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

Assessment of uncertainties in hot-wire anemometry and oil-film interferometry measurements for wall-bounded turbulent flows

In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are 0.44%, 0.23% and 0.22%, respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation. Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements

Effect of grid resolution on large eddy simulation of wall-bounded turbulence

The effect of grid resolution on large eddy simulation (LES) of wall-bounded turbulent flow is investigated. A channel flow simulation campaign involving systematic variation of the streamwise ($\Delta x$) and spanwise ($\Delta z$) grid resolution is used for this purpose. The main friction-velocity based Reynolds number investigated is 300. Near the walls, the grid cell size is determined by the frictional scaling, $\Delta x^+$ and $\Delta z^+$, and strongly anisotropic cells, with first $\Delta y^+ \sim 1$, thus aiming for wall-resolving LES. Results are compared to direct numerical simulations (DNS) and several quality measures are investigated, including the error in the predicted mean friction velocity and the error in cross-channel profiles of flow statistics. To reduce the total number of channel flow simulations, techniques from the framework of uncertainty quantification (UQ) are employed. In particular, generalized polynomial chaos expansion (gPCE) is used to create meta models for the errors over the allowed parameter ranges. The differing behavior of the different quality measures is demonstrated and analyzed. It is shown that friction velocity, and profiles of velocity and the Reynolds stress tensor, are most sensitive to $\Delta z^+$, while the error in the turbulent kinetic energy is mostly influenced by $\Delta x^+$. Recommendations for grid resolution requirements are given, together with quantification of the resulting predictive accuracy. The sensitivity of the results to subgrid-scale (SGS) model and varying Reynolds number is also investigated. All simulations are carried out with second-order accurate finite-volume based solver. The choice of numerical methods and SGS model is expected to influence the conclusions, but it is emphasized that the proposed methodology, involving gPCE, can be applied to other modeling approaches as well.Comment: 27 pages, The following article has been accepted by Physics of Fluids. After it is published, it will be found at https://aip.scitation.org/journal/phf. Copyright 2018 Saleh Rezaeiravesh and Mattias Liefvendahl. This article is distributed under a Creative Commons Attribution (CC-BY-NC-ND 4.0) Licens

A Validation Study of Full-Scale CFD Simulation for Sea Trial Performance Prediction of Ships

Shipping is a critical component of global trade but also accounts for a substantial portion of global greenhouse gas emissions. Recognising this issue, the International Maritime Organisation (IMO) has implemented new measures aimed at determining the energy efficiency of all ships and promoting continuous improvements, such as the Energy Efficiency Existing Ship Index (EEXI). As Computational Fluid Dynamics (CFD) can be used to calculate the EEXI value, RISE-SSPA1 and Flowtech have developed a CFD-based method for predicting full-scale ship performance with SHIPFLOW v7.0, which meets the new requirements of IMO. The method is validated through an extensive comparison study that examines the delivered power and propeller rotation rate between full-scale CFD predictions and high-quality sea trials using 14 common cargo ships of varying sizes and types. The comparison between the CFD predictions and 59 sea trials shows that both delivered power and RPM can be predicted with satisfactory accuracy, with an average comparison error of about 4% and 2%, respectively. The numerical methods used in this study differ significantly from the majority of the state-of-the-art CFD codes, highlighting their potential for future applications in ship performance prediction. Thorough validation with a large number of sea trials is essential to establish confidence in CFD-based ship performance prediction methods, which is crucial for the credibility of the EEXI framework and its potential to contribute to shipping decarbonisation

Stability results for viscous shock waves and plane Couette flow

NR 2014080

Wall-Modeled LES for Ship Hydrodynamics in Model Scale

A complete approach for wall-modeled large-eddy simulation (WMLES) is demonstrated for the simulation of the flow around a bulk carrier in the model scale. Essential components of the method are an a-priori estimate of the thickness of the turbulent boundary layer (TBL) over the hull and to use an unstructured grid with the appropriate resolution relative to this thickness. Expressions from the literature for the scaling of the computational cost, in terms of the grid size, with Reynolds number, are adapted in this application. It is shown that WMLES is possible for model scale ship hydrodynamics, with similar to 10(8) grid cells, which is a gain of at least one order of magnitude as compared with wall-resolving LES. For the canonical case of a flat-plate TBL, the effects of wall model parameters and grid cell topology on the predictive accuracy of the method are investigated. For the flat-plate case, WMLES results are compared with results from direct numerical simulation, RANS (Reynolds-averaged Navier-Stokes), and semi-empirical formulas. For the bulk carrier flow, WMLES and RANS are compared, but further validation is needed to assess the predictive accuracy of the approach