Pradhan, S and Kumaran, V
(2017)
*Separation analysis in a high-speed rotating cylinder for a binary gas mixture.*
In: 21st AIAA International Space Planes and Hypersonics Technologies Conference, Hypersonics 2017, 6 -9 March 2017, Xiamen; China.

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## Abstract

The solutions of the species balance equations linked with generalized Onsager equation for the secondary flow in a high-speed rotating cylinder (Pradhan & Kumaran (2011); Kumaran & Pradhan (2014)) are compared with the Direct Simulation Monte Carlo (DSMC) simulations for a binary gas mixture. The concentration fields are obtained for the secondary flow due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow, for stratification parameter (A) in the range (0.707-3.535), and Reynolds number (Re) in the range (102â��106) with aspect ratio (Z/D = 2, 4, 8). Two different types of cases have been considered, (a) no mass difference (Ïµa= (2â��m/(m1+m2)) = 0), and (b) with mass difference (Ïµa= 0.2, and 0.5) while calculating the secondary flow field in the analytical model. Here, the stratification parameter A = â��(mÂÎ©2R2)/(2kBT), and the Reynolds number Re = (Ï�wÎ©R2)/Âµ, where m is the molecular mass, Î© is the angular velocity of the cylinder, R is the cylinder radius, Ï�wis the wall density, Âµ is the viscosity and T is the temperature. The base flow is an isothermal solid body rotation in which there is a balance between the radial pressure gradient and the centrifugal force density for each species. Explicit expressions for the radial variation of the pressure, mass and mole fractions, and from these the radial variation of the viscosity, thermal conductivity and diffusion coefficient, are derived, and these are used in the computation of the secondary flow. For the secondary flow, the mass, momentum and energy equations in axisymmetric co-ordinates are expanded in an asymptotic series in a parameter Ïµ = (Ï�w(m1â�� m2)/(Ï�w1m1+ Ï�w2m2)), where Ïµ = (â��m/mav), where â��m is the difference in the molecular masses of the two species, and the average molecular mass mavis defined as mav= ((Ï�w1m1+ Ï�w2m2)/Ï�w), where Ï�w1and Ï�w2are the mass densities of the two species at the wall, and Ï�w= Ï�w1+ Ï�w2. The equation for the master potential and the boundary conditions are derived correct to O(Ïµ2). The leading order equation for the master potential contains a self-adjoint sixth order operator in the radial direction which is different from the generalized Onsager model (Pradhan & Kumaran (2011)), since the species mass difference is included in the computation of the density, viscosity and thermal conductivity in the base state. This is solved, subject to boundary conditions, to obtain the O(1) approximation for the secondary flow. The O(Ïµ) and O(Ïµ2) equations contain inhomogeneous terms which depend on the lower order solutions, and these are solved in a hierarchal manner to obtain the O(Ïµ) and O(Ïµ2) corrections to the master potential. The results of the Onsager hierarchy, up to O(Ïµ2), are compared with the results of DSMC simulations for a binary hard-sphere gas mixture for the concentration fields due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow. There is excellent agreement between the analytical solutions correct to O(Ïµ2) and the simulations, to within 15-20, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity and the ratio of the mass difference and the average mass(2â��m/(m1+m2)) is as high as 0.5. The leading order solutions do capture the qualitative trends, but are not in quantitative agreement. Â© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

Item Type: | Conference Paper |
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Publication: | 21st AIAA International Space Planes and Hypersonics Technologies Conference, Hypersonics 2017 |

Publisher: | American Institute of Aeronautics and Astronautics Inc, AIAA |

Additional Information: | cited By 0; Conference of 21st AIAA International Space Planes and Hypersonics Technologies Conference, Hypersonics 2017 ; Conference Date: 6 March 2017 Through 9 March 2017; Conference Code:190149 |

Keywords: | Aerodynamics; Aspect ratio; Boundary conditions; Cylinders (shapes); Flow velocity; Gas mixtures; Molecular mass; Momentum; Monte Carlo methods; Reynolds number; Secondary flow; Thermal conductivity; Thermal gradients; Viscosity, Binary hard spheres; Centrifugal Forces; Concentration fields; Direct simulation Monte Carlo; High-speed rotating; Quantitative agreement; Separation analysis; Stratification parameters, Gases |

Department/Centre: | Division of Mechanical Sciences > Chemical Engineering |

Date Deposited: | 18 Nov 2020 11:07 |

Last Modified: | 18 Nov 2020 11:07 |

URI: | http://eprints.iisc.ac.in/id/eprint/66283 |

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