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Research Papers: Fundamental Issues and Canonical Flows

Effect of Three-Dimensional Surface Topography on Gas Flow in Rough Micronozzles

[+] Author and Article Information
Han Yan

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China

Wen-Ming Zhang

Professor
State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: wenmingz@sjtu.edu.cn

Zhi-Ke Peng, Guang Meng

Professor
State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 22, 2014; final manuscript received January 15, 2015; published online March 4, 2015. Assoc. Editor: Ali Beskok.

J. Fluids Eng 137(5), 051202 (May 01, 2015) (9 pages) Paper No: FE-14-1324; doi: 10.1115/1.4029630 History: Received June 22, 2014; Revised January 15, 2015; Online March 04, 2015

The gas flow characteristics in rectangular cross section converging–diverging micronozzles incorporating the effect of three-dimensional (3D) rough surface topography are investigated. The fractal geometry is utilized to describe the multiscale self-affine roughness. A first-order slip model suitable for rough walls is adopted to characterize the slip velocities. The flow field in micronozzles is analyzed by solving 3D Navier–Stokes (N–S) equation. The results show that the dependence of mass flow rate on the pressure difference has a good agreement with the reported results. The presence of surface topography obviously perturbs the gas flow near the wall. Moreover, as the surface roughness height increases, this perturbation induces the supersonic “multiwaves” phenomenon in the divergent region, in which the Mach number fluctuates. In addition, the effect of 3D surface topography on performance is also investigated.

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Figures

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Fig. 1

The schematic of rough micronozzle with the enlarged view of the rough surface profile

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Fig. 2

The diagram of constructing rough micronozzles, including (a) points and the tiny region formed by four points and (b) Coons surfaces and the tiny volume formed by two corresponding surfaces

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Fig. 3

The computational domain and mesh details of micronozzles with different roughness parameters: (a) σ=0.2 μm, D=2.8; (b)σ=0.8 μm, D=2.8; (c) σ=0.4 μm, D=2.8; and (d) σ=0.4 μm, D=2.2

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Fig. 4

Comparisons of mass flow rates among the presented results with the experimental results [34], two-dimensional Burnett solution [7], and two-dimensional DSMC results [10]

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Fig. 5

The streamlines both in the whole region and in the near-wall region of rough micronozzles with different fractal dimension, (a) D = 2.2 and (b) D = 2.8

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Fig. 6

The contours of Mach number in (a) the smooth micronozzle and (b)–(f) the rough micronozzle

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Fig. 7

The contours of Mach number in different micronozzles: (a) smooth, (b) ε=2%, D=2.2, (c) ε=2%, D=2.8, and (d) ε=4%, D=2.8

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Fig. 8

The distributions along the centerline and the contours at the cross section of (a) Mach number and (b) static pressure in micronozzles with different surface roughness height

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Fig. 9

The distribution of (a) Mach number and (b) static pressure along the centerline in the smooth micronozzle and rough micronozzles with different fractal dimensions

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Fig. 10

Comparison of centerline Mach number in smooth and rough micronozzles with different scales

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Fig. 11

Dimensionless slip length affected by the size effect and the surface roughness

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Fig. 12

The distribution of dimensionless slip length on rough walls

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Fig. 13

The thrust loss induced by surface roughness for different stagnation pressure

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Fig. 14

The variation of thrust loss with the Reynolds numbers in rough micronozzles with different expansion ratios

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