New Dynamic Subgrid-scale Modelling Approaches for Large Eddy Simulation and Resolved Statistical Geometry of Wall-bounded Turbulent Shear Flow PDF Download
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Languages : en
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This dissertation consists of two parts, i.e. dynamic approaches for subgrid-scale (SGS) stress modelling for large eddy simulation and advanced assessment of the resolved scale motions related to turbulence geometrical statistics and topologies. The numerical simulations are based on turbulent Couette flow. The first part of the dissertation presents four contributions to the development of dynamic SGS models. The conventional integral type dynamic localization SGS model is in the form of a Fredholm integral equation of the second kind. This model is mathematically consistent, but demanding in computational cost. An efficient solution scheme has been developed to solve the integral system for turbulence with homogeneous dimensions. Current approaches to the dynamic two-parameter mixed model (DMM2) are mathematically inconsistent. As a second contribution, the DMM2 has been optimized and a modelling system of two integral equations has been rigorously obtained. The third contribution relates to the development of a novel dynamic localization procedure for the Smagorinsky model using the functional variational method. A sufficient and necessary condition for localization is obtained and a Picard's integral equation for the model coefficient is deduced. Finally, a new dynamic nonlinear SGS stress model (DNM) based on Speziale's quadratic constitutive relation [J. Fluid Mech., 178, p.459, 1987] is proposed. The DNM allows for a nonlinear anisotropic representation of the SGS stress, and exhibits a significant local stability and flexibility in self-calibration. In the second part, the invariant properties of the resolved velocity gradient tensor are studied using recently developed methodologies, i.e. turbulence geometrical statistics and topology. The study is a posteriori based on the proposed DNM, which is different than most of the current a priori approaches based on experimental or DNS databases. The performance of the DNM is further validated in terms of its cap.
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Languages : en
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Book Description
This dissertation consists of two parts, i.e. dynamic approaches for subgrid-scale (SGS) stress modelling for large eddy simulation and advanced assessment of the resolved scale motions related to turbulence geometrical statistics and topologies. The numerical simulations are based on turbulent Couette flow. The first part of the dissertation presents four contributions to the development of dynamic SGS models. The conventional integral type dynamic localization SGS model is in the form of a Fredholm integral equation of the second kind. This model is mathematically consistent, but demanding in computational cost. An efficient solution scheme has been developed to solve the integral system for turbulence with homogeneous dimensions. Current approaches to the dynamic two-parameter mixed model (DMM2) are mathematically inconsistent. As a second contribution, the DMM2 has been optimized and a modelling system of two integral equations has been rigorously obtained. The third contribution relates to the development of a novel dynamic localization procedure for the Smagorinsky model using the functional variational method. A sufficient and necessary condition for localization is obtained and a Picard's integral equation for the model coefficient is deduced. Finally, a new dynamic nonlinear SGS stress model (DNM) based on Speziale's quadratic constitutive relation [J. Fluid Mech., 178, p.459, 1987] is proposed. The DNM allows for a nonlinear anisotropic representation of the SGS stress, and exhibits a significant local stability and flexibility in self-calibration. In the second part, the invariant properties of the resolved velocity gradient tensor are studied using recently developed methodologies, i.e. turbulence geometrical statistics and topology. The study is a posteriori based on the proposed DNM, which is different than most of the current a priori approaches based on experimental or DNS databases. The performance of the DNM is further validated in terms of its cap.
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Category :
Languages : en
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Book Description
This dissertation consists of two parts, i.e. dynamic approaches for subgrid-scale (SGS) stress modelling for large eddy simulation and advanced assessment of the resolved scale motions related to turbulence geometrical statistics and topologies. The numerical simulations are based on turbulent Couette flow. The first part of the dissertation presents four contributions to the development of dynamic SGS models. The conventional integral type dynamic localization SGS model is in the form of a Fredholm integral equation of the second kind. This model is mathematically consistent, but demanding in computational cost. An efficient solution scheme has been developed to solve the integral system for turbulence with homogeneous dimensions. Current approaches to the dynamic two-parameter mixed model (DMM2) are mathematically inconsistent. As a second contribution, the DMM2 has been optimized and a modelling system of two integral equations has been rigorously obtained. The third contribution relates to the development of a novel dynamic localization procedure for the Smagorinsky model using the functional variational method. A sufficient and necessary condition for localization is obtained and a Picard's integral equation for the model coefficient is deduced. Finally, a new dynamic nonlinear SGS stress model (DNM) based on Speziale's quadratic constitutive relation [J. Fluid Mech., 178, p.459, 1987] is proposed. The DNM allows for a nonlinear anisotropic representation of the SGS stress, and exhibits a significant local stability and flexibility in self-calibration. In the second part, the invariant properties of the resolved velocity gradient tensor are studied using recently developed methodologies, i.e. turbulence geometrical statistics and topology. The study is a posteriori based on the proposed DNM, which is different than most of the current a priori approaches based on experimental or DNS databases. The performance of the DNM is further validated in terms of its cap.
Author: Hyun Ji Bae
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Category :
Languages : en
Pages :
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Book Description
Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motions is so large that the computational cost becomes prohibitive. In large-eddy simulation (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is modeled through a subgrid-scale (SGS) model. Given that accurate representation and prediction of turbulence is needed in many engineering and scientific applications, development of accurate yet computationally efficient SGS models is an important task. Additionally, wall models are necessary to overcome the prohibitive near-wall resolution requirements for the large scales in high-Reynolds-number turbulent flows. This study investigates a new SGS model, the anisotropic minimum-dissipation (AMD) model, which is constructed to provide the minimum eddy viscosity required to avoid energy pile-up in the smallest resolved scales. The AMD model is successfully applied in simulations of decaying grid turbulence for isotropic grids, and temporal mixing layer and turbulent channel flow for anisotropic grids. This model is more cost-effective than the dynamic Smagorinsky model (DSM) and appropriately switches off in laminar and transitional flows. The formulation of the AMD model is extended to the transport equation for scalar concentration to model the subfilter scalar flux. The performance of the model is tested in the simulation of high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the scalar model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. The accuracy of the SGS models is tested by studying the convergence properties in the outer region of a channel flow at moderate to high Reynolds numbers. As LES requires scale separation of the resolved and subgrid scales, the convergence study must be conducted in high-Reynolds-number flows. However, the analysis shows that the errors from the near-wall region are dominant for SGS models in usual LES grid resolutions, where the grid is not refined in the wall-parallel directions. For evaluation of SGS models, in order to overcome the grid requirements imposed by the near-wall turbulent eddies as well as the errors accumulated near the wall, a possible solution is to isolate the outer region of wall-bounded flows. This is made possible by one of two ways: suppressing the near-wall dynamics through a modified wall, or supplying the correct mean stress at the wall with a wall model. Theoretical analysis of the error scaling of SGS models for the mean velocity profile, turbulence intensities, and energy spectra is performed. The numerical convergence studies of the DSM and AMD models show that both models are first-order accurate in terms of the mean velocity profile, which is consistent with the theoretical assessments. Lastly, a new dynamic wall model based on the slip boundary condition is proposed. The use of the slip boundary condition for wall-modeled LES is motivated through theoretical analysis and a priori study of DNS data. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel and flat-plate turbulent boundary layer. The slip boundary condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. The requirements for the slip lengths to be used in conjunction with wall models are discussed, and the equation that connects the slip boundary condition with the stress at the wall is derived. A dynamic procedure based on the invariance of wall stress under test filtering is formulated for the slip condition, providing a dynamic slip wall model free of any a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow, and zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict mean and turbulence intensities for various flow configurations, Reynolds numbers, and grid resolutions.
Author: Seyedhadi Seyedi
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 0
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This study aims to propose novel solutions to the complex problem of turbulent flows using data-driven statistical and mathematical models. The proposed models reduce the huge computational cost of the direct numerical simulations and make them tractable while maintaining the important statistical features of the chaotic flows. Unlike the conventional models in the literature, the new proposed dynamic models take into account the inherent nonlocality of turbulence and predict the final statistical quantities with higher accuracy and correlations. First, we developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of the homogeneous isotropic turbulent flows (HIT). The model is based on a generalized (integer-to-noninteger) order Laplacian of the filtered velocity field, and a novel dynamic model has been formulated to avoid the need for tuning the model constant. Three data-driven approaches were introduced for the determination of the fractional-order to have a model which is totally free of any tuning parameter. Our analysis includes both the a priori and the a posteriori tests. In the former test, using a high-fidelity and well-resolved dataset from direct numerical simulations (DNS), we computed the correlation coefficients for the stress components of the subgrid-scale (SGS) stress tensor and the one we get directly from the DNS results. Moreover, we compared the probability density function of the ensemble-averaged SGS forces for different filter sizes. In the latter, we employed our new model along with other conventional models including static and dynamic Smagorinsky into our pseudo-spectral solver and tested the final predicted quantities. The results of the newly developed model exhibit an expressive agreement with the ground-truth DNS results in all components of the SGS stress and forces. Also, the model exhibits promising results in the VLES region as well as the LES region, which could be remarkably important for the cost-efficient nonlocal turbulence modeling e.g., in meteorological and environmental applications.Afterwards, we extend the same dynamic nonlocal idea to the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection-diffusion model, coding the corresponding super-diffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (non-integer) Laplacian exponent, where we on-the-fly calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreements with the ground-truth filtered DNS data in comparison to the conventional static and dynamic Prandtl-Smagorisnky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out a comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena at the same time and providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and VLES frameworks even with strong anisotropies, applicable to environmental applications.Finally, we developed a new dynamic tempered fractional subgrid-scale model, DTF, for the large and very large eddy simulation of turbulent flows. The nonlocality of the turbulent flows is the innate feature that can be seen in the non-Gaussian statistics of the velocity increments and can be addressed properly by the nonlocal models in terms of the fractional operators. Using kinetic transport, we developed a dynamic tempered fractional model that encompasses the three main characteristics of an ideal turbulence model: (i) nonlocal nature, (ii) dynamic model constant computations, and (iii) tempered and finite variance property. Several simulations of forced homogeneous isotropic and multi-layer temporal shear layer turbulent flows have been done in the a priori and a posteriori analyses. The results show that the new model is not only numerically stable and can maintain low- and high-order structures in long-range simulations, but it also provides better predictions than local models and nontempered models.
Author: P. Sagaut
Publisher: Springer Science & Business Media
ISBN: 9783540263449
Category : Computers
Languages : en
Pages : 600
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Book Description
First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineering From the foreword to the third edition written by Charles Meneveau: "... this meticulously assembled and significantly enlarged description of the many aspects of LES will be a most welcome addition to the bookshelves of scientists and engineers in fluid mechanics, LES practitioners, and students of turbulence in general."
Author: Tommy Kunhung Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 160
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Author: M. Lesieur
Publisher: Cambridge University Press
ISBN: 9780521781244
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Large-Eddy Simulations of Turbulence is a reference for LES, direct numerical simulation and Reynolds-averaged Navier-Stokes simulation.
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ISBN:
Category : Aeronautics
Languages : en
Pages : 1038
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Category : Dissertations, Academic
Languages : en
Pages : 848
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Author: Stavros Kassinos
Publisher: Springer Science & Business Media
ISBN: 3540342346
Category : Technology & Engineering
Languages : en
Pages : 440
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Book Description
The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.
