Gas flow through a micro-orifice due to small pressure difference

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Rarefied gas flow through a micro-orifice connecting two reservoirs at small pressure differences is considered in the whole range of rarefaction by the linearized BGK kinetic model equation. The problem is computationally challenging due to the five dimensional nature of the distribution function and techniques such as parallelization and numerical schemes of low memory requirements have been applied. Results include the distributions of density, velocity, temperature, as well as flow rates. The independence of flow rate in terms of the wall surface accommodation properties is confirmed.The European Community under the contract of Association EURATOM/Hellenic Republic

Flow rate measurement of rarefied binary gases in long rectangular microchannels

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The flow rate of binary gas mixtures through rectangular long microchannels is measured and compared to the numerical solution of the McCormack kinetic model. The microchannels are etched in silicon, and each individual channel has width=21, height=1.15, length=5000 μm. The measurement refers to He/Ar and Kr gas mixtures are based on the constant volume method. The microchannel is placed between an upstream and a downstream reservoir having different pressures. The flow through the microsystem is maintained by the pressure drop between the containers and the flow rate is determined from the pressure variations in reservoirs. In the case of He/Ar, measurements have been performed for several values of its concentration varying between zero and one, while in the case He/Kr only a concentration equal to 0.5 is considered. The pressure ratio between the two containers is in range of 3-7 and the corresponding average Knudsen numbers are in the range of 0.12-0.98. The results of the flow rate measurement are compared to the discrete velocity solution of the McCormack kinetic model and very good agreement between experiment and simulation has been obtained for all flow configurations. The relative discrepancy between the experimental and numerical results is in the range of the experimental uncertainty.The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 21550

Design of gas micro distribution systems consisting of long tubes

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.A novel algorithm is developed for the design of gaseous micro distribution systems consisting of long tubes based on linear kinetic theory. Provided that the geometry of the pipe network is fixed the algorithm is capable of estimating the mass flow rates through the pipes as well as the pressure heads at the nodes of the network. The pressure distribution along each pipe element may also be provided. The analysis is valid and the results are accurate in the whole range of the Knudsen number, while the involved computational effort is very small. This is achieved by successfully integrating the well known kinetic results for single tubes into a typical solver for designing gas pipe networks.The European Communities under the contract of Association EURATOM / Hellenic Republic

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

Transient micro heat transfer in a gas confined between parallel plates due to a sudden increase of the wall temperature

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The transient heat transfer problem through a rarefied gas confined between parallel plates maintained at different temperatures is investigated. The theoretical formulation is based on the linear BGK kinetic model subject to Maxwell diffuse reflection. The governing time dependent equation is solved by using the discrete velocity method. Results are presented for the number density, macroscopic velocity, heat flux and temperature distributions in the whole range of the Knudsen number. The results are compared with direct Monte Carlo simulations and good agreement is found for small temperature variations.This study is funded from the European Community's Seventh Framework Programme (ITN - FP7/2007-2013) under grant agreement n° 215504

Study of the thermomolecular pressure difference phenomenon in thermal creep flows through microchannels of triangular and trapezoidal cross sections

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.A detailed study of pressure and temperature driven flows through long channels of triangular and trapezoidal cross sections is carried out. The solution is based on the linearized Shakhov model subject to Maxwell boundary conditions and it is valid in the whole range of the Knudsen number. In addition to the dimensionless flow rates, a methodology is presented to estimate the pressure distribution along the channel, as well as the coefficient of the thermomolecular pressure difference

Physics of Fluids

The linearized binary model described by Hamel [Phys. Fluids 8, 418 (1964)] is used to obtain a set of kinetic equations and boundary conditions for the Couette flow problem. The derived set of two coupled integrodifferential equations is solved by iteration implementing standard discretization techniques. Highly accurate numerical results are presented for the mass velocity distribution and the total shear stress of the binary gas system.Dept of Energy Grant No. DE-AS05-80ER10711NSF DMS-831245

An analytical solution of the S-model kinetic equations

An analytical variation of the discrete ordinates method is used to establish a concise and accurate solution to the plane Poiseuille and thermal creep problems based on the S-model kinetic equations. The results are of high accuracy and include the flow rates and the heat fluxes of both problems for a wide range of Knudsen numbers and various values of the accommodation coefficient at the boundaries

The friction factor of a rarefied gas flow in a circular tube

An expression for the estimation of the Poiseuille number for internal rarefied flows is developed. The derived formula is given in terms of dimensionless quantities, which are obtained by the solution of the flow based on kinetic theory. The formulation is applied to the fully developed flow of a gas in a circular tube, and tabulated results of the Poiseuille number are presented in the whole range of the Knudsen number and for various values of the accommodation coefficient. Also, in the slip regime, a closed-form expression for the Poiseuille number is derived and a brief discussion on the proper estimation of the viscous slip coefficient is provided. © 2007 American Institute of Physics

Results on the viscous slip coefficient for binary gas mixtures

The viscous slip coefficients for the binary gas mixtures of Ne-Ar, He-Ar and He-Xe are estimated by solving the McCormack kinetic model equation subject to Maxwell diffuse-specular scattering boundary conditions. The kinetic equations are solved, by using a semi-analytical version of the discrete ordinates method. For each binary gas mixture the results are presented in table form for many values of the molar concentration of the species and the accommodation coefficients. It is found that the viscous slip coefficient strongly depends on the properties of the mixture (molar concentration, molecular mass ratios, accommodation coefficients) and some of the conclusions are generalized for other binary gas mixtures. It is also seen that the well-known Maxwell analytical result as well as the corresponding results of the complete solution of the kinetic equations for single gases are not valid. The results of the present work can be used for the effective implementation of the Navier-Stokes equations with slip boundary conditions when the flow of binary mixtures in the slip regime is investigated