Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition

In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.     

Numerical modeling for compartment fire environment under a solid-cone water spray

A mathematical model was developed for simulating the fire environment of a compartment under the action of a solid-cone water spray such as those discharged from a water mist fire suppression system. A smoke layer was induced by a fire in the compartment. The solid-cone water spray was discharged to act on the smoke layer, but not on the burning object. Under this condition of having a stable smoke layer, the compartment was divided into three regions. Region 1 is the upper hot smoke layer, Region 2 is the lower cool air layer and Region 3 is the solid-cone spray. The effects on the smoke layer development due to spray-induced flow were considered on the basis of mass, momentum and heat conservation. Water droplets of the solid-cone spray were divided into four typical classes based on the droplet distribution function.

The parameters including the smoke layer interface height, smoke temperature and air temperature, smoke flow rate through the opening and oxygen concentration in the air layer were investigated under various heat release rates, water application rates and volume mean diameters of the solid-cone spray. Effective hot gas entrainment and water vapor production suggested that the water spray should contain a variety of droplet size. In this way, a compartment fire can be controlled effectively through indirect interaction such as oxygen concentration depletion.     

具有蒸发液滴两相介质近壁流动的数学分析

在双连续介质理论框架下，采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程，给出了控制汽雾流的相似判据。对于沿曲面的流动，边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体驻点附近蒸汽－液滴边界层的数值计算结果。它们表明：由于蒸发，在边界层内近壁处形成了一个无液滴区域；在该区上边界处，液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加，甚至在自由来流中液滴质量浓度很低时此效应依然存在。     

Numerical modelling of EHD effects on heat transfer and bubble shapes of nucleate boiling

In this article, mathematical and numerical models are developed to study pure electrohydrodynamic (EHD) effects on heat transfer and bubble shapes when an initial bubble attached to a superheated horizontal wall in nucleate boiling. In the modelling of EHD effects on heat transfer, an undeformed bubble is considered; the electric body force and Joule heat are added to the momentum and energy equations; governing equations for heat, fluid flow and electric fields are coupled numerically and solved using a non-orthogonal body-fitted mesh system with necessary interfacial treatments at the gas–liquid boundary. While, to study the pure effect of EHD on the deformation of the bubble, the evaluation of a deformable bubble without heat transfer is simulated by volume of fluid (VOF) method based on an axial symmetric Cartesian coordinate system. The simulations indicate that EHD can effectively enhance heat transfer rate of nucleate boiling by influencing the motion of the ring vortex around the bubble and that bubble can be elongated due to the pull in axial direction and push in the negative radial direction by the electric field force.     

Three-dimensional numerical simulation of nonisotropic thermal density flow in a strongly curved open channel

The results from a 3D nonisotropic algebraic stress/flux turbulence model are presented to investigate the structure of thermal density flow and the temperature distribution in a strongly curved open channel (180° bend). The numerically simulated results show that (i) several secondary flows take place at the bend cross-section 90° of the curved open channel, the feature which is not found for the isothermal flows and thermal density flow in a straight channel, and (ii) the thermocline in a curved channel is thicker than that in a straight channel due to the secondary flows-induced strong mixing process taking place in the former. Such features may be ascribed to the complex interaction of the buoyant force, the centrifugal force and the Reynolds stresses taking place only in curved channels. The simulated results are in good agreement with available experimental data, which indicates that the developed model can be applied for predicting the motion of the nonisotropic thermal density flow in the curved open channel.     

Numerical modelling of bubbly flows with and without heat and mass transfer

In this paper, modelling gas–liquid bubbly flows is achieved by the introduction of a population balance equation combined with the three-dimensional two-fluid model. For gas–liquid bubbly flows without heat and mass transfer, an average bubble number density transport equation has been incorporated in the commercial code CFX5.7 to better describe the temporal and spatial evolution of the geometrical structure of the gas bubbles. The coalescence and breakage effects of the gas bubbles are modelled according to the coalescence by the random collisions driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Local radial distributions of the void fraction, interfacial area concentration, bubble Sauter mean diameter, and gas and liquid velocities, are compared against experimental data in a vertical pipe flow. Satisfactory agreements for the local distributions are achieved between the predictions and measurements. For gas–liquid bubbly flows with heat and mass transfer, boiling flows at subcooled conditions are considered. Based on the formulation of the MUSIG (multiple-size-group) boiling model and a model considering the forces acting on departing bubbles at the heated surface implemented in the computer code CFX4.4, comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter, interfacial area concentration, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter, interfacial area concentration and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress through the consideration of additional momentum equations or developing an algebraic slip model to account for the effects of bubble separation.     

Predictions of the gas–liquid flow in wet electrostatic precipitators

Based on Computational Fluid Dynamics (CFD), the present paper aims to simulate several important phenomena in a wet type ESP from the liquid spray generation to gas-droplet flow in electric field. A single passage between the adjacent plates is considered for the simulation domain. Firstly, the electric field intensity and ion charge density are solved locally around a corona emitter of a barbed wire electrode, which are applied to the entire ESP using periodic conditions. Next, the Euler–Lagrange method is used to simulate the gas-droplet flow. Water droplets are tracked statistically along their trajectories, together with evaporation and particle charging. Finally, the deposition density on the plate is taken as the input for the liquid film model. The liquid film is simulated separately using the homogenous Eulerian approach in ANSYS-CFX. In the current case, since the free surface of the thin water film is difficult to resolve, a special method is devised to determine the film thickness.As parametric study, the variables considered include the nozzle pressure, initial spray spreading patterns (solid versus hollow spray) and plate wettability. The droplet emission rate and film thickness distribution are the results of interest. Main findings: electric field has strong effect on the droplet trajectories. Hollow spray is preferred to solid spray for its lower droplet emission. The liquid film uniformity is sensitive to the plate wettability.     

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles

Magneto-hydrodynamics and thermal radiation effects on heat and mass transfer in steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid saturated porous media in the presence of the thermophoresis particle deposition effect is studied in this paper. The governing equations are transformed by special transformations. Brownian motion of particles and thermophoretic transport are considered in the flow equations. The magnetic field is considered to be applied. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically by the fourth-order Runge–Kutta method with shooting technique. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on the wall thermophoretic deposition velocity, concentration, temperature and velocity profiles.     

传导-辐射对沿垂直平面有热泳的瞬时自然对流的影响

研究存在热辐射时,热泳微粒的沉积,对沿垂直平面瞬态自然对流边界层流动的影响,垂直平面浸没在光密灰色流体中.分析中采用Rosseland扩散近似表示辐射热通量项.将控制方程简化为抛物线型的偏微分方程组,然后在整个时间段0≤τ<∞,利用有限差分法数值求解.还得到了小数值时间和大数值时间的渐近解,发现渐近解和数值解吻合很得好.而且,流体,20℃和1个标准大气压下的空气,即Prandtl数Pr为0.7时,用图形给出了不同物理参数,即热辐射参数Rd、表面温度参数θw和热泳参数λ,对瞬时的表面剪切应力τw、表面热传输率qw和组分浓度扩散率(传质率)mw的影响,以及对瞬时的速度、温度和浓度分布曲线的影响.     

Numerical simulation of the interaction between vortex ring and bubble plume

In present paper a three-dimensional Vortex-In-Cell method with two-way coupling effect was developed to study the bubble plume entrainment by a vortex ring. In this method the continuous flow was calculated by the three-dimensional Vortex-In-Cell method and the bubbles are tracked through bubble motion equation. Two-way coupling effect between continuous flow and dispersed bubbles is considered by introducing a vorticity source term, which is induced by the change of void fraction gradient in each computational cell. After validated by the comparison between experimental measurements and simulation results for the motion of vortex rings and the rising velocity of bubble plume, present method is implemented to simulate the interaction between an evolving vortex ring and a rising bubble plume. It was found that there is little effect of the bubble entrainment to the total circulation of vortex ring while the effect of bubble entrainment to the vortex ring structure is quite obvious. The bubble entrainment by the vortex ring not only changed the vorticity distribution in the vortex structure, but also displaced the positions of the vortex cores. The vorticity in the lower vortex core of the vortex ring decreases more than that in the upper vortex core of the vortex ring while the vortex core in the upper part of the vortex ring is displaced to the center of vortex ring by the entrained bubbles. Smaller bubbles are easier to be entrained by the large scale vortex structure and the transportation distance is in inverse proportion to bubble diameter.     

壁面效应对剪切稀化流体内气泡上浮特性的影响

数值研究了壁面效应对剪切稀化流体内气泡上浮运动特性的影响,气液两相的界面捕捉采用流体体积(VOF)法,剪切稀化流体流变特性和气液相间表面张力的计算分别采用Carreau模型和连续表面张力模型.详细研究了不同流变指数下,壁面效应对气泡形状、液相流场和气泡终端速度的影响.结果表明,强的壁面效应或弱的剪切稀化程度会限制气泡的变形和尾涡的形成,使气泡的终端速度减小;气泡终端速度最易受壁面效应的影响;强的壁面效应和强的剪切稀化程度会导致高剪切速率区域出现在壁面附近,引起壁面附近液相表观黏度大幅度的下降.     

Turbulent boundary layer on a plate. Reynolds analogy and new formulations of the temperature defect law

A consistent asymptotic theory describing hydrodynamic and thermal turbulent boundary layers on a flat plate in zero pressure gradient is developed. The fact that the flow depends on a limited number of governing parameters allows us to formulate algebraic closure conditions that relate the turbulent shear stress and turbulent heat flux to mean velocity and temperature gradients. As a result of an exact asymptotic solution of the boundary-layer equations, the known laws of the wall for the velocity and temperature and the velocity and temperature defect laws as well as the expressions for the skin-friction coefficient, Stanton number, and Reynolds-analogy factor are obtained. The latter implies two new formulations for the temperature defect law one of which is completely similar to the velocity defect law and does not contain the Stanton number and the turbulent Prandtl number, and the other does not contain the skin-friction coefficient. A heat-transfer law is obtained that relates only thermal quantities. The theoretical conclusions agree well with experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Falling film flow of a viscoelastic fluid along a wall

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non‐dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear‐thinning and shear‐thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain. Copyright © 2013 John Wiley & Sons, Ltd.     

底部加热肥皂泡上准二维湍流的数值模拟北大核心CSCD

底部加热的肥皂泡是一种全新的二维热对流模型,在实验中已发现肥皂泡上的岛涡运动规律与飓风轨迹规律一致.然而,肥皂泡的曲面特征对其准二维流场的数值模拟以及数据分析造成了较多困难.针对肥皂泡球面几何特征,该文介绍了其直接数值模拟(DNS)方法,及其流场空间波数谱、湍流通量和结构函数的计算分析方法.开展了Ra=3×10^(7),3×10^(9),3×10^(11)的数值计算,并获得了相应的波数谱、通量和湍流结构函数.计算结果表明,肥皂泡上速度的小尺度脉动特征满足Bo59的理论标度律,通过湍动能与拟涡能通量特征,发现在该准二维湍流场中存在湍流能量双级串现象.且随着Rayleigh数的增加,大尺度结构湍能量减小,更小尺度湍流结构能量增加.     

经过修正的层流流动的流动稳定性问题(Ⅲ)——经过修正的平行剪切流的非线性稳定性研究

本文根据文[1]给出的经过修正的层流流动的流动稳定性理论及平行剪切流中平均速度的一类修正剖面,研究了平行剪切流的非线性稳定性性质,并在本文的假设下,把背景湍流噪声的干扰引入了流动稳定性计算,对于平面Poiseuille流动和圆管Poiseuille流动,得到了与实验趋势相一致的结果.     

Hall current effect on MHD mixed convection flow from an inclined continuously stretching surface with blowing/suction and internal heat generation/absorption

Hydromagnetic heat transfer by mixed convection along an inclined continuously stretching surface, with power-law variation in the surface temperature or heat flux, in the presence of Hall current and internal heat generation/absorption has been studied. The surface is considered to be permeable to allow fluid suction or blowing, and stretching with a surface velocity varied according to a power-law. Two cases of the temperature boundary conditions were considered at the surface. The governing equations have been transformed into non-similar partial differential equations which have been integrated by the forth-order Runge–Kutta method. The effect of Hall parameter, magnetic parameter, dimensionless blowing/suction parameter, space and temperature dependent internal heat generation/absorption parameters and buoyancy force parameters on the temperature, primary and secondary flow velocity have been studied parametrically. All parameters involved in the problem affect the flow and thermal distributions except the temperature-dependent internal heat generation/absorption in the case of prescribed heat flux (PHF). Numerical values of the local skin-friction and the local Nusselt numbers for various parametric conditions have been tabulated.     

非线性边界滑移挤压膜流动

用一种包含初始滑移长度和临界剪切率的非线性边界滑移模型研究了两个球体间的挤压流体膜问题．研究发现初始滑移长度对低剪切率下的滑移行为起主要作用,而临界剪切率决定了高剪切率下的边界滑移程度．球体表面挤压流体膜的边界滑移量是与半径坐标相关的高度非线性函数．在挤压膜的中心点和远离中心点处由于低剪切率滑移量等于初始滑移长度,然而在高剪切率区域滑移长度迅速增加．球体挤压膜的流体动压力随着初始滑移长度的增加和临界剪切率的减小而减小,并且临界剪切率对流体动力的影响要比初始滑移长度大的多,当临界剪切率很小的情况下,流体动压随着最小膜厚的减小几乎不再增加．所用模型给出的理论预报和实验非常吻合．     

The simulation of micro droplet behavior of molten lead-free solder in inkjet printing process and its experimental validation

Micro droplets of molten lead-free solder were ejected at 230 °C using a piezoelectric inkjet printing process. The effect of the micro droplet formation of molten lead-free solder was investigated on the pulse time of the waveform. In this study, a numerical system for simulating the shape evolution of micro droplet of molten lead-free solder in the inkjet printing process was developed based on a solution algorithm (SOLA) scheme for the solution of velocity and pressure fields. It is coupled with the volume-of-fluid (VOF) and piecewise-linear interface construction (PLIC) techniques for the transport of mass and construction of the interface. For the treatment of surface tension effects, a CSF (continuum surface force) model is employed. The simulation results were validated with experimental observations. The numerical result was used to understand the mechanisms of the extrusion of the liquid column, the contraction of the liquid thread, and the pinch-off of the liquid thread at the nozzle exit.