Numerical Study of Gaseous Flow in Microchannels

Abstract

Low pressure gas flows are characterized in parallel plate channel and in rectangular microchannels. The main thrust of the dissertation is to investigate the effects of pressure ratio on flows in parallel plate channel and the effects of aspect ratio and Knudsen number on flows in rectangular microchannels. The slip flow regime which is not easily predicted by continuum assumption is investigated rigorously. The CFD software FLUENT is used for the investigation associated with a user defined function (UDF) to handle the wall boundary conditions. The flow domains are divided into two types-quadrilateral cells for parallel plate channel and hexahedral cells for rectangular channels. The flow is treated as steady, compressible and locally fully developed along with isothermal wall conditions and the density of the fluid is prescribed by using ideal gas law. The simulations are performed by control volume method and the results are compared and validated with the available existing results. The effects of varying pressure ratio on velocity, pressure distribution, friction factor and mass flow rate are examined for both slip and noslip boundary conditions in the parallel plate channel. The flow is assumed pressure driven with fixed outlet pressure and the inlet pressures are prescribed by the pressure ratios and the outlet pressure. The outlet Knudsen number is fixed to 0.058. The results obtained by slip and noslip model are quite different. Velocity and mass flow rate of slip flow model are always higher than those of noslip model. Pressure gradient is found very high although the channel pressure difference and Mach number is small. For both slip and noslip model pressure distribution is observed nonlinear and the deviation of pressure from linear distribution increases with the increase of pressure ratio. The Knudsen number increases towards downstream direction and the maximum Knudsen number is observed at the outlet where the density of the flow is the minimum. Friction factor of slip model is lower than that of noslip model and it decreases with the increase of pressure ratio. Mass flow rate increases with the increase of pressure ratio but it has no influence on friction coefficient . The friction coefficient with slip condition for outlet Knudsen number 0.058 is found 71.06 which is far below the conventional value of 96. The effects of aspect ratio and Knudsen number on flow variables in rectangular microchannels flow are investigated. Knudsen number is changed by changing the height of the channel. For different heights of the channels compressibility effects are considered and adjusted by changing the length of the channels. The result shows that the higher the Knudsen number, the higher the velocity. The velocity also increases with the distance from the inlet to the downstream position and is the maximum at the outlet. The wall velocity on the top/bottom and side walls is equal when the aspect ratio is 1 but with the decrease of aspect ratio the velocity difference occurs. For the aspect ratio less than 1, the velocity on the top/bottom wall is higher than the side wall. The velocity on the top/bottom wall decreases with the decrease of aspect ratio as long as AR<0.25 and for AR 0.25 the velocity coincides to an asymptotic value. The velocity does not decrease any more for further decrease of aspect ratio but the velocity on the side wall decreases gradually. The pressure deviation from linear distribution decreases with the increase of Knudsen number. Like a velocity, the wall shear stress on the top/bottom wall and side wall is equal for aspect ratio 1 but it increases with the decrease of aspect ratio. The difference of wall shear stress on the top/bottom and side walls occurs for aspect ratio less than 1 and the higher shear stress is found on the top/bottom wall. For the increase of Knudsen number the wall shear stress as well as friction coefficient decreases. At Knudsen number 0.03, the cross sectional average value of friction coefficient for aspect ratio 1 is 46.80 which increases to 81.38 for the decrease of aspect ratio to 0.0625. The ratio of slip over noslip mass flow rate M* increases with the increase of Knudsen number and decreases with the increase of pressure ratio. For the increase of Knudsen number from 0.02 to 0.1, the mass flow rate ratio increases form 1.098 to 1.15.