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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.

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Figures

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Fig. 1

Rough elements parameters

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Fig. 2

Sketch of computational domain

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Fig. 3

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

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Fig. 7

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

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Fig. 8

The rarefaction effect on the Poiseuille numbers in a rough channel

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Fig. 4

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

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Fig. 5

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

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Fig. 6

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

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