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.

scholarly journals Enstrophy Cascade and Smagorinsky Model of 2D Turbulent Flows

2001 ◽  
Vol 17 (3) ◽  
pp. 121-129
Author(s):  
Mei-Jiau Huang
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Smagorinsky Model ◽  
Large Wave ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Wave Numbers ◽  
Enstrophy Cascade ◽  
Stretching Effect

ABSTRACTDirect numerical simulations of 2D turbulent flows, freely decaying as well as forced, are performed to examine the mechanism of the enstrophy cascade and serve as a template of developing LES models. The stretching effect on the 2D vorticity gradients is emphasized on the analogy of the stretching effect on 3D vorticity. The enstrophy cascade rate, the Reynolds stresses and the associated eddy viscosity for 2D turbulence are correspondingly derived and investigated. Proposed herein is that the enstrophy cascade rate to be modeled in a large-eddy simulation can be and should be calculated using the only available large-eddy information, especially when the Reynolds number is not very large or when the flow is not stationary.The simulation results suggest all Kolmogorov's, Kraichnan's, and Saffman's similarity spectra. The Kolmogorov's spectrum appears in front of forced wave numbers and creates a subrange of a zero enstrophy cascade rate and a constant energy cascade rate. The Saffman's spectrum is the dissipation spectrum at large wave numbers. Kraichnan's spectrum shows up at intermediate wave numbers when the Reynolds number is sufficiently high. When the Smagorinsky model is employed for a large eddy simulation, its inability of capturing the significant reverse cascade phenomenon as observed in the DNS data becomes a fatal defect. Nonetheless, if only the mean cascade rate is concerned, the required Smagorinsky constant is evaluated using the DNS data and compared with the theoretical prediction of the Kraichnan's spectrum.

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.

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.

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

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.

An Anisotropic Subgrid Model for Large Eddy Simulation of Wall Bounded Turbulent Flows

2007 ◽  
Author(s):  
Sachin S. Badarayani ◽  
Kyle D. Squires
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Velocity Profile ◽  
Turbulent Flows ◽  
Model Parameters ◽  
Wall Region ◽  
Outer Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Near Wall

Large Eddy Simulation (LES) of high-Reynolds-number wall-bounded turbulent flows is prohibitively expensive if the energy-containing eddies in the near-wall region are resolved. This motivates the use of wall-layer models in which an approximate solution of the near wall dynamics is bridged to an LES of the outer flow. The main interest of the present work are wall-modeling strategies based on Detached Eddy Simulation (DES). In these approaches, the near-wall solution is closed using a Reynolds-averaged Navier Stokes model with a subgrid closure applied to the outer flow. As is well known, the original DES formulation applied directly as a wall model results in a shift in the velocity profile, corresponding to an under-estimation of the skin friction. A new formulation is proposed in this contribution in which the wall-parallel components of the modeled stress are reduced in order to lower the influence of the model and increase the resolved stress. The effectiveness of the new model is evaluated via comparison against DES predictions using the original and recently-proposed versions of the method. The effect of grid resolution and model parameters are also assessed using computations of turbulent channel flow at a Reynolds number based on friction velocity and channel halfwidth of 5000. The predictions show that the anisotropic form of the model stress yields an improved prediction of the mean velocity profile in better agreement with the logarithmic law and with larger resolved stress in the near-wall region.

Simulating flow separation from continuous surfaces: routes to overcoming the Reynolds number barrier

2009 ◽  
Vol 367 (1899) ◽  
pp. 2885-2903 ◽  
Author(s):  
Michael Leschziner ◽  
Ning Li ◽  
Fabrizio Tessicini
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Major Elements ◽  
Wall Layer ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Rans Models ◽  
High Reynolds ◽  
Near Wall

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

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