# Numerical simulations on performance of MEMS-based nozzles at moderate or low temperatures

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DOI: 10.1007/s10404-004-0008-5

- Cite this article as:
- Wang, M.R. & Li, Z.X. Microfluid Nanofluid (2004) 1: 62. doi:10.1007/s10404-004-0008-5

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## Abstract

Performance of microelectromechanical systems (MEMS)-based nozzles at moderate and low temperatures is numerically analyzed using the direct simulation Monte Carlo method. Considering the intermolecular attractive potential caused by low temperature, the generalized soft sphere collision model is introduced. The Larsen–Borgnakke model for the generalized sphere model is used to model the energy exchange between the translational and internal modes. The results for nozzle flows at an initial temperature of 300 K show that the temperature behind the throat is quite low and the intermolecular attractive potential cannot be ignored. Different working conditions in two-dimensional (2D) nozzles are simulated using the present method, including exit pressure, inlet pressure, initial temperature, nozzle geometry, and gas species. The effects on the nozzle performance are analyzed. Simulations on flows in a three-dimensional (3D) low aspect ratio flat nozzle show that the increased surface-to-volume ratio, which leads to high viscosity dissipation, causes a much lower flow characteristic and performance comparing with the 2D case.

### Keywords

DSMCFlow fieldGeneralized soft sphere modelMEMS-based nozzle### Nomenclature

*b*miss-distance impact parameter, m

*d*collision diameter, m

*D*_{t}throat width, m

*E*_{t}relative translational energy, J

*F*_{t}thruster force, N

*I*_{sp}specific impulse, s

*k*Boltzmann constant, J/K

*Kn*_{th}Knudsen number at throat, defined by averaged values

*m*molecular mass, kg

*m*_{r}reduced mass, kg

*n*gas number density, m

^{−3}*P*_{in}inlet pressure, Pa

*P*_{e}exit pressure, Pa

*Re*_{th}Reynolds number at throat, defined by averaged values

*T*gas temperature, K

*T*_{*}dimensionless temperature

*kT*/*ε**T*_{w}wall temperature, K

*T*_{in}inlet temperature, K

*Z*_{R}rotational relax number

*α*soft sphere scattering law

*β*_{j},*ω*_{j}parameters for the GSS model

*ε*depth of the potential well, J

*δ*dimensionless constant for polarization

*μ*gas viscosity, kg/m·s

*σ*low-velocity diameter, m

*σ*_{T}total collision cross-section, m

^{2}*ζ*_{R}rotational degree of freedom

*ζ*_{t}translational degree of freedom

- Γ(...)
gamma function

- Ω
^{(1,1)*} integral for the self-diffusion coefficient

- Ω
^{(2,2)*} integral for the viscosity