The dissertation is devoted to the research of thermohydrodynamic processes in porous media and in porous microchannel systems of different configuration.
Analytical and numerical methods for modeling thermophysical processes in porous microsystems are proposed. The continuous medium approach is used taking into account the boundary conditions of slippage for the first and the second order, which allows expanding the range of use of the Knudsen number. The Boltzmann lattice method (LBM) is applied to flat and round microchannels taking into account the porosity and slip conditions. Using the method of renormalization groups, a microscopic model of turbulence for porous media was developed. Based on this model, the equation for the effective kinematic viscosity is derived, taking into account the porosity of the medium. The perturbation method was used to study hydrodynamic and thermal instability. This analytical technique is adapted for the analysis of instability, which taking into account different physical and geometric conditions (porosity, slippage, etc.).
The results of hydrodynamic instability studding flow in a porous medium based on three-dimensional linear perturbations and in porous microchannels based on two-dimensional linear perturbations are presented. Increase in the critical values of the Reynolds number with increasing slippage and decrease in porosity due to an increase in the degree of filling of the velocity profile is shown. The instability criterion is determined taking into account nonlinear effects, which allowed to find the limit value of porosity at which turbulence can develop. The hydrodynamic instability of the flow with slippage in a curved porous microchannel between two fixed concentric cylinders is investigated. Calculations have shown that increasing the slippage coefficient, the porosity of the medium and the width of the channel leads to an increase in the filling of the undisturbed of velocity profile. It leads to an increase in the critical values of the Dean number and the critical wavelength of the perturbation, which determine the instability criteria for the flow.
Fluid flow and heat transfer during mixed convection in vertical flat and cylindrical microchannels with a porous structure have been studied taking into account the boundary conditions of first - order slippage. The influence of the Knudsen number is more pronounced in the wall area, in the central part of the channel the influence of the Rayleigh number prevails. At small Rayleigh numbers, the decrease in porosity intensifies heat transfer, and at large values of the Rayleigh number, the trend changes to the opposite. The effects of microflows are more pronounced in case of forced convection. Moreover, in the circular channel this tendency is more noticeable because in the circular channel the liquid is in contact with the wall across the entire cross section, while in the flat channel only two walls are in contact with the liquid, which significantly weakens the effect of free convection. Comparison of analytical results with numerical results based on the Boltzmann lattice method showed a discrepancy of less than 1%.
Analytical and numerical researches of heat transfer and fluid flow at forced convection in vertical flat and cylindrical porous microchannels with boundary conditions of slippage of the second order are carried out. Reducing the porosity causes increased heat transfer. At high Prandtl numbers, the temperature jump on the wall practically degenerates, which leads to an increase in the rate of heat transfer with an increase in the Knudsen number. At small Prandtl numbers, the effect of second-order parameters was not observed.
In general, the work shows that the proposed numerical and analytical modeling methods allow taking into account and analyzing the influence of a number of physical and geometric parameters on heat transfer and hydrodynamics in microporous structures. They also make it possible to determine the flow regimes in these microstructures. The research results can be used in the design and creation of new microchannel systems, as well as allow to optimize the most efficient operating parameters of existing ones.
Keywords: numerical simulating, analytical modeling, heat exchange, hydrodynamics, porosity, microchannel, slippage.
