Standard Large Eddy Simulation Research Articles

A super-grid approach for LES combustion closure using the Linear Eddy Model

LES–LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level ‘super-grid’ comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection–reaction–diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed ‘super-grid LEM’ or ‘SG-LEM’. The paper describes LEM reaction–diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES–LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES–LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.

A parameter-free LES model for anisotropic mesh adaptivity

Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method is tested using a flow past a sphere test case. The results are compared both qualitatively and quantitatively to results obtained with the standard Smagorinsky model, and demonstrate the better performance of our method with lower computational cost. This allows us to simulate large Reynolds number cases and compare our quantitative results to experimental results found in the literature, emphasising that our method produces good results at reasonable computational cost.

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Numerical Simulation Analysis of Flow Noise Characteristics of Underwater Vehicle

Based on the standard large eddy simulation and k-epsilon model, the steady flow field and navigation flow noise of the underwater vehicle shell are simulated. In this paper, the underwater vehicle model is established by referring to classic SUBOFF model. The standard k-epsilon method is used to study the pressure distribution characteristic, velocity distribution characteristic, and velocity vector distribution characteristic on and around the shell of the underwater vehicle at different speeds. The results indicate that the pressure increases with the increase of the speed and in the bow of the shell is the largest. A large eddy simulation was used to analyze the noise characteristics of sailing flow at different speeds. The results show that the sound pressure level of navigation flow noise is higher in the low-frequency band, and will increase with the increase in speed.

Time-series observation of the effects of kinetic energy conservation error on isotropic and anisotropic steady incompressible turbulence

The purpose of this study was to examine the effects of kinetic energy conservation error on isotropic and anisotropic steady incompressible turbulence fields. Results were obtained from time series of turbulent kinetic energy and static pressure fluctuation. A standard large-eddy simulation (LES) was used in the numerical analysis. The conservation error was generated using the Crank-Nicolson method. The result obtained using the fourth-order Runge-Kutta method was used to set results of reference. The effects of the conservation error on the mean value of the global turbulent kinetic energy were found to be small. On the other hand, it was found that the time series and mean values of static pressure fluctuation root mean square (rms) were sensitive to the conservation error. This discrepancy in the static pressure fluctuation rms was able to be reduced by adjusting the value of the model constant used in the LES. However, this adjusted model constant caused an error in the global turbulent kinetic energy. These results were found in both isotropic and anisotropic turbulence fields.

Quantification and mitigation of PIV bias errors caused by intermittent particle seeding and particle lag by means of large eddy simulations

In the present work, a standard large eddy simulation is combined with tracer particle seeding simulations to investigate the different PIV bias errors introduced by intermittent particle seeding and particle lag. The intermittency effect is caused by evaluating the velocity from tracer particles with inertia in a region where streams mix with different seeding densities. This effect, which is different from the vastly-discussed particle lag, is frequently observed in the literature but scarcely addressed. Here, bias errors in the velocity are analysed in the framework of a turbulent annular gaseous jet weakly confined by low-momentum co-flowing streams. The errors are computed between the gaseous flow velocity, obtained directly from the simulation, and the velocities estimated from synthetic PIV evaluations. Tracer particles with diameters of 0.037, 0.37 and 3.7 µm are introduced into the simulated flow through the jet only, intermediate co-flowing stream only and through both regions. Results quantify the influence of intermittency in the time-averaged velocities and Reynolds stresses when only one of the streams is seeded, even when tracers fulfil the Stokes-number criterion. Additionally, the present work proposes assessing unbiased velocity statistics from large eddy simulations, after validation of biased seeded simulations with biased PIV measurements. The approach can potentially be applied to a variety of flows and geometries, mitigating the bias errors.

Towards DES/DDES computation of the flow field and heat transfer adopting elliptic relaxation and local correlation based transition approaches

As Large–Eddy Simulation (LES) shall remain too expensive in the following few decades for the ever increasing number of engineering complexities, researches have shifted much of the attention and effort to hybrid formulations incorporating Reynolds–Averaged Navier– Stokes (RANS) equations and LES in a certain ways. The long term goal of this research activity is to develop accurate hybrid RANS/LES methods. These approaches are particularly appealing in massively separated flows since they offer good prediction performance and they can be considered a good trade–off, in terms of computational resources, if compared with standard LES techniques. In particular with this work we want to deeply investigate Detached–Eddy Simulation (DES) based on: (i) elliptic relaxation turbulence model; (ii) Spalart Allmaras local correlation based transition model (LCTM). Specifically, we analyze v2–f DES approach for the convective heat transfer around a sphere at Re = 5000 (with Pr = 0.71) and we compare these results with the so called delayed version of the model. At the same time we also investigate the LCTM version of the SA model, in the DES context.

Velocity Field and Scalar Field Measurements of Turbulent Buoyant Round Jets in a Two-Layer Stratified Environment

Results reported in the literature have shown that the turbulence models currently implemented in computational fluid dynamics (CFD) commercial codes (e.g., ANSYS-CFX, STAR-CCM+, and FLUENT) have a tendency to overestimate thermal stratification and underestimate turbulent mixing when buoyancy effects become dominant with respect to momentum effects. Also, standard large eddy simulation models cannot fully capture the behavior of jets interacting with stratified environments because the assumption of turbulence isotropy of the smaller scales breaks down. Because of light diffraction and image distortion, it is challenging to apply nonintrusive optical flow measurements, like particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), to get experimental data for CFD validations when there are density variances involved in the flow. However, a refractive index matching (RIM) technique that has been recently developed in our Experimental and Computational Multiphase Flow Laboratory allows us to perform high-resolution measurements of velocity fields and scalar fields for turbulent buoyant jet flow in the presence of density differences as high as 8.6%. To form a fully turbulent round free jet, an experimental facility was designed with a jet nozzle diameter of 2 mm, located at the bottom of a cubic tank with 30-cm side length. The jet flow is established by a servo-engine-driven piston to eliminate possible fluctuations introduced by the motor. A high-fidelity synchronized PIV/PLIF system was utilized in conjunction with RIM to measure the velocity and concentration fields in the self-similar regions of a jet flow with a density difference of 3.16% for aqueous solutions. With Reynolds numbers of 4000 and 10 000, the jet impinging with a two-layer stably stratified environment is compared to the positively buoyant jet with lighter fluid injected into denser surroundings. Detailed quantifications of the measurement uncertainties are also carried out. The experimental results are presented in terms of turbulent statistics and the analysis of jet penetration depths.

An Implicit Algebraic Turbulence Closure Scheme for Atmospheric Boundary Layer Simulation

Abstract Turbulence parameterization plays a critical role in the simulation of many weather regimes. For challenging cases such as the stratocumulus-capped boundary layer (SCBL), traditional schemes can produce unrealistic results even when a fine large-eddy-simulation (LES) resolution is used. Here we present an implicit generalized linear algebraic subfilter-scale model (iGLASS) to better represent unresolved turbulence in the simulation of the atmospheric boundary layer, at both standard LES and so-called terra incognita (TI) resolutions. The latter refers to a range of model resolutions where turbulent eddies are only partially resolved, and therefore the simulated processes are sensitive to the representation of unresolved turbulence. iGLASS is based on the truncated conservation equations of subfilter-scale (SFS) fluxes, but it integrates the full equations of the SFS turbulence kinetic energy and potential energy to retain “memory” of the SFS turbulence. Our evaluations suggest iGLASS can perform significantly better than traditional eddy-diffusivity models and exhibit skills comparable to the dynamic reconstruction model (DRM). For a neutral boundary layer case run at LES resolution, the simulation using iGLASS exhibits a wind profile that reasonably matches the similarity-theory solution. For an SCBL case with 5-m vertical resolution, iGLASS maintains more realistic cloud water profiles and boundary layer structure than traditional schemes. The SCBL case is also tested at TI resolution, and iGLASS also exhibits superior performance. iGLASS permits significant backscatter, whereas traditional models allow forward scatter (diffusion) only. As a physics-based approach, iGLASS appears to be a viable alternative for turbulence parameterization.

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 standard (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. 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, ≈1% error in the above quantities, was achieved for channel flow using a mildly dissipative second-order accurate scheme for the convective fluxes applied on an isotropic grid with 27000 cells per δ3-cube, where δ is the channel half-height. In the case of flow over a BFS, this combination led to the best agreement with experimental data. 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. Program SummaryProgram Title: libWallModelledLESProgram Files doi:http://dx.doi.org/10.17632/m8dnsnp4nd.1Licensing provisions: GPLv3Programming language: C++Nature of problem: Large-eddy simulation (LES) is a scale-resolving turbulence modelling approach providing a high level of predictive accuracy. However, LES of high Reynolds number wall-bounded flows is prohibitively computationally expensive due to the need for resolving the inner region of turbulent boundary layers (TBLs) [1]. This inhibits the application of LES to many industrially relevant flows [2] and prompts for the development of novel modelling techniques that would modify the LES approach in a way that allows it to retain its accuracy (at least away from walls) yet significantly lower its computational cost. Solution method: Wall-modelled LES (WMLES) is an approach that is based on complementing LES with special near-wall modelling that allows to leave the inner layer of TBLs unresolved by the computational grid. Many types of wall models have been proposed [1,3], commonly tested within the framework of in-house research codes. Here, an open-source library implementing several wall models is presented. The library is based on OpenFOAM, which is currently the most widely used general-purpose open-source software for computational fluid dynamics. The developed library can be directly applied to both academic and industrial flow cases, leading to a wider adoption of wall modelling and better understanding of its strengths and limitations.[1] J. Larsson, S. Kawai, J. Bodart, and I. Bermejo-Moreno. Large eddy simulation with modeled wall-stress: recent progress and future directions. Mechanical Engineering Reviews, 3(1):1-23, 2016.[2] J. Slotnick, A. Khodadoust, J. Alonso, D. Darmofal, W. Gropp, E. Lurie, D. Mavriplis. CFD vision 2030 study: A path to revolutionary computational aerosciences, Tech. rep., NASA, 2014.[3] S. T. Bose and G. I. Park. Wall-modeled large-eddy simulation for complex turbulent flows. Annual Review of Fluid Mechanics, 50(1):535–561, 2018.

Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation

Explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation (LES). We use a differential filter, namely the inverse Helmholtz operator, which is readily applied to unstructured meshes. The filter is invertible, which allows the sub-filter scale (SFS) stresses to be exactly reconstructed in terms of the filtered solution. Unlike eddy viscosity models, the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime. The sub-grid scale (SGS) stresses are not recoverable by reconstruction, but the second-order finite element method used here is an adequate source of numerical dissipation in lieu of an SGS model. Results for incompressible turbulent channel flow at Re τ = 180 are presented which show that explicit filtering and exact SFS reconstruction is a significant improvement over the standard LES approach of implicit filtering and eddy-viscosity SGS modelling.

Improving Large-Eddy Simulation of Neutral Boundary Layer Flow across Grid Interfaces

Abstract Increasing computational power has enabled grid resolutions that support large-eddy simulation (LES) of the atmospheric boundary layer. These simulations often use grid nesting or adaptive mesh refinement to refine the grid in regions of interest. LES generates errors at grid refinement interfaces, such as resolved energy accumulation, that may compromise solution accuracy. In this paper, the authors test the ability of two LES formulations and turbulence closures to mitigate errors associated with the use of LES on nonuniform grids for a half-channel approximation to a neutral atmospheric boundary layer simulation. Idealized simulations are used to examine flow across coarse–fine and fine–coarse interfaces, as would occur in a two-way nested configuration or with block structured adaptive mesh refinement. Specifically, explicit filtering of the advection term and the mixed model are compared to a standard LES formulation with an eddy viscosity model. Errors due to grid interfaces are evaluated by comparison to uniform grid solutions. It is found that explicitly filtering the advection term provides significant benefits, in that it allows both mass and momentum to be conserved across grid refinement interfaces. The mixed model reduces unphysical perturbations generated by wave reflection at the interfaces. These results suggest that the choice of LES formulation and turbulence closure can be used to help control grid refinement interface errors in atmospheric boundary layer simulations.

Large eddy simulation using the general circulation modelICON

AbstractICON (ICOsahedral Nonhydrostatic) is a unified modeling system for global numerical weather prediction (NWP) and climate studies. Validation of its dynamical core against a test suite for numerical weather forecasting has been recently published by Zängl et al. (2014). In the present work, an extension of ICON is presented that enables it to perform as a large eddy simulation (LES) model. The details of the implementation of the LES turbulence scheme in ICON are explained and test cases are performed to validate it against two standard LES models. Despite the limitations that ICON inherits from being a unified modeling system, it performs well in capturing the mean flow characteristics and the turbulent statistics of two simulated flow configurations—one being a dry convective boundary layer and the other a cumulus‐topped planetary boundary layer.

A framework for large eddy simulation of Burgers turbulence based upon spatial and temporal statistical information

We present a novel theoretical framework that has the potential not only to improve the reliability and computational efficiency of large-eddy simulation (LES) predictions for turbulent flows but also promises to address a major drawback of many existing constructs of LES, namely, inaccurate predictions for the underlying spatiotemporal structure. In our proposed framework, subgrid models are constructed based upon information that is consistent with the underlying spatiotemporal statistics of the flow. Unlike many pre-existing LES approaches, the proposed subgrid models include non-Markovian memory terms whose origins can be related to the optimal prediction formalism. These optimal subgrid models are studied within the context of the forced Burgers equation. Results indicate that the proposed models perform better than standard LES models by virtue of their ability to better preserve the underlying spatiotemporal statistical structure of the flow. Furthermore, the presence of coarse-grained temporal information in our subgrid models allows for faster simulations (resulting in about an order of magnitude reduction in computational time, in comparison to conventional LES) through the use of larger time steps.

Controlling entrainment in the smoke cloud using level set-based front tracking

Although large-eddy simulation (LES) has been shown to produce a reasonable representation of the turbulent circulations within the stratocumulus-topped boundary layer, it has difficulties to accurately predict cloud-top entrainment rates. In this paper, we present a front-tracking algorithm for LES to untangle the numerical and physical contributions to entrainment. Instead of resolving the cloud-top inversion, we treat it as a discontinuity separating the boundary layer from the free atmosphere and use the level set method to track its location. We apply our method to the smoke cloud test case as presented by Bretherton et al. (1999) which is simpler than stratocumulus in that it is only driven by radiative cooling avoiding evaporative feedbacks on entrainment. We present three-dimensional LES results with and without use of the level set method varying the grid resolution and the flux limiter. With the level set method, we prescribe zero entrainment and use this case to evaluate our method’s ability to maintain a non-entraining smoke-cloud layer. We use an empiricallybased entrainment law to estimate numerical errors. With the level set method, the prescribed entrainment rate was maintained with errors about one order of magnitude smaller than the entrainment errors found in the standard LES. At the same time, the dependence of the entrainment errors on the choice of the limiter was reduced by more than a factor of 10.

Detached Eddy Simulation of Turbulent Flow in Stirred Tank Reactor

The difficulties associated with the use of the standard LES (Large Eddy Simulation) models, particularly in near-wall regions, has lead to the development of hybrid models that attempt to combine the best aspects of RANS (Reynolds Averaged Navier Stokes) and LES methodologies in a single solution strategy. An example of a hybrid technique is the detached-eddy simulation (DES). In this paper, application of DES model is made in the analysis of turbulent flow generated in impeller driven (Rushton Impeller) stirred tank reactor in order to understand the flow behavior especially around the impeller region and near the wall of the tank. The simulated result is compared with Experimental results of Wu and Patterson [1]. DES is found more accurate against the experimental result in predicting the turbulent flow of velocity profile than the LES model which ultimately increases its interest in turbulent flow analysis.

Large Eddy Simulation of Wind Turbine Wakes in Prescribed Neutral and Non-Neutral Atmospheric Boundary Layers

Large eddy simulation (LES) of an infinitely long wind farm in a fully developed flow is carried out based on solution of the incompressible Navier-Stokes equations. The wind turbines are modeled as equivalent rotating actuator disks by applying aerodynamic loads on the flow field using tabulated aerodynamic lift and drag coefficients to save computational time. As a substitute to standard wall modeling LES, a ''prescribed mean shear" profile (hereafter called PMS) approach has been implemented and analysed for generating the desired turbulent shear flow. It is applied on Neutral, Stable and Convective atmospheric boundary layers in presence of the -actuator disc represented- wind turbines and qualitatively meaningful results of mean and fluctuating velocity field is obtained. The effect of four different sub-grid scale (SGS) models on the flow structure is investigated and it is seen that subgrid scale modeling (in particular, the Mix-O and Smagorinsky models) improves the accuracy of the simulations. An optimal grid resolution is also proposed for this kind of simulation.

A New Inlet Boundary Conditon for LES

It is known that the inlet boundary condition is still a problem for tubulence simulation. In this paper a numerical procedure to generate inflow turbulence based on the digital filter technique (Autoregressive Moving Average (ARMA) model) is presented suitable for Large Eddy Simulation (LES) models and validated to realize the inflow turbulence and this approach is adopted to investigate the flow characteristics in the empty domain based on standard and dynamic LES models.

MODELS FOR THE LARGE EDDY SIMULATION EQUATIONS TO DESCRIBE MULTI-SPECIES MIXING OCCURING AT SUPERCRITICAL PRESSURE

An existing database of direct numerical simulations (DNS) representing mixing of species under supercritical pressure (supercritical-ρ) conditions has been investigated for the purpose of understanding the modeling of the gradient of the filtered pressure, the divergence of the filtered heat flux, and the divergence of the filtered species mass flux, all in the context of large eddy simulation (LES). The analysis consists of two separate parts. The activities of all terms appearing in the LES equations are first evaluated, and the dominant terms for each of the transport equations are identified. These data are used to check whether the standard LES assumptions−i.e., that the three above quantities are equal to the gradient of the pressure and the divergences of the fluxes computed from the filtered flow field, respectively−that are routinely used for atmospheric-ρ flows, continue to be valid also in the realm of supercritical-ρ conditions. Having found that these assumptions do not hold under supercritical-ρ conditions, alternative modeling strategies for these terms are proposed, and their accuracy with respect to the standard LES assumptions is assessed.

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.