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

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

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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Shimane, R., Kumagai, S., Hashizume, H., Ohta, T., Ito, M., Hori, M., and Sasaki, M., 2014, “Localized Plasma Irradiation Through a Micronozzle for Individual Cell Treatment,” Jpn. J. Appl. Phys., 53(11S), p. 11RB03. [CrossRef]
Lu, Z., Barnard, D., Shaikh, T. R., Meng, X., Mannella, C. A., Yassin, A. S., Agrawal, R. K., Wagenknecht, T., and Lu, T.-M., 2014, “Gas-Assisted Annular Microsprayer for Sample Preparation for Time-Resolved Cryo-Electron Microscopy,” J. Micromech. Microeng., 24(11), p. 115001. [CrossRef] [PubMed]
Bayt, R. L., 1999, “Analysis, Fabrication and Testing of a MEMS-Based Micropropulsion System,” Aerospace Computational Design Laboratory, Department of Aeronautics & Astronautics, Massachusetts Institute of Technology, Report No. FDRL TR-99-1.
Torre, F. L., Kenjeres, S., Kleijn, C. R., and Moerel, J.-L. P., 2010, “Effects of Wavy Surface Roughness on the Performance of Micronozzles,” J. Propul. Power, 26(4), pp. 655–662. [CrossRef]
Watvisave, D., Bhandarkar, U., and Puranik, B., 2013, “Investigation of Wall Effects on Flow Characteristics of a High Knudsen Number Nozzle,” Nanoscale Microscale Thermophys. Eng., 17(2), pp. 124–140. [CrossRef]
Moríñigo, J. A., and Hermida-Quesada, J., 2010, “Solid–Gas Surface Effect on the Performance of a MEMS-Class Nozzle for Micropropulsion,” Sens. Actuators, A, 162(1), pp. 61–71. [CrossRef]
Ketsdever, A. D., Clabough, M. T., Gimelshein, S. F., and Alexeenko, A. A., 2005, “Experimental and Numerical Determination of Micropropulsion Device Efficiencies at Low Reynolds Numbers,” AIAA J., 43(3), pp. 633–641. [CrossRef]
Nagai, H., Naraoka, R., Sawada, K., and Asai, K., 2008, “Pressure-Sensitive Paint Measurement of Pressure Distribution in a Supersonic Micronozzle,” AIAA J., 46(1), pp. 215–222. [CrossRef]
San, O., Bayraktar, I., and Bayraktar, T., 2009, “Size and Expansion Ratio Analysis of Micro Nozzle Gas Flow,” Int. Commun. Heat Mass Transfer, 36(5), pp. 402–411. [CrossRef]
Sebastião, I. B., and Santos, W. F., 2014, “Numerical Simulation of Heat Transfer and Pressure Distributions in Micronozzles With Surface Discontinuities on the Divergent Contour,” Comput. Fluids, 92(20), pp. 125–137. [CrossRef]
Louisos, W., and Hitt, D., 2012, “Viscous Effects on Performance of Three-Dimensional Supersonic Micronozzles,” J. Spacecr. Rockets, 49(1), pp. 51–58. [CrossRef]
Xie, C., 2007, “Characteristics of Micronozzle Gas Flows,” Phys. Fluids, 19(3), p. 037102. [CrossRef]
Sun, Z.-X., Li, Z.-Y., He, Y.-L., and Tao, W.-Q., 2009, “Coupled Solid (FVM)–Fluid (DSMC) Simulation of Micro-Nozzle With Unstructured-Grid,” Microfluid. Nanofluid., 7(5), pp. 621–631. [CrossRef]
Darbandi, M., and Roohi, E., 2011, “Study of Subsonic–Supersonic Gas Flow Through Micro/Nanoscale Nozzles Using Unstructured DSMC Solver,” Microfluid. Nanofluid., 10(2), pp. 321–335. [CrossRef]
Zhang, W.-M., Meng, G., and Wei, X., 2012, “A Review on Slip Models for Gas Microflows,” Microfluid. Nanofluid., 13(6), pp. 845–882. [CrossRef]
Bhattacharyya, S., and Nayak, A., 2010, “Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels,” ASME J. Fluids Eng., 132(4), p. 041103. [CrossRef]
Yan, X., and Wang, Q., 2009, “Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes,” ASME J. Fluids Eng., 131(10), p. 101201. [CrossRef]
Cho, C.-C., and Chen, C.-L., 2013, “Characteristics of Transient Electroosmotic Flow in Microchannels With Complex-Wavy Surface and Periodic Time-Varying Electric Field,” ASME J. Fluids Eng., 135(2), p. 021301. [CrossRef]
Xiong, R., 2011, “Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms,” ASME J. Fluids Eng., 133(3), p. 031102. [CrossRef]
Duan, Z., and Muzychka, Y., 2008, “Effects of Corrugated Roughness on Developed Laminar Flow in Microtubes,” ASME J. Fluids Eng., 130(3), p. 031102. [CrossRef]
Duan, Z., and Muzychka, Y., 2010, “Effects of Axial Corrugated Roughness on Low Reynolds Number Slip Flow and Continuum Flow in Microtubes,” ASME J. Heat Transfer, 132(4), p. 041001. [CrossRef]
Bahrami, M., Yovanovich, M., and Culham, J., 2006, “Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes,” ASME J. Fluids Eng., 128(3), pp. 632–637. [CrossRef]
Zhang, W.-M., Meng, G., and Wei, K.-X., 2012, “Numerical Prediction of Surface Roughness Effect on Slip Flow in Gas-Lubricated Journal Microbearings,” Tribol. Tras., 55(1), pp. 71–76. [CrossRef]
Ngalande, C., Lilly, T., Killingsworth, M., Gimelshein, S., and Ketsdever, A., 2006, “Nozzle Plume Impingement on Spacecraft Surfaces: Effects of Surface Roughness,” J. Spacecr. Rockets, 43(5), pp. 1013–1018. [CrossRef]
Sucec, J., 2014, “An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient,” ASME J. Fluids Eng., 136(8), p. 081103. [CrossRef]
Chen, Y., Zhang, C., Shi, M., and Peterson, G. P., 2012, “Slip Boundary for Fluid Flow at Rough Solid Surfaces,” Appl. Phys. Lett., 100(7), p. 074102. [CrossRef]
Sayles, R. S., and Thomas, T. R., 1978, “Surface Topography as a Nonstationary Random Process,” Nature, 271(5644), pp. 431–434. [CrossRef]
Chen, Y., Zhang, C., Shi, M., and Peterson, G., 2009, “Role of Surface Roughness Characterized by Fractal Geometry on Laminar Flow in Microchannels,” Phys. Rev. E, 80(2), pp. 1–7. [CrossRef]
Zhang, C., Chen, Y., Deng, Z., and Shi, M., 2012, “Role of Rough Surface Topography on Gas Slip Flow in Microchannels,” Phys. Rev. E, 86(1), p. 016319. [CrossRef]
Zhang, C., Deng, Z., and Chen, Y., 2014, “Temperature Jump at Rough Gas–Solid Interface in Couette Flow With a Rough Surface Described by Cantor Fractal,” Int. J. Heat Mass Tranfer, 70, pp. 322–329. [CrossRef]
Majumdar, A., and Bhushan, B., 1990, “Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces,” ASME J. Tribol., 112(2), pp. 205–216. [CrossRef]
Majumdar, A., and Tien, C., 1990, “Fractal Characterization and Simulation of Rough Surfaces,” Wear, 136(2), pp. 313–327. [CrossRef]
Yan, W., and Komvopoulos, K., 1998, “Contact Analysis of Elastic–Plastic Fractal Surfaces,” J. Appl. Phys., 84(7), pp. 3617–3624. [CrossRef]
Salomon, D., 2007, Curves and Surfaces for Computer Graphics, Springer, New York.
Maxwell, J. C., 1879, “On Stresses in Rarified Gases Arising From Inequalities of Temperature,” Philos. Trans. R. Soc. London, 170, pp. 231–256. [CrossRef]
Lockerby, D. A., Reese, J. M., Emerson, D. R., and Barber, R. W., 2004, “Velocity Boundary Condition at Solid Walls in Rarefied Gas Calculations,” Phys. Rev. E, 70(1), p. 017303. [CrossRef]
Hao, P.-F., Ding, Y.-T., Yao, Z.-H., He, F., and Zhu, K.-Q., 2005, “Size Effect on Gas Flow in Micro Nozzles,” J. Micromech. Microeng., 15(11), p. 2069. [CrossRef]


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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. 1

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

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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. 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. 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. 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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