Regularization modeling and Computational error minimization for large-eddy simulation

Bernard Geurts: University of Twente, The Netherlands - 13th October 2010


The large number of degrees of freedom of realistic turbulence poses serious challenges to numerical approaches aimed at understanding and controlling such flows. While the Navier-Stokes equations are commonly accepted to precisely describe turbulent flow, alternative coarsened descriptions need to be developed for engineering applications. These coarsened descriptions aim at capturing the primary features of a flow, at considerably reduced computational effort. Such coarsening introduces a ‘closure’ problem that requires additional phenomenological modeling. A prime example of this is large-eddy simulation in which a spatial filtering is applied to smoothen the small 'sub-filter' scales in a turbulent flow. Careful analysis and fundamental understanding of turbulence and numerical methods is needed to achieve successful closure and accurate computational strategies. Predictions of LES are principally limited by shortcomings in the closure modeling and errors in the numerical treatment. Sub-filter modeling will be reviewed, with emphasis on regularization modeling. In addition, a systematic framework for estimating these errors is presented in which error-decomposition is a central element. The error-landscape concept is introduced and applied to homogeneous, isotropic, decaying turbulence and turbulent channel flow at high Reynolds numbers. 




  Compressible turbulent channel and pipe flow: similarities and differences.

Prof. Rainer Friedrich, TU Munchen, Germany - 18th May 2010


Direct numerical simulation (DNS) is used to explore similarities and differences between fully developed supersonic turbulent plane channel and axisymmetric non- swirling pipe flow bounded by isothermal walls. The comparison is based on equal- friction Mach number, friction Reynolds number, Prandtl number, ratio of specific heats and viscosity exponent. The channel half-width and pipe radius are chosen to define the Reynolds numbers. To what extent and why mean flow quantities, second-order turbulence statistics and terms in the Reynolds stress equations coincide or diverge in both flows are investigated. The role of the fluctuating pressure in causing characteristic differences among correlations involving pressure fluctuations is identified via a Green-function-based analysis of the pressure field.





  Development of one- and two-equation models in Large-Eddy Simulation

Sergei G. Chumakov, Center for Turbulence Research (CTR) - Stanford University - 23rd October 2009


Large Eddy Simulation (LES) is a rapidly evolving approach to numerical modeling of turbulent flows, in which only the large-scale motions of the floware computed directly, and the effect of small-scale motions is modeled via subgrid models.One-equation subgrid models for LES use auxiliary quantities to close the equation of motions, and these quantities are calculated by adding an extra transport equation to the problem. One-equation models tend to be more accurate and have wide application area than zero-equation models such as classical Smagorinsky model.Advantages of one-equation models include (but are certainly not limited to) memory effects which become extremely important at transient high Reynolds number flows, for which the local equilibrium assumption is not valid.I will discuss several different approaches and present a new model for the dissipation rate of subgrid-scale kinetic energy - a work in progress that leads to a two-equation model that combines characteristic features of two very different one-equation approaches developed recently.





  Arguments in favor of universality of compressible turbulent wall & bounded flows, based on LES of compressible channel flow. Christophe Brun, Univ. Orleans/LEGI Grenoble , France - 4th July 2007

The scope of the present contribution is related to the design of physically based wall treatment for compressible turbulent boundary layer simulations. In order to reach such goal there is a need to first address the issue of the universality of the structure of the turbulence in non hypersonic compressible boundary layers (M < 5). This is presently performed based on wall resolved Large Eddy Simulation of fully developed isothermal channel flows for Re = 3000 and Re = 4880 in the Mach number range 0.3 < M < 3 and involving possible local adverse pressure gradient effects. In such context, the compressibility essentially affects the large scales of the turbulent flow and is driven by a ’coupling between sound and thermal fields’ described by Morkovin (1961) in the following way : ’The coupling occurs primarly through spatial and timewise variation of density, viscosity and heat conductivity’. The first consequence of this coupling is a full analogy between the velocity and the temperature field which can be derived as Strong Reynolds Analogy (SRA) related to turbulent stresses and turbulent heat fluxes. A second consequence of the ’coupling between sound and thermal fields’ concerns the universality of the structure of the turbulence which is expressed by Morkovin (1961) in the following terms : ’The large scale motion (mean velocity field) should be statistically coupled to the thermal field almost exclusively through mean values of ro, μ, lambda, and the generalized law of the wall so that with a variable lateral stretching factor, it may resemble the incompressible motion.’ Aerodynamic flow configurations generally feature turbulent boundary layer separation induced by strong adverse pressure gradients. This effect is presently accounted for to propose a near-wall scaling for compressible separating boundary layers. In addition to the standard friction velocity u(tau) and to the friction temperature T(tau) (based on wall heat flux, Carvin et al. 1988), we consider a pressure gradient based velocity up = abs( μ/ro^2 . dp/dx)^1/3 (Simpson 1983) and define a combined friction/pressure gradient velocity u(tau.p) = sqrt(up^2 + u(tau)^2) (Manhart et al. 2007), a pressure gradient based temperature Tp = up^2 /2Cp and a combined friction/pressure gradient temperature T(tau.p) = Tp + T(tau) . The ratios alfa = u(tau)^2 /u(tau.p)^2 [0, 1] and beta = T(tau)/T(tau.p) [0, 1] quantify which effect, friction or pressure gradient is preponderant. Laws of the wall are derived for the velocity and the total temperature. The account for the adverse streamwise pressure gradient in the present extendednew scaling clearly improves the velocity and temperature law of the wall with respect to the classical linear scaling.






LES and hybrid LES/URANS simulations in industrial applications: Fluid-Structure interaction and bi-phase flows.

Aristeu Silveira-Neto, Univ. Federal da Uberlândia, Brasil - 3rd July 2007







Unbalanced vortex stretching in nonstationary turbulence: Charles Speziale's work on unbalanced vortex stretching revisited

Robert Rubinstein, NASA Langley Research Center - 19th July 2007


Unbalanced vortex stretching in nonstationary turbulence: Charles Speziale's work on unbalanced vortex stretching revisited Turbulence modeling is based on Kolmogorov's theory of a universal homogeneous statistically steady state; indeed, models often assume that this theory describes the small scales of motion responsible for energy transfer even in flows that are far from steady and homogeneous. One crucial feature of the Kolmogorov theory is the prediction that at high enough Reynolds number, the large scales of motion become independent of viscosity, and we can speak of a high Reynolds number `fixed point.' Associated to this idea is a famous problem posed by Tennekes and Lumley: if the enstrophy balance in a turbulent flow is to be independent of viscosity, then two terms of order Re^{1/2}, representing enstrophy generation by vortex stretching and enstrophy destruction by vorticity, must cancel, leaving an $O(Re0)$ remainder.The failure of any number of theoretical investigations to justify this balance led Charles Speziale to investigate the possibility of `unbalanced vortex stretching' in turbulence, leading to novel predictions for decaying turbulence and homogeneous shear flow.We will revisit this work, showing that unbalanced vortex stretching occurs in transient turbulence  dynamics,but that in self-similar turbulent flows, the Tennekes-Lumley balance is recovered. This analysis implies that whereas the Kolmogorov theory does indeed represent a statistical {\em attractor} for the small scales of motion, it is not a permanent feature. Implications of unbalanced vortex stretching for modeling transient flows will be considered.






Coherent structures in the separated shear layer on the side of a square cylinder: a multiscale problem.


Christophe Brun, Univ. Orleans/LEGI Grenoble, France - 2nd July 2007


The scope of the present contribution is related to the design of proper signal processing tools to identify and understand, from both experimental and numerical data, the main coherent structures present in a turbulent flow. We will consider the case of the separated shear layer on the side of a square cylinder for a Reynolds number ranging from Re = 1000 to Re = 200000 which is a typical multiscale problem. Unsteady analysis based on LES at intermediate Reynolds numbers and LDV/PIV at high Reynolds numbers are carried out. For numerics, 2D and 3D visualisations are performed based on iso-vorticity contours and isovalues of the Q-criterion (2nd invariant of the velocity gradient tensor). The storage of huge time data bank allows for building time dependent movies for the main coherent structures. For experiments, smoke visualisations provide a qualitative description of the flow which can be viewed as the behaviour of a passive scalar. A special care was taken to obtain very high sampling frequency in order to capture properly the smallest coherent structures related to the present multiscale problem, based on a time 1D wavelet analysis.





Large Eddy Simulation Techniques for Physically Complex Flows

J. A. Domaradzki, 8th November, 2006


 Traditional turbulence models have been developed for incompressible, constant density flows governed by Navier-Stokes equations written in the inertialframe of reference. These assumptions must be relaxed when additional physi-cal phenomena are present. For instance, effects of compressibility, stratification(both stable and unstable), electromagnetic fields, as well as transformations to non-inertial systems of coordinates change the governing equations by introduc-ing additional terms in the momentum equation and/or extra equations for thedensity, energy, temperature, magnetic field in MHD, etc. The most obvious complication in large eddy simulations (LES) for such flows is the presence ofadditional unclosed terms in the equations, beyond the classical subgrid-scale(SGS) stress in the momentum equation, that require new modeling assumptions. The models for the additional unknowns are usually based on analogieswith modeling the SGS stress, e.g., for a SGS heat flux known as the Reynoldsanalogy. Even in situations that the equations of motion are changed by theaddition of merely linear terms that do not require modeling, as is the case of turbulence in a rotating frame of reference, models for the seemingly unmodified SGS stress term must be changed to capture the new physics. The classicalapproaches to modeling new physical phenomena will be reviewed and a com-peting technique based on the Truncated Navier-Stokes (TNS) equations will bedescribed. The TNS method has a potential advantage over classical methodsin that it is universal, being applicable in the same form to turbulent flows with different physics, without a need for new closure assumptions. It has been implemented previously to simulate classical "simple" flows: isotropic turbulence andchannel flow, and later validated for several physically complex flows, includ-ing compressible turbulence. Few examples of application of TNS to physicallycomplex turbulent flows will be reviewed: Rayleigh-Benard convection, rotatingturbulence, and stably stratified flows.



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