the computations with the AMD and Bardina models alone. The results obtained with the two-layer AMD–Bardina model are particularly remarkable: both first- and second-order statistics are extremely well predicted and even the inflection of the mean velocity in the channel center is captured. Hence, a very promising model is obtained for large-eddy simulations of wall-bounded turbulent flows at moderate and high Reynolds numbers.

Numerical modelling of wall-bounded turbulent flows based on the CABARET scheme

In this study, the classical problem of turbulent plane channel flow at Rem = 13750 and Rem = 21900 is investigated using a numerical algorithm based on the CABARET scheme. Simulations are performed on the fine grids, resolving all the spatial scales of the turbulence according to a direct numerical simulation approach, as well as on coarse grids standard for large eddy simulation of wall-bounded turbulent flows. In the latter case, in order to obtain a more accurate representation of the momentum transfer towards the wall, artificial boundary conditions are introduced. It allows modelling with high accuracy the mean flow characteristics. Numerical results obtained by the CABARET scheme are compared with numerical results obtained by pseudospectral method.

Turbulent Inflow Generation Through Buoyancy Perturbations with Colored Noise

An inflow generation method for large-eddy simulations of wall-bounded turbulent flows is presented. The method builds upon the work of Muñoz-Esparza et al. (“A Stochastic Perturbation Method to Generate Inflow Turbulence in Large-Eddy Simulation Models: Application to Neutrally Stratified Atmospheric Boundary Layers,” Physics of Fluids, Vol. 27, No. 3, 2015, Paper 035102). In the present adaptation of the original idea, colored noise is generated in the temperature field by adding white noise as source term perturbations in the filtered form of the temperature transport equation. Perturbation boxes introduced within a buffer zone near the inlet encompass multiple computational cells to induce a volumetric buoyancy effect. The amplitudes of the source term perturbations are determined by assigning a bulk Richardson number based on the size of the perturbation box and the height-dependent velocity profile. The temperature field with colored noise is then coupled to the incompressible flowfield within a buffer zone only via the Boussinesq approximation. A turbulent-channel flow and a backward-facing step with a spatially evolving boundary layer upstream of the step are simulated to assess the predictive performance of the inflow generation technique. The results are in good agreement with direct numerical simulation benchmark data, both for the first- and second-order statistics of turbulence. It is also found that the same set of parameters works well in both cases studied.

Extended integral wall-model for large-eddy simulations of compressible wall-bounded turbulent flows

Wall-modeling is required to make large-eddy simulations of high-Reynolds number wall-bounded turbulent flows feasible in terms of computational cost. Here, an extension of the integral wall-model for large-eddy simulations (iWMLESs) for incompressible flows developed by Yang et al. [“Integral wall model for large eddy simulations of wall-bounded turbulent flows,” Phys. Fluids 27(2), 025112 (2015)] to compressible and isothermal flows is proposed and assessed. The iWMLES approach is analogous to the von Kármán-Pohlhausen integral method for laminar flows: the velocity profile is parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer momentum equation. It allows non-equilibrium effects such as pressure gradient and convection to be included at a computing cost similar to analytical wall-models. To take into account density variations and temperature gradients, the temperature profile is also parameterized and the integral compressible boundary layer energy equation is considered. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of validity. Instead of solving a set of differential equations as wall-models based on the thin boundary layer equation approach, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers. For low Mach number cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with those of Direct Numerical Simulation (DNS). For supersonic flows, the results are in good agreement with the DNS data, especially the mean velocity quantities and the wall friction, while standard analytical wall-models show their limits.

Wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling of external flows

The recent development of the adaptive-anisotropic wavelet-collocation method, which incorporates the use of coordinate transforms, opens new horizons for wavelet-based simulations of wall-bounded turbulent flows. The new wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes approach for computational modelling of turbulent flows is presented. The proposed methodology that is integrated with anisotropic wavelet-based mesh refinement is demonstrated for a two-equation eddy-viscosity turbulence model. The performance of the method is assessed by conducting numerical simulations of the turbulent flow past a circular cylinder at subcritical Reynolds number. The present study demonstrates both the feasibility and the effectiveness of the new wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling procedure for external flows.

Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows

In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%–15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method’s advantages are illustrated for the simulation of a developing wind-farm boundary layer.

Integral wall model for large eddy simulations of wall-bounded turbulent flows

A new approach for wall modeling in Large-Eddy-Simulations (LES) is proposed and tested in various applications. To properly include near-wall physics while preserving the basic economy of equilibrium-type wall models, we adopt the classical integral method of von Karman and Pohlhausen (VKP). A velocity profile with various parameters is proposed as an alternative to numerical integration of the boundary layer equations in the near-wall zone. The profile contains a viscous or roughness sublayer and a logarithmic layer with an additional linear term that can account for inertial and pressure gradient effects. Similar to the VKP method, the assumed velocity profile coefficients are determined from appropriate matching conditions and physical constraints. The proposed integral wall-modeled LES (iWMLES) method is tested in the context of a pseudo-spectral code for fully developed channel flow with a dynamic Lagrangian subgrid model as well as in a finite-difference LES code including the immersed boundary method and the dynamic Vreman eddy-viscosity model. Test cases include a fully developed half-channel at various Reynolds numbers, a fully developed channel flow with unresolved roughness, a standard developing turbulent boundary layer flows over smooth plates at various Reynolds numbers, over plates with unresolved roughness, and a case with resolved roughness elements consisting of an array of wall-mounted cubes. The comparisons with data show that the proposed iWMLES method provides accurate predictions of near-wall velocity profiles in LES while, similarly to equilibrium wall models, its cost remains independent of Reynolds number and is thus significantly lower compared to existing zonal or hybrid wall models. A sample application to flow over a surface with truncated cones (representing idealized barnacle-like roughness elements) is also presented, which illustrates effects of subgrid scale roughness when combined with resolved roughness elements.

Anisotropic Adaptation for Transonic Flows with Turbulent Boundary Layers

Simulation of wall-bounded turbulent flows poses significant challenges and requires tightly controlled mesh spacing and structure near the walls. Semistructured or hybrid meshes are often used for turbulent boundary layer flows. These meshes not only account for complex geometry but also maintain highly anisotropic, graded, and layered elements near the walls. However, for engineering flow problems, the mesh spacing required to achieve a given level of accuracy cannot be determined a priori and, therefore, an adaptive approach becomes essential. For wall-bounded turbulent flows, such an approach must incorporate the structure of the turbulent boundary layer and associated flow physics to guide the adaptive process. This paper introduces a new approach for boundary layer adaptivity, wherein flow physics indicators are used in combination with interpolation-based or numerical error indicators. The effectiveness of the current technique is demonstrated by applying them to two aerodynamic problems involving transonic turbulent flows.

Large Eddy Simulation of a Free Circular Jet

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components u'u'¯, v'v'¯, and u'v'¯ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

Constrained large-eddy simulation of wall-bounded compressible turbulent flows

A constrained large-eddy simulation (CLES) approach is developed for wall-bounded compressible turbulent flows based on its incompressible analogue [Chen et al., “Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows,” J. Fluid Mech. 703, 1–28 (2012)]. In the new CLES approach, both the subgrid-scale (SGS) stress and the SGS heat flux are decomposed into an averaged part and a fluctuating part in the near-wall region with the mean SGS stress and heat flux constrained by prescribed Reynolds stress model and turbulent heat flux model, respectively. The Smagorinsky SGS models are employed to approximate the SGS stress and heat flux in the remaining region of the flow domain. The present CLES method is validated by simulating the compressible turbulent channel flows at various Reynolds numbers and Mach numbers. The mean velocity profiles, mean temperature profiles, and other statistical quantities and turbulent structures are obtained and well compared among the present approach, direct numerical simulation (DNS), detached eddy simulation (DES) and traditional large eddy simulation (LES). The results demonstrate that the dual constraint of Reynolds stress and turbulent heat flux plays a non-trivial role in enhancing the ability of LES for wall-bounded compressible flows. In addition, the Reynolds and Mach numbers effects on the mean and statistical quantities as well as the turbulence structures are investigated using the proposed CLES method. The main conclusions are in very good agreement with those drawn by other authors using DNS method. All the results manifest that the present CLES technique is an encouraging and useful tool for wall-bounded compressible turbulent flows.

Вихреразрешающее моделирование пристенных турбулентных течений

Вихреразрешающее моделирование пристенных турбулентных течений

The effect of lattice models within the lattice Boltzmann method in the simulation of wall-bounded turbulent flows

This study investigated the effect of 3D lattice models (D3Q19 and D3Q27 lattices) on the simulation results of wall-bounded turbulent flows in a circular pipe and in a square duct. The LES with the Smagorinsky subgrid-scale (SGS) model was adopted for the turbulence simulation. To improve the credibility of our results on the lattice model effect, a comprehensive sensitivity study was performed of boundary treatment techniques and collision models, as well as grid sizes in the simulation of the turbulent pipe flows. Through the turbulent circular pipe flow simulation, it was discovered that the D3Q27 lattice model could achieve the rotational invariance in terms of long-time-averaged turbulence statistics and generated the results comparable to the DNS data, while the D3Q19 lattice model broke the rotational invariance and produced unreasonable data. In the turbulent square duct flow simulation, the rotational invariance was evaluated by comparing the results before and after rotating the geometry by 45° about a center. As in the circular pipe flow simulation, the D3Q19 lattice model could not achieve the rotational invariance while the D3Q27 lattice model could. The D3Q19 lattice model also produced poor results compared to those from the D3Q27 lattice model. These defects of the D3Q19 lattice model could be explained by the planes consisting of 2D lattices with five velocities (called defective planes in this study) in the D3Q19 lattice model, based on White and Chong’s [14] hypothesis. The defective planes had a deficiency in the momentum transfer of flow and turbulence, thus breaking the rotational invariance and causing the inaccurate results for tested problems.

Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows

AbstractIn the traditional hybrid RANS/LES approaches for the simulation of wall-bounded fluid turbulence, such as detached-eddy simulation (DES), the whole flow domain is divided into an inner layer and an outer layer. Typically the Reynolds-averaged Navier–Stokes (RANS) equations are used for the inner layer, while large-eddy simulation (LES) is used for the outer layer. The transition from the inner-layer solution to the outer-layer solution is often problematic due to the lack of small-scale dynamics in the RANS region. In this paper, we propose to simulate the whole flow domain by large-eddy simulation while enforcing a Reynolds-stress constraint on the subgrid-scale (SGS) stress model in the inner layer. Both the algebraic eddy-viscosity model and the one-equation Spalart–Allmaras (SA) model have been used to constrain the Reynolds stress in the inner layer. In this way, we improve the LES methodology by allowing the mean flow of the inner layer to satisfy the RANS solution while small-scale dynamics is included. We validate the Reynolds-stress-constrained large-eddy simulation (RSC-LES) model by simulating three-dimensional turbulent channel flow and flow past a circular cylinder. Our model is able to predict mean velocity, turbulent stress and skin-friction coefficients more accurately in turbulent channel flow and to estimate the pressure coefficient after separation more precisely in flow past a circular cylinder compared with the pure dynamic Smagorinsky model (DSM) and DES using the same grid resolution. Furthermore, the computational cost of the RSC-LES is almost the same as that of DES.

G102 内層を取り除いた壁乱流の数値シミュレーション(GS1-1 乱流関連,一般セッション)

G102 内層を取り除いた壁乱流の数値シミュレーション(GS1-1 乱流関連,一般セッション)

A low Reynolds number variant of partially-averaged Navier–Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier–Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k– ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results – at a reduced CPU time – as compared to the Dynamic Smagorinsky model.

Leray- α simulations of wall-bounded turbulent flows

The Leray- α model reduces the range of active scales of the Navier–Stokes equations by smoothing the advective transport. Here we assess the potential of the Leray- α model in its standard formulation to simulate wall-bounded flows. Three flow cases are considered: plane channel flow at Re τ = 590 , Rayleigh–Bénard convection at Ra = 10 7 and Pr = 1, and a side-heated vertical channel at Ra = 5 × 10 6 and Pr = 0.7. The simulations are compared to results from a well resolved and coarse DNS. It is found that for all three flow cases, the variance in the velocity field increases as the filter width parameter a is increased, where a is connected to the filter width as α i = a Δ x i , with Δ x i the local grid size. Furthermore, the viscous and diffusive wall regions tend to thicken relative to the coarse DNS results as a function of a. In the cases where coarse DNS overpredicts wall gradients (as for Rayleigh–Bénard convection and the side-heated vertical channel), the thickening is beneficial. However, for the plane channel flow, coarse DNS underpredicts the wall-shear velocity, and increasing a only degrades the results. It is shown that buoyancy effects need to be included with care, because of the close relation of turbulent heat flux and the production of turbulent kinetic energy.

Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows

In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu, Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified asvT=(Csδ)2(|S|—|〈S〉|): the magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|;CSis the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbersReτ= 395 andReτ= 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.