Olga Rovenskaya

Numerical Investigation of Microflow Over Rough Surfaces: Coupling Approach

A numerical analysis of the flow field in rough microchannel is carried out decomposing the computational physical domain into kinetic and continuum subdomains. Each domain size is determined by the value of a proper threshold parameter, based on the local Knudsen number and local gradients of macroparameters. This switching parameter is computed from a preliminary Navier–Stokes (NS) solution throughout the whole physical domain. The solution is then advanced in time simultaneously in both kinetic and continuum domains: The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes domains, taking care of the conservation of momentum, energy, and mass through the interface. The roughness geometry is modeled as a series of triangular obstructions with a relative roughness up to a maximum of 5% of the channel height. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions 0.001 ≤ Ma ≤ 0.75 and a Reynolds number up to 170. To estimate rarefaction effect, the flow at Knudsen number ranging from 0.01 to 0.08 and fixed pressure ratio has been considered. Accuracy and discrepancies between full Navier–Stokes, kinetic, and coupled solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.

Numerical Analysis of Rarefaction and Compressibility Effects in Bent Microchannels

Numerical investigation of a gas flow through microchannels with a sharp, 90 degrees bend is carried out using Navier-Stokes (N-S) equations with the classical Maxwell first-order slip boundary condition, including the tangential gradient effect due to the wall curvature, and Smoluchowski first order temperature jump definition. The details of the flow structure near the corner are analyzed, investigating the competing effects of rarefaction and compressibility on the channel performances. The flow characteristics in terms of velocity profiles, slip velocity distribution along inner and outer wall, pressure, average Mach number along central line of the channel have been presented. The results showed that impact of the bend on the channel performances is smaller at high rarefaction levels. The behaviour of pressure and velocity away from the bend is similar to that of a straight microchannel; however, the asymmetry in the flow at the bend, with high velocities and high velocity gradients on its inner side, has a strong impact on wall slip velocities. The presence of a recirculation is detected on both the inner and outer walls of the corner for larger Reynolds. However, rarefaction may delay the onset of recirculation. It is also observed that the mass flux through a bend microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure difference.Copyright

Coupling Kinetic and Continuum Equations for Micro Scale Flow Computations

A hybrid method, coupling the direct numerical solution of the Bhatnagar-Gross-Krook (BGK) kinetic equation and hydrodynamic (Navier-Stokes) equations is presented. The computational physical domain is decomposed into kinetic and continuum sub-domains using an appropriate criterion based on the local Knudsen number and proper gradients of macro-parameters, computed via a preliminary Navier-Stokes solution throughout the whole physical domain. The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy, and mass through the interface. The advantage of the presented hybrid algorithm is that it easily allows the coupling of existing codes for the numerical solution of the BGK and Navier-Stokes equations. To validate and estimate the efficiency of the proposed method the simulation of the monatomic gas flow through a slit has been considered for outlet to inlet pressure ratio of 0.1, 0.5, and 0.9, and a wide range of Knudsen number. The comparison of local parameters (density, velocity, and temperature) with pure kinetic solutions shows satisfactory agreement with those computed by the hybrid solver.

Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels

A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.

Conjugate Heat Transfer Performances for Gaseous Flows in Short Micro Channels

A fully conjugate heat transfer analysis of gaseous flow, within slip flow regime, in short microchannels is presented. A Navier Stokes code, coupled with Maxwell slip and Smoluchowski temperature jump models, is adopted.The main focus is on the interaction between compressibility and heat transfer; in particular, due to the link between temperature and velocity field in highly compressible flow, it is important to recast the channel performance parameters in order to take into account the flow cooling due to the conversion between internal and kinetic energy. Results are presented for Nusselt number and a corrected heat sink thermal resistance, as well as resulting wall temperature.Copyright

Effect of surface roughness: comparison between continuum and kinetic approaches

In the present work a numerical analysis of the flow field in rough microchannels is carried out using two approaches: Navier-Stokes equations provided with first order slip-boundary condition and kinetic S-model equation with Maxwell diffuse reflecting boundary condition. An implicit scheme is used for the solution of S-model equation and an algorithm allowing massive parallelization in both physical and velocity spaces has been developed. The roughness geometry is modelled as a series of triangular obstructions with relative roughness e equals to 1.25%, 2.5% and 5%. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions and a Reynolds number up to 170. To estimate rarefaction effect the flow at Knudsen number ranging from 0.01 to 0.08 and fixed pressure ratio has been considered. Accuracy and discrepancies between full Navier - Stokes and S-model solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.

Numerical Investigation of Rough Surfaces: Coupling Approach

A numerical analysis of the flow field in rough microchannel is carried out decomposing the computational physical domain into kinetic and continuum sub-domains. Each domain size is determined by the value of a proper threshold parameter, based on the local Knudsen number and local gradients of macro-parameters. This switching parameter is computed from a preliminary Navier–Stokes solution throughout the whole physical domain. The solution is then advanced in time simultaneously in both kinetic and continuum domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes domains, taking care of the conservation of momentum, energy and mass through the interface.The roughness geometry is modeled as a series of triangular obstructions with a relative roughness up to a maximum of 5% of the channel height. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions and a Reynolds number up to 100. Accuracy and discrepancies between full Navier Stokes, kinetic and coupled solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.Copyright