Specific features of unsteady exhaustion of a gas–particle medium into vacuum

Results of an analysis of two-dimensional unsteady exhaustion of a one-velocity gas–particle medium into vacuum for limiting equilibrium cases of heat transfer between the phases are reported. Domains of existence of a one-dimensional Riemann wave and a lateral expansion wave, as well as boundaries of the flow expansion region are determined. Under thermal equilibrium conditions, the reverse flow is found to occupy a large domain extending beyond the boundaries defined by angles of expansion for an ideal gas and for a gas–particle mixture with thermally insulated phases. Exhaustion of a nonequilibrium (in terms of velocities and temperatures) two-phase medium into vacuum is numerically simulated. It is demonstrated that a barrel-shaped structure with wave expansion of the gas and a combined discontinuity in the expanding gas–particle mixture is formed.     

The Onset of Convection in an Anisotropic Porous Layer Using a Thermal Non-Equilibrium Model

The stability of a horizontal fluid saturated anisotropic porous layer heated from below and cooled from above is examined analytically when the solid and fluid phases are not in local thermal equilibrium. Darcy model with anisotropic permeability is employed to describe the flow and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is implemented to compute the critical Rayleigh number and the corresponding wavenumber for the onset of convective motion. The effect of thermal non-equilibrium and anisotropy in both mechanical and thermal properties of the porous medium on the onset of convection is discussed. Besides, asymptotic analysis for both very small and large values of the interphase heat transfer coefficient is also presented. An excellent agreement is found between the exact and asymptotic solutions. Some known results, which correspond to thermal equilibrium and isotropic porous medium, are recovered in limiting cases.     

Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model

Nanoparticle(drug particle) dispersion is an important phenomenon during nanodrug delivery in the bloodstream by using multifunctional carrier particles. The aim of this study is to understand the dispersion of drug particle(nanoparticle) transport during steady blood flow through a microvessel. A two-phase fluid model is considered to define blood flow through a microvessel. Plug and intermediate regions are defined by a non-Newtonian Herschel-Bulkley fluid model where the plug region appears due to the aggregation of red blood cells at the axis in the vessel. The peripheral(porous in nature)region is defined by the Newtonian fluids. The wall of the microvessel is considered to be permeable and characterized by the Darcy model. Stress-jump and velocity slip conditions are incorporated respectively at the interface of the intermediate and peripheral regions and at the inner surface of the microvessel. The effects of the rheological parameter, the pressure constant, the particle volume fraction, the stress jump constant, the slip constant,and the yield stress on the dispersion are analyzed and discussed. It is observed that the non-dimensional pressure gradient and the yield stress enhance the dispersion rate of the nanoparticle, while the opposite trends are observed for the velocity slip constant, the nanoparticle volume fraction, the rheological parameter, and the stress-jump constant.     

Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas

Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture \(K_p\) , and the ratio of the density of solid particles to the initial density of the gas \(G_a\) are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.     

泡内气体热力学性质对空泡溃灭的影响

数值研究固壁附近轴对称空泡溃灭问题. 忽略泡内气体与周围流体之间的质量和热交换, 假设气体瞬时处于热平衡状态, 通过引入不同的热力学模型, 考察泡内气体在空泡溃灭过程中的作用. 采用原始变量的Navier-Stokes方程作为流场的控制方程, 用流体体积方法跟踪运动空泡壁. 数值结果显示空泡溃灭过程中, 伴随空泡变形, 空泡发出多个高压脉冲和高速射流. 对于不同的热力学模型, 等温, 绝热和准绝热过程, 绝热过程能够最大程度抑制空泡溃灭, 从而减弱空泡溃灭对固壁造成的空蚀破坏. 在绝热及其类似过程中, 出现空泡回弹现象.     

Effect of local thermal non-equilibrium on unsteady heat transfer by natural convection of a nanofluid over a vertical wavy surface

This paper uses thermal non-equilibrium model to study transient heat transfer by natural convection of a nanofluid over a vertical wavy surface. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three-temperature model is applied to represent the local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. Finite difference method is used to solve the dimensionless governing equations of the problem. The obtained results are displayed in 2D graphs to illustrate the influences of the different physical parameters on local skin-friction coefficient, local Nusselt numbers for fluid, particle and solid phases and local Sherwood number. The results for velocity component, nanoparticle volume fraction, fluid temperature, particle temperature and solid-matrix temperature are presented in 3D graphs as a function of the axial and transverse coordinates. All the obtained results are discussed.     

What is the Correct Definition of Average Pressure?

Use of a correct definition of average pressure is important in numerical modeling of oil reservoirs and aquifers, where the simulated domain can be very large. Also, the average pressure needs to be defined in the application of pore-network modeling of (two-phase) flow in porous media, as well as in the (theoretical) upscaling of flow equations. Almost always the so-called intrinsic phase-volume average operator, which weighs point pressure values with point saturation values, is employed. Here, we introduce and investigate four other potentially plausible averaging operators. Among them is the centroid-corrected phase-average pressure, which corrects the intrinsic phase-volume average pressure for the distance between the centroid of the averaging volume and the phase. We consider static equilibrium of two immiscible fluids in a homogeneous, one-dimensional, vertical porous medium domain under a series of (static) drainage conditions. An important feature of static equilibrium is that the total potential (i.e., the sum of pressure and gravity potentials) is constant for each phase over the whole domain. Therefore, its average will be equal to the same constant. It is argued that the correct average pressure must preserve the fact that fluid potentials are constant. We have found that the intrinsic phase-volume average pressure results in a gradient in the total phase potential, i.e., the above criterion is violated. In fact, only the centroid-corrected operator satisfies this criterion. However, at high saturations, use of the centroid-corrected average can give rise to negative values of the difference between the average nonwetting and wetting phase pressures. For main drainage, differences among various averaging operators are significantly less because both phases are present initially, such that the difference between the centroids of phases, and the middle of the domain are relatively small.     

Ideal gas flow behind a finite-amplitude shock wave

The equations of one-dimensional (with a plane of symmetry) adiabatic motion of an ideal gas are transformed to a form convenient for studying flows between a moving piston and a shock wave of variable intensity. The solution is found for the equations of a motion containing a shock wave which propagates through a quiescent gas with variable initial density and constant pressure. This solution contains four arbitrary constants and, in a particular case, gives an example of adiabatic shockless compression by a piston of a gas initially at rest.     

Experimental investigation of TiO2/water nanofluid laminar forced convective heat transfer through helical coiled tube

Coiled tubes and nanofludics are two significant techniques to enhance the heat transfer ability of thermal equipments. The forced convective heat transfer and the pressure drop of nanofluid inside straight tube and helical coiled one with a constant wall heat flux were studied experimentally. Distilled water was used as a host fluid and Nanofluids of aqueous TiO₂ nanoparticles (50 nm) suspensions were prepared in various volume concentrations of 0.25–2 %. The heat transfer coefficient of nanofluids is obtained for different nanoparticle concentrations as well as various Reynolds numbers. The experiments covered a range of Reynolds number of 500–4,500. The results show the considerable enhancement of heat transfer rate, which is due to the nanoparticles present in the fluid. Heat transfer coefficient increases by increasing the volume concentration of nanoparticles as well as Reynolds number. Moreover, due to the curvature of the tube when fluid flows inside helical coiled tube instead of straight one, both convective heat transfer coefficient and the pressure drop of fluid grow considerably. Also, the thermal performance factors for tested nanofluids are greater than unity and the maximum thermal performance factor of 3.72 is found with the use of 2.0 % volume concentration of nanofluid at Reynolds number of 1,750.     

Similar solution of laminar boundary layer equations with a flame front

This paper is devoted to the general question of the effect of chemical reactions taking place in the boundary layer with the release of heat on the heat transfer, mass transfer, and friction. In the most general formulation the problem is associated with extremely complex computations because of the presence of many components in the mixture of gases. Moreover, to date the chemical kinetics have received little study, and there are simply no reliable data that can be used in the calculations. Therefore we consider in the following a simplified case in which the chemical reaction proceeds in an infinitely narrow region-a flame front. Mathematically this front is a surface of discontinuity of the concentration and temperature derivatives. Physically this corresponds to the limiting case of chemical equilibrium, in which equilibrium occurs with complete combustion and is realized at moderate temperatures and quite high pressures.This formulation of the problem simplifies the calculation considerably, since the gas mixture may be considered everywhere binary. In this case it is not necessary to introduce into consideration either the chemical kinetics or the chemical equilibrium constants. Moreover, in the case of this formulation we may make use of a similar solution of the boundary layer equations. The extreme simplification of the computations does not alter the physical essence of the problem-the effect of the heat sources within the boundary layer on friction, heat transfer and mass transfer. A large number of computations was made to permit clarification of the specific nature of the dependences of the coefficients of friction, and heat and mass transfer on the rate of fuel injection.Several studies have been published in which a similar assumption was made. Avduevskii and Obroskova [1] consider the case when the flame front is located right at the wall. Harnett and Eckert [2] calculated the boundary layer for a flame front on the assumption that the physical parameters do not depend on temperature. This assumption gives a picture which is inaccurate both quantitatively and qualitatively. Finally, when the present study was nearly completed, the article of Libby and Pierucci [3] appeared. In that study the external flow (air) is a mixture of oxygen and an inert gas (argon). Therefore there is a three-component mixture in the boundary layer at every point. This significantly complicates the computation. At the same time, the dependence of the physical parameters on temperature and the concentrations of the mixture components is taken in simplified form (an unjustified simplification, in our view). The authors of [3] carried out only a limited number of computations, which did not make it possible to clarify the characteristic features of the variation of the friction, heat transfer, and mass transfer coefficients as a function of the rate of combustible gas injection.Notation x coordinate along plate in flow direction - y coordinate along normal to plate - u, v velocity components - T absolute temperature - c mass concentration - volume concentration - density - c_p specific heat at constant pressure - viscosity coefficient - D diffusion coefficient - h specific enthalpy - heat conductivity - M Mach number in external stream - k adiabatic exponent in external stream The author wishes to thank V. S. Avduevskii for guiding this investigation.     

Free Convection Heat Transfer From A Sphere In A Porous Medium Using A Thermal Non-equilibrium Model

This work studies the free convection heat transfer from a sphere with constant wall temperature embedded in a fluid-saturated porous medium using a thermal non-equilibrium model. The governing equations are transformed into boundary-layer partial differential equations by the coordinate transform, and the obtained governing equations are then solved by the cubic spline collocation method. The temperature distributions for fluid and solid phases are shown for different values of the porosity scaled thermal conductivity ratio, the interphase heat transfer parameter, and the streamwise coordinate. The effects of the porosity scaled thermal conductivity ratio and the interphase heat transfer parameter between solid and fluid phases on the local Nusselt numbers for fluid and solid phases are examined. Results show the local Nusset number for the porous medium can be increased by increasing the porosity scaled thermal conductivity ratio. Moreover, the thermal non-equilibrium effect is more significant for low values of the porosity scaled thermal conductivity ratio or the interphase heat transfer parameter.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Experimental and numerical investigations on the performance of dehumidifying desiccant beds composed of silica-gel and thermal energy storage particles

Enhanced efficiency of the adsorption process in the dehumidifier is a key element for improved performance of desiccant cooling systems. Due to the exothermic nature of the adsorption process, the dehumidification and cooling capacity are limited by significant temperature changes in the adsorption column. In the present study, the effects of integration of sensible and latent heat storage particles in the desiccant bed for in situ management of released adsorption heat are investigated. For this purpose, column experiments are performed using an initially dry granular bed made of silica-gel particles or a homogeneous mixture of silica gel and inert sensible or latent heat storage particles. The packed bed is subject to a sudden uniform air flow at selected values of temperature and humidity. Also, a packed bed numerical model is developed that includes the coupled non-equilibrium heat and moisture transfer in the solid and gas phases. Investigations of the heat and mass transfer characteristics are reported using the composite structure and the results are compared with the base case of simple silica gel bed. Improved desiccant cooling system performance can be obtained by appropriate adjustment of desiccant cycle operation and proper choice of the volume ratio of thermal energy storage particles.     

Rayleigh-Bénard convection heat transfer in nanoparticle suspensions

Natural convection heat transfer of nanofluids in horizontal enclosures heated from below is investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than like a conventional solid-liquid mixture, which implies that all the convective heat transfer correlations available for single-phase flows can be extended to nanoparticle suspensions, provided that the thermophysical properties appearing in them are the nanofluid effective properties calculated at the reference temperature. In this connection, two empirical equations, based on a wide variety of experimental data reported in the literature, are developed for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity, whereas the other effective properties are evaluated by the traditional mixing theory. The heat transfer enhancement that derives from the dispersion of nano-sized solid particles into the base liquid is calculated for different operating conditions, nanoparticle diameters, and combinations of solid and liquid phases. One of the fundamental results is the existence of an optimal particle loading for maximum heat transfer across the bottom-heated enclosure. In particular, for any assigned combination of suspended nanoparticles and base liquid, it is found that the optimal volume fraction increases as the nanofluid average temperature increases, and may either increase or decrease with increasing the nanoparticle size according as the flow is laminar or turbulent. Moreover, the optimal volume fraction has a peak at a definite value of the Rayleigh number of the base fluid, that depends on both the average temperature of the nanofluid and the diameter of the suspended nanoparticles.     

Meso-level simulation of gas hydrate dissociation inlow-permeability sediments

This paper presents a meso-level simulation of gas hydrate dissociation in low-permeability marine sediments. Interstitial pores are defined to describe fluid flow and particle movement. The proposed model couples multiphase fluid flow with particle movement to simulate the thermodynamics of gas hydrate dissociation triggered by sharp temperature rises. Hydrates respond quickly to temperature rise in low-permeability sediments. Dissociation causes pore pressure to rise rapidly to equilibrium then steadily increase above equilibrium pressure. Lower permeability sediment builds up greater excess pore pressure as the dissipation of pore pressure is constrained.     

Incompleteness of the flashing of a supersaturated liquid and sonic ejection of the produced phases

For an adiabatic, constant flowrate and frictionless flow of a supersaturated liquid, the equations of evolution are established owing to a variable which is a flashing index. The graphical solution in the pressure volume diagram shows that the flashing is choked when the phases produced are expelled at the local sonic velocity. Comparison is made between theory and existing experimental results for hot water, the agreement is satisfactory.     

Steady natural convection flow of a particulate suspension through a circular pipe

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long pipe. The wall of the pipe is maintained at a constant temperature. The particle phase is endowed by an artificial viscosity which may be used to model particle-particle interaction in dension suspensions. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Closed-form solutions for the velocity and temperature profiles are obtained. For the assumptions employed in the problem, the temperatures of both phases in the pipe are predicted to be uniform. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the velocity profiles of both the fluid and particle phases.     

Thermo-Osmosis Effect in Saturated Porous Medium

In this paper, the thermo-poroelasticity theory is used to investigate the quasi-static response of temperatures, pore pressure, stress, displacement, and fluid flux around a cylindrical borehole subjected to impact thermal and mechanical loadings in an infinite saturated poroelastic medium. It has been reported in literatures that coupled flow known as thermo-osmosis by which flux is driven by temperature gradient, can significantly change the fluid flux in clay, argillaceous and many other porous materials whose permeability coefficients are very small. This study presents a mathematical model to investigate the coupled effect of thermo-osmosis in saturated porous medium. The energy balance equations presented here fulfill local thermal non-equilibrium condition (LTNE) which is different from the local thermal equilibrium transfer theory, accounting for that temperatures of solid and fluid phases are not the same and governed by different heat transfer equations. Analytical solutions of temperatures, pore pressure, stress, displacement, and fluid flux are obtained in Laplace transform space. Numerical results for a typical clay are used to investigate the effect of thermo-osmosis. The effects of LTNE on temperatures, pore pressure, and stress are also studied in this paper.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Self-similar solution of cylindrical shock wave propagation in a rotational axisymmetric mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has a variable azimuthal fluid velocity together with a variable axial fluid velocity. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. The shock Mach number is not infinite, but has a finite value. The azimuthal and axial component of the fluid velocity in the ambient medium are assumed to be vary and obey power laws, and the density of the ambient medium is taken to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of the variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of the density of solid particles to the initial density of the gas are investigated.