Large eddy simulation of a confined square cavity with natural convection based on compressible flow equations

Large eddy simulation of natural convection in a confined square cavity is described. The use of a complex compressible code with an artificial acoustic stiffness correction method, allows the use of higher time steps for a faster time and statistical convergence. We consider a broadly studied experimental case, consisting of a natural convective flow in a confined square cavity, with vertical walls heated at different rates (active walls), set at Ra = 1.58 × 10⁹. Turbulent boundary layers developing on the active walls and a vertical stable stratification characterize the mean flow. It is shown here that the results of this study match the experimental results reported in literature; for instance, mean velocity results. Although results for rms velocity fluctuations are barely over-predicted, the peak region is properly represented, while the greatest disagreements are found in the turbulent heat flow rate (velocity–temperature correlations). Turbulent structures were identified using different visualization methods and statistical studies. The authors found that the boundary layers on the active walls almost reach the fully turbulent regime, tending toward the laminar regime along the horizontal walls.     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ_∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.For some research studies in small domains, Δ_∥ is made much smaller than δ, and LES content is generated intentionally. However for natural DES applications in useful domains, it is preferable to over-ride the DES limiter and maintain RANS behavior in boundary layers, independent of Δ_∥ relative to δ. For this purpose, a new version of the technique – referred to as DDES, for Delayed DES – is presented which is based on a simple modification to DES97, similar to one proposed by Menter and Kuntz for the shear–stress transport (SST) model, but applicable to other models. Tests in boundary layers, on a single and a multi-element airfoil, a cylinder, and a backward-facing step demonstrate that RANS function is indeed maintained in thick boundary layers, without preventing LES function after massive separation. The new formulation better fulfills the intent of DES. Two other issues are discussed: the use of DES as a wall model in LES of attached flows, in which the known log-layer mismatch is not resolved by DDES; and a correction that is helpful at low cell Reynolds numbers.     

The use of turbulent inflow conditions for the modelling of a high aspect ratio jet

The aim of this work is to investigate the capabilities of a turbulent inflow method. The application selected for this study is the high aspect ratio jet. The complexities associated to the numerical modelling of a high aspect ratio jet are embedded in its physical complexity. Consequently, the numerical modelling does not only require a high mesh resolution, but furthermore it requires a careful mesh construction, inflow conditions and subgrid-scale modelling to make an accurate computation of the unsteady flow phenomena. The results indicate that increased grid resolution and enhanced turbulence modelling reduce the effect of the imposed flow fluctuations. It is concluded that for a high aspect ratio free-jet turbulent inflow conditions are effective if the mesh resolution is insufficient to trigger shear-layer instabilities. Applied with sufficient mesh resolution the onset of vortex motions will occur in the shear layer, hence there is limited inflow sensitivity.     

Large Eddy Simulations of convergent–divergent channel flows at moderate Reynolds numbers

The paper is focused on the study of fully turbulent channel flows, using Large Eddy Simulations (LES), in order to address the effects of adverse pressure gradient regions. Analyses of the effects of streak instabilities, which have been shown to be relevant in such regions, are extended to moderate Reynolds numbers. The work considers two different channel geometries in order to further separate influences from wall curvature, flow separation and adverse pressure gradients. Turbulent kinetic energy and Reynolds stress budgets are investigated at separation and re-attachment points. The numerical approach used in the present work is based on the incompressible Navier–Stokes equations, which are solved by a pseudo-spectral methodology for structured grids. Wall-resolved LES calculations are performed using the WALE subgrid scale model. The study shows that the streak instability mechanism persists at higher Reynolds numbers with and without wall curvature in the adverse pressure gradient regions. Moreover, the observed effects are also present regardless of the existence of flow separation regions. Finally, the study of turbulent kinetic energy budgets indicates that, independently of the flow condition, there are well-defined patterns for such turbulent properties at separation and re-attachment points.     

Effect of secondary flow on droplet distribution and deposition in horizontal annular pipe flow

In horizontal annular dispersed pipe flow the liquid film at the bottom is thicker and rougher than at the top of the pipe. A turbulent pipe flow experiencing a variation of roughness along the pipe wall will show a secondary flow. Such secondary flow, consisting of two counter-rotating cells in the cross-section of the tube, can change the distribution of the droplets inside the pipe and their deposition at the wall. Here, we compare the behaviour of the droplets (dispersed phase) with and without secondary flow, using large-eddy simulations. It is shown that the presence of secondary flow increases the droplet concentration in the core of the pipe and the droplet deposition-rate at the top of the pipe.     

A scaling analysis for point–particle approaches to turbulent multiphase flows

Simple dimensional arguments are used in establishing three different regimes of particle time scale, where explicit expression for particle Reynolds number and Stokes number are obtained as a function of nondimensional particle size (d/η)$(d/\eta )$ and density ratio. From a comparative analysis of the different computational approaches available for turbulent multiphase flows it is argued that the point–particle approach is uniquely suited to address turbulent multiphase flows where the Stokes number, defined as the ratio of particle time scale to Kolmogorov time scale (_τp/_τk)$({\tau }_p/{\tau }_k)$, is greater than 1. The Stokes number estimate has been used to establish parameter range where point–particle approach is ideally suited. The point–particle approach can be extended to handle “finite-sized” particles whose diameter approach that of the smallest resolved eddies. However, new challenges arise in the implementation of Lagrangian–Eulerian coupling between the particles and the carrier phase. An approach where the inter-phase momentum and energy coupling can be separated into a deterministic and a stochastic contribution has been suggested.     

Novel Implementation and Assessment of a Digital Filter Based Approach for the Generation of LES Inlet Conditions

A novel implementation of a digital filter based inlet condition generator for Large Eddy Simulation (LES) is presented. The effect of using spatially varying turbulence scales as inputs is investigated; it is found that this has impact on both accuracy and affordability, and has prompted the algorithm implementation changes described in the paper. LES of a channel flow with a periodically repeating constriction was used as a test case. The accuracy of the present simulation using a streamwise periodic boundary condition (PBC) was first established by comparison with a previously published highly resolved LES study. Post-processed statistics from the PBC simulation were then input into a Digital Filter Generator (DFG) algorithm. Three time series were created using the DFG for subsequent use as LES inlet conditions. In the first, as well as inputting the spatially varying first and second moments of the velocity field over the inlet plane from the PBC simulation, the turbulence scales input into the DFG were chosen to be spatially uniform with values specified by an area weighted average across the channel inlet height. In the second and third time-series, the turbulence scales were allowed to change in the wall normal direction, their variation again being deduced from the PBC simulation. These various time series were then used as inlet boundary conditions for LES prediction of the same flow case. Analysis of the results and comparison to the PBC predictions showed that the use of spatially varying turbulence scales increased the accuracy of the simulation in some important areas. However, the cost of generating unsteady inlet conditions using the DFG approach increased significantly with the use of spatially varying turbulence scales. Consequently, a new technique applied as part of the DFG approach is described (used as an ‘on the fly’ method), which significantly reduces the cost of generating LES inlet conditions, even when spatially non-uniform turbulent scales are used.     

A stress transport equation model for simulating turbulence at any mesh resolution

Prior work has demonstrated the effectiveness of using two-equation closures as the basis for universal, self-adapting turbulence models that are effective at any mesh resolution (Perot and Gadebusch in Phys. Fluids 19:115105, 2007). In order to demonstrate the broad applicability of the fundamental approach, the same behavior is now demonstrated for a second-moment closure (SMC). The SMC has the advantage over the earlier two-equation universal closure of being more accurate in the coarse mesh limit and of having a natural mechanism for backscattering energy from the modeled to the resolved turbulent fluctuations. The mathematical explanation for why Reynolds averaged (RANS) transport equation closures are applicable at any mesh resolution, including the large eddy simulation (LES) regime, is reviewed. It is demonstrated that for the problem of isotropic decaying turbulence, the SMC model produces good predictions at any mesh resolution and with arbitrary initial conditions. In addition, it is shown that the proposed model automatically adapts to the mesh resolution provided. The self-adaptive nature of the method is clearly observed when different initial conditions are used. It is shown that classic RANS models (often thought to produce steady and smooth solutions) can produce three-dimensional, unsteady, and chaotic solutions when generalized correctly and when provided with sufficient mesh resolution. The implications of these observations on the fundamental theories of RANS and LES turbulence modeling are discussed.      

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.