Investigations of microscale fluid-thermal phenomena based on the deterministic Boltzmann-ESBGK model

Xiaohui Guo, Purdue University

Abstract

Fluid and thermal problems are widely encountered in micro/nano-scale devices, the characteristic lengths of which are from hundreds of microns down to tens of nanometers. A great number of such devices involve fundamental components like microchannels, capillaries, membranes and cantilever beams. Continuum assumptions that lead to classical governing equations such as Navier-Stokes equations and Fourier Laws break down when the characteristic size shrinks by an order of millions. In addition, conventional sensors, actuators and controllers turn to be insufficient to depict the flow, thermal, or electrical fields in micro-devices without impacting the original conditions greatly. Therefore, the development of numerical methods becomes indispensable in design and performance analysis of micro-electro-mechanical systems (MEMS). The main goal of this PhD research is the development, implementation and application of comprehensive deterministic Boltzmann-ESBGK modeling framework to micro-scale fluid-thermal phenomena. Investigation of gas flows in short rectangular microchannels has been carried out to understand the rarefaction effects on the reduced mass-flow-rate as well as the non-equilibrium effects on the temperature components. At high Knudsen numbers, the reduced mass-flow-rate only depends on the pressure ratio and the temperature components deviate at the channel exit. For gas flows in long microchannels with and without constrictions, the Navier-Stokes equations with first-order slip boundary conditions are solved. Numerical results accurately predict the entrance pressure drop comparing to high-resolution experimental data using pressure-sensitive-paint (PSP). Simultions show clearly that the compressibility effects become less important than the rarefaction effects at low pressures. The coupled gas-phonon Boltzmann solver has been developed. The reduced distribution functions are used in the two-dimensional code to reduce the computational cost. The physical space is discretized in Cartesian coordinate, while the velocity space is discretized in polar coordinate. The Gaussian-Hermite quadrature is applied to the velocity magnitude. Boundary conditions including temperature, pressure, symmetry as well as far-field are implemented. The interfacial gas-phonon coupling is solved based on conservations of mass, momentum and energy. Good agreements have been obtained from comparisons of current simulations with other numerical models, analytical solutions and experimental data for benchmark cases. The work on temperature-driven microflows includes two major parts: contact thermal resistance over constrictions and thermal transpiration flows in a closed system. The verification of heat transfer at gas-solid surfaces is conducted by comparison with theoretical solutions, where the infinite thin constrictions are considered. For finite constrictions, the heat flux through the interface can be much less than analytical predictions. The coupling effects in thermal transpiration flows can not be ignored when gas flows are in transitional and free-molecular regimes. The effective temperature gradient should be calculated using the wall temperatures at the entrance and exit of the channel, which are different from the temperatures at the inlet and outlet chamber. In addition, when the phonon mean-free-path becomes comparable to the membrane thickness, the assumption for linear wall temperature distribution becomes invalid. The deterministic Boltzmann solver has been also applied to micro-scale aerodynamic damping problems. Based on fifty simulations over a broad range of Knudsen number and geometry, a compact model in the form of a rational function is generated. The fitting is examined by various statistical criteria. The developed compact model is accurate for cantilever/squeeze-film damping problems with small amplitude vibrations by comparison with experimental measurements with various geometries and flow conditions. The compact model is also used to conduct uncertainty quantification with input probability distribution functions (PDFs) of geometry and environment parameters. The results agree well with the generalized polynomial chaos (gPC) predictions. In rarefied transitional flow regime, the damping force is highly non-linear. It is shown that the bias between the averaged damping coefficient and the damping coefficient of the averaged input value can be over 10% at ambient pressure conditions.

Degree

Ph.D.

Advisors

Alexeenko, Purdue University.

Subject Area

Aerospace engineering

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