Non-equilibrium gas flow and heat transfer in a bottom heated square microcavity

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The flow of a rarefied gas in a square enclosure with a bottom wall at high temperature and the other three walls at the same low temperature is investigated. The flow configuration is simulated both deterministically, using the non-linear Shakhov kinetic model and stochastically, using the DSMC method. Excellent agreement between the two approaches is obtained. The flow is characterized by the reference Knudsen number and the temperature ratio. It is found that along the side walls the velocity of the gas is not necessarily from cold-to-hot regions due to thermal creep, but from hot-to-cold as well. The effect of the flow parameters to this configuration, including the not well theoretically defined flow from hot-to-cold, is investigated and results are provided in the whole range of the Knudsen number for small, moderate and large temperature differences

Solving the Boltzmann equation deterministically by the fast spectral method : application to gas microflows

Based on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearised Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the Onsager-Casimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearised Boltzmann equation. Then, a number of two-dimensional micro flows in the transition and free molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearised Boltzmann equation. For thermally driven flows in the free molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearised Poiseuille and thermal creep flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearised Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel

Application of discrete unified gas kinetic scheme to thermally induced nonequilibrium flows

In this article, we present the applications of the discrete unified gas kinetic scheme (DUGKS) for simulating thermal induced non-equilibrium flows. Four different types of thermally induced flows, including the thermal creep flow, thermal edge flow, radiometric flow and temperature discontinuity induced flow have been simulated in a wide range of Knudsen numbers. The numerical results have been compared with direct simulation Monte Carlo (DSMC) solutions and show that the Shakhov model based DUGKS can be faithfully used for such thermally induced nonequilibrium flows. In particular, due to the asymptotic preserving property of the DUGKS, the flow features in the near continuum flows can be captured efficiently. The extremely low-speed character of such flows is also in favor of the current deterministic model equation solver

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios

Direct Simulation of the Thermal Transpiration of Rarefied Gases in Short Channels

Thermal transpiration (also referred to as thermal creep, thermal diffusion and thermomolecular flux) is the process by which a gas under the influence of a temperature gradient will flow through a channel from a cold region to a hotter one. This dissertation presents molecular simulations of thermally induced flow in the transition and free molecular regime using the probabilistic modeling technique referred to as Direct Simulation Monte Carlo (DSMC). We show how the thermomolecular flux can create a pressure increase which can be used as a pumping mechanism as well as present results of the net flux as a function of temperature, gas density, channel length, and accommodation coefficient.This disseration begins with a presentation of the historical background which led up to kinetic gas theory and inspired Martin Knudsen and his pump idea. We describe the Knudsen pump idea in depth and outline the experimental progress and various Knudsen pump designs in the last 100 yeas. We then take a comprehensive look at the various types of micropumps and their pumping mechanisms. The last section of the review focuses specifically on gas phase pumps and the performance of existing Knudsen pumps.Afterwards, we provide the basic kinetic theory of thermal transpiration and describe the work in that area in the previous century. We then present the modern methods for solving the thermal transpiration method including an analysis of the strengths and weaknesses of each method. We discuss at length the DSMC method, the errors involved in the method and the simulation parameters for my set of simulations.Our DSMC simulations give the most complete DSMC results for both open and closed systems with the focus being on the thermomolecular flow through short channels throughout the transition and free molecular regimes. To our knowledge, our results are the first DSMC results to include both multiple pressure differences and temperature gradients and use those plots to derive maximum values for the flux, flowrate and pressure drop. We provide the first flowfield velocity profiles for both transition regime and free molecular regime flows as well as flux values for a variety of pressures differences at all Knudsen numbers. We also provide the pressure differences and pressure ratios when there is zero molecular flux along with flux data for pore arrays.The results shown here are the first DSMC simulations looking at thermal transpiration for different aspect ratios and different tangential momentum accommodation coefficients for Knudsen numbers in the transition (0.110) regimes. We have run over 300 simulations where a single run takes anywhere from 12 hours to 7 days of computational time. For each flux or pressure difference data point, we ran several simulations at varying pressures using a single number density (Knudsen number) and temperature gradient.Finally we provide four design scenarios which utilize the simulations results in various ways. We show how this phenomenon applies both to rarefied gases flowing through meso-sized channels as well as dense gases through micro/nano-channels. These designs show how the simulation results predict that a 1cm2 array of pores could achieve a maximum pressure difference of 7kPa and a maximum flowrate of over 1×108 sccm. The designs also emphasize the validity and usefulness of the DSMC simulations as well as provide the reader with a clearer understanding of the physics behind thermal transpiration and the potential performance of a Knudsen pump

Octant Flux Splitting Information Preservation DSMC Method for Thermally Driven Flows

We present the octant flux splitting DSMC method as an efficient method for simulating non-equilibrium flows of rarefied gas, particularly those arising from thermal loading. We discuss the current state-of-the-art flux splitting IP-DSMC technique and show that it fails to capture the shear stresses created by thermal gradients. We present the development of the octant flux splitting IP-DSMC as well as degenerate 2D, 1D, and 0D forms and apply the method to a number of problems including thermal transpiration, with satisfactory results. (c) 2007 Elsevier Inc. All rights reserved

Si-Micromachined Knudsen Pumps for High Compression Ratio and High Flow Rate.

This dissertation focuses on Si-micromachined Knudsen pumps. Knudsen pumps exploit thermal transpiration that results from the free-molecular flow in non-isothermal channels. The absence of moving parts, without frictional loss and mechanical failure, provides significantly higher reliability. For a high compression ratio, 48 stages are cascaded in series in a single chip of 10.35 × 11.45 mm2 area. A five-mask, single-wafer process is used for monolithic integration of the designed Knudsen pump. The pressure levels of each stage are measured by integrated Pirani gauges. Using 1.35 W, the fabricated pumps evacuates the encapsulated cavities from 760 to 50 Torr and from 250 to 5 Torr. Multistage Knudsen pumps are further explored using a two-part architecture. To increase the compression ratio, 162 stages are serially cascaded. The two-part architecture uses 54 stages designed for the pressure range of 760-50 Torr, and 108 stages designed for lower pressures. This approach provides greater compression ratio and speed than using a uniform design for each stage in the 48-stage Knudsen pump. The design has a footprint of 12 × 15 mm2. Using 0.39 W, the evacuated chamber is reduced from 760 to 0.9 Torr, resulting in a compression ratio of 844. The vacuum levels were sustained beyond 37 days of continuous operation. The dynamic calibration of microfabricated Pirani gauges is explored for increasing pressure measurement accuracy in the 162-stage Knudsen pump. Test results demonstrated that dynamic calibration can be significantly more accurate than conventional static calibration when Pirani gauges are embedded deep within a microfluidic pathway. Si-micromachined single-stage Knudsen pumps are explored for generating high-flow rates. A high density of thermal transpiration flow channels is arrayed in parallel for combined pumping operation. A design with 0.4 × 106 parallel channels in a footprint of 16 × 20 mm2 generates a measured 211 sccm air flow at a pressure difference of 92 Pa, using 37.2 W. The low-temperature atomic layer deposition (ALD) of Al2O3 is investigated for vacuum seals in wafer-level vacuum packaging applications. The conformal coverage provided by ALD Al2O3 is shown to seal micromachined cavities. Lifetime tests extending out to 19 months are reported.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102498/1/sdan_1.pd