Analysis of Interaction between Turbulence generated by Settling Particles and Oscillating Grid Turbulence
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In order to study turbulence modulation in solid-liquid two-phase flows, in particular effects of slip velocity between the two phases on turbulence structure of the fluid phase, interaction between turbulence generated by settling particles and the oscillating grid turbulence is calculated using the turbulence model based on the one-point closures. The calculated values either for the turbulence due to settling particles or for the oscillating grid turbulence agree well with the experimental data in the previous studies. And the model predicts that mixing of particles decays turbulence of the fluid phase.Keywords:
Settling
Turbulence Modeling
Reynolds decomposition
The paper discusses the state-of-the-art of turbulence modeling and presents possible ways for improvement in the future turbulence models. Based on a set of turbulence closure postulations, a variation of second-order turbulence models, such as the Reynolds stress model (RSM), the algebraic stress model (k-ε-A), and the eddy viscosity model (k-ε-E), are obtained. Examples of prediction made are free shear flows, cavity flows, and flows past an off-set channel. Although a complete turbulence model does not exist at the present time, some prediction capability has been achieved by the secondorder turbulence model. The incompleteness of turbulence modeling may be attributed to the inadequacy of isotropic dissipation and single turbulent scale postulations. Use of multiple turbulence scale concepts, including use of fractal dimension of turbulent eddies may improve turbulence prediction.
Turbulence Modeling
Reynolds decomposition
Reynolds stress
Closure (psychology)
Eddy
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The accuracy to which a turbulent boundary layer or wake can be predicted numerically depends on the validity of the turbulence closure model used. The modeling of turbulence physics is one of the most difficult problems in computational fluid dynamics (CFD). In fact, it is one of the pacing factors in the development of CFD. In general, there are three main approaches to the description of trubulence physics. First is turbulence modeling in which the Reynolds averaged Navier-Stokes equations are used and some closure approximation is made for the Reynolds stresses. A second approach to turbulence is large eddy simulation (LES) in which the computational mesh is taken to be fine enough that the large scale structure of the turbulence can be calculated directly. An empirical assumption must be made for the small scale sub-grid turbulence. The third approach is direct simulation. In this technique the Navier-Strokes equations are solved directly on a mesh which if fine enough to resolve the smallest length scale of the turbulence. The Reynolds averaged equations are not used and no closure assumption is required. These last two approaches require extensive computer resources and as such are not engineering tools. The purpose of the work was to investigate the various engineering turbulence models for accuracy and ease of programming. This involved comparison of the models with each other and with experimental data.
Turbulence Modeling
Closure (psychology)
Reynolds decomposition
Reynolds stress
Large-Eddy Simulation
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This paper summarizes application of the turbulence model to study the characteristic of flow field and the pattern of mass mixing diffusion transportation. The research present situation and new development trend on the turbulence model are analysed in detail. Moreover, the viewpoint on environmental hydraulics problem solved by turbulence model is put forward, and the traits of zero-equation turbulence model, one-equation turbulence model, two-equation k-a turbulence model and the revised anisotropic k-a turbulence model, the Reynolds stress model, the algebraic Reynolds stress model, the low-Reynolds flow model and the senior simulation of turbulence flow are discussed.
Turbulence Modeling
Reynolds stress
Reynolds decomposition
Hydraulics
Convection–diffusion equation
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to Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards Real World Turbulence.
Turbulence Modeling
Reynolds decomposition
Homogeneous isotropic turbulence
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to Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards Real World Turbulence.
Turbulence Modeling
Reynolds decomposition
Homogeneous isotropic turbulence
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The eddy viscosity turbulence models were applied to predict the flows through a cascade, and the prediction performances of turbulence models were assessed by comparing with the experimental results for a controlled diffusion(CD) compressor blade. The original k-ω turbulence model and k-ω shear stress transport(SST) turbulence model were used as two-equation turbulence model which were enhanced for a low Reynolds number flow and the Baldwin-Lomax turbulence model was used as algebraic turbulence model. Farve averaged Navier-Stokes equations in a two-dimensional, curvilinear coordinate system were solved by an implicit, cell-centered finite-volume computer code. The turbulence quantities are obtained by lagging when the mean flow equations have been updated. The numerical analysis was made to the flows of CD compressor blade in a cascade at three different incidence angles (40, 43.4, 46 degrees). We found the reversion in the prediction performance of original k-ω turbulence model and k-ω SST turbulence model when the incidence angle increased. And the algebraic Baldwin-Lomax turbulence model showed inferiority to two-equation turbulence models.
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Reynolds decomposition
Reynolds stress
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Preface 1.Introduction to Turbulence 1.1.Historical View 1.2.Navier-Stokes(N-S) Equations:Validity for Turbulence 1.3.Averaging Processes 1.4.Averaged Incompressible Turbulence Equations 1.5.Turbulence Closure Problem 1.6.Summary 2.Second-Order Closure Turbulence Model 2.1.Turbulence Model Postulations 2.2.Modeling of uiuj, k, E, and uiO Equations 2.3.Summary of the Second-Order Turbulence Model 2.4.Determination of Turbulence Model Constants 2.5.Summary and Conclusion 3.Discussions of Turbulence Models 3.1.Variation of Second-Order Turbulence Models 3.2.Turbulent Flow Predictions:One(Free-Shear Flows) 3.3.Problem Function 3.4.Two-Scale Second-Order Turbulence Model 4.Near-Wall Turbulence 4.1.Introduction 4.2.Wall Functions 4.3.Low-Reynolds-Number Turbulence Models 4.4.Two-Layer Model 4.5.Direct Numerical Simulation(DNS) 4.6.Turbulent Flow Predictions:Two(Wall-Shear Flows) 4.7.Other Near-Wall Turbulence Models 4.8.Summary 5.Applications of Turbulence Models 5.1.Introduction 5.2.Turbulent Flow Predictions:Three(Two-Dimensional Separated Flows) 5.3.Turbulent Flow Past Disc Type Valves 5.4.Third-Order Closure Model 5.5.Three-Dimensional Flows 5.6.Turbulence Flow Predictions:Four(Three-dimensional Flows) 5.7.Anistrophic Turbulence Models 5.8.Conclusion 6.Turbulent Buoyant Flows 6.1.Introduction 6.2.Equation of State 6.3.Boussinesq Approximation 6.4.Averaged Turbulence Equations 6.5.Turbulent Transport Equations 6.6.Turbulence Modeling of Turbulent Buoyant Flows 6.7.Summary of the Turbulence Model 6.8.Turbulent Flow Predictions:Five (Buoyant Flows) 6.9.Two-Scale Turbulence Review Quotes Concept 7.Closure Bibliography Index
Turbulence Modeling
Reynolds decomposition
Kolmogorov microscales
Closure (psychology)
Closure problem
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Reynolds averaged Navier–Stokes (RANS) turbulence models are usually concerned with modeling the Reynolds stress tensor. An alternative approach to RANS turbulence modeling is described where the primary modeled quantities are the scalar and vector potentials of the turbulent body force—the divergence of the Reynolds stress tensor. This approach is shown to have a number of attractive properties, most important of which is the ability to model nonequilibrium turbulence situations accurately at a cost and complexity comparable to the widely used two-equation models such as k-e. Like Reynolds stress transport equation models, the proposed model does not require a hypothesized constitutive relation between the turbulence and the mean flow variables. This allows nonequilibrium turbulence to be modeled effectively. However, unlike Reynolds stress transport equation models, the proposed system of partial differential equations is much simpler to model and compute. It involves fewer variables, no realizability c...
Reynolds stress
Turbulence Modeling
Reynolds decomposition
Realizability
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An overview of the second-order closure turbulence models is presented in this paper. Models studied include the k-ε-eddy viscosity model, k-ε-nonlinear Reynolds stress model, differential Reynolds stress model, k-ε algebraic stress model, near-wall second-order closure model, low-Reynolds number model, two-layer model, and multiscale model, which cover the efforts of scientists and engineers over the past 50 years. However, at the present time, there exists no unified turbulence model. Each model applies successfully to some turbulent flows, while it predicts unsatisfactory results for other flows, especially for flows that are very different from those for which the models were calibrated. To improve the prediction accuracy and the applicability of the existing turbulence models, modifying, or even remodeling, the ε equation, the dissipation rate of turbulent kinetic energy, and pressure-strain terms of the Reynolds stress, uiuj¯, equations is necessary.
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Turbulence Modeling
Closure (psychology)
Reynolds decomposition
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Turbulence Modeling
Reynolds stress
Closure (psychology)
Magnetic Reynolds number
Reynolds decomposition
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