Large Eddy Simulation Of Turbulent Flow Research Articles

Revisiting the modelling framework for the unresolved scalar variance

The unresolved scalar variance in large-eddy simulations of turbulent flows is a fundamental physical and modelling parameter. Despite its importance, relatively few algebraic models have been developed for this important variable with the most prominent models to date being the classic scale-similarity and gradient models. In this work a new generalized modelling framework based on reconstruction has been developed, which in contrast to classic modelling approaches allows the construction of base static variance models of arbitrary accuracy. It is demonstrated that higher-order reconstructions naturally lead to base static variance models of increased accuracy, and that the classic scale-similarity and gradient models are subsets of more general and higher-order models. The classic scale-similarity assumption for developing dynamic models is also revisited, and it is demonstrated that this can essentially be reinterpreted as a two-level reconstruction approach. Based on this result, a new general methodology is proposed that allows the construction of dynamic models for any given base static model, and a corresponding general reconstruction operator, algebraic or iterative. Consequently, improved static and dynamic models for the scalar variance are developed. The newly developed models are then thoroughly tested a priori using two high-fidelity direct numerical simulation databases corresponding to two substantially different flame and flow configurations, and are shown to outperform classic algebraic models for the variance.

Large-eddy simulations of turbulent flows in arrays of helical- and straight-bladed vertical-axis wind turbines

Effects of helical-shaped blades on the flow characteristics and power production of finite-length wind farms composed of vertical-axis wind turbines (VAWTs) are studied numerically using large-eddy simulation (LES). Two helical-bladed VAWTs (with opposite blade twist angles) are studied against one straight-bladed VAWT in different array configurations with coarse, intermediate, and tight spacings. Statistical analysis of the LES data shows that the helical-bladed VAWTs can improve the mean power production in the fully developed region of the array by about 4.94%–7.33% compared with the corresponding straight-bladed VAWT cases. The helical-bladed VAWTs also cover the azimuth angle more smoothly during the rotation, resulting in about 47.6%–60.1% reduction in the temporal fluctuation of the VAWT power output. Using the helical-bladed VAWTs also reduces the fatigue load on the structure by significantly reducing the spanwise bending moment (relative to the bottom base), which may improve the longevity of the VAWT system to reduce the long-term maintenance cost.

Stochastic Dynamical Modeling of Wind Farm Turbulence

Low-fidelity engineering wake models are often combined with linear superposition laws to predict wake velocities across wind farms under steady atmospheric conditions. While convenient for wind farm planning and long-term performance evaluation, such models are unable to capture the time-varying nature of the waked velocity field, as they are agnostic to the complex aerodynamic interactions among wind turbines and the effects of atmospheric boundary layer turbulence. To account for such effects while remaining amenable to conventional system-theoretic tools for flow estimation and control, we propose a new class of data-enhanced physics-based models for the dynamics of wind farm flow fluctuations. Our approach relies on the predictive capability of the stochastically forced linearized Navier–Stokes equations around static base flow profiles provided by conventional engineering wake models. We identify the stochastic forcing into the linearized dynamics via convex optimization to ensure statistical consistency with higher-fidelity models or experimental measurements while preserving model parsimony. We demonstrate the utility of our approach in completing the statistical signature of wake turbulence in accordance with large-eddy simulations of turbulent flow over a cascade of yawed wind turbines. Our numerical experiments provide insight into the significance of spatially distributed field measurements in recovering the statistical signature of wind farm turbulence and training stochastic linear models for short-term wind forecasting.

Multi-Level Solution Strategies for Implicit Time Discontinuous Galerkin Discretizations

The discontinuous Galerkin method and related flavors of high-order spectral element methods provide many well-known benefits for the spatial discretization of partial differential equations such as the Navier–Stokes equations. However, practical problems of engineering relevance such as large-eddy simulation of turbulent flows over complex geometries are computationally intractable by standard explicit time integration methods, necessitating the use of implicit methods. The efficient solution of the nonlinear algebraic systems arising from implicit time integration methods applied to DG discretizations of nonlinear PDEs is challenging; standard linearization methods result in very stiff block-sparse systems with prohibitive computational and memory requirements. This paper presents a low-memory, computationally efficient, implicit solution method that combines a framework of nonlinear polynomial multigrid, adaptive explicit Runge–Kutta smoothers, implicit Jacobian-free coarse level smoothers, nonlinear Krylov subspace acceleration and adaptive time stepping using feedback control of the nonlinear solver convergence rate.

An efficient model for subgrid-scale velocity enrichment for large-eddy simulations of turbulent flows

In some applications of large-eddy simulation (LES), in addition to providing a closure model for the subgrid-scale stress tensor, it is necessary to also provide means to approximate the subgrid-scale velocity field. In this work, we derive a new model for the subgrid-scale velocity that can be used in such LES applications. The model consists in solving a linearized form of the momentum equation for the subgrid-scale velocity using a truncated Fourier-series approach. Solving within a structured grid of statistically homogeneous sub-domains enables the treatment of inhomogeneous problems. It is shown that the generated subgrid-scale velocity emulates key properties of turbulent flows, such as the right kinetic energy spectrum, realistic strain–rotation relations, and intermittency. The model is also shown to predict the correct inhomogeneous and anisotropic velocity statistics in unbounded flows. The computational costs of the model are still of the same order as the costs of the LES.

Near-wall vortices and thermal simulation of coupled-domain transpiration cooling by a recursive regularized lattice Boltzmann method

The present study aims to reveal the near-wall vortices and the effects of flow states in coupled-domain transpiration cooling using a recursive regularized thermal lattice Boltzmann method (RR-TLBM). Large-eddy simulations of turbulent flow and heat transfer have been conducted on high-resolution computational grids using a desktop-level computer with CUDA 11.6. Results indicate that the near-wall flow structures present spatial characteristics along the streamwise direction. The vortex evolution promotes the downstream heat dissipation, even though turbulence impairs the effective cooling area. The spanwise evolvement of vortices strengthens the mixing of coolant and hot gas, and small-scale structures are beneficial for turbulent heat transfer. Moreover, the transition onset occurs earlier at higher Reynolds numbers, and it weakens the downstream cooling. The cooling performance of the derived coolant film is improved as the Reynolds number varies from 5 × 103 to 3 × 104 with a blowing ratio of F = 10%, whereas the local cooling is impaired at the high Reynolds numbers exceeding 5 × 104. The variation in flow states has little influence on the cooling performance at the Reynolds numbers larger than 3 × 106. On the other hand, our in-house RR-TLBM solver is highly stable and efficient for the simulation of flow and heat transfer with high Reynolds numbers. Simultaneously, a high computational performance of 1127 million lattices updated per second is achieved for our simulation of a coupled-domain turbulent flow and heat transfer, using the desktop-level computer with three Tesla V100 graphics processing units.

Experimental and numerical investigation of flow over spiral grooved cylinders

This study experimentally and numerically investigates the performance of a circular cylinder with a spiral grooved surface in terms of reducing wind drag. Its application in the overhead high-power conductor plays a vital role, especially in typhoon conditions. Wind tunnel tests have shown that at the critical Reynolds number (Re), the coefficients of wind drag decrease to a greater extent in a spiral grooved cylinder than in a smooth circular one. Moreover, a cylinder with a shallow groove and a small number of spirals could reduce the coefficient of drag in typhoon conditions. To gain an insight into the underlying fluid mechanism, a large-eddy simulation of turbulent flow from a critical to a super-critical Re has been carried out to approximate the flow separation and turbulent eddies over the spiral grooved cylinder. The results of the wind tunnel test have been used as a benchmark for the numerical results. The flow characteristics have been established about the near-wall flow separation and far wake flow, the pressure coefficient, the skin-friction coefficient, drag coefficient, and Q-criterion field.

Local dynamic gradient Smagorinsky model for large-eddy simulation

The dynamic Smagorinsky model for large-eddy simulation of turbulent flow is often applied with some kind of spatial averaging to prevent the instability of simulations. This paper demonstrates that the local model constant of the dynamic Smagorinsky model has a singularity if spatial averaging is not applied. The paper identifies the large local values arising from this singularity as a source of numerical instability and proposes an alternative dynamic model without the singularity. This local dynamic model has improved stability and provides good results in simulations of canonical turbulent flows.

Effect of secondary currents on the flow and turbulence in partially filled pipes

Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Large-eddy simulations (LES) are widely used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired coarsening approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for both physical understanding and modelling even in that simple case. For example, an alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Non-uniform resolution can be represented in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. Potential extensions of the theory to more complex physics such as multiphase flows are briefly discussed.

LES of Turbulent Flow through Square Duct with Rounded Corners

In the present study, large eddy simulation (LES) for turbulent flows through square ducts with four rounded corners is performed using immersed boundary (IB) method. The geometrical shape of the duct is determined by an equation |y|α+ |z|α= Rα with a deformation parameter α. The distribution and magnitude of the mean secondary flow with α≧4 is almost close to those of the square-duct case. The center position of secondary circulation flows with α≦4 approaches the square-side bisector in contrast to the square-duct case. The profiles of the Reynolds stress and behaviour of the instantaneous turbulent structures in case of α≧4 are similar with those in square duct case.

Reynolds number effect on statistics of turbulent flows over periodic hills

The wall-resolved large-eddy simulations of turbulent flows over periodic hills are carried out to study the Reynolds number effect on flow statistics. Five different Reynolds numbers ranging from 2800 to 37 000 are considered. The present simulations are validated by comparing the time-averaged flow statistics with those from the literature. The Reynolds number effect is first examined on the skin friction and pressure coefficients, the isosurfaces of p′ and Q criteria, and the vertical profiles of flow statistics. The results show that (1) at most locations the magnitude of friction coefficient decreases with the increase in Reynolds number, while the pressure coefficient varies in the opposite direction; (2) smaller turbulence structures arise at higher Reynolds numbers; and (3) the mean velocities and Reynolds stresses in general exhibit asymptotic behaviors with the increase in Reynolds number. The statistical properties of turbulence structures are further examined via the probability density function and time correlation of velocity fluctuations. At last, the dynamics in the separation bubble is investigated by examining the flow statistics and the budget equation of mean kinetic energy (MKE) on the coordinate with its origin fixed at the recirculation center, and the power spectral density of the velocity fluctuations. Similarities are in general observed for the mean velocities, Reynolds stresses, and the MKE budget in the rear part of the separation bubble. The mean convection term and turbulence convection term are observed playing a key role on the decrease in bubble size with the increase in Reynolds number.

Constrained large-eddy simulation of turbulent flow over rough walls

Structures of wall turbulence due to the mean shear created by the wall are generated. Numerical tests are performed with the rough-wall-like mean shear imposed in the near-wall region without resolving the surface roughness in the constrained large-eddy simulation. The results indicate that the major effects of roughness on wall turbulence can be well reproduced.

Subgrid-scale helicity equation model for large-eddy simulation of turbulent flows

A new one-equation eddy-viscosity model based on subgrid-scale (SGS) helicity is introduced in this paper for large-eddy simulation (LES) of turbulent flows. First, the governing equation of SGS helicity is deduced from the incompressible Navier–Stokes equations, and it reflects the transfer of the small-scale helicity that has been filtered out. We deduce a certain functional relation between the eddy viscosity and SGS helicity based on the kinetic energy and helicity spectra in the homogeneous and isotropic helical turbulence. For improving the accuracy, each unclosed term in the governing equation of SGS helicity is modeled independently, and the coefficients of these unclosed terms are constants or are determined dynamically. The new one-equation eddy-viscosity model is first tested and validated in the simulation of the homogeneous and isotropic helical turbulence. The a priori tests from the direct numerical simulation of forced homogeneous and isotropic turbulence show that the energy and helicity fluxes exhibit scale invariance in the inertial subrange. Additionally, the a posteriori tests demonstrate that the constant-coefficient and dynamic SGS helicity equation models can predict both the energy and helicity spectra more precisely than the common SGS models. For the LES of channel flow, the SGS helicity equation model can accurately predict the mean velocity, the turbulent stress, and the viscous shear stress and supply more abundant flow structures than the compared SGS model under the same grid resolution.

Commutative recursive filters for explicit-filter large-eddy simulation of turbulent flows

A recursive filtering technique is developed to improve the computational efficiency of explicit-filter large-eddy simulation in highly parallelized computational environments. In parallel computations on a partitioned domain, unlike in non-recursive explicit filtering in which the number of ghost cell layers for storing neighbor cell values to ensure communication with neighbor partitions is increased rapidly as the stencil of the filter becomes wider, the present recursive filtering technique requires only a single layer of ghost cells for storing immediate neighbor cell values regardless of the stencil width of the filter. A generalized algorithm for construction of recursive filters with desired filter widths is developed. The computational efficiency of the proposed recursive filtering technique over the conventional non-recursive broad-band filtering techniques in terms of memory usage and computational time is presented.

Large-Eddy Simulation of Turbulent Flow over Wavy Wall with Different Wave Steepness

Large-eddy simulation (LES) with dynamic one-equation subgrid-scale stress model was utilized to study the characteristics of turbulent flow over sea-surface generalized as two-dimensional wavy wall with different wave steepness. The statistical characteristics of turbulent field and pressure distribution were presented in detail. The simulation results showed that the separation zones induce stronger convection as the wave steepness increases. Reynolds shear stress near the wall boundary showed positive correlation with the wave steepness, while in the outer region, time-averaged turbulent fields seemed to be insensitive with the wall boundary. The equivalent velocity profiles obtained from the spatial averaging of the time-averaged velocity indicated that lower velocity occurred as the increase of wave steepness due to the increased pressure-induced form drag. The vortex structures were also visualized and showed vertically-bent characteristics which induced negative Reynolds shear stress at the stoss side as the increase of wave steepness that is equivalent to the effect of wave age.

Constrained large-eddy simulation of turbulent flow over inhomogeneous rough surfaces

In this work we extend the method of the constrained large-eddy simulation (CLES) to simulate the turbulent flow over inhomogeneous rough walls. In the original concept of CLES, the subgrid-scale (SGS) stress is constrained so that the mean part and the fluctuation part of the SGS stress can be modelled separately to improve the accuracy of the simulation result. Here in the simulation of the rough-wall flows, we propose to interpret the extra stress terms in the CLES formulation as the roughness-induced stress so that the roughness inhomogeneity can be incorporated by modifying the formulation of the constrained SGS stress. This is examined with the simulations of the channel flow with the spanwise alternating high/low roughness strips. Then the CLES method is employed to investigate the temporal response of the turbulence to the change of the wall condition from rough to smooth. We demonstrate that the temporal development of the internal boundary layer is just similar to that in a spatial rough-to-smooth transition process, and the spanwise roughness inhomogeneity has little impact on the transition process.

Large-eddy simulation of turbulent flows over an urban building array with the ABLE-LBM and comparison with 3D MRI observed data sets

In this article we describe the details of an ABLE-LBM (Atmospheric Boundary Layer Environment-Lattice Boltzmann Model) validation study for urban building array turbulent flow simulations. The ABLE-LBM large-eddy simulation results were compared with a set of 3D magnetic resonance image (MRI) velocimetry data. The ABLE-LBM simulations used the same building layout and Reynolds numbers operated in the laboratory water channel. The building set-up was an evenly spaced orthogonal array of cubic buildings (height = H) with a central tall building (height = 3H) in the second row. Two building orientations, angled with 0°and 45° wind directions, were simulated with ABLE-LBM. The model produced horizontal and vertical fields of time-averaged velocity fields and compared well with the experimental results. The model also produced urban canyon flows and vortices at front and lee sides and over building tops that were similar in strength and location to the laboratory studies. The turbulent kinetic energy associated with these two wind directions were also presented in this simulation study. It is shown that the building array arrangement, especially the tall building, has a great effect on turbulent wind fields. There is a Karman vortex street on the lee side of the tall building. High turbulent intensity areas are associated with the vortex shedding motions at building edges. In addition, the wind direction is a very important factor for turbulent wind and kinetic energy distribution. This validation study indicated that ABLE-LBM is a viable simulation model for turbulent atmospheric boundary layer flows in the urban building array. The computational speed of ABLE-LBM using the GPU has shown that real-time LES simulation is realizable for a computational domain with several millions grid points.

Large-eddy simulations of turbulent flow in a channel with streamwise periodic constrictions

Abstract

An adaptation of the immersed boundary method for turbulent flows over three-dimensional coastal/fluvial beds

A modification of the immersed boundary method is presented, using the discrete-forcing concept, for the large-eddy simulation of turbulent flows over coastal/fluvial beds. The method was adapted to be compatible with the usual surveying practice to obtain the bathymetry of coastal/fluvial beds, i.e., point measurements of water depth. An efficient fluid/solid point identification process and an improved trilinear interpolation algorithm were implemented for more accurate boundary forcing expressions and easier algorithm implementation. The temporal and spatial discretizations of the filtered Navier–Stokes equations were based on a time-splitting projection scheme and second-order finite-differences, respectively. The method was applied to the simulation of an oscillatory flow over bed ripples and a unidirectional flow over bed dunes. The accuracy of the computational results was verified by comparison to existing numerical and experimental results in the literature.