The Interfacial Slip Effect And Its Influencing Mechanism Between A Porous Medium And Fluid Region

The fluid flow, heat or mass transfer in the porous media are encountered in a wide range of industrial and agricultural processes or environmental situations, such as the nuclear waste dealing, heat pump, drying process, solar collectors, fuel cells, crude oil extraction and so on. While among them, the transport phenomena in systems partially filled with a porous medium has gained widely applications. However, the fluid flow and heat transfer mechanism is very complex, in which the dynamical characteristics of fluid (slip effect) at the porous/fluid interface play an important role. Nowadays, after the research enthusiasm on natural convection in a porous medium or fluid region, study efforts have been focused on problems in partially porous systems. Most important of all, the slip effect at the interface is the key factor in developing accurate models in multi-media involving flow and heat transfer. Therefore, objective of this dissertation is aim to thoroughly investigate the slip effect at a porous/fluid interface and its influence on natural convective flow and heat transfer in cavities.On the basis of volume averaged method, two-domain model on natural convection and heat transfer is founded and then the stress slip conditions at the interface could be deduced. The point continuity and momentum equations are developed in pore scale. By using averaging operators, the continuity and momentum equations could be derived in a representational elemental volume(REV) in mesoscopic scale. The equation is reduced to Navier-Stokes equations in clear fluid region and expressed as Darcy-Brinkman-Forchheimer equation in homogeneous porous region. To develop the boundary condition at the interface, the integral of momentum equation without any length-scale constraints over the volume of whole cavity is formed and also the integral of momentum equations in homogeneous porous medium and fluid region. By using the difference between the former and latter, the boundary condition of slip effect as well as the expression of stress slip coefficient at the interface could be derived. After that heat transfer could be analyzed by the same method as mensioned above. The REV energy equation in mesoscopic scale could be deduced by using averaging operator on the point heat transfer equations of liquid and solid phases in pore scale. And then the energy equations in homogeneous porous medium and fluid region could be obtained. With an assumption of local thermal equilibrium, continuous temperature and heat flux at the interface are satisfied. As is mentioned above, two-domain models on natural convection and heat transfer including a homogeneous porous medium and clear fluid region are constructed. In order to achieve mechanism in macroscopic scale, averaging values of parameters based on REV would be substituted into standard transport equations.The macroscopic scale models are solved by using finite element method combined with weak constraint at the porous/fluid interface, then slip effect and influences on convective flow and heat transfer are mainly focused on in numerical simulation. The key in obtaining flow and temperature fields is proper interfacial condition with a determination of stress slip coefficient. Permeability and interfacial area corresponding to porosity could be calculated by three empirical correlations; thereby the viscous stress slip coefficients are determined under some conditions. Influences of viscous stress slip and inertial stress slip conditions on flow and heat transfer are compared with continuity condition by using vertical velocity and average heat transfer velocity along the left wall. The numerical results on flow show that affected by viscous stress slip, velocity differences between the interface become large and the differences become famous with increasing porosity in the former two empirical correlations. Reverse flow appears at the interface when the third correlation is used, and the phenomenon would disappear untilε>0.9. Inertial stress slip leads to smaller velocity differences at the interface, thus more smooth profile in velocity could be found. Comparing with continuous condition, influence of inertial stress slip condition on flow is small exceptε>0.9 and limited in a strip region near the interface. The comparisons of numerical results in Nusselt nunber show that influences on heat transfer of viscous stress slip are related with porosity and pore size. Nusselt number increases with increasing pore size whenε>0.7 influenced by viscous stress slip, and increased or decreased whileε<0.7. There is a critical permeability in heat transfer under viscous stress slip condition, and the value varies with empirical correlation. When permeability is larger than the critical value, Nusselt number is larger than the value obtained by continuity condition, conversely Nusselt number is smaller than the value in continuity condition. Inertial stress slip at the interface leads to an increase of Nusselt number for any porosity, and the growth is accelerated. Influenced by inertial stress slip condition, Nusselt number would always become small slightly, but the influence is very small. The natural convective flow filed in an constructedly invisible partially porous cavity is measured by using particle image velocimetry(PIV), and the fluid dynamical characteristics at porous/fluid interface is mainly focused on. Multiple Rayleigh number conditions can be attained by setting different temperature differences between vertical walls. After static flow fields are shot by PIV, streamlines, velocity and shear rate could be obtained by cross-correlation calculation and image post-processing. The viscous stress slip coefficient could be calculated by velocities, shear stresses and permeability obtained from above empirical correlations. Test results shown that in a given porosity, viscous stress slip coefficient would vary with permeability, height of the interface and Rayleigh number. For the convenience in practice, average value of viscous stress slip coefficients along the height of the interface is expressed an average viscous stress slip coefficient in the cavity. Formula involving Rayleigh number is obtained by the polynomial fitting method.Numerical results are compared with experiment results to testify each other. The mathematical model is solved by using experimental average viscous stress slip coefficient in the interfacial condition The comparisons show agreeable streamlines when Ra～104～106 and discrepancy for Ra being 107. An agreement could be found by comparing vertical velocity distribution of numerical and experimental results. At the same time the results indicate that the test values in the porous medium are smaller than the numerical results. The reason might be attributed to several factors:firstly the walls are not smooth; secondly, the resistance of rods in test is different from ones of porous in simulation, thirdly at the interface, direction of velocity affected by rods may be deviated from vertical direction.There are many factors on slip effect at the porous/fluid interface in narual convection and heat transfer, including fluid property, flow conditions and interfacial structure and so on. At first the slip effect at the interface is analyzed in this dissertation. Then influence of slip effect on natural convection and heat transfer in simulation are thoroughly investigated. After that the flow conditions in the cavity especially at the interface are tested by PIV and the viscous stress slip coefficients are obtained. Finally numerical results are compared with experimental results. The present results may act as the basis to some thermal engineering fields in partially porous cavities.