Choked flows in open capillary channel

A forced liquid flow through an open capillary channel with free liquid surfaces is investigated. Since the free surfaces can only withstand a certain difference between the liquid pressure and the ambient pressure the flow rate in the channel is limited. The maximum flow rate is achieved when the surfaces collapse. A theoretical approach is presented which shows that the limitation of flow rate occurs due to choking. This theory confirms the results of an experiment performed on board the sounding rocket TEXUS‐37 to measure the maximum stationary volume flux of a forced flow through an open capillary channel.     

扰动的Couette－Poiseuille流的特征值的计算

本文考虑的问题是二维粘性渠流。对0到2000之间的雷诺数,计算了平稳扰动的Couette-Poiseuille流的下游特征值,其特征方程类似于Orr-Sommerfeld方程。所用的方法是谱方法和初值方法(复合矩阵方法).就几种有趣的流量,给出了相应的特征值的计算结果。这些特征值确定了扰动的衰减率。     

Global subsonic Euler flows in an infinitely long axisymmetric nozzle

In this paper, we consider global subsonic compressible flows through an infinitely long axisymmetric nozzle. The flow is governed by the steady Euler equations and has boundary conditions on the nozzle walls. Existence and uniqueness of global subsonic solution are established for an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The results give a strictly mathematical proof to the assertion in Bers (1958) [2]: there exists a critical value of the incoming mass flux such that a global subsonic flow exists uniquely in a nozzle, provided that the incoming mass flux is less than the critical value. The existence of subsonic flow is obtained by the precisely a priori estimates for the elliptic equation of two variables. With the assumptions on the nozzle in the far fields, the asymptotic behavior can be derived by a blow-up argument for the infinitely long nozzle. Finally, we obtain the uniqueness of uniformly subsonic flow by energy estimate and derive the existence of the critical value of incoming mass flux.     

Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no-slip condition, continuity of velocity and stresses at interfaces along with Happle's no-couple stress condition as the boundary conditions. The expressions for the linear velocity, micro-rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro-rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work.     

黄河小型清沟封冻过程现场模拟实验与实测数据分析

利用黄河封冻阶段的冰层,开16m2敞流水面模拟清沟,通过雷达测冰厚的方法,观测敞流水面因冰花封冻过程,并测量敞流水面封冻后冰盖厚度分布,并用费氏台观察冰晶体结构.通过将实测冰厚数据绘成等高线图以及冰厚剖面图,证实封河过程中,由周边向中间封冻的清沟除了与冰冻度日有关外,还与清沟下水流速度和方向以及冰花含量有关.水流携带冰花流至清沟时,冰花会漂浮在清沟中.由于水的粘性作用,水流使清沟中的水起动,然后冲击下游冰壁引起涡旋.涡旋场在清沟上游形成较平静区域,可以积累大量冰花;而在下游冰壁处水体运动活跃,冰花无法堆积.经过长时间冻结,上游处冰花被冻结成为较厚的冰花冰,而下游逐渐冻结成较薄的冰花冰.之后,柱状冰在冰花冰下开始生长.最后经过1个月的冻结,形成了敞流水面下游处冰较薄,上游处冰较厚的非对称冻结厚度分布,并在与水流垂直的方向表现为对称冻结厚度分布.     

Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction

Analytical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously vertical permeable surface in the presence of a radiation, a first-order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed.     

Making the semi-implicit space-time conservation-element solution-element method of Jerez et al. more explicit

In the beginning of the nineties a NASA-group around S. C. Chang started to work on a new method for unsteady flow computation with seemingly good results. Thereby elements are space-time domains. Within solution-elements state and flux variables are linearized satisfying the underlying differential equation, within conservation-elements space-time flux is conserved. Proceeding this way for one-dimensional pipe flow Jerez et al. include source terms with all cross-section dependencies making the method semi-implicit. We show that by taking simple measures as - accounting for cross-sections in state and flux variables of mass and energy or - subtracting spatially integrated source terms from the flux the method may become more or completely explicit, particularly helpful when chemical species transport is involved. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fractal graph model of capillary type systems

Abstract

We consider blood flow in a vessel with an attached capillary system. The latter is modelled with the help of a corresponding fractal graph whose edges are supplied with ordinary differential equations obtained by the dimension-reduction procedure from a three-dimensional model of blood flow in thin vessels. The Kirchhoff transmission conditions must be satisfied at each interior vertex. The geometry and physical parameters of this system are described by a finite number of scaling factors which allow the system to have self-reproducing solutions. Namely, these solutions are determined by the factors’ values on a certain fragment of the fractal graph and are extended to its rest part by virtue of these scaling factors. The main result is the existence and uniqueness of self-reproducing solutions, whose dependence on the scaling factors of the fractal graph is also studied. As a corollary we obtain a relation between the pressure and flux at the junction, where the capillary system is attached to the blood vessel. This relation leads to the Robin boundary condition at the junction and this condition allows us to solve the problem for the flow in the blood vessel without solving it for the attached capillary system.     

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case.     

Global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles

In this paper, we establish existence of global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles by combining variational method, various elliptic estimates and a compensated compactness method. More precisely, it is shown that there exist global subsonic flows in nozzles for incoming mass flux less than a critical value; moreover, uniformly subsonic flows always approach to uniform flows at far fields when nozzle boundaries tend to be flat at far fields, and flow angles for axially symmetric flows are uniformly bounded away from π/2; finally, when the incoming mass flux tends to the critical value, subsonic-sonic flows exist globally in nozzles in the weak sense by using angle estimate in conjunction with a compensated compactness framework.     

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.     

Note on the uniqueness of subsonic Euler flows in an axisymmetric nozzle

In this paper, we consider the uniqueness of globally subsonic compressible flows through an infinitely long axisymmetric nozzle. The flow is governed by the steady Euler equations and satisfies no-flow boundary conditions on the nozzle walls. We will show that for given mass flux and Bernoulli’s function in the upstream, the subsonic flow is unique in the class of all axisymmetric solutions, which possess the asymptotic behaviors at the far fields. This result extends the uniqueness of solutions in the previous paper Du and Duan (2011) [1].     

Existence of solutions for a finite nonlinearly hyperelastic rod

A theoretical investigation of a mathematical model for the capillary-tissue fluid exchange, including the characteristics and influence of the boundaries and media through which the fluid flows, has been studied. Filtration from the cylindrical capillary into the concentrically surrounding tissue-space and flow from a capillary into the tissue across the thin membrane are analyzed in detail. It has been observed that the filtration efficiency of the functional unit decreases as the peripherallayer viscosity increases, and that contrary to the results of Apelblat, Katziv-Kutchalsky and Silborberg (Biorheology2 (1974), 1–49), the slip velocity plays dominant role on filtration efficiency. It is also noted that he filtration efficiency decreases as the slip velocity at the porous boundary increases.     

Wave–Mean-Flow Interactions in a Forced Rossby Wave Packet Critical Layer

This paper describes the nonlinear critical layer evolution of a zonally localized Rossby wave packet forced in mid-latitudes and propagating horizontally on a beta plane in a zonal shear flow. The wave packet has an amplitude that varies slowly in the zonal direction. Numerical solutions of the governing nonlinear equations show that the wave–mean-flow interactions differ from those that would result with a monochromatic forcing. With the localized forcing, the net absorption of the disturbance at the critical layer continues for large time, because there is an outward flux of momentum in the zonal direction. Further insight into the mechanism for this and other aspects of the evolution of the critical layer is obtained through an approximate asymptotic analysis which is valid for large time.     

Contact angle effects on microdroplet deformation using CFD

In this paper we use computational fluid dynamics (CFD) to study the effect of contact angle on droplet shape as it moves through a contraction. A new non-dimensional number is proposed in order to predict situations where the deformed droplet will form a slug in the contraction and thus have the opportunity to interact with the channel wall. It is proposed that droplet flow into a contraction is a useful method to ensure that a droplet will wet a channel surface without a trapped lubrication film, and thus help ensure that a slug will remain attached to the wall downstream of the contraction. We demonstrate that when a droplet is larger than a contraction, capillary and Reynolds numbers, and fluid properties may not be sufficient to fully describe the droplet dynamics through a contraction. We show that, with everything else constant, droplet shape and breakup can be controlled simply by changing the wetting properties of the channel wall. CFD simulations with contact angles ranging from 30° to 150° show that lower contact angles can induce droplet breakup while higher contact angles can form slugs with contact angle dependent shape.     

Computational modelling of slug flow in a capillary microreactor

The benefits of slug flow capillary microreactor exhibit the ability to adjust two individual transport mechanisms, i.e., convection inside the slug and diffusion between two consecutive slugs. The mass transfer rate is enhanced by internal circulation, which arises due to the shear between slug axis and continuous phase or capillary wall. The knowledge of circulation patterns within the slug plays an important role in the design of a capillary microreactor. Apart from this, well defined slug flow generation is a key activity in the development of methodology to study hydrodynamics and mass transfer. In the present paper we discuss computational fluid dynamics (CFD) modelling aspects of internal circulations (single phase) and slug flow generation (two-phase).     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

On mass flux through a torus in Stokes flow

The symmetrical flow of a viscous fluid past a torus is considered with particular reference to the mass flux through the central hole. Asymptotic expressions are obtained when the hole is small and when it is relatively large, and are compared with the results of a numerical computation.     

Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.