Pradhan, S
(2017)
*Analysis of high-speed rotating flow in polar (r - Î¸) coordinate.*
In: 8th AIAA Theoretical Fluid Mechanics Conference, 05-09 June 2017, Denver, United States.

## Abstract

The generalized analytical model for the radial boundary layer in a high-speed rotating cylinder is formulated for studying the secondary radial flow due to insertion of mass, momentum and energy into the rotating cylinder in the polar (r-Î¸) plane. The analytical solution includes the sixth order differential equation for the radial boundary layer at the cylindrical surface in terms of master potential (Î§), which is derived from the equations of motion in a polar (r-Î¸) plane. 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 solid-body rotation. Additional assumptions in the analytical model include constant temperature in the base state (isothermal condition), and high Reynolds number, but there is no limitation on the stratification parameter. In this limit, the gas flow is restricted to a boundary layer of thickness (Re-1/3R) at the wall of the cylinder. Here, the stratification parameter (Formula presented.). This quantity(A) is the ratio of the peripheral speed (Î©R) to the most probable molecular speed (Formula presented.), the Reynolds number Re = (Ï�wÏ�R2)/Âµ, where m is the molecular mass, Ï� and R are the rotational speed and radius of the cylinder, kB is the Boltzmann constant, T is the gas temperature, Ï�w is the gas density at wall, and Âµ is the gas viscosity. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the meridional and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and meridional directions for the generalized analytical equation) are obtained. The solutions for the secondary radial flows are determined in terms of these eigenvalues and eigenfunctions. The major advantage of the present formulation is that it is not restricted to the asymptotic limit of high stratification parameter, and the shock type solutions (Rankine-Hugoniot relations) are obtained simultaneously. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 10) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified. In a high speed rotating field we examine the mass flow rate through the stationary intake tube. The simulations show that the scaled mass flow rate m/(HÏ�) increases progressively from zero, at the stagnation condition, to 0.024 as the equilibrium back pressure is reduced. Here, H is the total gas holdup. The slow down of the circumferential velocity of the bulk of the rotating fluid due to the presence of stationary intake tube is studied for stratification parameter in the range 0.707 - 3.535, and found significant slow down (between 8 to 28), which induces the secondary radial flow towards the axis, and it further excites the secondary axial flow, which could be very important for the centrifugal gas separation processes. An important finding is that the stagnation pressure (no mass flow through the intake tube) is strongly affected by the wall gap, as well as with stratification parameter indicating a strong coupling between the local temperature, density, pressure and velocity fields. Â© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

Item Type: | Conference Paper |
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Publication: | 8th AIAA Theoretical Fluid Mechanics Conference, 2017 |

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

Additional Information: | The copyright of this article belongs to American Institute of Aeronautics and Astronautics |

Keywords: | Boundary conditions; Boundary layers; Cylinders (shapes); Density of gases; Eigenvalues and eigenfunctions; Equations of motion; Flow of gases; Fluid mechanics; Gases; Mass transfer; Mathematical operators; Monte Carlo methods; Radial flow; Reynolds number; Rotational flow; Velocity, Direct simulation Monte Carlo; DSMC simulation; High-speed rotating; Homogeneous boundary condition; Linearization approximation; Rankine-Hugoniot relations; Rarefied gas flow; Stratification parameters, Analytical models |

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

Date Deposited: | 07 Apr 2021 09:42 |

Last Modified: | 07 Apr 2021 09:42 |

URI: | http://eprints.iisc.ac.in/id/eprint/66213 |

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