Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Iterative process acceleration of calculation of unsteady,viscous, compressible,and heat‐conductive gas flows

In this paper, extrapolation technique is introduced in the Semi‐Implicit Method for Pressure‐Linked Equations ‐ Time Step (SIMPLE‐TS) finite volume iterative algorithm for calculation of compressible Navier–Stokes–Fourier equations subject of slip and jump boundary conditions. The initial state, required by the iterative solver in simulation of unsteady flow problems, is approximated in time by Lagrange polynomial extrapolation in each node. The approach is applicable to a parallel code in a straightforward way due to algorithmic independence of the neighboring nodes in the computational grid. A criterion is proposed to determine the order of extrapolation polynomial and stop the extrapolation execution, when the local steady state is reached. The approach is tested on different microflow problems: Couette flow, flow past a square in a microchannel at subsonic and supersonic speeds, and convective Rayleigh–Bénard flow of a rarefied gas. The acceleration varies from 1.14‐fold to 2.8‐fold. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling,parameterisation and simulation-based optimisation of a microflow-control actuator

A synthetic jet is considered to control microflows, where the Knudsen number is between 0.001 and 0.1. The flow is modelled with the compressible, 2D Navier–Stokes equations. The wall boundary conditions are modified for the slip velocity and the temperature jump encountered for this Knudsen number range. The membrane motion is modelled as a moving boundary. After a validation using experimental results available only for a macroflow over a hump, the present study focuses on developing a design optimisation methodology for micro-synthetic jets in micro-scale, laminar crossflow. First, single-variable optimisations are performed. As compared to the baseline case, the optimisations yield 2, 15, 15 and 200% increase in actuation efficiency for the cases varying the orifice width, the orifice height, the cavity height and the frequency, respectively. Then, multi-variable shape optimisation is performed. Compared to the baseline case, the optimisation using shape parameters results in a 7-fold increase in the actuation efficiency, while the optimisation with Bezier polynomials results in more than a 10-fold increase.     

Variable slip coefficient in binary lattice Boltzmann models

We present a new method in order to obtain variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. We present the Boundary layer theory. We study both the single-and multi-fluid BGK-type models as well. The boundary slip and the Knudsen layer are analyzed in detail. Benchmark simulations are carried out in order to compare the analytical derivation with the numerical results. Excellent agreement is found between the two analytical formalism and the numerical simulations.      

Experimental Analysis of Gas Micro-Convection Through Commercial Microtubes

In this article, an experimental campaign devoted to analyzing the forced micro-convection features of heated gas flows through commercial stainless-steel microtubes having inner diameters of 172 μm and 750 μm is described. The experimental results obtained by heating the microtubes with an imposed uniform heat flux (H-boundary condition) at the external wall, in terms of Nusselt numbers, are compared to the predictions of the classical correlations validated for conventional pipes and to the correlations proposed for gas flows through microtubes under laminar and transitional conditions (100 < Re < 4,000). The cross-sections of the tested microtubes enabled the analysis of the effects of wall axial heat conduction on the Nusselt number. It was observed that the Nusselt number is strongly dependent on the Reynolds number in the laminar regime, and this fact is explained in the article with the effects of wall axial heat conduction and the difficulties in the experimental determination of the right exit bulk temperature of the gas flow, which cannot be ignored in the thermal analysis. The agreement between the Gnielinski correlation and the experimental Nusselt number is poor, especially for low Reynolds numbers, if one uses the average gas bulk temperature, obtained as the arithmetic mean between the inlet and outlet gas bulk temperature, in the definition of the experimental Nusselt number. On the contrary, the agreement with the Gnielinski correlation improves if the local wall-gas temperature difference near the exit of the microtube is used instead. The experimental results presented in the article demonstrate that the criteria for the design of accurate micro-convection tests can be quite different from those for the analysis of forced convection through conventional pipes.