Numerical analysis of boiling on high heat-flux and high subcooling condition using MPS-MAFL

This paper shows the numerical simulation study on the growth of the bubble in the transient pool boiling using moving particle semi-implicit with meshless advection using flow-directional local grid (MPS-MAFL) method. The growth process of a bubble with the different initial radii is calculated in a high heat-flux and high subcooling condition. The smaller initial radius is, the earlier the growth starts. The initial bubble radius has little effect on the growth initiation time and the bubble departure radius.     

ANALYSIS OF MOVING BOUNDARY PROBLEM FOR BUBBLE COLLAPSE IN BINARY SOLUTIONS

Bubble collapse in a binary solution with simultaneous heat and mass transfer is studied under a nonspherically symmetrical condition. A numerical technique is presented in this paper that is suitable for solving the axisymmetric moving boundary problem. Making use of the boundary-fitted curvilinear coordinate system and the Lagrangian method, this finite difference technique is able to dynamically track the evolving bubble shape and size during the collapsing process through adaptive grid regeneration. The grid moving velocity is incorporated as an integral part of the governing equations. The numerical results demonstrate that the combined effect of zero shear stress condition, the decreasing curvature, and short life span results in the absence of a wake behind a collapsing bubble.     

气化炉液池内单个高温气泡传热、传质的数值模拟

建立了气、液间传热传质数学模型,对单个热气泡在上升过程中与处于蒸发阶段的水之间的传热、传质规律进行了数值研究,获得了气泡半径、气泡温度、水蒸发速率以及蒸发量随时间的变化规律.研究表明:在水恒温蒸发阶段,由于传热传质的共同作用,气泡半径随着气泡的上升而变小,并逐渐趋于稳定;随着气、液间温度差的增大,气泡半径缩小得越快;在气泡与水开始接触时,水的蒸发速率及气泡内的水蒸汽增量最大;气泡温度在较短时间内急剧下降,并趋于稳定;随着气泡半径的缩小,气泡冷却速率提高;但随着接触时间的继续增加,对气体的冷却效果却无明显作用.     

Approximate Solution for the Heat-Transfer-Controlled Growth of a Steadily Translating Vapor Bubble

The existing analytical solution for the problem of the heat-transfer-controlled growth of a spherical vapor bubble moving with a constant velocity under the assumptions of a thin thermal boundary layer and potential flow results in a complicated integral equation for the bubble radius and is too unwieldy to be used in multiphase flow models. The goal of this work is to suggest for this problem an approximate solution that gives correct asymptotic behavior and yields a simpler expression for the bubble growth rate. Comparison with the exact solution showed that this way a good approximation can be obtained.     

A level-set method for ultrasound-driven bubble motion with a phase change

A level-set (LS) method is presented for computation of ultrasound-driven bubble motion including the effect of liquid and vapor compressibility as well as the effect of liquid–vapor phase change. The semi-implicit pressure correction formulation is implemented into the LS method to avoid the serous time-step restriction in low Mach number (or near incompressible) flows. The numerical results for one-dimensional compressible flows and spherical bubble motion in a periodic acoustic field show good agreement with the analytical solutions. The effects of phase change and ambient temperature on the ultrasound-driven bubble motion are quantified.     

Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

A Piecewise Linear Interface-Capturing Volume-of-Fluid Method Based on Unstructured Grids

A piecewise linear interface calculation (PLIC) technique on triangular unstructured grids is proposed for the volume-of-fluid (VOF) method. For an interface cell, a straight line segment is set to approximate the actual interface by the gradient of the volume fraction function. Three gradient models are discussed, and the results show that the gradient model introduced from the moving particle semi-implicit method is of the highest accuracy. Mass flux is calculated in a Eulerian scheme depending on the relationship between the line segment and each boundary of the cell. It is proved that the combination of geometric and algebraic methods is most precise, because both geometric interface position and algebraic mass conservation are considered. Numerical experiments are conducted on unstructured grids generated by the traditional Delaunay triangulation method and the bubble packing method (BPM), which can produce much more regular triangular cells than the Delaunay method (see Wu and Chen, Numerical Heat Transfer B, vol. 58; pp. 343–369, 2010). Compared with Young's PLIC-VOF, our method is of satisfactory accuracy and sharpness. The deformation errors on the BPM grid are even smaller than those by the PLIC method on a structured grid. In addition, it is observed that the accuracy is higher on the unstructured grid, with better quality.     

Modeling aspects of vapor bubble condensation in subcooled liquid using the VOF approach

Direct contact condensation of a vapor bubble during subcooled boiling flow scenario has diverse applications in many fields such as thermal, chemical, and nuclear energies. The present work aims at the exploration of the underlying physics of single vapor bubble condensation in subcooled water following the volume of fluid method approach using ANSYS FLUENT 14.5. This work emphasizes on the modeling of the mass transfer rate using interfacial jump conditions for investigating the effect of various parametric conditions on the collapse phenomenon. A comparative study is also performed between the interface jump approach and the models based on the proposed empirical correlations to assess the condensation heat transfer (in terms of the collapse rate and Nusselt number) and bubble shape. The mass transfer model based on the interfacial jump condition is found to be the more realistic among all models for capturing the collapse rate as well as its shape.     

A sharp-interface level-set method for compressible bubble growth with phase change

A sharp-interface level-set method is presented for simulating the growth and collapse of a compressible vapor bubble. The interface tracking method is extended to include the effects of bubble compressibility and liquid-vapor phase change by incorporating the ghost fluid method to efficiently implement the matching conditions of velocity, stress and temperature at the interface. The numerical results for one-dimensional compressible flows and spherical bubble growth show good agreement with the exact solutions. The level-set method is applied to investigate the effects of phase change, ambient temperature and wall on the compressible bubble growth and collapse.     

Collapse of one-component vapor bubble with translatory motion

Theoretical analysis of one-component vapor bubble collapse with translatory motion in uniformly subcooled liquid has been carried out. The bubble is spherical and flow in the region surrounding the bubble is potential. General solution is obtained in which the function R = R(τ) is defined implicitly by integral equation. General solution is reduced to the quasi steady state and quasi linear problem. Quasi steady state solution is used to obtain a set of simple and explicit expressions by which the bubble radius is determined in function of time. The results of theoretical analysis are compared with those given by other authors and available experimental data. The agreement between compared experimental data and theoretical results is very good.     

制备生物柴油中超声空化过程的研究

建立了超声波辅助制备生物柴油中空化气泡运动的动力学模型,采用MATLAB对模型方程进行数值模拟,探讨超声频率、声压幅值、空化泡的初始半径和环境压力对空化泡运动的影响.模拟结果表明,随着超声波频率的增加,空化效应减弱;超声声压较小时,超声波空化为稳态空化过程,随着声压的增加,空化气泡半径变化幅度增加,空化气泡所带来的空化效应必然增加;气泡的原始半径为超声波频率对应的共振尺寸时,空化情况最为激烈,声化效果最好;环境压力变化时,气泡运动的振幅差别不大.经分析得到提高生物柴油产率的较佳条件,即较低频率、较大声压幅值、气泡直径为共振尺寸、普通大气压.该研究可为超声在制备生物柴油中的应用提供基础理论依据.     

Meshless analysis of the substrate temperature in plasma spraying process

The substrate temperature plays a very important role in coating formation and its quality during the thermal spraying. Heating effect of the plasma and particle flux on the substrate is explored in detail in terms of different spraying distances using the meshless local Petrov–Galerkin method (MLPG). Based on this approach, a 3D transient heat transfer model is derived rigorously, in which the moving least-squares (MLS) method is introduced to construct the shape functions. A quartic spline function is selected as the weight function of the MLS scheme and also the test function for the discretized weak form, in which the penalty technique is used to treat the essential boundary conditions. For comparison, the finite element method (FEM) is also adopted to solve the same problem. It is found that the computed temperature is in very good agreement with the empirical data and better than that obtained using FEM, which validates the meshless formulation. Both numerical and experimental results indicate that the spraying distance has a crucial influence on heating effect of the plasma jet and particle flux onto the substrate.     

Diffusion and reaction controlled dissolution of oxygen microbubbles in blood

A model for the dissolution of a bubble in blood is presented in this paper. The gas inside the bubble is oxygen and the collapse of the bubble is controlled by the diffusion of the gas from the bubble surface into the surrounding blood. The diffusion is facilitated by the oxygen uptake reaction between the dissolved gas and the hemoglobin, which is described using the Hill saturation curve. The model consists of a system of coupled differential equations describing the related mass transfer physics in an expanding computational domain, which follows the moving interface between the shrinking bubble and the surrounding blood. The main findings regarding the important collapse time of microbubbles in blood indicate that this time may vary from 10 s to 2 or 3 h depending on the size of the bubbles and on the parameters which specify the blood conditions.     

Theoretical model for fast bubble growth in small channels with reference to startup of capillary pumped loops used in spacecraft thermal management systems

A capillary pumped loop (CPL) is a closed two-phase loop in which capillary forces developed in a wicked evaporator passively pump the working fluid over long distances to dissipate heat from electronic and power sources. Because it has no moving parts and requires minimal power to sustain operation, the CPL is considered an enabling technology for thermal management of spacecraft. While the steady-state operation of a CPL is fairly well understood, its thermal response during startup remains very illusive. During the startup, initial vapor bubble growth in the evaporator is responsible for liquid acceleration that results in a differential pressure spike. A large pressure spike can deprime the evaporator by forcing vapor into the evaporator’s liquid-saturated wick, which is the only failure mode of a CPL other than fluid loss or physical damage to the loop. In this study, a numerical transient 3D model is constructed to predict the initial bubble growth. This model is used to examine the influence of initial system superheat, evaporator groove shape and size, and wick material. A simplified model is also presented which facilitates the assessment of parametric influences by analytic means. It is shown how these design parameters may be optimized to greatly reduce the bubble growth rate and therefore help prevent a deprime.     

Experimental and numerical study of microwave drying in unsaturated porous material

The drying of unsaturated porous material due to microwave drying (2.45GHz) has been investigated numerically and experimentally. Most importantly, this work focuses on the influence of moisture content on each mechanism (vapor diffusion and capillary flow) during microwave drying process. Based on a model combining the electric field and heat-mass transport equations show that the variation of initial moisture content and particle size changes the degree of penetration and rate of absorbed energy within the material. The small bead size leads to much higher capillary forces resulting in a faster drying time.     

Meshless local Petrov–Galerkin approach for coupled radiative and conductive heat transfer

A meshless local Petrov–Galerkin approach is employed for solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media. The meshless local Petrov–Galerkin approach with upwind scheme for radiative transfer is based on the discrete ordinate equations. The moving least square approximation is used to construct the shape function. Three particular test cases for coupled radiative and conductive heat transfer are examined to verify this new approximate method. The dimensionless temperatures and the dimensionless heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the meshless local Petrov–Galerkin approach has a good accuracy in solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media.     

Numerical simulation of compression of the single spherical vapor bubble on a basis of the uniform model

The problem of the response of a single spherical vapor bubble is considered for the case of an abrupt increase of pressure in the surrounding infinite liquid. The mathematical model adopted is based on the assumption of the uniformity of pressure, temperature and density throughout the bubble volume. The temperature field around the bubble is calculated using the energy equation for the liquid. Thermal–physical characteristics, exclusive of specific heats of the liquid and vapor, are considered to be temperature-dependent. A notable feature of the model is the exact fulfillment of the integral law of conservation of system energy, disregarding the relatively small vapor kinetic energy. The initial bubble radius and the pressure rise in the liquid were varied in the calculations. It was found that the temperature increment in the bubble due to vapor condensation and heat exchange with the liquid is approximately two orders of magnitude less than that due to adiabatic compression. To study the effect of condensation, calculations were performed in which phase transitions were artificially blocked at the bubble boundary. It was found that the character of the process in the latter case changes both quantitatively and qualitatively; in particular, the temperature increment increases by about an order of magnitude.     

An adaptive time-stepping semi-Lagrangian method for incompressible flows

The semi-Lagrangian method is widely applied to solving the advection term of the Navier–Stokes (N–S) equations whereas the role of time step is often unclear. This article proposed an adaptive time-stepping method, which first calculates local adaptive time step based on truncation error coefficient functions, and then to obtain global time step based on an averaging function for all grid points. The new method was tested for solving 1-D and 2-D advections with different initial time steps and grid resolutions, and the transient incompressible N–S equations. Better simulation accuracy can be achieved than the cases with constant time steps.     

Simulations of Droplet Spreading and Solidification Using an Improved SPH Model

Smoothed particle hydrodynamics (SPH) method as one of the meshless Lagrangian methods has been widely used to simulate problems with free surface. The traditional SPH method suffers from so-called tensile instability, which may eventually result in numerical instability or complete blowup during the simulation of bubble/droplet dynamics. A new pressure-correction equation is proposed to efficiently transport the local pressure to the neighboring area during the impact of incompressible/compressible fluid and reduce the disorder of particle distribution. Consequently, the accuracy and the efficiency of the SPH method can be dramatically improved. New treatments to the surface tension and solidification are also proposed to manipulate SPH particles near the free surface and the solidification interface. The improved SPH method has been used to simulate droplet impact, spreading, and solidification. It is evident that the new method can handle the droplet contraction problem without causing numerical instability. The numerically predicted flattening ratio of the splat due to droplet impact is in good agreement with the analytical prediction. The results demonstrate that the improved SPH model is a powerful tool to study droplet spreading and solidification.     

Development of a Moving and Stationary Mixed Particle Method for Solving the Incompressible Navier-Stokes Equations at High Reynolds Numbers

In the current particle method, we propose a new semi-implicit particle method for more effectively solving the incompressible Navier-Stokes equations at a high Reynolds number. Within the Lagrangian framework, the convective terms in the equations of motion are eliminated, without the problem of convective numerical instability. Also, the crosswind diffusion error generated normally in the case of a large angle difference between the velocity vector and the coordinate line disappears. Only the Laplacian operator for the velocity components and the gradient operator for the pressure need to be approximated on the basis of particle interaction through the currently proposed kernel function. As the key to getting better predicted accuracy, the kernel function is derived subject to theoretical constraint conditions. In the conventional moving-particle method, it is almost impossible to get convergent solution at a high Reynolds number. To overcome this simulation difficulty so that the moving-particle method is applicable to a wider range of flow simulations, a new solution algorithm is proposed for solving the elliptic-parabolic set of partial differential equations. In the momentum equations, calculation of the velocity components is carried out in the particle-moving sense. Unlike the traditional moving-particle semi-implicit method, the pressure values are not calculated at the particle locations being advected along the flowfield. After updating the fluid particle locations within the Lagrangian framework, we interpolate the velocities at uniformly distributed pressure locations. In the current semi-implicit solution algorithm, pressure is governed by the elliptic differential equation with the source term being contributed entirely to the velocity gradient terms. The distribution of particle locations can become highly nonuniform in cases involving a high Reynolds number and under conditions having an apparently vortical flow. As a result, the elliptic nature of the pressure can be considerably destroyed in the course of Lagrangian motion. To retain the embedded ellipticity in the incompressible viscous flow equations, the Poisson equation adopted for the calculation of pressure is solved in a mathematically more plausible fixed uniform mesh so as to get not only fourth-order accuracy for the pressure but also to enhance ellipticity in the pressure Poisson equation. Moreover, the velocity–pressure coupling can be more enhanced in the semi-implicit solution algorithm. The proposed moving and stationary mixed particle semi-implicit solution algorithm and the particle kernel will be demonstrated to be suitable to simulate high-Reynolds number fluid flows by investigating the lid-driven cavity flow problem at Re = 100 and Re = 1,000. Besides the validation of the proposed semi-implicit particle method in the fixed domain, the broken-dam problem is also solved to demonstrate the ability of accurately capturing the time-evolving free surface using the proposed semi-implicit particle method.