Large Eddy Simulation Of Flow Research Articles

Transient energy transfer and cascade analysis for stratified turbulent channel flows

A comprehensive and fine-grained transient analysis of the kinetic budget equation in the spectral and spatial domains for channel flow subjected to stable stratification is performed, through a series of large eddy simulations (LES) at a bulk Reynolds number of 2200 and for Froude numbers of 0.5, 2.0, 4.5 and 6.8, thereby covering a range of stratification strengths from high to low. The dynamic Smagorinsky eddy viscosity-based sub-grid scale (SGS) model is used for closure. Validation of the methodology is carried out by comparing the turbulent flow LES results to previously published channel flow results. The analysis is focussed on the effect of stratification on the energy cascade process of an initially turbulent flow in a channel configuration. The terms in the kinetic budget equation, in the homogeneous and inhomogeneous directions, are compared for different Froude numbers to assess the effects of weak and strong stratification on turbulent statistics. Transient results are plotted to highlight the role played by different terms in the budget equation and to understand the formation of the gravity waves in the core or outer regions of the wall-bounded flow in the presence of stratification. The energy cascade reveals some interesting observations about the functions of viscous diffusion, pressure diffusion, and inhomogeneous energy transfer in the initial phase of the development of flow, which in turn helps to explain the stationary waves observed in the presence of strong stratification.

Influence of LES Inflow Conditions on Simulations of a Piloted Diffusion Flame

This study investigates the influence of different turbulent inflow conditions on the Large Eddy Simulation (LES) of turbulent combustion problems. Four turbulent inflow conditions are studied, including two Synthetic turbulence methods (White Noise and Random Spot), and two Precursor simulation methods (Library and Library-Rescale). The simulation results are compared with experimental measurements. While the White Noise method yields a longer flame with poor agreement against experiments, the Random Spot method has good predictions initially but overpredicts turbulent fluctuations downstream. The results obtained by the Library and Library-Rescale methods are similar, and the discrepancies mainly lie in the region around the centerline. By rescaling the turbulent inlet library to match the experimental profiles, the Library Rescale method improves the prediction of turbulence fluctuations near the nozzle. The present study shows the pronounced sensitivity of LES accuracy in turbulent jet flames to the choice of turbulent inflow conditions.

Large-Eddy Simulations of Flow over a Backward-Facing Ramp with a Wall-Mounted Cube

Passive flow control devices, such as vortex generators (VGs), can effectively modulate the turbulent boundary layer flow near regions of adverse pressure gradients, but the interactions between the salient flow structures produced by VGs and those of the separated flow are not fully understood. In this study, a spatially evolving turbulent boundary layer interacting with a wall-mounted cube ahead of a backward-facing ramp is investigated using wall-resolved large-eddy simulations for a Reynolds number of 19,600, based on the inlet boundary layer thickness and freestream velocity. Different cube configurations are examined to isolate the effects of cube height and streamwise position. The large counter-rotating flow produced by the larger cubes generated more turbulent kinetic energy, thereby resulting in smaller separated regions over the ramp. Although significantly lower levels of turbulent kinetic energy dissipation than production are observed in the outer flow regions of the horseshoe vortex and in the induced counter-rotating flow, the spatial distribution of dissipation is similar to that of the turbulent kinetic energy. When the upstream position of an isolated single cube, relative to the leading ramp edge, is more than three cube heights, the streamwise decay of the counter-rotating flow results in lower levels of turbulent kinetic energy.

A-priori evaluation of data-driven models for large-eddy simulations in Rayleigh–Bénard convection

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. The models’ development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh–Bénard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L2 norm of the grid cell ΔL2 as the length scale, demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scale for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths.

Large eddy simulation of flow over a circular cylinder with a neural-network-based subgrid-scale model

A neural-network-based large eddy simulation is performed for flow over a circular cylinder. To predict the subgrid-scale (SGS) stresses, we train two fully connected neural network (FCNN) architectures with and without fusing information from two separate single-frame networks (FU and nFU, respectively), where the input variable is either the strain rate (SR) or the velocity gradient (VG). As the input variables, only the grid-filtered variables are considered for the SGS models of G-SR and G-VG, and both the grid- and test-filtered variables are considered for the SGS models of T-SR and T-VG. The training data are the filtered direct numerical simulation (fDNS) data at $Re_d=3900$ based on the free-stream velocity and cylinder diameter. Using the same grid resolution as that of the training data, the performances of G-SR and G-VG (grid-filtered inputs) and T-SR-FU and T-VG-FU (grid- and test-filtered inputs with fusion) are better than those of the dynamic Smagorinsky model and T-SR-nFU and T-VG-nFU (grid- and test-filtered inputs without fusion). These FCNN-based SGS models are applied to untrained flows having different grid resolutions from that of training data. Although the performances of G-SR and G-VG are degraded, T-SR-FU and T-VG-FU still provide good performances. Finally, T-SR-FU and T-VG-FU trained at $Re_d = 3900$ are applied to higher-Reynolds-number flows ( $Re_d = 5000$ and 10 000) and their results are also in good agreements with those of fDNS and previous experiment, indicating that adding the test-filtered variables and fusion increases the prediction capability even for untrained Reynolds number flows.

Swing and reverse swing of a cricket ball: laminar separation bubble, secondary vortex and wing-tip-like vortices

Large eddy simulation of flow past a cricket ball with its seam at $30^\circ$ to the free stream is carried out for $5 \times 10^4 \le Re \le 4.5 \times 10^5$ . Three regimes of flow are identified on the basis of the time-averaged swing force coefficient ( $\bar {C}_Z$ ) – no swing (NS), conventional swing (CS, $\bar {C}_Z>0$ ) and reverse swing (RS, $\bar {C}_Z<0$ ). The effect of seam on the boundary layer is investigated. Contrary to the popular belief, the boundary layer does not transition to a turbulent state in the initial stages of CS. The seam energizes the laminar boundary layer and delays its separation. The delay is significantly larger in a region near the poles, whose extent increases with an increase in $Re$ causing $\bar {C}_Z$ to increase. Here $\bar {C}_Z$ assumes a near constant value in the later stage of CS. The boundary layer transitions to a turbulent state via formation of a laminar separation bubble (LSB) in the equatorial region and directly, without a LSB, in the polar region. The extent of the LSB shrinks while the region of direct transition near the poles increases with an increase in $Re$ . A LSB forms on the non-seam side of the ball in the RS regime. A secondary vortex is observed in the wake bubble. While it exists on the non-seam side for the entire range of $Re$ considered, the mixing in the flow introduced by the seam causes it to disappear beyond a certain $Re$ on the seam side. The pressure difference between the seam and non-seam sides sets up wing-tip-like vortices. Their polarity reverses with the switch from the CS to RS regime.

Assessment of Machine Learning Wall Modeling Approaches for Large Eddy Simulation of Gas Turbine Film Cooling Flows: An a Priori Study

Abstract In this work, a priori analysis of machine learning (ML) strategies is carried out with the goal of data-driven wall modeling for large eddy simulation (LES) of gas turbine film cooling flows. High-fidelity flow datasets are extracted from wall-resolved LES (WRLES) of flow over a flat plate interacting with the coolant flow supplied by a single row of 7-7-7 shaped cooling holes inclined at 30 degrees with the flat plate at different blowing ratios (BR). The WRLES are performed using the high-order Nek5000 spectral element computational fluid dynamics (CFD) solver. Light gradient boosting machine (LightGBM) is employed as the ML algorithm for the data-driven wall model. Parametric tests are conducted to systematically assess the influence of a wide range of input flow features (velocity components, velocity gradients, pressure gradients, and fluid properties) on the accuracy of ML wall model with respect to prediction of wall shear stress. In addition, the use of spatial stencil and time delay is also explored within the ML wall modeling framework. It is shown that features associated with gradients of the streamwise and spanwise velocity components have a major impact on the prediction fidelity of wall model, while the effect of gradients of wall-normal velocity component is found to be negligible. Moreover, adding flow feature information from an x-y-z spatial stencil significantly improves the ML model accuracy and generalizability compared to just using local flow features from the matching location. Overall, highest prediction accuracy is achieved when both spatial stencil and time delay features are incorporated within the data-driven wall modeling paradigm.

A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at $Re_\tau = 1000$ and at centreline Mach numbers of $M_c= 0.76$ and $1.5$ are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth–Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at $M_c= 0.25$ with those of reference incompressible DNS data at $Re_\tau = 1000$ and $5200$ . Finally, the proposed wall model is also applied to a turbulent channel flow at $M_c=1.5$ and $Re_\tau =5200$ .

Evolution of clusters of turbulent reattachment due to shear layer instability in flow past a circular cylinder

We perform large eddy simulations of flow past a circular cylinder for the Reynolds number (Re) range, 2×103≤Re≤4×105, spanning subcritical, critical, and supercritical regimes. We investigate the spanwise coherence of the flow in the critical and supercritical regimes using complex networks. In these regimes, the separated flow reattaches to the surface in a turbulent state due to the turbulence generated by the shear layer instability. In the early critical regime, the turbulent reattachment does not occur simultaneously at all span locations. It occurs incoherently along the span in clusters. We treat strong surface pressure fluctuations due to the shear layer instability as extreme events and construct time-varying spatial proximity networks where links are based on synchronization between events. This analysis unravels the underlying complex spatiotemporal dynamics by enabling the estimation of characteristics of clusters of turbulent reattachment via the concept of connected components. In the critical regime, the number and size of the clusters increase with the increase in Re. At higher Re in the supercritical regime, they coalesce to form bigger clusters, resulting in increase in spanwise coherence of turbulent reattachment. We find that the size and number of clusters govern the variation of the time-averaged coefficient of drag (C¯D) in the critical and supercritical regimes. C¯D exhibits power-law distribution with the largest cluster size (C¯D∝S¯CL−25) and the most probable cluster size [C¯D∝E(SC)−25].

Explicit and implicit large eddy simulations of variable-density low-speed flows

The application of the Non-oscillatory Forward-in-Time (NFT) class of solvers to facilitate conventional explicit Large Eddy Simulations (LES) and implicit LES (ILES) of low-speed turbulent flow encompassing substantial local density variations is explored. Schemes solving two different sets of Low Mach Number (LMN) equations are proposed with the aim of capturing variable-density effects arising from either a non-isothermal distribution in single-species flow or compositional variation occurring in a binary-species mixing under isothermal conditions. Both schemes employ the semi-implicit NFT integrators based on the Multidimensional Positive Definite Advection Transport Algorithm and a non-symmetric Krylov subspace solver for the variable-coefficient Poisson problems arising from different treatments applied to the non-zero velocity divergence term in the two sets of the LMN equations. The developments are successfully validated using three diverse test cases, differentially heated cavity flow, non-isothermal free-jets, and a helium plume. The reported simulations show that both the dynamic Smagorinsky model in LES and ILES subgrid-scale treatments yield similar accuracy in capturing turbulent effects for the considered flows.

Large eddy simulations of flow past an inclined circular cylinder: Insights into the three-dimensional effect

The flow past an inclined cylinder is simulated using large eddy simulations to study the three-dimensional wake flow effects on the forces on the cylinder at Re = 3900. Four inclination angles of α = 0°, 30°, 45°, and 60° are considered. The validity of the independence principle (IP) at the four investigated angles is examined. The results suggest that IP can predict the vortex shedding frequency at 0° ≤ α ≤ 60°, while it fails to predict the drag, lift, and pressure coefficients variations because the three-dimensional effect is neglected for IP. A comprehensive analysis is performed to provide insights into the three-dimensional effects on the drag and lift forces caused by α. The flow velocities, the Reynolds stress, and the spanwise characteristic length of the flow structures are discussed in detail. It is found that the recirculation length reaches its maximum at α = 45°, which results in the smallest drag coefficient and lift force amplitudes. The spanwise characteristic lengths of the vortices are similar for all cases, while spanwise traveling patterns are observed only for α > 0°. A force partitioning analysis is performed to quantify the correlations between the forces and the spanwise and cross-spanwise vortices. It reveals that for α = 30°, the drag force becomes dominated by the cross-spanwise vorticity. With the increasing α, the dominant contribution gradually changes from the cross-spanwise to the spanwise vorticity, and the cross-spanwise vorticity contribution to the drag force further becomes negative at α = 60°.

High-Order Implicit Large Eddy Simulation using Entropically Damped Artificial Compressibility

Performing industrial scale incompressible Large Eddy Simulation (LES) remains particularly challenging due to computational cost limitations. Recently, the Entropically Damped Artificial Compressibility (EDAC) method was introduced, which does not require coupled global solves or pseudo-time stepping. Parallel to this, high-order unstructured methods, such as the Flux Reconstruction (FR) approach, have been proposed for Implicit LES (ILES) of compressible turbulent flows. This work presents EDAC with FR as an ILES framework for incompressible flows. Results from a Taylor–Green vortex, turbulent channel flow, and transitional and turbulent flow over an SD7003 airfoil demonstrate the approach is accurate and stable for solutions polynomials of degree ps≤4, while some instabilities were observed beyond this. Higher-order solutions were found to be significantly more accurate than their lower-order counterparts compared to reference direct numerical simulation, and had lower divergence error even with less strict incompressibility factors. These results demonstrate that combining EDAC with FR provides a simple, accurate, efficient, and stable framework for performing ILES of incompressible flows. Additionally, this fully explicit framework does not require coupled solvers, pseudo-time stepping, or explicit subgrid scale models.

A Mapping Model of Propeller RANS and LES Flow Fields Based on Deep Learning Methods

In this work, we propose a deep-learning-based mapping model for simulating and predicting the flow field of Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) of propellers. The model employs image processing and computer vision methods to process the two-dimensional propeller RANS and LES simulation data. First, images are obtained by simulating the flow fields with the location data used to acquire a set of features specific to the corresponding positions. Second, the regression models for the flow fields and the mapping between the two different flow fields are established to predict the LES flow field at that position. Specifically, we utilize a deep convolutional neural network (CNN) for feature extraction from the flow field, which is then integrated with a nonlinear module for the purposes of regression and mapping. The effectiveness and accuracy of the proposed model in flow field prediction are demonstrated by its application to propeller RANS and LES simulations. It is shown that the overall error rate between the LES flow field predictions generated using this method and actual flow field data is 7.92%. Additionally, we also evaluate the model’s generalization ability, stability, and robustness by testing it on the data of propeller flow fields at different Reynolds numbers. The results verify the applicability of the proposed model in various problems of flow field simulation and prediction.

Effects of taper ratio on the aerodynamic forces and flow field of two tandem square cylinders

To explore the influence of taper ratio on aerodynamic characteristics of tandem square cylinders, three-dimensional (3D) large eddy simulations of flow around two tandem square cylinders at the Reynolds number (Re) = 2 × 103 are carried out with a spacing ratio G/D = 4, where G is the cylinder center-to-center distance and D is the cylinder width. Different taper ratios of ξ = 0%, 5%, 10%, and 15% are considered. The influence of taper ratio on aerodynamic coefficient, wind pressure coefficient, mean, and instantaneous flow fields are comprehensively studied. The mechanism of variation in flow fields is revealed, and the mathematical relationship between the taper ratio and aerodynamic characteristics is established, which can provide theoretical reference for design and construction of tandem structures. The results indicate that the taper ratio has significant influence on the mean force coefficient, fluctuating force coefficient, surface mean and fluctuating pressure coefficients, and vortex shedding frequency (fvs). As increase in the taper ratio, the mean force in the along-wind direction, fluctuating force in the across-wind direction, and surface pressure of the two cylinders will be decreased, but the vortex shedding frequency will be increased. The taper ratio has negligible influence on the flow separation location of the upstream cylinder. However, reattachment location of the shear layer moves backward along the leeward surface of the downstream cylinder, and width of the shear layer gradually becomes narrower and closer to surface of the two cylinders. The vortex shedding strength and vortex energy distribution of the two cylinders will be reduced as a result of the narrower shear layer. Meanwhile, coherence and periodicity of the vortex shedding will also be weakened, which results in reduction in the aerodynamic forces and increase in the vortex shedding frequency.

Large-eddy simulation of free-surface turbulent flow in a non-prismatic channel

Abstract Hydraulic engineering applications require a good knowledge of turbulent behaviour in non-prismatic channels. This paper aims to predict turbulent behaviour using large-eddy simulation (LES). The model channel has a warped transition. We perform two-phase LES of free-surface flow and validate the results using experimental data and benchmark solution. We discuss rigorous strategies for model set-up, parameter selection and parametric value assignment, including parameters in spectrum synthesiser (SS) and vortex method (VM) for inlet turbulence. The predicted flow displays complex structures due to eddy motions translated from upstream and locally generated by asymmetrical separation in the transition. The history of the flow dynamics may affect the flow development. The predicted velocity, energy spectrum, root-mean-square error, hit-rate and factor-of-two compare well with measurements and benchmark solution. Mapping mean-velocity distribution from experimental data, combined with SS, gives satisfactory inlet condition; alternatively, a 1/7th power-law for the mean-velocity, combined with VM, is acceptable. This paper uses the Okubo–Weiss parameter to delineate instantaneous coherent structures. The LES methods are reliable, efficient and cost-effective. As compared to the simulation of prismatic channels, the flow dynamics in non-prismatic channels exhibit flow separation and turbulence interactions, which increase the flow-complexity, while offering results with crucial practical applications.

A graphics-accelerated deep neural network approach for turbomachinery flows based on large eddy simulation

In turbomachinery, strongly unsteady rotor–stator interaction triggers complex three-dimensional turbulent flow phenomena such as flow separation and vortex dynamics. Large eddy simulation (LES) is an advanced numerical method that has recently been used to resolve large-scale turbulent motions and model subgrid-scale turbulence in turbomachinery. To largely reduce the computing cost of LES for turbomachinery flow, a graphics processing unit (GPU)-accelerated deep neural network-based flow field prediction approach is explored, which combines convolutional neural network autoencoder (CNN-AE) with long short-term memory (LSTM). CNN-AE extracts spatial features of turbomachinery flow by mapping high-dimensional flow fields into low-dimensional space, while LSTM is used to predict the temporal evolution of fluid dynamics. Automatic mixed precision (AMP) is employed to achieve rapid neural network training using Nvidia GTX 1080 Ti GPU, which shows a significant speedup compared with that without AMP. We evaluated the proposed CNN-AE-LSTM (CAL) method against gated recurrent units (GRU) and simple recurrent network (SRN) on two types of turbomachinery, i.e., centrifugal and axial flow pumps. The results show that the proposed CAL shows better capability of capturing the vortex structure details of turbomachinery. When predicting the temporal vorticity field, the mean square error of CAL results is 0.105%–0.124% for centrifugal pumps and 0.071%–0.072% for axial flow pumps. Meanwhile, the structural similarity index measure of the CAL results is 92.51%–92.77% for centrifugal pumps and 93.81%–94.61% for axial flow pumps. The proposed CAL is noticeably better than GRU and SRN in terms of both mean square error and structural similarity index measure.

Collocated Finite Difference Method in General Coordinates for Simulation of Flow Over Arbitrary Geometry

A finite difference method to be used in simulations of turbulent flows such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) has been developed and verified for basic benchmark flows. The method is constructed using the general curvilinear coordinate system with the collocated grid arrangement of the variables so that it can be easily applied to various engineering flows including hydraulic applications involving complex geometry and moving boundary. The computer code is verified by test calculation of steady laminar internal flow in a curved cavity and an external flow above a curved hill. Furthermore the same code is used to conduct a DNS of fully-developed turbulent flow in a two-dimensional open channel and a LES of flow over curved hill. All results indicate that the method is sound with sufficient accuracy for the intended applications.

Large eddy simulation of flow over a three-dimensional hill with different slope angles

Large eddy simulation of flow over a three-dimensional hill with different slope angles

Numerical study on spray characteristics of liquid jets in supersonic crossflow

The spray characteristics of liquid jets in supersonic crossflow at different injection jet-gas momentum ratios are investigated numerically. The compressible two-phase flow large eddy simulation (LES) method is based on the Eulerian-Lagrangian scheme. The average droplet volume fraction is defined to quantify spray concentration distribution, which can also reflect the oscillation boundary of the spray. The LES predicted the spray boundaries at different injection jet-gas momentum ratios in the central and cross-sectional planes, which agree reasonably well with the experiment. Two sets of counter-rotating vortex pair (CVP) are in the gas-liquid mixing region. As injection momentum ratio q increases, the upper CVP increases. Still, the absolute size of the wall CVP remains almost unchanged, which means that the relative size of the wall CVP to the upper CVP becomes smaller. As q increases, the spray's overall distribution position is generally upward, and the number of droplets entering the near-wall region becomes small. Thus, droplet-wall interactions are weakened. The spray body increases with the increase of q, while the spray foot decreases gradually. In the central plane, the coherent structures near the wall are mainly composed of splashed droplets, and this phenomenon gradually weakens as q increases. Although the increase of q can increase the total droplet mass flow rate, the proportion of the droplet mass flow rate in the near-wall region to the total mass flow rate decreases, and the droplet mass flow rate in the near-wall region decreases.

Toward the use of LES for industrial complex geometries. Part II: Reduce the time-to-solution by using a linearised implicit time advancement

The strong increase in computational power observed during the last few years has allowed to use Large Eddy Simulation (LES) for industrial configurations. Nevertheless, the time-to-solution is still too large for a daily use in the design phases. The objective of this work is to develop a new time integration method to reduce the time-to-solution of LES of incompressible flows by allowing the use of larger time step. The projection method, probably the most commonly used method in the context of LES of incompressible flow, is generally applied using explicit time advancement which constrains the time-step value for stability reasons (CFL and Fourier constraints). The time step can then be small with respect to the physical characteristic times of the studied flow. In this case, an implicit time advancement method, which is unconditionally stable, can be used. However, this leads to non-linear resolution of momentum equation which can strongly increase time-to-solution because of non-linear iterations inside a physical iteration. To relax the stability constraints while minimising the computational cost of an iteration, a linearised implicit time advancement based on Backward Differentiation Formula (BDF) scheme is proposed in this work. The linearisation is performed using an extrapolated velocity field based on the previous fields. This time integration is first evaluated on a turbulent pipe test case. It is observed a time-to-solution up to five times lower than the explicit time integration while keeping the same accuracy in terms of mean and fluctuating velocity fields. To incorporate this new time advancement method in the automatic mesh convergence developed in Part I, a time-step control method based on the local truncation error is used. The resulting automatic time-step and mesh procedure is evaluated on a turbulent round jet case and on PRECCINSTA configuration, a swirl burner which is a representative case of an industrial aeronautical injection system. This new procedure leads to a time-to-solution up to three times lower than the previous procedure, presented in Part I.