Department of Mathematics

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Author: search.filters.author.Rana, AnirudhSubject: search.filters.subject.Rarefied Gas Flow

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    A finite difference scheme for non-Cartesian mesh: Applications to rarefied gas flows
    (AIP, 2022-07) Rana, Anirudh
    A novel numerical scheme based on the finite-difference framework is developed, which allows us to model moderately rarefied gas flows in irregular geometries. The major hurdle in constructing numerical methods for rarefied gas flows is the prescription of the velocity-slip and temperature-jump boundary conditions as well as the discretization of an intricate set of partial differential equations. The proposed scheme is demonstrated to solve the non-linear coupled constitutive relations model along with the corresponding non-linear slip and jump boundary conditions. The computation of the discretized weights is proposed using two approaches: (i) polynomial shape functions and (ii) a generalized inverse distance approach. The non-linear terms are discretized using the fixed-point iteration method. The numerical method is validated for the Laplace equation over an annulus, and results are presented for a lid-driven curved cavity and a triangular lid-driven cavity, which delineates its performance on a skewed non-Cartesian grid. The results are validated with direct simulation Monte Carlo data from the literature, and a robust convergence for the solutions is demonstrated.
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    Rarefied gas flow past a liquid droplet: Interplay between internal and external flows
    (ARXIV, 2022-10) Rana, Anirudh
    Experimental and theoretical studies on millimeter-sized droplets suggest that at low Reynolds number the difference between the drag force on a circulating water droplet and that on a rigid sphere is very small (less than 1%) (LeClair et al. 1972), which is not the case when the droplet is of micrometer/nanometer size. The goal of this article is to study the effects of internal motion within a spherical micro/nano droplet -- such that its diameter is comparable to the mean free path of the surrounding gas -- on the drag force and its overall dynamics. To this end, the problem of a slow rarefied gas flowing over an incompressible liquid droplet is investigated analytically by considering the internal motion of the liquid inside the droplet and also by accounting for kinetic effects in the gas. Detailed results for different values of the Knudsen number, the ratio of the thermal conductivities and the ratio of viscosities are presented for the pressure and temperature profiles inside and outside the liquid droplet. The results for the drag force obtained in the present work are in good agreement with the theoretical and experimental results existing in the literature.
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    A review of rarefied gas flow in irregular micro/nanochannels
    (IOP, 2021-10) Rana, Anirudh
    In today's complex micro–electro–mechanical systems (MEMS), investigation of flow through irregular micro/nanochannels, such as bended channels, variable cross-sectional area channels, and those with rough surfaces, can contribute considerably to efficient designing of the microdevices and to gain a better understanding of the flow structure in these geometries. The present paper reviews the prominent studies published in literature on rarefied gas flow through these types of complex geometries. The main focus of the study is to explore the physical aspects of the findings and the analyses provided in support of the results. Finally, the areas in which a gap exists in literature and could be subjects of future studies are introduced.
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    H -theorem and boundary conditions for the linear R26 equations: application to flow past an evaporating droplet
    (CUP, 2021-08) Rana, Anirudh
    Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate the second law of thermodynamics and the Onsager reciprocity relations for certain boundary value problems, and, hence, are not physically admissible. We further prove that the linearised R26 (LR26) equations possess a proper H-theorem (second-law inequality) by determining a quadratic form without cross-product terms for the entropy density. The establishment of the H-theorem for the LR26 equations in turn leads to a complete set of boundary conditions that are physically admissible for all processes and comply with the Onsager reciprocity relations. As an application, the problem of a slow rarefied gas flow past a spherical droplet with and without evaporation is considered and solved analytically. The results are compared with the numerical solution of the linearised Boltzmann equation, experimental results from the literature and/or other macroscopic theories to show that the LR26 theory with the physically admissible boundary conditions provides an excellent prediction up to Knudsen number ≲1 and, consequently, provides transpicuous insights into intriguing effects, such as thermal polarisation. In particular, the analytic results for the drag force obtained in the present work are in an excellent agreement with experimental results even for very large values of the Knudsen number.
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    Evaporation-driven vapour microflows: analytical solutions from moment methods
    (CUP, 2018-03) Rana, Anirudh
    Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier–Stokes–Fourier, regularised 13-moment and regularised 26-moment frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number ≲1, whilst providing clear insight into non-equilibrium phenomena occurring adjacent to the interface.