0
Research Papers

Numerical Investigation of Microflow Over Rough Surfaces: Coupling Approach

[+] Author and Article Information
Olga Rovenskaya

e-mail: olga.rovenskaya@uniud.it

Giulio Croce

e-mail: giulio.croce@uniud.it
DIEG,
University of Udine,
Via delle Scienze 208,
Udine 33100, Italy

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received June 29, 2012; final manuscript received February 26, 2013; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101005 (Sep 11, 2013) (8 pages) Paper No: HT-12-1329; doi: 10.1115/1.4024500 History: Received June 29, 2012; Revised February 26, 2013

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mala, G. M., and Li, D., 1999, “Flow Characteristics of Water in Microtubes,” Int. J. Heat Mass Transfer, 20, pp. 142–148. [CrossRef]
Wu, P. Y., and Little, W. A., 1983, “Measurement of Friction Factor for the Flow of Gases in Very Fine Channels Used for Microminiature Joule–Thomson Refrigerator,” Cryogenics, 23, pp. 273–277. [CrossRef]
Wu, P. Y., and Little, W. A., 1984, “Measurement of the Heat Transfer Characteristics of Gas Flow in Fine Channel Heat Exchangers Used for Microminiature Refrigerators,” Cryogenics, 24, pp. 415–420. [CrossRef]
Choi, S. B., Barron, R. F., and Warrington, R. O., 1991, “Fluid Flow and Heat Transfer in Microtubes,” ASME J. Dyn. Syst., Meas., Control, 32, pp. 123–133.
Morini, G. L., 2004, “Single-Phase Convective Heat Transfer in Microchannels: A Review of Experimental Results,” Int. J. Therm. Sci., 43(7), pp. 631–651. [CrossRef]
Kandlikar, S., Schmitt, D., Carrano, A., and Taylor, J., 2005, “Characterization of Surface Roughness Effects on Pressure Drop in Single-Phase Flow in Minichannels,” Phys. Fluids, 17(10), pp. 1–11. [CrossRef]
Croce, G., D'Agaro, P., and Nonino, C., 2007, “Three-Dimensional Roughness Effect on Microchannel Heat Transfer and Pressure Drop,” Int. J. Heat Mass Transfer, 50, pp. 5249–5259. [CrossRef]
Turner, S. E., Lam, L. C., Faghri, M., and Gregory, O. J., 2004, “Experimental Investigation of Gas Flow in Microchannels,” ASME J. Heat Transfer, 126, pp. 753–762. [CrossRef]
Lorenzini, G., Morini, G. L., and Salvigni, S., 2010, “Laminar, Transitional and Turbulent Friction Factors for Gas Flows in Smooth and Rough Microchannels,” Int. J. Therm. Sci., 49, pp. 248–255. [CrossRef]
Demsis, A., Prabhu, S. V., and Agrawal, A., 2010, “Influence of Wall Conditions on Friction Factor for Flow of Gases Under Slip Conditions,” Exp. Therm. Fluid Sci., 34, pp. 1448–1455. [CrossRef]
Tang, G. H., Li, Z., He, Y. L., and Tao, W. Q., 2007, “Experimental Study of Compressibility, Roughness and Rarefaction Influences on Microchannel Flow,” Int. J. Heat Mass Transfer, 50, pp. 2282–2295. [CrossRef]
Hu, Y., Werner, C., and Li, D., 2003, “Influence of Three-Dimensional Roughness on Pressure-Driven Flow Through Microchannels,” ASME J. Fluid Eng., 125, pp. 871–879. [CrossRef]
Croce, G., and D'Agaro, P., 2005, “Numerical Simulation of Roughness Effect on Microchannel Heat Transfer and Pressure Drop in Laminar Flow,” J. Phys. D: Appl. Phys., 38(10), pp. 1518–1530. [CrossRef]
Valses, R., Miana, J., Pelegay, L., Nunez, L., and Putz, T., 2007, “Numerical Investigation of the Influence of Roughness on the Laminar Incompressible Fluid Flow Through Annular Microchannels,” Int. J. Heat Mass Transfer, 50, pp. 1865–1878. [CrossRef]
Kleinstreuer, C., and Koo, J., 2004, “Computational Analysis of Wall Roughness Effects for Liquid Flow in Micro-Conduits,” ASME J. Fluid Eng., 126, pp. 1–9. [CrossRef]
Koo, J., and Kleinstreuer, C., 2005, “Analysis of Surface Roughness Effects on Heat Transfer in Micro-Conduits,” Int. J. Heat Mass Transfer, 48, pp. 2625–2634. [CrossRef]
Sun, H., and Faghri, M., 2003, “Effect of Surface Roughness on Nitrogen Flow in a Microchannel Using the Direct Simulation Monte Carlo Method,” Numer. Heat Transfer, Part A, 43, pp. 1–8. [CrossRef]
Cao, B., Chen, M., and Guo, Z., 2004, “Rarefied Gas Flow in Rough Microchannels by Molecular Dynamics Simulation,” Chin. Phys. Lett., 21(9), pp. 1777–1779. [CrossRef]
Liu, C., Yanga, J., and Ni, Y., 2011, “A Multiplicative Decomposition of Poiseuille Number on Rarefaction and Roughness by Lattice Boltzmann Simulation,” Comp. Math. Appl., 61, pp. 3528–3536. [CrossRef]
Ji, Y., Yuan, K., and Chung, J., 2006, “Numerical Simulation of Wall Roughness on Gaseous Flow and Heat Transfer in a Microchannel,” Int. J. Heat Mass Transfer, 49, pp. 1329–1339. [CrossRef]
Croce, G., and D'Agaro, P., 2007, “Compressibility and Rarefaction Effects on Pressure Drop in Rough Microchannels,” Heat Transfer Eng., 28(8–9), pp. 688–695. [CrossRef]
Hakak Khadem, M., Shams, M., and Hossainpour, S., 2009, “Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness,” Int. J. Aerosp. Mech. Eng., 3(4), pp. 204–210. Available at http://www.waset.org/journals/ijame/v3/v3-4-33.pdf
Croce, G., and D'Agaro, P., 2009, “Compressibility and Rarefaction Effects on Heat Transfer in Rough Microchannels,” Int. J. Therm. Sci., 48(2), pp. 252–260. [CrossRef]
Colin, S., 2012, “Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer,” ASME J. Heat Transfer, 134(2), pp. 1–13. [CrossRef]
Shakhov, E. M., 1974, A Method for Calculating Rarefied Gas Flows, Nauka, Moscow.
Carlson, H. A., Roveda, R., Boyd, I. D., and Candler, G. V., 2004, “A Hybrid CFD-DSMC Method of Modeling Continuum-Rarefied Flows,” AIAA Paper No. 2004-1180.
Lockerby, D. A., Reese, J. M., and Struchtrup, H., 2009, “Switching Criteria for Hybrid Rarefied Gas Flow Solvers,” Proc. R. Soc. London, 465, pp. 1581–1598. [CrossRef]
Kolobov, V. I., Arslanbekov, R. R., Aristov, V. V., Frolova, A. A., and Zabelok, S. A., 2007, “Unified Solver for Rarefied and Continuum Flows With Adaptive Mesh and Algorithm Refinement,” J. Comput. Phys., 223, pp. 589–608. [CrossRef]
Croce, G., 1995, “Viscous 3D Cascade Flow Analysis Using an RNG Algebraic Turbulence Mode,” ASME Paper No. 95-CTP-78.
Croce, G., and Rovenskaya, O., 2010, “Numerical Analysis of Rarefaction and Compressibility Effects in Bent Microchannels,” ASME Paper No. ICNMM2010-30489.
Pulliam, T. H., 1986, “Artificial Dissipation Models for the Euler Equations,” AIAA J., 24, pp. 1931–1940. [CrossRef]
Asako, Y., Pi, T., Turner, S. E., and Faghri, M., 2002, “Effect of Compressibility on Gaseous Flows in Micro-Channels,” Int. J. Heat Mass Transfer, 46, pp. 3041–3050. [CrossRef]
Rovenskaya, O., and Croce, G., 2013, “Coupling Kinetic and Continuum Equations for Micro Scale Flow Computations,” Heat Transfer Eng., 34(2–3), pp. 192–203. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Rough elements parameters

Grahic Jump Location
Fig. 2

Sketch of computational domain

Grahic Jump Location
Fig. 3

CNS criteria for Kn = 0.01 (top) and Kn = 0.04 (bottom), p0i/pe = 2

Grahic Jump Location
Fig. 4

The rarefaction effect on the Poiseuille number in a smooth channel p0i/pe = 1.1

Grahic Jump Location
Fig. 5

Average Poiseuille number via average Re at p0i/pe = 2 (top) and p0i/pe = 3 (bottom)

Grahic Jump Location
Fig. 6

Local Poiseuille number distribution via local Ma at p0i/pe = 2 (top) and p0i/pe = 3 (bottom) for ε = 0, ε = 5%

Grahic Jump Location
Fig. 7

Streamlines at p0i/pe = 2, Kn = 0.04, kinetic (thick), and NS (thin) solutions

Grahic Jump Location
Fig. 8

The rarefaction effect on the Poiseuille numbers in a rough channel

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In