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Binary gas mixture in a high speed channel

Pradhan, S (2017) Binary gas mixture in a high speed channel. In: Engineering Sciences and Fundamentals 2017 - Core Programming Area at the 2017 AIChE Annual Meeting, 29 - 3 November 2017, Minneapolis, p. 593.

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Official URL: https://doi.org/10.1016/j.engfailanal.2022.106442


The viscous, compressible flow in a 2D wall-bounded channel, with bottom wall moving in positive x direction, simulated using the direct simulation Monte Carlo (DSMC) method, has been used as a test bed for examining different aspects of flow phenomenon and separation performance of a binary gas mixture at Mach number Ma = (Uw/√ γkBTw/m) in the range 0.1 < Ma < 30, and Knudsen number Kn = (1/(√2πd2ndH) in the range 0.1 < Kn < 10. Here, H is the channel width, Uw is the wall velocity, ρm is the volumeaveraged gas density, Tw is the wall temperature, m, and d are the molecular mass and molecular diameter, nd is the number density, μw is the molecular viscosity based on the temperature at the isothermal wall, and kB is the Boltzmann constant. The generalized analytical model is formulated which includes the fifth order differential equation for the boundary layer at the channel wall in terms of master potential (χ), which is derived from the equations of motion in a 2D rectangular (x - y) coordinate. The starting point of the analytical model is the Navier-Stokes, mass, momentum and energy conservation equations in the 2D rectangular (x - y) coordinate, where x and y are the streamwise and wall-normal coordinates. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a compressible Couette flow. Additional assumptions in the analytical model include high aspect ratio (length of the channel L is large compared to the width H), constant temperature in the base state (isothermal condition), and low Reynolds number. In this limit, the gas flow is restricted to a boundary layer of thickness (Re-1/2H) at the wall of the channel. Here, the Reynolds number Re = (ρmUwH/μw). The solutions of the generalized analytical model in a high-speed channel are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be compared with care. The commonly used 'diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a 'temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10%.

Item Type: Conference Paper
Publication: Engineering Sciences and Fundamentals 2017 - Core Programming Area at the 2017 AIChE Annual Meeting
Publisher: AIChE
Additional Information: The copyright for this article belongs to AIChE.
Keywords: Aerodynamics; Analytical models; Aspect ratio; Boundary conditions; Boundary layers; Channel flow; Density of gases; Flow of gases; Gas engineering; Gas mixtures; Isotherms; Monte Carlo methods; Navier Stokes equations; Reynolds number; X-Y model, Direct simulation Monte Carlo; Direct simulation Monte Carlo method; DSMC simulation; Energy conservation equations; Fifth order differential equation; High-speed channels; Linearization approximation; Rarefied gas flow, Gases
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 27 Jul 2022 04:57
Last Modified: 27 Jul 2022 04:57
URI: https://eprints.iisc.ac.in/id/eprint/74672

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