Study of subsonic–supersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver

Abstract

We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging-diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the NavierStokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier-Stokes equations.

Detailed investigation of flow and thermal field in micro/nano nozzles using Simplified Bernoulli Trial (SBT) collision scheme in DSMC

“…T =ṁ e u e (7) where ṁ e and u e are the mass flow rate and velocity values, respectively. In addition, subscript 'e' refers to the nozzle exit section.…”

“…The behavior was investigated for two conditions, single and array patterns of nozzles. Darbandi and Roohi [7] studied the effects of gas/surface interactions (diffuse/specular reflections) and Knudsen number on the flow field in micro/nanoscale nozzles. Sebastião et al [8,9] simulated arrayarranged convergent-divergent micro nozzles by using DSMC.…”

Optimization of machining parameters for micro-machining nozzle based on characteristics of surface roughness

“…This additional momentum transfer can be accounted for by introducing a roughness-viscosity in a manner similar to the eddy-viscosity concept in the turbulent flow model. Darbandi et al [10] study the effects gas/surface interactions on the flow field in micro/nanoscale nozzles and show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle. Li et al [11] considered surface roughness effects on gas flows through long microtubes.…”

Study of the effects of preheated wall/plates in microthruster systems

“…Due to expansion of flow in the divergent section, the rarefied region is increased toward the end of nozzle. It is demonstrated by Darbandi and Roohi (2011) that solving the flow using the NS solver in the divergent section is not accurate even in the centerline. Therefore, the DSMC solver is used to simulate the entire divergent section and the NS solver is used for simulation of the convergent section of the micronozzle.…”