Investigation of rarefied gas flow in microchannels of non-uniform cross section

Study of rarefied gas flow in converging and diverging cross sections is crucial to the development of micro-nozzles and micro-thrusters. In other practical cases too, a microchannel may not always be straight and may include diverging and converging sections in the flow path. In this context, isothermal rarefied gas flow in microchannels of longitudinally varying cross section is studied experimentally in this work. The primary objective is to investigate the existence of Knudsen minimum in microchannels of varying cross sections. The effect of geometrical cross section and fluid properties on the Knudsen minimum are also investigated by performing experiments on three divergence angles (4°, 8°, and 12°) and three different gases (argon, nitrogen, and oxygen) to prove the robustness of the result. The Knudsen minimum, which is one of the characteristic features of rarefied flows, is experimentally observed for the first time in a microchannel of varying cross section. The position of the Knudsen minimum (at Kn ≈ 1) is seen to depend only weakly on the divergence angle and fluid properties.

[1]  Ramesh K. Agarwal,et al.  Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime , 2001 .

[2]  P. Perrier,et al.  Mass flow rate measurements in gas micro flows , 2006 .

[3]  J. Maurer,et al.  Second-order slip laws in microchannels for helium and nitrogen , 2003 .

[4]  Stéphane Colin,et al.  Validation of a Second-Order Slip Flow Model in Rectangular Microchannels , 2004 .

[5]  A. Agrawal,et al.  Experimental study of rarefied gas flow near sudden contraction junction of a tube , 2014 .

[6]  M. Knudsen.  Die Gesetze der Molekularstrmung und der inneren Reibungsstrmung der Gase durch Rhren , 1909 .

[7]  Felix Sharipov,et al.  Rarefied gas flow through a long rectangular channel , 1999 .

[8]  A. Agrawal,et al.  Heat transfer coefficient of gas flowing in a circular tube under rarefied condition , 2010 .

[9]  Amit Agrawal,et al.  Survey on measurement of tangential momentum accommodation coefficient , 2008 .

[10]  A. Agrawal,et al.  Flow map and measurement of void fraction and heat transfer coefficient using an image analysis technique for flow boiling of water in a silicon microchannel , 2009 .

[11]  A. Agrawal,et al.  The Burnett equations in cylindrical coordinates and their solution for flow in a microtube , 2014, Journal of Fluid Mechanics.

[12]  S. Colin,et al.  A novel experimental setup for gas microflows , 2010 .

[13]  Anupam Agrawal,et al.  Modeling of Navier-Stokes equations for high Knudsen number gas flows , 2012 .

[14]  W. G. Pollard,et al.  On Gaseous Self-Diffusion in Long Capillary Tubes , 1948 .

[15]  A. Agrawal,et al.  Behaviour of rarefied gas flow near the junction of a suddenly expanding tube , 2013, Journal of Fluid Mechanics.

[16]  T. Veltzke,et al.  An analytically predictive model for moderately rarefied gas flow , 2012, Journal of Fluid Mechanics.

[17]  S. Loyalka.  Kinetic Theory of Thermal Transpiration and Mechanocaloric Effect. I , 1971 .

[18]  F. Sharipov,et al.  Rarefied gas flow through a long tube of variable radius , 2005 .

[19]  Carlo Cercignani,et al.  Variational Approach to Boundary‐Value Problems in Kinetic Theory , 1966 .

[20]  P. Perrier,et al.  Effects of two transversal finite dimensions in long microchannel: Analytical approach in slip regime , 2012 .

[21]  Felix Sharipov,et al.  Data on Internal Rarefied Gas Flows , 1998 .

[22]  M. Ho,et al.  Rarefied gas flow through a long rectangular channel of variable cross section , 2014 .

[23]  P. Perrier,et al.  Mass flow rate measurements in microtubes: From hydrodynamic to near free molecular regime , 2011 .

[24]  A. Agrawal.  A Comprehensive Review on Gas Flow in Microchannels , 2011 .

[25]  David Emerson,et al.  A high-order moment approach for capturing non-equilibrium phenomena in the transition regime , 2009, Journal of Fluid Mechanics.

[26]  Carlo Cercignani,et al.  Flow of a Rarefied Gas between Two Parallel Plates , 1963 .

[27]  T. Veltzke,et al.  Erratum to: The gas flow diode effect: theoretical and experimental analysis of moderately rarefied gas flows through a microchannel with varying cross section , 2015 .

[28]  Abhishek Agrawal,et al.  Analytical solution of gaseous slip flow in long microchannels , 2007 .

[29]  Howard Brenner,et al.  Predicting enhanced mass flow rates in gas microchannels using nonkinetic models. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  V. S. Duryodhan,et al.  Low Mach number slip flow through diverging microchannel , 2015 .

[31]  A. Agrawal,et al.  Analytical solution of plane Poiseuille flow within Burnett hydrodynamics , 2014 .

[32]  A. Agrawal,et al.  Slip flow through a converging microchannel: experiments and 3D simulations , 2015 .

[33]  Amit Agrawal,et al.  Analytical solution of plane Couette flow in the transition regime and comparison with Direct Simulation Monte Carlo data , 2014 .

[34]  Timothée Ewart,et al.  Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes , 2007, Journal of Fluid Mechanics.

[35]  S. Tison,et al.  Experimental data and theoretical modeling of gas flows through metal capillary leaks , 1993 .

[36]  C. Cercignani,et al.  Cylindrical Poiseuille Flow of a Rarefied Gas , 1966 .

[37]  F. Sharipov,et al.  Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section , 2009 .