Mixing Model Based on Parameterized Scalar Profiles

The composition fields in turbulent reacting flows are affected by turbulent transport (macromixing), molecular diffusion (micromixing), and chemical reactions. In the joint velocity-composition probability density function transport equation the highly nonlinear macromixing and chemical reaction terms appear in closed form. This is a considerable advantage over second moment closure methods. Micromixing on the other hand requires modelling and especially for turbulent combustion accurate mixing models are crucial. In this paper we present an approach to model the mixing of scalars, e.g. species mass fractions or temperature, based on considering one-dimensional parameterized scalar profiles (PSP). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mixing model providing statistics of the conditional scalar dissipation rate

Joint composition probability density function (PDF) methods are used for the numerical simulation of turbulent reactive flows. Here, other than in classical Reynolds averaged Navier–Stokes (RANS) or large eddy simulation (LES) approaches, the highly non-linear chemical source term appears in closed form. On the other hand, mixing models are required for the closure of the molecular diffusion term. In the present work, the joint statistics of the scalar and the scalar dissipation rate provided by the parameterized scalar profile (PSP) mixing model are validated. The goal is to combine the PDF method with a flamelet approach, where the scalar dissipation rate plays a crucial role in determining the contribution of the chemical source term. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixing in simple models for turbulent diffusion

Simple turbulent diffusive models are proposed as conceptual tools for exploring scenarios involving mixing of stratified flows. Applications include the dynamics of the ocean's top mixed layer, shear instability, breaking internal waves, and turbulent stirring of sharp interfaces. A novel measure of mixing is developed, based on arguments from statistical physics. It is shown that, under turbulent diffusion, this measure grows, and that there are strong indications that, under stirring, flows tend to settle down at a maximum of this measure, subject to global dynamical constraints. © 2004 Wiley Periodicals, Inc.     

Hybrid LES-RANS Modeling of Complex Turbulent Flows

The paper describes a state-of-the-art hybrid LES-URANS method for the simulation of complex internal and external turbulent flows. Relying on a unified LES-URANS approach with a soft interface the methodology is designed for wall-bounded non-equilibrium flows. The unsteady Reynolds-averaged Navier-Stokes (URANS) mode within the hybrid approach is taken into account by an explicit algebraic Reynolds stress model (EARSM), which guarantees an appropriate representation of the anisotropic near-wall turbulence. All non-closed terms in the transport equation of the turbulent kinetic energy are modeled by enhanced formulations using the EARSM (production and diffusion term) and the splitting of the dissipation rate into a homogeneous and an inhomogeneous contribution. The former is expressed analytically by a Taylor series expansion of the homogeneous lateral Taylor microscale in the vicinity of the wall guaranteeing the correct asymptotic behavior. The latter is incorporated into the diffusion term. The interface location between the large-eddy simulation (LES) mode and the URANS mode is determined automatically on-the-fly based on the modeled turbulent kinetic energy and the distance to the wall. For transitional (external) flows an additional dynamic transition criterion is applied which determines the laminar and the turbulent flow regimes and is combined with the existing interface criterion. An internal flow over a periodic arrangement of hills and an external flow past a SD7003 airfoil with a laminar separation bubble are taken into account for a detailed evaluation of the method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD analysis in hydromagnetic casting process of clad steel slabs

A novel continuous casting process for clad steel slabs has been developed by suppressing the mixing of molten steels in the mold pool of continuous casting strand with a level DC magnetic field (LMF) installed in the mold. In this process, two molten steels of different chemical composition are discharged by two nozzles into the upper and the lower pools respectively to solidify in the outer and the inner layers as a clad steel slabs. The mechanism of separation into two layers has been elucidated by using a three dimensional MHD analysis. The numerical prediction employing Maxwell's equation, Ohm's law, and the turbulent flow model shows that the mixing of the different type of steels is suppressed by the electromagnetic dividing of the upper and the lower recirculating flows. The principle of the new process has also been verified by steel casting trials of the stainless-steel clad steel slabs with an 8-ton scale pilot continuous casting machine.     

Physical Modelling of Point Source Dispersion Inside Atmospheric Boundary Layer

One of the most important problems in the turbulence theory is the process of turbulent mixing. Although many theoretical and experimental studies on the structure functions of a passive scalar as well as the probability density functions of its increment and gradient in a turbulent fluid have been published so far, the instantaneous feature of an advected scalar has not been explored very well. There are only a few experimental studies on a scalar concentration fluctuation analysis in turbulent flows. In this study the time‐series of both longitudinal velocity component and concentration analysis are to be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heat Transfer in Rotor/Rotor and Rotor/Stator Cavity: Physics,Correlations and Numerical Modeling

The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

Prandtl's Mixing Length Model - Revisited

The paper is concerned with a modification of Prandtl's mixing length model of Reynolds stresses in fully developed turbulent channel flows. Here it is a well established fact that Prandtl's model falls short to describe the Reynolds stresses correctly very close to the wall. Furthermore, the resulting solution of the time averaged velocity fails to describe the channel flow correctly from the wall to its center. To overcome these shortcomings, the only characteristic mixing length in Prandtl's model is replaced by separate mixing lengths for velocity fluctuations parallel to the wall and normal to the wall, respectively. The modified model describes the mean velocity, all Reynolds stresses, and the functional dependence between Reynolds number based on the mean velocity and the one based on the friction velocity. For all Reynolds numbers these results - and corresponding results for the production terms of Reynolds stresses and the energy balance of the mean flow - agree quantitatively with experimental data and with data obtained by numerical simulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavelet filtering to study mixing in 2D isotropic turbulence

This paper presents the application of coherent vortex simulation (CVS) filtering, based on an orthogonal wavelet decomposition of vorticity, to study mixing in 2D homogeneous isotropic turbulent flows. The Eulerian and Lagrangian dynamics of the flow are studied by comparing the evolution of a passive scalar and of particles advected by the coherent and incoherent velocity fields, respectively. The former is responsible for strong mixing and produces the same anomalous diffusion as the total flow, due to transport by the coherent vortices, while mixing in the latter is much weaker and corresponds to classical diffusion.     

Cross-relaxation dynamics on anomalous saturation processes in low pressure supersonic cw HF chemical laser amplifier

It is assumed that both translational and rotational nonequilibrium cross-relaxations play a role simultaneoulsy in low pressure supersonic cw HF chemical laser amplifier. For two-type models of gas flow medium with laminar and turbulent flow diffusion mixing, the expressions of saturated gain spectrum are derived respectively, and the numerical calculations are performed as well. The numerical results show that turbulent flow diffusion mixing model is in the best agreement with the experimental result. Project supported by the National Natural Science Foundation of China (Grant No. 19474036) and by the Laboratory of Hih-temperature Gas Dynamics. Insititute of Mechanics, Chinese Academy of Sciences (Grant No. KJ951-E-202).     

Modelling Intermediate Species in Partially Premixed Turbulent Combustion Based on the LES-FGM Method北大核心CSCD

The LES of partially premixed turbulent flame MRB in TU Darmstadt was conducted based on the flamelet-tabulated combustion model FGM, and effects of premixed and partially premixed tabulations on the modelling results were studied. The results show that, different methods of tabulation exhibit limited influences on the predictions of the flame structure, velocity, and major species, but using a partially premixed tabulation largely improves the reliability of modelling intermediate minor species CO and H2. The underlying reason lies in a better inclusion of the fuel-air mixing effects through the partially premixed tabulation, which is built based on laminar counter-flow flames. Adding extra transport equations for the intermediate species improves the predictions of intermediate species, especially given a premixed tabulation adopted; meanwhile, the stretch effects in this turbulent flame are ignorable. The results are significant to guide the high-fidelity simulation of partially premixed turbulent flames based on the flamelet-tabulated combustion model. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Modified k – ω Model for Simulation of Cavitating Flows

Although cavitating flows are generally turbulent, the interaction of turbulence and cavitation dynamics is still not well understood. In general, two‐equation models are employed, which were originally developed for single‐phase flows. Therefore they fail by handling cavitation based flow phenomena with very high density variations (dependent on operating condition up to 40000:1). This sudden change of the density causes strong pressure gradients, secondary flows and local compressibility. The aim of this study is to enhance the Wilcox's k‐? model with empirical correlations in order to simulate turbulent cavitating flows more precisely and effciently.     

Effects of plane strain on inhomogeneous turbulence

The influence of the mean plane strain on the turbulence transportation is investigated by large eddy simulation (LES) in the shearless turbulence mixing layer. It is found that the mean strains enhance the turbulent fluctuations in the mixing region. Compression in the inhomogeneous direction can greatly increase the transport of turbulent kinetic energy by triple correlation terms, while stretching in the inhomogeneous direction decreases the turbulence transportation. The gradient diffusion models for turbulent transportation are evaluated and it is found that the intermittency consideration can improve the prediction ability of the gradient-type models for the triple correlation terms. Project supported by the Sino-French Laboratory in Beijing and the National Natural Science Foundation of China (Grant No. 19572041).     

Simulation of mass transport in series arrays of membranes with “active” solute flow

The behaviour of the volume and solute flows across a series array of several membranes is investigated by simulation, using a model based on the linear thermodynamics of irreversible processes. Locally linear phenomenological equations are integrated along the direction of the flows, giving non-linear flow-force relationships whose shape is in good agreement with the observations. The simulation also shows that an asymmetry of the array is required, in order to obtain both the non-linearity of the flows and the coupling between the water and solute transport, when the former is coupled to a chemical reaction (metabolism coupled ‘active transport).     

Numerical simulation of the performance of a snow fence with airfoil snow plates by FVM

The aim of this work is to analyze the efficiency of a snow fence with airfoil snow plates to avoid the snowdrift formation, to improve visibility and to prevent blowing snow disasters on highways and railways. In order to attain this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (snow particles) and fluid phase (air). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, we have used a particle transport model termed as Lagrangian particle tracking model, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 15,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. Finally, the conclusions of this work are exposed.     

Nonhydraulic Effects in Particle-Driven Gravity Currents in Deep Surroundings

In this article, we present an approach to modeling the flow of particle-driven gravity currents produced by the sudden release of well-mixed, fixed-volume suspensions into deep surroundings. Our model accounts for the initial turbulent energy of mixing in the release volume, characteristic of the classical lock–release experiments, as well as the spatiotemporal variability in the driving buoyancy forces attributable to particle settling. We show that, in contrast to compositionally driven flows, particle-driven flows cannot be described consistently in terms of shallow water theory. Specifically, we show that the presence of particles in the flow dynamics produces significant horizontal velocity shear, thereby changing the flow configuration in important ways from flows assumed to be governed by the shallow water equations. These new flow properties are calculated and contrasted with flow properties derived on the basis of the shallow water equations to show that the shallow water analysis misses dynamical features of the flow. We also show that our model provides significant improvement over the previous shallow water-based models in predicting the experimentally determined deposition patterns associated with the lock–release experiments.     

Notes on modelling of environmental transport in wetland

This paper presents an effort towards a basic model for environmental transport of momentum, heat and mass transfer in the wetland. To smear out the discontinuity between the two phases of water and solid in the wetland, the continuum models distinctively applying for the water body and solid frame are transformed via the technique of phase average to give equations for a virtual single-phase flow in the entire domain of the wetland. Then to filter out the vortex and fluctuation common in the wetland flow, the operation of large eddy simulation (LES) is applied to yield a basic model for practical simulation. With reference to the modelling of flows in porous media and turbulent flows, closure relations are presented for the correlation terms due to the phase average and large eddy simulation.     

Variation of drag coefficient with wind wave development

Turbulent air flows over developing wind waves in the air-sea boundary layer are numerically simulated without considering wave breaking. Influences of wind waves on air flows are considered using a model of significant wave and surface roughness, with a formula proposed for calculating the surface roughness. κ-ε model is adopted to simulate turbulent flows. The results of the drag coefficient and turbulence characteristics agree well with the observations. Project supported by the National Natural Science Foundation of China (Grant No. 19332010).     

A dynamic subgrid-scale model for the large eddy simulation of stratified flow

A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa’s eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis