A Library for Wall-Modelled Large-Eddy Simulation Based on OpenFOAM Technology

This work presents a feature-rich open-source library for wall-modelled large-eddy simulation (WMLES), which is a turbulence modelling approach that reduces the computational cost of traditional (wall-resolved) LES by introducing special treatment of the inner region of turbulent boundary layers (TBLs). The library is based on OpenFOAM and enhances the general-purpose LES solvers provided by this software with state-of-the-art wall modelling capability. In particular, the included wall models belong to the class of wall-stress models that account for the under-resolved turbulent structures by predicting and enforcing the correct local value of the wall shear stress. A review of this approach is given, followed by a detailed description of the library, discussing its functionality and extensible design. The included wall-stress models are presented, based on both algebraic and ordinary differential equations. To demonstrate the capabilities of the library, it was used for WMLES of turbulent channel flow and the flow over a backward-facing step (BFS). For each flow, a systematic simulation campaign was performed, in order to find a combination of numerical schemes, grid resolution and wall model type that would yield a good predictive accuracy for both the mean velocity field in the outer layer of the TBLs and the mean wall shear stress. The best result was achieved using a mildly dissipative second-order accurate scheme for the convective fluxes applied on an isotropic grid with 27000 cells per $\delta^3$-cube, where $\delta$ is the thickness of the TBL or the half-height of the channel. An algebraic model based on Spalding's law of the wall was found to perform well for both flows. On the other hand, the tested more complicated models, which incorporate the pressure gradient in the wall shear stress prediction, led to less accurate results

Systematic Study of Accuracy of Wall-Modeled Large Eddy Simulation using Uncertainty Quantification Techniques

The predictive accuracy of wall-modeled large eddy simulation is studied by systematic simulation campaigns of turbulent channel flow. The effect of wall model, grid resolution and anisotropy, numerical convective scheme and subgrid-scale modeling is investigated. All of these factors affect the resulting accuracy, and their action is to a large extent intertwined. The wall model is of the wall-stress type, and its sensitivity to location of velocity sampling, as well as law of the wall's parameters is assessed. For efficient exploration of the model parameter space (anisotropic grid resolution and wall model parameter values), generalized polynomial chaos expansions are used to construct metamodels for the responses which are taken to be measures of the predictive error in quantities of interest (QoIs). The QoIs include the mean wall shear stress and profiles of the mean velocity, the turbulent kinetic energy, and the Reynolds shear stress. DNS data is used as reference. Within the tested framework, a particular second-order accurate CFD code (OpenFOAM), the results provide ample support for grid and method parameters recommendations which are proposed in the present paper, and which provide good results for the QoIs. Notably, good results are obtained with a grid with isotropic (cubic) hexahedral cells, with $15\, 000$ cells per $\delta^3$, where $\delta$ is the channel half-height (or thickness of the turbulent boundary layer). The importance of providing enough numerical dissipation to obtain accurate QoIs is demonstrated. The main channel flow case investigated is ${\rm Re}_\tau=5200$, but extension to a wide range of ${\rm Re}$-numbers is considered. Use of other numerical methods and software would likely modify these recommendations, at least slightly, but the proposed framework is fully applicable to investigate this as well

Flow dynamics in the closure region of an internal ship air cavity

Accurate prediction of air leakage is crucial for the design of ship air lubrication systems based on internal cavities. Currently, the flow dynamics that govern the leakage remain largely unexplored, and the goal of this work is to elucidate them by means of numerical simulation. A geometrically simple test cavity is considered, and a simulation of the flow is conducted using large-eddy simulation coupled with a Volume of Fluid interface capturing method. The flow in the closure region is shown to be highly unsteady and turbulent. The cause of this is identified to be the pressure gradient on the beach wall of the cavity, occurring due to the stagnation of the flow. This pressure gradient pushes the air–water interface upwards, making it steeply inclined. As a result, the flow separates from the interface and forms a recirculation zone, in which air and water are mixed by means of overturning waves and turbulent entrainment Swarms of air bubbles leak periodically. Upstream of the closure region, the phase and length of the wave are found to be well-predicted using existing approximations based on linear flow theory. However, for the corresponding prediction of the amplitude of the wave the agreement is worse

Flow dynamics in the closure region of an internal ship air cavity

This work is dedicated to providing a detailed account of the flow dynamics in the closure region of an internal ship air cavity. A geometrically simple multiwave test cavity is considered, and a simulation of the flow is conducted using large-eddy simulation coupled with an algebraic Volume of Fluid interface capturing method. Results reveal that the flow in the closure region is highly unsteady and turbulent. The main cause of this is established to be the pressure gradient occurring due to the stagnation of the flow on the beach wall of the cavity. The pressure gradient leads to a steep incline in the mean location of the air-water interface, which, in turn, leads to the flow separating from it and forming a recirculation zone, in which air and water are mixed. The separated flow becomes turbulent, which further facilitates the mixing and entrainment of air. Swarms of air bubbles leak periodically. Upstream of the closure region, the phase and length of the wave are found to be well-predicted using existing approximations based on linear flow theory. However, for the corresponding prediction of the amplitude of the wave the agreement is worse, with the estimates under-predicting the simulation results

Predictive accuracy of wall-modelled large-eddy simulation on unstructured grids

The predictive accuracy of wall-modelled LES is influenced by a combination of the subgrid model, the wall model, the numerical dissipation induced primarily by the convective numerical scheme, and also by the density and topology of the computational grid. The latter factor is of particular importance for industrial flow problems, where unstructured grids are typically employed due to the necessity to handle complex geometries. Here, a systematic simulation-based study is presented, investigating the effect of grid-cell type on the predictive accuracy of wall-modelled LES in the framework of a general-purpose finite-volume solver. Following standard practice for meshing near-wall regions, it is proposed to use prismatic cells. Three candidate shapes for the base of the prisms are considered: a triangle, a quadrilateral, and an arbitrary polygon. The cell-centre distance is proposed as a metric to determine the spatial resolution of grids with different cell types. The simulation campaign covers two test cases with attached boundary layers: fully-developed turbulent channel flow, and a zero-pressure-gradient flat-plate turbulent boundary layer. A grid construction strategy is employed, which adapts the grid metric to the outer length scale of the boundary layer. The results are compared with DNS data concerning mean wall shear stress and profiles of flow statistics. The principle outcome is that unstructured simulations may provide the same accuracy as simulations on structured orthogonal hexahedral grids. The choice of base shape of the near-wall cells has a significant impact on the computational cost, but in terms of accuracy appears to be a factor of secondary importance

Large-Eddy Simulation of a Classical Hydraulic Jump: Influence of Modelling Parameters on the Predictive Accuracy

Results from large-eddy simulations of a classical hydraulic jump at inlet Froude number two are reported. The computations were performed using the general-purpose finite-volume-based code OpenFOAM\uae, and the primary goal was to evaluate the influence of the modelling parameters on the predictive accuracy, as well as establish the associated best-practice guidelines. A benchmark simulation was conducted on a grid with a 1 mm-cell-edge length to validate the solver and provide a reference solution for the parameter influence study. The remaining simulations covered different selections of the modelling parameters: geometric vs. algebraic interface capturing, three mesh resolution levels, and four choices of the convective flux interpolation scheme. Geometric interface capturing led to better accuracy, but deteriorated the numerical stability and increased the simulation times. Interestingly, numerical dissipation was shown to systematically improve the results, both in terms of accuracy and stability. Strong sensitivity to the grid resolution was observed directly downstream of the toe of the jump

An improved air entrainment model for stepped spillways

Numerical modelling of flow in stepped spillways is considered, focusing on a highly economical approach combining interface capturing with explicit modelling of air entrainment. Simulations are performed on spillways at four different Froude numbers, with flow parameters selected to match available experimental data. First, experiments using the model developed by Lopes et al. (Int. J. Nonlin. Sci. Num., 2017) are conducted. An extensive simulation campaign is used to carefully evaluate the predictive accuracy of the model, the influence of various model parameters, and sensitivity to grid resolution. Results reveal that, at least for the case of stepped spillways, the number of parameters governing the model can be reduced. A crucial identified deficiency of the model is its sensitivity to grid resolution. To improve the performance of the model in this respect, modifications are proposed for the interface detection algorithm and the transport equation for the volume fraction of entrained air. Simulations using the improved model formulation demonstrate better agreement with reference data for all considered flow conditions. A parameter-free criterion for predicting the inception point of air entrainment is also tested. Unfortunately, the accuracy of the considered conventional turbulence models proved to be insufficient for the criterion to work reliably