Turbulence: the filtering approach

1992 ◽  
Vol 238 ◽  
pp. 325-336 ◽  
Author(s):  
M. Germano
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Small Scale ◽  
Mean Values ◽  
Eddy Simulation ◽  
Turbulent Field ◽  
Large Eddy ◽  
Different Levels

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 Unfortunately, in the case of a general implicit or explicit filtering operator the Reynolds rules of the mean are no longer valid, and the classical analysis of the turbulence in terms of mean values and fluctuations is not so simple.In this paper a new operatorial approach to the study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.

scholarly journals Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

2021 ◽  
Author(s):  
Mohammad Khalid Hossen ◽  
Asokan Mulayath Variyath ◽  
Jahrul M Alam
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Physical Space ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy

In large eddy simulation (LES) of turbulent flows, the most critical dynamical processes to be considered by dynamic subgrid models to account for an average cascade of kinetic energy from the largest to the smallest scales of the flow is not fully clear. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study some essential statistical characteristics of vortex stretching and its role in dynamic approaches of modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. This technique is a single unified approach to studying a wide range of length scales in the turbulent flow. In addition, it also provides a rational basis for the statistical characteristics a subgrid model must serve in physical space to ensure an appropriate cascade of kinetic energy. Results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

scholarly journals Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

Aerospace ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 375
Author(s):  
Mohammad Khalid Hossen ◽  
Asokan Mulayath Variyath ◽  
Jahrul M. Alam
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Joint Probability ◽  
Energy Dissipation Rate ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Individual

In large eddy simulation (LES) of turbulent flows, dynamic subgrid models would account for an average cascade of kinetic energy from the largest to the smallest scales of the flow. Yet, it is unclear which of the most critical dynamical processes can ensure the criterion mentioned above. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study essential statistical characteristics of vortex stretching. Our numerical results demonstrate that vortex stretching rate provides the energy dissipation rate necessary for modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. The individual and the joint probability of vortex stretching and strain amplification show that vortex stretching rate is highly correlated with the energy cascade rate. Sheet-like flow structures are correlated with viscous dissipation, and vortex tubes are more stretched than compressed. The overall results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

On Homogenization-Based Methods for Large-Eddy Simulation

2002 ◽  
Vol 124 (4) ◽  
pp. 892-903 ◽  
Author(s):  
L. Persson ◽  
C. Fureby ◽  
N. Svanstedt
Keyword(s):  
Large Eddy Simulation ◽  
Large Scale ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Practical Importance ◽  
Small Scale ◽  
Homogeneous Material ◽  
Mean Flow ◽  
Eddy Simulation ◽  
Large Eddy

The ability to predict complex engineering flows is limited by the available turbulence models and the present-day computer capacity. In Reynolds averaged numerical simulations (RANS), which is the most prevalent approach today, equations for the mean flow are solved in conjunction with a model for the statistical properties of the turbulence. Considering the limitations of RANS and the desire to study more complex flows, more sophisticated methods are called for. An approach that fulfills these requirements is large-eddy simulation (LES) which attempts to resolve the dynamics of the large-scale flow, while modeling only the effects of the small-scale fluctuations. The limitations of LES are, however, closely tied to the subgrid model, which invariably relies on the use of eddy-viscosity models. Turbulent flows of practical importance involve inherently three-dimensional unsteady features, often subjected to strong inhomogeneous effects and rapid deformation that cannot be captured by isotropic models. As an alternative to the filtering approach fundamental to LES, we here consider the homogenization method, which consists of finding a so-called homogenized problem, i.e. finding a homogeneous “material” whose overall response is close to that of the heterogeneous “material” when the size of the inhomogeneity is small. Here, we develop a homogenization-based LES-model using a multiple-scales expansion technique and taking advantage of the scaling properties of the Navier-Stokes equations. To study the model simulations of forced homogeneous isotropic turbulence and channel flow are carried out, and comparisons are made with LES, direct numerical simulation and experimental data.

scholarly journals Developments in turbulence research: a review based on the 1999 Programme of the Isaac Newton Institute, Cambridge

2001 ◽  
Vol 436 ◽  
pp. 353-391 ◽  
Author(s):  
J. C. R. HUNT ◽  
N. D. SANDHAM ◽  
J. C. VASSILICOS ◽  
B. E. LAUNDER ◽  
P. A. MONKEWITZ ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Small Scale ◽  
Isaac Newton ◽  
Eddy Simulation ◽  
Isaac Newton Institute ◽  
Large Eddy ◽  
Eddy Structures

Recent research is making progress in framing more precisely the basic dynamical and statistical questions about turbulence and in answering them. It is helping both to define the likely limits to current methods for modelling industrial and environmental turbulent flows, and to suggest new approaches to overcome these limitations. Our selective review is based on the themes and new results that emerged from more than 300 presentations during the Programme held in 1999 at the Isaac Newton Institute, Cambridge, UK, and on research reported elsewhere. A general conclusion is that, although turbulence is not a universal state of nature, there are certain statistical measures and kinematic features of the small-scale flow field that occur in most turbulent flows, while the large-scale eddy motions have qualitative similarities within particular types of turbulence defined by the mean flow, initial or boundary conditions, and in some cases, the range of Reynolds numbers involved. The forced transition to turbulence of laminar flows caused by strong external disturbances was shown to be highly dependent on their amplitude, location, and the type of flow. Global and elliptical instabilities explain much of the three-dimensional and sudden nature of the transition phenomena. A review of experimental results shows how the structure of turbulence, especially in shear flows, continues to change as the Reynolds number of the turbulence increases well above about 104 in ways that current numerical simulations cannot reproduce. Studies of the dynamics of small eddy structures and their mutual interactions indicate that there is a set of characteristic mechanisms in which vortices develop (vortex stretching, roll-up of instability sheets, formation of vortex tubes) and another set in which they break up (through instabilities and self- destructive interactions). Numerical simulations and theoretical arguments suggest that these often occur sequentially in randomly occurring cycles. The factors that determine the overall spectrum of turbulence were reviewed. For a narrow distribution of eddy scales, the form of the spectrum can be defined by characteristic forms of individual eddies. However, if the distribution covers a wide range of scales (as in elongated eddies in the ‘wall’ layer of turbulent boundary layers), they collectively determine the spectra (as assumed in classical theory). Mathematical analyses of the Navier–Stokes and Euler equations applied to eddy structures lead to certain limits being defined regarding the tendencies of the vorticity field to become infinitely large locally. Approximate solutions for eigen modes and Fourier components reveal striking features of the temporal, near-wall structure such as bursting, and of the very elongated, spatial spectra of sheared inhomogeneous turbulence; but other kinds of eddy concepts are needed in less structured parts of the turbulence. Renormalized perturbation methods can now calculate consistently, and in good agreement with experiment, the evolution of second- and third-order spectra of homogeneous and isotropic turbulence. The fact that these calculations do not explicitly include high-order moments and extreme events, suggests that they may play a minor role in the basic dynamics. New methods of approximate numerical simulations of the larger scales of turbulence or ‘very large eddy simulation’ (VLES) based on using statistical models for the smaller scales (as is common in meteorological modelling) enable some turbulent flows with a non-local and non-equilibrium structure, such as impinging or convective flows, to be calculated more efficiently than by using large eddy simulation (LES), and more accurately than by using ‘engineering’ models for statistics at a single point. Generally it is shown that where the turbulence in a fluid volume is changing rapidly and is very inhomogeneous there are flows where even the most complex ‘engineering’ Reynolds stress transport models are only satisfactory with some special adaptation; this may entail the use of transport equations for the third moments or non-universal modelling methods designed explicitly for particular types of flow. LES methods may also need flow-specific corrections for accurate modelling of different types of very high Reynolds number turbulent flow including those near rigid surfaces.This paper is dedicated to the memory of George Batchelor who was the inspiration of so much research in turbulence and who died on 30th March 2000. These results were presented at the last fluid mechanics seminar in DAMTP Cambridge that he attended in November 1999.

Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Nagendra Dittakavi ◽  
Aditya Chunekar ◽  
Steven Frankel
Keyword(s):  
Large Eddy Simulation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Vapor Cavity ◽  
Eddy Simulation ◽  
Downstream Region ◽  
Large Eddy ◽  
Venturi Nozzle

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the AUSM+-up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

Large Eddy Simulation of a Free Circular Jet

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Trushar B. Gohil ◽  
Arun K. Saha ◽  
K. Muralidhar
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Experimental Results ◽  
Entrainment Rate ◽  
Smagorinsky Model ◽  
Potential Core ◽  
Eddy Simulation ◽  
Large Eddy

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components u'u'¯, v'v'¯, and u'v'¯ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

Large Eddy Simulation of Turbulent Axial Flow Along an Array of Rods

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
F. Abbasian ◽  
S. D. Yu ◽  
J. Cao
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Axial Flow ◽  
Dominant Frequency ◽  
Turbulence Structure ◽  
Circular Array ◽  
Central Difference ◽  
Eddy Simulation ◽  
Large Eddy

Large eddy simulation (LES) is employed in this paper to model the axial flow along a circular array of rods with a focus on anisotropic large-scale turbulence. The circular array consists of four whole rods and eight half rods, with a pitch-to-diameter ratio of 1.08. A dynamic Smagorinsky model with SIMPLE coupling method and a bounded central difference scheme are used to reduce numerical errors. The high demands for computations of the three-dimensional turbulent flows are afforded through parallel processing and utilization of 20 processors. The numerical results obtained using LES are compared with independent experimental data available in the literature; good agreement is achieved. The LES model was developed to accurately predict (i) the dependence of turbulence intensity and dominant frequency on the gap size and (ii) the turbulence structure in different directions.

WAVELET MULTI-RESOLUTION ANALYSIS ON LARGE-EDDY SIMULATION OF TURBURLENT FLOW BEHIND A VEHICLE EXERNAL MIRROR

2013 ◽  
Vol 11 (04) ◽  
pp. 1360007 ◽  
Author(s):  
A. RINOSHIKA ◽  
Y. ZHENG ◽  
E. SHISHIDO
Keyword(s):  
Large Eddy Simulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Wake Flow ◽  
Small Scale ◽  
Three Dimensional Flow ◽  
Eddy Simulation ◽  
Multi Resolution Analysis ◽  
Large Eddy ◽  
Resolution Analysis

The three-dimensional orthogonal wavelet multi-resolution technique was applied to analyze flow structures of various scales around an externally mounted vehicle mirror. Firstly, the three-dimensional flow of mirror wake was numerically analyzed at a Reynolds number of 105 by using the large-eddy simulation (LES). Then the instantaneous velocity and vorticity were decomposed into the large-, intermediate- and relatively small-scale components by the wavelet multi-resolution technique. It was found that a three-dimensional large-scale vertical vortex dominates the mirror wake flow and makes a main contribution to vorticity concentration. Some intermediate- and relatively small-scale vortices were extracted from the LES and were clearly identifiable.

Large-Eddy Simulation of Turbine Rim Seal Flow

2018 ◽  
Author(s):  
Alexej Pogorelov ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Flow Field ◽  
Large Eddy Simulation ◽  
Level Set ◽  
Large Scale ◽  
Stokes Equations ◽  
Axial Flow ◽  
Dominant Mode ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Impact

The flow field in a complete one-stage axial-flow turbine with 30 stator and 62 rotor blades is investigated by large-eddy simulation (LES). To solve the compressible Navier-Stokes equations, a massively parallelized finite-volume flow solver based on an efficient Cartesian cut-cell/level-set approach, which ensures a strict conservation of mass, momentum and energy, is used. This numerical method contains two adaptive Cartesian meshes, one mesh to track the embedded surface boundaries and a second mesh to resolve the fluid domain and to solve the conservation equations. The overall approach allows large scale simulations of turbomachinery applications with multiple relatively moving boundaries in a single frame of reference. The relative motion of the geometries is described by a kinematic motion level-set interface method. The focus of the numerical analysis is on the flow inside the cavity between the stator and the rotor disks. Full 360° computations of the turbine stage with a single lip rim seal geometry are conducted. First, the impact of the mesh resolution on the LES results is analyzed. Second, the LES results are compared to experimental data, followed by a detailed analysis of the flow field inside the rotor-stator wheel space. A dominant mode unrelated to the rotor frequency and its harmonics is identified, which shows a major impact on the ingress of the hot gas into the rotor-stator wheel space.

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