Pradhan, S
(2017)
*The generalized onsager model and dsmc simulations of high-speed rotating flows in a multiply connected domain.*
In: 47th AIAA Fluid Dynamics Conference, 2017, 5 - 9 June 2017, Denver.

## Abstract

The generalized Onsager model for the radial boundary layer and of the generalized Carrier- Maslen model for the axial boundary layer in a highspeed rotating cylinder ((S. Pradhan & V. Kumaran, J. Fluid Mech., 2011, vol. 686, pp. 109-159); (V. Kumaran & S. Pradhan, J. Fluid Mech., 2014, vol. 753, pp. 307-359)), are extended to a multiply connected domain, created by the product and waste baffles. For a single component gas, the analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. In both cases, the equations are linearized in the perturbation to the base flow, which is a solid-body rotation. An explicit expression for the baffle stream function is obtained using the boundary layer solutions. The equations are restricted to the limit of high Reynolds number and (length/radius) ratio, but there is no limitation on the stratification parameter. The linear operators in the generalized Onsager and generalized Carrier-Maslen equations in a multiply connected domain with product and waste baffles are still self-adjoint, and so the eigenfunctions form a complete orthogonal basis set. However, the differential operator depends explicitly on the stratification parameter, and so it is necessary to evaluate the eigenvalues and eigenfunctions numerically. 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 axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth and second order in the radial and axial directions for the generalized Onsager equation, and fourth and second order in the axial and radial directions for the generalized Carrier- Maslen equation) are determined. The solutions for the secondary flows in a multiply connected domain with product and waste baffles are determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched 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 the wall temperature ((S. Pradhan & V. Kumaran, J. Fluid Mech., 2011, vol. 686, pp. 109-159); (V. Kumaran & S. Pradhan, J. Fluid Mech., 2014, vol. 753, pp. 307-359))). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 15%.

Item Type: | Conference Paper |
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Publication: | 47th AIAA Fluid Dynamics Conference, 2017 |

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

Additional Information: | The copyright for this article belongs to American Institute of Aeronautics and Astronautics Inc, AIAA. |

Keywords: | Boundary conditions; Boundary layers; Mathematical operators; Monte Carlo methods; Reynolds number; Rotational flow, Analysis and simulation; Direct simulation Monte Carlo; DSMC simulation; High-speed rotating; Homogeneous boundary condition; Multiply connected domain; Rarefied gas flow; Stratification parameters, Eigenvalues and eigenfunctions |

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

Date Deposited: | 18 Jul 2022 04:37 |

Last Modified: | 18 Jul 2022 04:37 |

URI: | https://eprints.iisc.ac.in/id/eprint/74608 |

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