PARALLEL ADAPTIVE SIMULATION OF A PLUNGING LIQUID JET

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, capturing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method （FEM） was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pool＇s surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.     

Study on Hydrodynamics Characteristics of a Single Bubble in Viscoelastic Fluid at Low Weissenberg Numbers北大核心CSCD

The VOF method was used to numerically study the upward motion of a single bubble in viscoelastic fluid, and the Oldroyd-B model was applied to describe the fluid viscoelastic property. At low Weissenberg numbers (Wi≤1), the effects of the viscous force, the relaxation time, the surface tension and the viscosity ratio on the rising motion of the bubble were studied. The results show that, under relatively large viscous and elastic forces (such as Ga= 2, Wi≥0.5 and β = 0.2), the bubble exhibits the phenomenon of “a pointed rear end”, and this phenomenon intensifies with the increase of the elasticity and the decrease of the surface tension. Otherwise, under a relatively weak elasticity (such as Wi= 0.1), the phenomenon of “a pointed rear end” disappears, and the bubble bears a hat-like shape. For a large surface tension (such as Eo = 1), the bubble bears a longitudinally elongated ellipse-like shape without distinct tail features. The effect of the surface tension on the bubble in viscoelastic fluid is like that in viscous fluid. The bubble has 2 types of rising motions, namely, “continuous acceleration” to a stable velocity and “acceleration-deceleration-reacceleration” to a stable velocity, and the bubble rising velocity in viscoelastic fluid is higher than that in pure viscous fluid. The elastic stress around the bubble is influenced by the viscosity and the relaxation time of the fluid, and with the decrease of the fluid viscosity or/ and the increase of the relaxation time, the incidence of the elastic stress becomes wide. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

First Principle Study on the Influence Mechanism of Impurity Gas O2 on the Adsorption Properties of Alloy ZrCo北大核心CSCD

The adsorption behavior of impurity gases on the surface of alloy ZrCo has an important influence on its hydrogen storage performance. The adsorption behavior of O2 on the ZrCo(110) surface was investigated with the first principles based on the pseudopotential plane wave method. The results of adsorption energy and charge analysis show that, the most stable geometry configuration was B3 (the Zr—Co bridge site) where the adsorption energy was –8.124 eV. The analysis of the density of states and the differential charge density show that, the adsorption behavior of O2 on the ZrCo(110) surface is a strong chemical adsorption, where the oxygen-oxygen bond breaks. The essence of bonding between atom O and the ZrCo(110) surface atom is that the electron orbit of atom O overlaps with the electron orbit of the surface atom, i.e. the 2s and 2p orbital electrons of atom O overlapped with the 4p and 4d orbital electrons of atom Zr and the 3d orbital electrons of atom Co on the surface. The research results make senses in revealing the poisoning mechanism of alloy ZrCo in impurity gases. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Determination of Unknown Boundary in the Composite Materials with Stefan-Boltzmann Conditions

Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary （or corrosion） by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Nonuniform Approach to Terminal Velocity for Single Mode Rayleigh-Taylor Instability

Abstract The temporal development of a single mode Rayleigh-Taylor instability consists of three stages:the linear, free fall and terminal velocity regimes. The purpose of this paper is to report on new phenomenaobserved in the approach to terminal velocity. Our numerical study shows an unexpected nonuniform approachto terminal velocity. The nonuniformity applies especially to the spikes, which are fingers of heavy fluid fallinginto the light fluid, but it also applies to the rising bubbles of light fluid. For spikes especially our results callinto question the meaningfulness of a terminal velocity for moderate values of the Atwood number A. After ashort time period of pseudo-terminal plateau, the spike velocity increases to a significantly higher maximum,followed by a decrease. This phenomena appears to be due to a slow evolution in the shape of the spike andbubble. We find a relation between the spike (bubble) acceleration and the tip curvature. In correlation with anincrease in the spike velocity, th     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Two-scale analysis method for predicting heat transfer performance of composite materials with random grain distribution

A two-scale analysis (TSA) method for predicting the heat transfer performance of composite materials with the random distribution of same-scale grains is presented. First the representation of the materials with the random distribution is briefly described. Then the two-scale analysis formulation of heat transfer behavior of the materials with random grain distribution of small periodicity is formally derived by means of     

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.     

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.     

Numerical study of dynamics of single bubbles and bubble swarms

A systematic computational study of the dynamics of gas bubbles rising in a viscous liquid is presented. Two-dimensional simulations are carried out. Both the dynamics of single bubbles and small groups of bubbles (bubble swarms) are considered. This is a continuation of our previous studies on the two-bubble coalescence and vortex shedding [A. Smolianski, H. Haario, P. Luukka, Vortex shedding behind a rising bubble and two-bubble coalescence: a numerical approach, Appl. Math. Model. 29 (2005) 615–632]. The proposed numerical method allows us to simulate a wide range of flow regimes, accurately capturing the shape of the deforming interface of the bubble and the surface tension effect, while maintaining the mass conservation. The computed time-evolution of bubble’s position and rise velocity shows a good agreement with the available experimental data. At the same time, the results on the dynamics of bubble interface area, which are, up to our knowledge, presented for the first time, show how much the overall mass transfer would be affected by the interface deformation in the case of the bubble dissolution. Another set of experiments that are of interest for chemical engineers modelling bubbly flows concerns the bubble swarms and their behavior in different bubble-shape regimes. The ellipsoidal and spherical shape regimes are considered to represent, respectively, the coalescing and non-coalescing bubble swarms. The average rise velocities of the bubble swarms are computed and analyzed for both regimes.     

The dynamics of the growth of vapour bubbles in a superheated liquid

The boiling of a superheated liquid is investigated assuming that, in the initial state, the liquid and a vapour bubble (or a system of vapour bubbles) are in mechanical and thermal equilibrium. It is shown that the state of a mixture of a liquid and bubbles is unstable due to the action of capillary forces. Linear and non-linear solutions are constructed describing the emergence of the system from the unstable state and also the unbounded growth of a single bubble and the transition into a stable vapour-liquid state when there are bubbles distributed throughout the volume in the initial state.     

Steady-state solutions in a nonlinear pool boiling model

We consider a relatively simple model for pool boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling fluid via a nonlinear boundary condition imposed on the fluid–heater interface. This results in a standard heat equation with a nonlinear Neumann boundary condition on part of the boundary. In this paper, we analyse the qualitative structure of steady-state solutions of this heat equation. It turns out that the model allows both multiple homogeneous and multiple heterogeneous solutions in certain regimes of the parameter space. The latter solutions originate from bifurcations on a certain branch of homogeneous solutions. We present a bifurcation analysis that reveals the multiple-solution structure in this mathematical model. In the numerical analysis a continuation algorithm is combined with the method of separation-of-variables and a Fourier collocation technique. For both the continuous and discrete problem a fundamental symmetry property is derived that implies multiplicity of heterogeneous solutions. Numerical simulations of this model problem predict phenomena that are consistent with laboratory observations for pool boiling processes.     

Boiling heat transfer on a sphere with turbulent vapour film

The theoretical study investigates turbulent film boiling on a sphere immersed in the stagnant liquid. It begins by assuming the surface temperature of the sphere is isothermal. The result shows that the boiling heat transfer under the turbulent vapour shows that both the temperature and the velocity present a non-linear distribution. Besides, the increase of the thermal radiation, wall temperature and buoyancy effects can enhance the heat transfer efficiency. Furthermore, a comparison between the results of the present study and those reported in a previous theoretical study of laminar film boiling is provided. It is found that turbulent film boiling with higher Rayleigh number will have higher Nusselt number.     

网络股泡沫大小测度研究

网络股泡沫是最能反映网络泡沫本质的表现形式，本文利用理性预期理论，构建了网络股泡沫大小的测度模型，说明网络股泡沫的存在，在此基础上确定了网络股泡沫大小的测度指标，并以雅虎公司股票为例对泡沫的大小进行了测度，结果符合网络泡沫的实际情况。     

基于马氏域变的房地产泡沫存在概率研究

借鉴股票市场泡沫的研究方法,采用非齐次马氏域变思想对我国2001年1月到2010年12月的房地产市场泡沫进行了分析.通过Johansen协整检验方法从房价数据中分离出泡沫成份,使用极大似然估计方法估计出房价泡沫在两状态下的方差和转移概率的相关参数,进而求出各时期房价泡沫存在的概率.实证结果表明:第一,样本期间大部分时期内我国房地产价格存在泡沫的概率较小,但2009年4月至12月房价存在泡沫的概率较大;第二,提高贷款利率能够减小从无泡沫到有泡沫的概率,同时增加从有泡沫到无泡沫的概率.     

Heat flux effect on the droplet entrainment and deposition in annular flow dryout

This paper discusses the internal mass transfer process in annular flow dryout. The emphasis is put on the order of magnitude estimation of respective hydrodynamic and thermal mechanisms and the analysis of the heat flux effect on droplet entrainment and deposition. A simple interfacial turbulence model is developed to characterize the turbulence intensity suppression due to interface tension. The heat flux effect on droplet entrainment depends on the competition between the shear force decrease due to vapor effusion and the bubble emission: in low flow condition, the bubble emission outweighs the shear force decrease, thus the net effect is to increase the droplet entrainment; in high flow condition, the situation may reverse. The heat flux impact on droplet deposition is significant only for very fine droplets (less than 1 μm) because of the coupled effect of interface turbulence damping and the radial vapor effusion due to evaporation, but for droplets of medium and large sizes the heat flux effect is negligible. The analysis is then used to develop constitutive equations for droplet entrainment and deposition rates to take into account the interaction between thermal and hydrodynamic mechanisms, which gives improved CHF prediction for limiting quality regime (LQR) CHF experimental data.     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.