Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer

Numerical simulation is used to study the Kolmogorov flow in a shear layer of a compressible inviscid medium. A periodic permanent force applied to the flow gives rise to a vortex cascade of instabilities. The influence exerted by the size of the computational domain, the initial conditions, and the amplitude of the force on the formation of an instability cascade and the transition to turbulence is studied. It is shown that the mechanism of the onset of turbulence has an essentially three-dimensional nature. For the turbulent flows computed, the classical Kolmogorov ?5/3 power law holds in the inertial range.     

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     

Mixed convection turbulent film condensation on a sphere

The present paper reports a research on condensation heat transfer of an isothermal sphere with an external flow of vapor. The high tangential velocity of the vapor flow is determined from potential flow theory. The transition criterion of the onset turbulence has been given in the local film Reynolds number (Re_Γ). An eddy diffusivity model along with an expression by [H. Kato, N.N. Shiwaki, M. Hirota, On the turbulent heat transfer by free convection from a vertical plate, Int. J. Heat Mass Transfer, 11(1968) 1117–1125] is used to model turbulence. And the local liquid–vapor interfacial shear which occurs for high velocity vapor flow across a sphere surface is defined by the Colburn analogy. The paper then presents analytical analysis for the local dimensionless film thickness and heat transfer characteristics for the film condensation. And a comparison with those generated by previous theoretical of laminar condensation is discussed. The comparison shows the heat transfer coefficient of turbulent film condensation is higher than laminar film condensation under the high vapor velocity.     

An improved dynamic subgrid-scale model and its application to large eddy simulation of stratified channel flows

In the present paper, a new dynamic subgrid-scale (SGS) model of turbulent stress and heat flux for stratified shear flow is proposed. Based on our calculated results of stratified channel flow, the dynamic subgrid-scale model developed in this paper is shown to be effective for large eddy simulation (LES) of stratified turbulent shear flows. The new SGS model is then applied to the LES of the stratified turbulent channel flow to investigate the coupled shear and buoyancy effects on the behavior of turbulent statistics, turbulent heat transfer and flow structures at different Richardson numbers.     

Numerical calculation of turbulent corner flows

Numerical predictions are presented of the hydrodynamic characteristics of developing and fully-developed turbulent flow in a square duct. The turbulent stresses in the plane of the cross-section, gradients of which cause the familiar secondary flows, are approximated by gradients in the axial mean velocity. Two distinct approximations are investigated, one of which specifies some of the model ‘constants’ as functions of the gradient of the length scale to account for wall effects. The stresses in the axial momentum equation are calculated from an eddy viscosity deduced from the K-W model of turbulence, K being the turbulence energy and W, a measure of the time-mean-square-vorticity fluctuations. The approximation incorporating wall effects generally performs better than the other when compared with fully-developed flow-data. This same approximation also compares favourably with data for developing flow and predictions based on K-? models in the literature.     

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．     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Energy dissipation bounds for hear flows for a model in large eddy simulation

This report gives an upper bound for the time average of the energy dissipation rate, including energy dissipation due to viscous dissipation and turbulent diffusion in a model for the motion of large eddies in a turbulent flow. The bound is only a function of the reference velocity U, the domain diameter L, the eddy size δ, and surprisingly, the Reynolds number.     

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.     

On dispersion of settling particles from an elevated source in an open-channel flow

Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface is investigated numerically when the settling particles are released from an elevated continuous line-source. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection–diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the ‘log-wake law’ velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.     

MHD turbulence in a channel with spanwise field

We study turbulent channel flow of an electrically conducting liquid with a homogeneous magnetic field imposed in the spanwise direction. The Lorentz force is modelled using the quasistatic approximation. Direct and large–eddy simulations are performed for hydrodynamic Reynolds numbers Re=10000 and Re=20000 and the Hartmann number varying in a wide range. The main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall–normal direction. Comparing the results from direct and large–edddy simulations we show that the dynamic Smagorinsky model accurately reproduces the flow transformation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

表示湍流场的一种新设想

本文仿照量子场论中描述基本粒子产生湮灭的方法来描述湍流中涡旋的产生和消灭.因为当某一基本粒子存在的时候,我们可以认为它是一个不变实体,而湍流中涡旋则在时间过程中不断变化和耗散,所以在类比应用量子场论方法时首先要解决怎样的湍流涡旋可认为是同一个涡旋.根据线性化理论的特点,我们认为在时间过程中按相似性规律变化时湍流涡旋才算是同一个涡旋,而把不具有相似性的涡旋出现或消失,看成是方程(2.6)中相互作用项φ_i所引起的湮火和产生的结果.然后,我们采用和量子场论相类似的产生算符和消灭算符来描述湍流涡旋系统所处的状态.最后,我们利用原N-S方程中相互作用项来构成涡旋相互作用的“Schr?dinger”方程以描述其状态的变化.这样就得类似于量子场论的湍流涡旋相互作用理论.     

Monte Carlo simulation of boundary layer transition

A statistical method for simulating a boundary layer transition flow is proposed as based on experimental data on the kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate placed in an incompressible fluid. The method determines intermittency with allowance for overlapping spots, which makes it possible to determine the forces on the plate surface and the flow field near the transition region if the mean streamwise velocity field in a developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multiparameter transition models, this approach avoids the use of nonphysical parameter values.     

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.     

Invariant solution for an axisymmetric turbulent free jet using a conserved vector

An axisymmetric turbulent free jet described by an effective viscosity, which is the sum of the kinematic viscosity and the kinematic eddy viscosity, is investigated. The conservation laws of the jet are derived using the multiplier method. A second conserved vector, in addition to the elementary conserved vector, exists provided the effective viscosity has a special form. The Lie point symmetry associated with the elementary conserved vector is obtained and used to generate the invariant solution. The analytical solution is derived when the effective viscosity depends only on the distance along the jet. The numerical solution is obtained when the effective viscosity depends also on the distance across the jet. The eddy viscosity causes an apparent increase in the viscosity of the mean flow which produces an increase in the width of the jet due to an increase in diffusion and also a decrease in the maximum mean velocity along the axis of the jet.     

Evaluating flame turbulence scale in diffusion combustion of diesel fuels

This paper presents results of mathematical simulations of dynamic flame behavior that occurs in burning diesel fuel, as well as experimental data on turbulent flame eddies provided by infrared thermography. The comparison of the simulated and experimental data documents a good match between the parameters of flame thermodynamics and the combustible gas flow in a turbulent eddy. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics of laminar-turbulent transition in three dimensional Rayleigh–Benard convection

This paper proposes a new approach to analysis of incompressible 3D fluid motion in Rayleigh–Benard convection in transition from laminar to turbulent regimes. Number of test series were conducted. The analysis indicated that in different test series laminar-turbulent transition follows either the subharmonic bifurcation cascade of two-dimensional tori or the subharmonic bifurcation cascade of limit cycles. Cycles up to the third period were found in the system that indicated the end of the Sharkovskii sequence. All bifurcation cascades agree with the Feigenbaum–Sharkovskii–Magnitskii (FSM) scenario.     

Convergence of finite element approximations of large eddy motion

Fluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are solved numerically. This report considers “numerical errors” in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 689–710, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10027.     

A two-algebraic turbulence model for compressible flow in turbomachinery cascade

The objective of this study is to examine the Baldwin–Lomax turbulence model in a finite volume solver to introduce a computer code for complex two–dimensional flows in turbomachinery. The turbulent model was tested with investigating the turbulent flow over a flat plate and other test cases. Three test cases are presented and the computed results are compared with experimental data. The calculated velocity profile agreed well with the experimental data in plate test case and the solver is validated in test case of flow over a semi NACA–0012 airfoil. The solver is used for flow through a multi–blade cascade of an axial compressor in design condition to show its capability of multi–block solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian simulation of particle deposition in a turbulent boundary layer in the presence of thermophoresis

Knowledge of particle deposition in turbulent flows is often required in engineering situations. Examples include fouling of turbine blades, plate-out in nuclear reactors and soot deposition. Thus it is important for numerical simulations to be able to predict particle deposition. Particle deposition is often principally determined by the forces acting on the particles in the boundary layer. The particle tracking facility in the CFD code uses the eddy lifetime model to simulate turbulent particle dispersion, no specific boundary layer being modelled. The particle tracking code has been modified to include a boundary layer. The non-dimensional yplus, y⁺, distance of the particle from the wall is determined and then values for the fluid velocity, fluctuating fluid velocity and eddy lifetime appropriate for a turbulent boundary layer used. Predictions including the boundary layer have been compared against experimental data for particle deposition in turbulent pipe flow. The results giving much better agreement. Many engineering problems also involve heat transfer and hence temperature gradients. Thermophoresis is a phenomena by which small particles experience a force in the opposite direction to the temperature gradient. Thus particles will tend to deposit on cold walls and be repulsed by hot walls. The effect of thermophoresis on the deposition of particles can be significant. The modifications of the particle tracking facility have been extended to include the effect of thermophoresis. A preliminary test case involving the deposition of particles in a heated pipe has been simulated. Comparison with experimental data from an extensive experimental programme undertaken at ISPRA, known as STORM (Simplified Tests on Resuspension Mechanisms), has been made.