Large Eddy Simulation Of Turbulent Flow Research Articles

Solvable model in renormalization group analysis for effective eddy viscosity.

This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).

Large-eddy simulation of turbulent flow in a channel with rib roughness

Turbulent flow in a channel with transverse rib roughness on one wall is investigated by large-eddy simulation (LES). The spacing of the roughness elements is varied to reproduce the so-called d- and k-type roughness, and an intermediate roughness between the two. The time–mean and instantaneous flows are analyzed. The LES results agree with the rather limited laboratory observations in flows with rib roughness, and provide new insights into the effects of roughness on the mean flow as well as the turbulence structure. In d-type roughness, the outer flow almost rides over the roughness layer, in the mean, with the separation eddies confined to the gaps between the ribs. For intermediate roughness, between the d-type and k-type, the mean separation region is about the same size as the cavity between the ribs, but the outer flow is affected by large turbulent eddies emanating from the roughness layer. For k-type roughness, separation and reattachment occur between two adjoining ribs, much larger and more frequent eddies are thrown into the outer flow, resulting in strong interaction between the roughness layer and the outer flow. Time and space averaged velocity profiles show the well-known downward shift of the semi-logarithmic portion of the law of the wall. This result is quite surprising in view of the grossly varying spatial structure of the instantaneous flow.

Suboptimal feedback control of turbulent flow over a backward-facing step

The objective of the present numerical study is to increase mixing in turbulent flow behind a backward-facing step using a systematic feedback control method. Spatially and temporally varying blowing and suction with zero-net mass flow rate are provided at the step edge, based on the sensing of the spanwise distribution of the wall pressure fluctuations at a downstream location. The cost functional to be increased is the root-mean-square spanwise pressure-gradient fluctuations at the sensing location, which may be associated with mixing behind the backward-facing step. Given the cost functional, the actuation at the step edge is determined through the suboptimal feedback control procedure of Choi et al. (1993). Large-eddy simulations of turbulent flow are conducted at a Reynolds number of 5100 based on the step height and free-stream velocity. The results of suboptimal feedback controls are compared with those of non-feedback single-frequency actuations. In case of the suboptimal control, velocity and vorticity fluctuations substantially increase downstream of the backward-facing step as well as in the recirculation zone. As a result, the reattachment length is significantly reduced, as compared to those of uncontrolled flow and flow with single-frequency actuations. A simple open-loop control method is devised from the suboptimal feedback control result, producing nearly the same mixing enhancement as the feedback control.

A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids

A second-order-accurate finite difference discretization of the incompressible Navier–Stokes is presented that discretely conserves mass, momentum, and kinetic energy (in the inviscid limit) in space and time. The method is thus completely free of numerical dissipation and potentially well suited to the direct numerical simulation or large-eddy simulation of turbulent flow. The method uses a staggered arrangement of velocity and pressure on a structured Cartesian grid and retains its discrete conservation properties for both uniform and nonuniform gird spacing. The predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids. The capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of H. Choi and P. Moin (1994, J. Comput. Phys.113, 1), where the effect of computational time step on the computed turbulence was investigated. The present fully conservative scheme achieved turbulent flow solutions over the entire range of computational time steps investigated (Δt+=Δtu2τ/ν=0.4 to 5.0). Little variation in statistical turbulence quantities was observed up to Δt+=1.6. The present results differ significantly from those reported by Choi and Moin, who observed significant discrepancies in the turbulence statistics above Δt+=0.4 and the complete laminarization of the flow at and above Δt+=1.6.

Large-eddy simulation of the turbulent flow through a heated square duct

Large-eddy simulations of a compressible turbulent square duct flow at low Mach number are described. First, we consider the isothermal case with all the walls at the same temperature: good agreement with previous incompressible DNS and LES results is obtained both for the statistical quantities and for the turbulent structures. A heated duct with a higher temperature prescribed at one wall is then considered and the intensity of the heating is varied widely. The increase of the viscosity with temperature in the vicinity of the heated wall turns out to play a major rôle. We observe an amplification of the near-wall secondary flows, a decrease of the turbulent fluctuations in the near-wall region and, conversely, their enhancement in the outer wall region. The increase of the viscous thickness with heating implies a significant augmentation of the size of the characteristic flow structures such as the low- and high-speed streaks, the ejections and the quasi-longitudinal vorticity structures. For strong enough heating, the size limitation imposed by the lateral walls leads to a single low-speed streak located near the duct central plane surrounded by two high-speed streaks on both sides. Violent ejections of slow and hot fluid from the heated wall are observed, linked with the central low-speed streak. A selective statistical sampling of the most violent ejection events reveals that the entrainment of cold fluid, originated from the duct core, at the base of the ejection and its subsequent expansion amplifies the ejection intensity.

Large-eddy simulations of turbulent flow in a rotating square duct

The turbulent flow at low Reynolds numbers in a rotating straight square duct was simulated using the large-eddy simulation technique. The rotation axis is parallel to two opposite walls of the duct, and the pressure-driven flow is assumed to be fully developed, isothermal and incompressible. The Reynolds number based on the friction velocity (Reτ=300) was kept constant in the range of the rotational numbers studied (0⩽Roτ⩽1.5) Computations were carried out using a second-order finite volume code with a localized one-equation dynamic subgrid scale model. Simulations of rotating channel flows were initially carried out and were seen to be in agreement with experiments and direct numerical simulations reported in the literature. The study of the flow in a rotating square duct revealed the influence of the Coriolis force on the spatial distribution of the average velocity fields and Reynolds stresses. At low rotation rates, turbulence-driven secondary flows developed near the corners convect the rotation-generated cross-stream currents. At moderate and high rotation rates, the mean secondary flow structure consists essentially of two large counter-rotating cells convecting low/high momentum fluid from the stable/unstable side to the unstable/stable side. Inspection of the terms of the transport equations of the average axial velocity and vorticity components shows the mechanisms responsible for the changes in the average flow structure. Spatial distributions of the Reynolds stresses are mainly influenced by the changes that rotation induces in the main strain rates. It has been found that, globally, at the low Reynolds number studied, rotation tends to significantly reduce the overall turbulence level of the flow.

A vortex-based model for the subgrid flux of a passive scalar

A model for the flux of a passive scalar by the subgrid motions in the large-eddy simulation of turbulent flow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar field by an elemental subgrid vortex. This gives a tensor gradient-diffusion expression for the local flux of the scalar with subgrid turbulent diffusivity which depends upon the subgrid energy, the local cell size, and the vortex orientation in space. The scalar-flux subgrid model is tested by comparison of the results of 323 large-eddy simulation of passive-scalar transport by forced isotropic turbulence in the presence of a mean scalar gradient, with the direct-numerical simulation results of Overholt and Pope [Phys. Fluids 8, 2128 (1996)]. The present large-eddy simulation results predict that at large Taylor–Reynolds numbers, the ratio of the scalar variance to the squared product of the scalar gradient with the dissipation length of the turbulence, is asymptotic to a nearly constant value c′2/(α1 Lε)2≈0.36.

A parallel, finite-volume algorithm for large-eddy simulation of turbulent flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting (FDS), and second-order MacCormack time marching. A systematic and consistent means of evaluating the surface and volume integrals of the control volume is described. Parallel implementation is done using the message-passing programming model. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. For the first time, a finite volume method with Roe FDS was used for LES of turbulent flow in a square duct, and the effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe FDS adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3–5% of the standard Roe FDS dissipation is needed.

Large-Eddy Simulations: Where Are We and What Can We Expect?

Recent subgrid models for large-eddy simulations of turbulent flows are evaluated, particularly the dynamic-Smagorinsky combination, with emphasis on identifying the reasons for their success and the limits of their applicability. The argument is made that they reproduce the turbulent dissipation relatively well, but their main advantage is that they are robust to errors in that they have a built-in mechanism to adjust the dissipation without substantially modifying the larger scales. The question of the stresses is considered next. It is found that it is an intrinsic property of subgrid models that the stresses are essentially unpredictable, and the models considered are indeed found not to reproduce them correctly, even on the average. In particular, the stress-strain correlation is low in real turbulence, and because eddy viscosity models assume that both are proportional, they always result in either the wrong energy spectrum or the wrong stresses. This is confirmed by simulations of shear flows, where it is shown that the error of the mean flow can only be made small if the subgrid stresses are negligible. Stresses are however large-scale quantities that are carried by the resolved scales if the resolution is fine enough

Large-eddy simulation of turbulent flow over a two-dimensional cavity with temperature fluctuations

Large-eddy simulation of turbulent flow over a plane free cavity and over a plane symmetric cavity was performed. The Smagorinsky sub-grid scale turbulence model was used. The compressible formulation and the MacComarck finite volume method were employed. The dynamic and thermal behavior of a thermal capacitor were analyzed. This behavior presents strong dependence on the geometry and the temperature fluctuation frequency which is imposed in the entrance of capacitor and a little dependence on the Reynolds Number.

A new dynamic two-parameter mixed model for large-eddy simulation

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

Suitability of Upwind-Biased Finite Difference Schemes for Large-Eddy Simulation of Turbulent Flows

We have simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization. Detailed comparisons of turbulence statistics and energy spectra in the downstream wake region (7.0 < x/D < 10.0) have been made with the results of Beaudan and Moin and with experiments to assess the impact of numerical diffusion on the flowfield. Based on these comparisons, conclusions are drawn on the suitability of higher-order upwind schemes for LES in complex geometries.

Stability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows

Stability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows

Large-Eddy Simulation of Turbulent Flow in a Curved Pipe

In this paper, we use Large-Eddy Simulation (LES) to compute a fully-developed turbulent flow in a curved pipe. The results allow us to study how the curvature influences the mean velocity profile and also various turbulent statistics. We find reasonable agreement with the few experiments that are available. Our simulation also allows a detailed study of secondary motion in the cross section of the pipe which are caused by the centrifugal acceleration due to the pipe curvature. It is known that this secondary motion may consist of one, two, or three circulation cells. In our simulation results we find one circulation cell.

Large-eddy simulations of turbulent flow with heat transfer in simple and complex geometries using Harwell-FLOW3D

Large-eddy simulation (LES) results are presented and discussed for the turbulent flow with heat transfer in different geometrical configurations, including a plane channel, a channel bearing transverse square ribs on one of the walls, and a crossed-corrugated air heater. They were obtained using the computational fluid dynamics (CFD) code Harwell-FLOW3D (Release 2), finite-volume grids having up to 42 3 nodes, and the Smagorinsky subgrid model with several variants regarding near-wall damping and wall boundary conditions. The first problem (plane turbulent Poiseuille flow with heat transfer) was mainly used as a benchmark to investigate the influence of numerical methods (pressure-velocity coupling algorithm, discretization scheme for the advection terms, time stepping and value of the time step, number of grid points) and modelling options (magnitude of the Smagorinsky constant, near-wall damping, form of the wall boundary conditions, subgrid Prandtl number) against experimental data and literature LES-direct simulation (DS) results. The two problems in complex geometries were studied with the main purpose of testing the potentialities of LES as a predictive tool of engineering and industrial interest when coupled with a powerful general-purpose CFD code.

A dynamic localization model for large-eddy simulation of turbulent flows

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A dynamic localization model for large-eddy simulation of turbulent flows

In a previous paper, Germano, et al. (1991) proposed a method for computing coefficients of subgrid-scale eddy viscosity models as a function of space and time. This procedure has the distinct advantage of being self-calibrating and requires no a priori specification of model coefficients or the use of wall damping functions. However, the original formulation contained some mathematical inconsistencies that limited the utility of the model. In particular, the applicability of the model was restricted to flows that are statistically homogeneous in at least one direction. These inconsistencies and limitations are discussed and a new formulation that rectifies them is proposed. The new formulation leads to an integral equation whose solution yields the model coefficient as a function of position and time. The method can be applied to general inhomogeneous flows and does not suffer from the mathematical inconsistencies inherent in the previous formulation. The model has been tested in isotropic turbulence and in the flow over a backward-facing step.

A spatiotemporal decomposition of a fully inhomogeneous turbulent flow field

The three-dimensional orthogonal spatial modes and their temporal counterparts have been extracted from a large-eddy simulation of turbulent flow over a surface-mounted cube, using a space-time symmetric version of proper orthogonal decomposition (POD), proposed by Aubry et al. (1991). A relatively small domain of interest, located immediately above the top face of the flow obstacle, has been selected for the application of POD. Within that volume of interest, time records of the velocity field have been sampled at 6000 locations simultaneously. The space-time duality of POD can be demonstrated by deriving two alternative eigenvalue problems for either the orthogonal spatial modes or the orthogonal temporal modes. For a particular case, the choice between the two alternatives can be done on the basis of computational convenience and of data-storage requirements. The results show that the first spatiotemporal mode can be identified with the mean flow. The second spatiotemporal mode is dominated by the alternating vortex shedding from the side edges of the flow obstacle. A Fourier analysis of the second temporal mode leads to a Strouhal number of S=0.125 which corresponds to the measured Strouhal number for the vortex shedding (Martinuzzi, 1992). The third and the fourth spatiotemporal modes are connected with the rolls created at the horizontal leading edge of the cube. For the flow field investigated, the dual space-time point of view of POD is rather realistic in the sense that the first four spatiotemporal modes can actually be observed in the flow.

Large-eddy simulation of turbulent flow above and within a forest

A large-eddy simulation has been performed of an atmospheric surface layer in which the lower third of the domain is occupied by a drag layer and heat sources to represent a forest. Subgridscale processes are treated using second-order closure techniques. Lateral boundaries are periodic, while the upper boundary is a frictionless fixed lid. Mean vertical profiles of wind velocity derived from the output are realistic in their shape and response to forest density. Similarly, vertical profiles of Reynolds stress, turbulent kinetic energy and velocity skewness match observations, at least in a qualitative sense. The limited vertical extent of the domain and the artificial upper boundary, however, cause some departures from measured turbulence profiles in real forests. Instantaneous turbulent velocity and scalar fields are presented which show some of the features obtained by tower instrumentation in the field and in wind tunnels, such as the vertical coherence of vertical velocity and the slope of structures revealed by temperature patterns.

Turbulence: the filtering approach

Explicit or implicit filtered representations of chaotic fields like spectral cut-offs or numerical discretizations are commonly used in the study of turbulence and particularly in the so-called large-eddy simulations. Peculiar to these representations is that they are produced by different filtering operators at different levels of resolution, and they can be hierarchically organized in terms of a characteristic parameter like a grid length or a spectral truncation mode. Unfortunately, in the case of a general implicit or explicit filtering operator the Reynolds rules of the mean are no longer valid, and the classical analysis of the turbulence in terms of mean values and fluctuations is not so simple.In this paper a new operatorial approach to the study of turbulence based on the general algebraic properties of the filtered representations of a turbulence field at different levels is presented. The main results of this analysis are the averaging invariance of the filtered Navier—Stokes equations in terms of the generalized central moments, and an algebraic identity that relates the turbulent stresses at different levels. The statistical approach uses the idea of a decomposition in mean values and fluctuations, and the original turbulent field is seen as the sum of different contributions. On the other hand this operatorial approach is based on the comparison of different representations of the turbulent field at different levels, and, in the opinion of the author, it is particularly fitted to study the similarity between the turbulence at different filtering levels. The best field of application of this approach is the numerical large-eddy simulation of turbulent flows where the large scale of the turbulent field is captured and the residual small scale is modelled. It is natural to define and to extract from the resolved field the resolved turbulence and to use the information that it contains to adapt the subgrid model to the real turbulent field. Following these ideas the application of this approach to the large-eddy simulation of the turbulent flow has been produced (Germano et al. 1991). It consists in a dynamic subgrid-scale eddy viscosity model that samples the resolved scale and uses this information to adjust locally the Smagorinsky constant to the local turbulence.