A MULTIPLE-TIME-SCALE TURBULENCE MODEL BASED ON VARIABLE PARTITIONING OF THE TURBULENT KINETIC ENERGY SPECTRUM

A multiple-time-scale turbulence model based on a single point closure and a simplified split-spectrum method is presented. In the model the effect of the ratio of the production rate to the dissipation rate on the eddy viscosity is modeled using multiple time scales and a variable partitioning of the turbulent kinetic energy spectrum. Example problems included are a wall-jet flow, a wake-boundary-layer interaction flow, a backward-facing step flow, and a confined coaxial swirling jet. The multiple-time-scale turbulence model yields significantly improved computational results compared with those obtained using the k-c turbulence model. It is also shown that the present turbulence model can resolve the viscous superlayer of turbulent flows.     

The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

The melting and solidification stages of a continuous copper–nickel dissimilar metal conduction mode laser welding have been simulated numerically in this study. The heat, mass and momentum transports in molten metal pool have been analysed using both laminar and turbulent flow models separately for the same process parameters. The phase change aspects related to solidification and melting are accounted for by a modified enthalpy–porosity technique while the turbulent transport is modelled by a high Reynolds number k–ε model. It has been observed that temperature fields obtained from both laminar and turbulent transport simulations are qualitatively similar to each other. The molecular thermal diffusivity of the molten metal mixture is found to be in the same order of magnitude as eddy thermal diffusivity, as a result of which the thermal field gets marginally affected by fluid turbulence. By contrast, eddy viscosity remains much greater than molecular viscosity, which leads to greater amount of momentum diffusion in the case of a turbulent molten metal pool, in comparison to that obtained from the corresponding laminar simulation. This is reflected in the reduction in maximum velocity magnitude in the turbulent simulation in comparison to the maximum velocity obtained from laminar simulation. In the case of species transport, the turbulent mass diffusivity is found to be about 10⁷–10⁸ times greater than molecular mass diffusivity. As a result, the species field in turbulent simulation shows characteristics of better mixing between two dissimilar molten metals than the species field obtained using the laminar transport model. The species distribution obtained from turbulent transport is shown to be in better agreement with experimental data reported in literature than the corresponding mass fraction distribution obtained from laminar simulation. It is also found that species distribution in the molten pool is principally determined by advective and diffusive transport during the melting stage and species transport by advection and eddy diffusion in turbulent pool increasingly weakens with decreasing temperature during the cooling following the laser melting stage.     

Scalar transport in a turbulent jet

A model equation for the scalar dissipation rate, based on the Two Scale Direct Interaction Approximation (TSDIA) of Yoshizawa [1] was solved and applied to a turbulent round jet in conjunction with turbulence modelling based on the eddy viscosity and diffusivity. The model coefficients were adjusted by using a similarity analysis for the round jet. This led to an improvement in the prediction of concentration fluctuations on the axis of a jet with respect to results obtained with the equal length scales model. The turbulent Schmidt number, no longer assigned an ad-hoc constant value, displays experimentally observed behaviour in the jet.     

Effects of turbulence model and interfacial shear on heat transfer in turbulent falling liquid films

An improved method is presented for the prediction of heat transfer coefficients in turbulent falling liquid films with or without interfacial shear for both heating or condensation. A modified Mudawwar and El-Masr's semi-empirical turbulence model, particularly to extend its use for the turbulent falling film with high interfacial shear, is used to replace the eddy viscosity model incorporated in the unified approach proposed by Yih and Liu. The liquid film thickness and asymptotic heat transfer coefficients against the film Reynolds number for wide range of interfacial shear predicted by both present and existing methods are compared with experimental data. The results show that, in general, predictions of the modified model agree more closely with experimental data than that of existing models.     

Modifications to Reynolds-averaged Navier–Stokes turbulence models for the wind flow over buildings

The standard k–ε turbulence model is well known to perform poorly in the stagnation regions in front of buildings where it over-predicts the turbulent kinetic energy, k. It is less well known that this error is compounded by an excess decay of the turbulence over and behind a building so that k is eventually under-estimated in the building wake. A new formulation of the eddy viscosity in the standard k–ε turbulence model was developed and compared with previous modifications designed for stagnation regions. The new formulation provides more accurate values of k and it showed similar results for streamwise mean velocity predicted by the shear stress transport turbulence model. A blend between the new model and the standard eddy viscosity model provides the best overall prediction of the mean velocities and turbulence.     

LES of Stably Stratified Flow with Varying Thermophysical Properties

Large eddy simulations of stably stratified, turbulent channel flow subjected to a large temperature gradient have been performed by considering a broad spectrum of stratification. Due to a large thermal gradient across the channel, temperature-dependent fluid properties like viscosity (µ), density (ρ), and thermal conductivity (κ) are considered as variables. With increased stratification, a cluster of laminar patches appears in the near-wall region, and turbulent momentum and buoyancy fluxes are suppressed drastically in the core of the channel due to the formation of internal gravity waves. Variable viscosity results in flow relaminarization on the hot side of the channel (where viscosity is higher). Density tends to stablize the flow by blocking the upward movement of thermal plumes, while thermal conductivity pays the toll for viscosity at high Reynolds number. A mechanistic model for wall heat transfer is developed for buoyancy-effected flows. We have observed qualitatively and quantitatively the pronounced modifications in turbulent structure and flow statistics.     

A new heat eddy diffusivity equation for calculation of heat transfer to drag reducing turbulent pipe flows

A new semi-empirical equation of heat eddy diffusivity in terms of friction drag reduction ratio and Weissenburg number is presented. The proposed equation was validated with heat transfer experimental results of Kwack [1] and our recent experimental results, both for aqueous solutions of polyacrylamide (Separan AP-273) for concentrations ranging from 10 to 1000 ppm in turbulent flow through pipes under constant wall heat flux condition. The predictions of heat transfer coefficients with the use of the proposed equation are in good agreement with both sets of independent experimental results. The results of this study indicate that the proposed equation for eddy diffusivity of heat has predictive capability provided experimental measurements of pressure drop and the fluid time scale are available. The fluid time scale for these prediction was estimated using the Powell-Eyring fluid model and apparent viscosity measurements.     

湍流燃烧亚格子线性涡模型研究

湍流燃烧的亚格子模式一直是限制大涡模拟在湍流燃烧中应用的主要困难,介绍了湍流燃烧亚格子模型———亚格子线性涡模型.回顾了该模型的发展历程并给出了其当前形式,指出了该模型建立过程与其他湍流燃烧亚格子模型相比的长处,指出了该模型的不足.对亚格子线性涡模型在湍流燃烧大涡模拟中的应用进行了总结评述,重点分析了该模型应用于超声速燃烧存在的问题.     

Planar momentum-dominated regime of small-scale hydrogen leakage

The geometry of the source of hydrogen leakage is essential in forming hydrogen flow and distribution in air. For example, if the geometry of the source is circular, the behavior of leakage flow becomes axisymmetric and a radial jet is constructed. On the other hand, if the geometry of the source is planar, the behavior of hydrogen leakage becomes planar and a planar jet is constructed. Throughout this article, the problem of momentum-dominated regime of a planar slow-leak hydrogen–air jet resulting from a hydrogen leakage from a planar source is considered. We derive a set of analytical expressions for selected physical turbulent properties. Several quantities of interest are obtained, including the cross-stream velocity, the Reynolds stresses, the velocity-concentration correlation, the dominant turbulent kinetic energy production term, the turbulent eddy viscosity, the turbulent eddy diffusivity, and the turbulent Schmidt number. Moreover, the normalized jet-feed material density and the normalized momentum flux density are correlated.     

Numerical simulation of separated flows in channels

The work deals with numerical modelling of turbulent flows in channels with an expansion of the cross-section where flow separation and reattachment occur. The performance of several eddy viscosity models and an explicit algebraic Reynolds stress model (EARSM) is studied. The used test cases are flows in channels with various backward facing steps where the step is perpendicular or inclined and the top wall is parallel or deflected. Furthermore, a channel with the circular ramp is considered. The numerical solution is achieved by the finite volume method or by the finite element method. The results of both numerical approaches are compared.     

Integral solutions for selected turbulent quantities of small-scale hydrogen leakage: A non-buoyant jet or momentum-dominated buoyant jet regime

In this paper, the integral method is used to derive a complete set of results and expressions for selected physical turbulent properties of a non-buoyant jet or momentum-dominated buoyant jet regime of small-scale hydrogen leakage. Several quantities of interest, including the cross-stream velocity, Reynolds stress, velocity-concentration correlation (radial flux), dominant turbulent kinetic energy production term, turbulent eddy viscosity and turbulent eddy diffusivity are obtained. In addition, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated. Throughout this paper, experimental results from Schefer et al. [Schefer RW, Houf WG, Williams TC. Investigation of small-scale unintended releases of hydrogen: momentum-dominated regime. Int J Hydrogen Energy 2008;33(21):6373–84] and other works for the momentum-dominated jet resulting from small-scale hydrogen leakage are used in the integral method. For a non-buoyant jet or momentum-dominated regime of a buoyant jet, both the centerline velocity and centerline concentration are proportional with z⁻¹. The effects of buoyancy-generated momentum are assumed to be small, and the Reynolds number is sufficient for fully developed turbulent flow. The hydrogen–air momentum-dominated regime or non-buoyant jet is compared with the air–air jet as an example of non-buoyant jets. Good agreement was found between the current results and experimental results from the literature. In addition, the turbulent Schmidt number was shown to depend solely on the ratio of the momentum spread rate to the material spread rate.     

耦合天然气详细反应机理的三维湍流预混火焰结构数值预测

以具有279机理的天然气燃烧为例,分别采用涡耗散概念EDC湍流燃烧模型、修正的涡旋破碎EBU湍流燃烧模型以及基于时均值的Arrhenius关系,对燃烧室内复杂的湍流反应流进行了三维数值模拟,并对预测结果进行了分析．结果表明,EDC模型可以较好地反映湍流化学作用,并且能够较好地描述各基元反应,从而为工程实际复杂燃烧情况下其有害排放、中间物质、自由基和痕迹物质生成机理的研究提供基础。     

多流体模型在燃气轮机燃烧室三维反应流中的应用

对一种模型燃气轮机燃烧室中的三维反应流进行了数值模拟，模型燃烧室的燃料是CH4，燃烧类型是预混燃烧，在数值模拟过程中，采用了Spalding于1995年提出来的多流体模型来对燃烧室中的湍流预混燃烧进行了数值模拟，在数值模拟过程中考虑了辐射问题，采用了六通量辐射模型。通过数值模拟给出了速度，压力，湍流脉动动能，湍流动能耗散率，焓值，湍流粘度，温度，密度，燃烧产物质量分数，氧的质量分数，燃料/空气混合比，燃料质量分数，空间三个方向的辐射热通量以及各种流体的质量分数等变量的分布情况，此外，还采用传统的旋涡破碎模型对此燃烧室进行了数值模拟，并对两种方法的结果进行了分析比较，由分析可以看出多流体模型的结果接近于实际情况，对模型燃烧室进行三维反应流数值模拟的工作为今后对实际燃烧室反应流的数值模拟打下了一定的基础。     

Influence d'ondulations de faible amplitude sur la convection turbulente dans un ecoulement en conduite axisymetrique: Experience et prevision numerique

The influence of weak undulations on the turbulent flow in an axisymmetric pipe is studied through experimental investigations and numerical modelling using the eddy viscosity concept. Cross-section variations, wall curvature effects and the occurrence of reverse flow produce drastic changes in the flow structure. The calculation model has been extended to the numerical prediction of heat convection. Results obtained on the distribution of local heat transfer coefficients and on overall properties confirm that the Reynolds analogy is no longer valid in such a complex flow.     

A Study of LES Stress and Flux Models Applied to a Buoyant Jet

Large eddy simulation (LES) stress and scalar flux subgrid scale models are evaluated in the context of buoyant jets. Eddy viscosity, eddy diffusivity (including formulations of the generalized gradient diffusion hypothesis), “structure” (Bardina and Leonard), mixed, and dynamic models are scrutinized. The performance of the models is examined in terms of the main flow variables and also with respect to the “internal” behavior of the models in terms of the relative contributions to the turbulent kinetic energy budget.     

锅炉一次风管道内流场特性数值模拟及其优化研究

为了改善锅炉烟风管道内二次流所引起的流体流动不均、振动等问题,本文采用重整化群k-ε模型计算了锅炉一次风管道中冷、热风阀门、弯管曲率等影响因素对管内流体流动特性的影响,并给出了在管道中安装导流板减小二次流的最佳方案。通过模拟结果发现,加装导流板后管内的流动湍动程度明显减弱。     

Substantiating a fractal-based algebraic reaction closure of premixed turbulent combustion for high pressure and the Lewis number effects

A comprehensive set of nearly 100 atmospheric and high-pressure flame data of Kobayashi et al. are a good source for numerical analysis to address two main aspects in premixed turbulent combustion—high-pressure influence and effects of fuel type on the reaction rate. The present work deals with the lucid and realizable fractal-based reaction rate closure from Lindstedt and Váos (LV model) for premixed flames in the thin-flame limit. In this study, the reaction source term is customized on the eddy viscosity closure of turbulent transport, for practical reasons. Computed results from the LV model show the right qualitative trends with the experimental findings, as a function of turbulence. However, quantitative predictions of the original model are partly too low, and preclude the effects of pressure and fuel type on the reaction rate. With an extensive parametric study, based on numerical findings as well as on theoretical argumentation, the LV model is substantiated for these two effects. Results from the proposed tuned LV model are found to be in very good agreement with most of the measured data.     

三维紊流燃烧室流场的数值计算

运用圆柱从标系对单管回流燃烧室进行了数值模拟。紊流粘度模型采用k-ε双方程紊流模型来估算紊流粘度,燃烧模型采用EBU旋涡破碎燃烧模型来估算化学反应速度,热辐射模型采用比较简单的DTRM模型来计算热辐射量。计算结果能比较准确地反映燃烧室流场的流动状态,同时也为复杂形状的燃烧室造型提供了方法。     

Simple two-layer model for temperature distribution in the inner part of turbulent boundary layers in adverse pressure gradients

A simple one-point closure for the inner region of turbulent boundary layers subjected to adverse pressure gradient is introduced. The use of local wall variables leads to self-similarity for the temperature distribution but not the velocity. A turbulent velocity scale directly related to the pressure parameter that maintains constant the total shear stress in the inner layer is used to define an eddy viscosity and diffusivity. The predicted velocity and temperature profiles agree reasonably well with the experiments. The essence of the formulation explains why the turbulent heat flux scaled by the local inner variables is merely unaffected contrarily to the Reynolds shear stress distribution in wall units that is significantly sensitive to the imposed pressure gradient.     

四角切圆燃烧炉内颗粒湍流扩散数值模拟

基于四角切圆燃烧锅炉内湍流流动及各向同性的假设,得出炉内和点的特征频率。同时采用特征频率－频谱随机轨道模型及随机轨道模型对炉内颗粒的湍流扩散进行了数值模拟。计算结果表明,特征频率－频谱随机轨道模型更能反映出颗粒湍流扩散中受涡结构的影响的特征,更接近实验结果。