Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour

We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool

Kinetic calculation of rarefied gaseous flows in long tapered rectangular microchannels

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.Gaseous flows in microsystems have attracted considerable attention in fluid dynamic communities over the last few years. When the size of the device is in the range of microns, the molecular mean free path becomes comparable with the device size, and the details of the molecular interactions need to be taken into account. The proper description of such microflows requires the consideration of the velocity distribution function of the molecules and kinetic equations. The scope of the present paper is to discuss the determination of the behavior of pressure driven rarefied gas flows in microchannels at the kinetic level. As a new application of the methodology, preliminary results are presented for pressure driven flows of single gases through long rectangular tapered microchannels, which have constant widths but varying depths along the axis of the channel. The kinetic calculation is based on the solution of the linearized Bhatnagar-Gross- Krook (BGK) equation and refers to the determination of the mass flow rate through the channel and the axial distribution of the pressure. The BGK equation is solved by the discrete velocity method. It is shown that the mass flow rate exhibits the diodicity effect, which means that the flow rate depends on the orientation of the channel. If the gas flows from the larger cross section towards the smaller one, the flow rate is larger than in the opposite situation. The pressure profile strongly varies near the small cross section, and it has a quite different character than in the case of channels with uniform cross sections. The tapered microchannel might be useful for separating the different gaseous components in engineering applications

Microchannel fluid flow and heat transfer by lattice boltzmann method

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.Micro flow has become a popular field of interest due to the advent of micro electromechanical systems (MEMS). In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional micro channel fluid flow. We simulated fluid flow and heat transfer inside microchannel, the prototype application of this study is micro-heat exchangers. The main incentive to look at fluidic behaviour at micron scale is that micro devices tend to behave much differently from the objects we are used to handling in daily life. The choice of using LBM for micro flow simulation is a good one owing to the fact that it is based on the Boltzmann equation which is valid for the whole range of the Knudsen number. Slip velocity and temperature jump boundary conditions are used for the microchannel simulations with Knudsen number values covering the slip flow. The lattice Bhatnagar-Gross-Krook single relaxation time approximation was used. The results found are compared with the Navier-Stokes analytical and numerical results available in the literature and good matches are observed

Modern Lattice Boltzmann methods for multiphase micro-flows

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.During the last decade, the Lattice Boltzmann (LB) method has captured an increasing attention as an efficient tool for the numerical simulation of complex fluids, particularly multi-phase and multi-component flows. In this paper, we revisit the basic features of two modern variants of lattice Boltzmann models for non-ideal fluids, which offer promising perspectives for the numerical simulation of complex micro- flows.This study is funded from the European Project INFLUS, NMP3-CT-2006-031980

Numerical Simulation of Microflows with Moment Method

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.A series of hyperbolic moment equations is derived for the Boltzmann equation with ES-BGK collision term. These systems can be obtained through a slight modification in the deduction of Grad’s moment equations, and such a method is suitable for deriving systems with moments up to any order. The systems are equipped with proper wall boundary conditions so that the number of equations in the boundary conditions is consistent with the hyperbolic structure of the moment system. Our numerical scheme for solving the hyperbolic moment systems is of second order, and a special mapping method is introduced so that the numerical efficiency is highly enhanced. Our numerical results are validated by comparison with the DSMC results. Through the numerical solutions of systems with increasing number of moments, the convergence of the moment method is clearly observed

A thermal lattice Boltzmann model for micro/nano-flows

The dynamic behavior of charged micro and nanofluids plays a crucial role in a large variety of industrial and biological processes. Such dynamic behavior is characterized by the simultaneous occurrence of several competing mechanisms, such as electrostatic interactions, viscous dissipation and hydrodynamic effects, often taking place in complex geometries. This paper focuses on a thermal lattice Boltzmann model for micro/nano-flows

Multiscale lattice Boltzmann approach to modeling gas flows

For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost