Browsing by Author "Rana, Anirudh Singh"

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Capturing non-equilibrium in hypersonic flows: Insights from a two-temperature model in polyatomic rarefied gases
(AIP, 2024) Rana, Anirudh Singh
The study utilizes a two-temperature model to analyze non-equilibrium in normal shocks within hypersonic flows in polyatomic rarefied gases. Derived from the extended second law of thermodynamics, this model separates translational and internal temperatures in polyatomic gases, providing a more accurate depiction of non-equilibrium gas flow compared to classical theories like the Navier–Stokes and Fourier (NSF) system. Notably, the analysis reveals that the two-temperature model incorporates an additional contribution to the heat flux due to the gradient of the dynamic temperature, resulting in improved accuracy, especially for high Mach numbers. Results show that the model gives satisfactory shock density and temperature profiles up to Mach 10, with very good agreement observed up to Mach 6.1 compared to the classical NSF model. We conduct an order of magnitude analysis on the dynamic temperature and heat flux gradients appearing in the new constitutive equation using the Mott-Smith method. This analysis highlights the impact of these terms on accurately modeling polyatomic gas behavior in high-speed flows. The effects of bulk viscosity and incoming temperature on shock profiles are also investigated, contributing to a better understanding of shock wave structures in polyatomic gases and their implications for hypersonic flow dynamics.
Coupled constitutive relations for two-temperature model for polyatomic gases: Linear analysis, light scattering, and shock propagation
(AIP, 2025-07) Rana, Anirudh Singh
This article presents a new two-temperature coupled constitutive relations (CCR) model for polyatomic gases, developed using CCR based on classical irreversible thermodynamics. The model includes nonlinear terms in entropy and heat flux to better capture non-equilibrium phenomena. It offers a significant improvement over the one-temperature CCR model recently introduced by Rana and Barve [“A second-order constitutive theory for polyatomic gases: Theory and applications,” J. Fluid Mech. 958, A23 (2023)] and simplifies the complex behavior of polyatomic gases, providing a practical alternative to the Boltzmann equation or molecular dynamics simulations. The proposed model accurately describes steady-state shocks and Rayleigh–Brillouin light scattering, showing particular advantages in rarefied flow scenarios. Additionally, the model exhibits strong stability and consistency in capturing non-equilibrium processes, making it suitable for a wide range of flow conditions.
Dispersion of neutral solutes in viscoelastic microflows under combined electroosmotic and pressure forcing
(AIP, 2025-08) Rana, Anirudh Singh
This study examines the transport of a neutral, fully miscible solute in the fully developed flow of a viscoelastic fluid through a microchannel, influenced by both electroosmotic and pressure-driven forces. The viscoelastic behavior is modeled using the simplified Phan-Thien–Tanner (sPTT) constitutive equation. To capture the nonlinear viscoelastic effects on solute dispersion and concentration distribution, Mei's multi-scale homogenization technique is employed. A detailed parametric study, supported by graphical analysis, reveals that the maximum Taylor dispersion coefficient and most efficient solute diffusion occur when electroosmotic and pressure forces favour each other, the electroosmotic parameter (based on the Debye–Hückel approximation) is minimal—corresponding to a thick electrical double layer (EDL)—and the sPTT viscoelastic parameter is high. In the Newtonian case, increasing the electroosmotic parameter (i.e., reducing EDL thickness) significantly enhances transverse concentration. In purely electroosmotic non-Newtonian flows (absence of pressure), optimal velocity and flow rate are achieved when both the electroosmotic and viscoelastic parameters are large. In the general non-Newtonian case with both electroosmotic and pressure forces, favoring forces lead to a sharp increase in the Taylor dispersion coefficient at low electroosmotic parameter values, with a more gradual increase at higher values. These results are relevant for designing electro-bio-microfluidic systems that utilize non-Newtonian biopolymer solutions for enhanced species separation and controlled biochemical transport.
Evaporating jets and phase transition in rarefied conditions
(AIP, 2025-05) Rana, Anirudh Singh
This work examines the evaporation and condensation phenomena at small scales, focusing on how surface deformations affect mass and heat transfer under temperature-driven and pressure-driven conditions. The rarefaction effects arising at these scales cannot be accurately captured by the classical continuum theories such as Navier–Stokes–Fourier equations. To address this limitation, the coupled constitutive relations (CCR) are employed to describe the process. The thermodynamically admissible boundary conditions for both partial and complete evaporation and condensation are presented by determining the reciprocity coefficients for the CCR model. The problem is solved using the method of fundamental solutions (MFS), which is a meshless numerical scheme. Numerical results from the MFS are validated with an analytic solution for a circular cross section of an evaporating jet. Furthermore, the effect of cross-sectional deformations on evaporation and condensation is demonstrated by evaluating mass and heat transfer characteristics wherein spherical harmonics are used to generate deformed shapes. An error analysis is performed to showcase the accuracy and convergence of the MFS. The results provide an understanding of the modeling of phase-change phenomena in micro- and nanoscale systems.
Exploring external rarefied gas flows through the method of fundamental solutions
(APS, 2025-01) Rana, Anirudh Singh
The well-known Navier-Stokes-Fourier equations of fluid dynamics are, in general, not adequate for describing rarefied gas flows. Moreover, while the Stokes equations—a simplified version of the Navier-Stokes-Fourier equations—are effective in modeling slow and steady liquid flow past a sphere, they fail to yield a nontrivial solution to the problem of slow and steady liquid flow past an infinitely long cylinder (a two-dimensional problem essentially); this is referred to as Stokes' paradox. The paradox also arises when studying these problems for gases. In this paper, we present a way to obtain meaningful solutions for two-dimensional flows of rarefied gases around objects by circumventing Stokes' paradox. To this end, we adopt an extended hydrodynamic model, referred to as the CCR model, consisting of the balance equations for the mass, momentum, and energy and closed with the coupled constitutive relations. We determine an analytic solution of the CCR model for the problem and compare it with a numerical solution based on the method of fundamental solutions. Apart from addressing flow past a circular cylinder, we aim to showcase the capabilities of the method of fundamental solutions to predict the flow past other objects in two dimensions for which analytic solutions do not exist or are difficult to determine. For that, we investigate the problem of rarefied gas flow past an infinitely long semicircular cylinder
A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows
(2025-04) Rana, Anirudh Singh
In this work, we explore the method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific fundamental solutions, we propose a generic approach that systematically computes the fundamental solutions for any linear moment system without predefined source terms. The generalized framework is first introduced using a simple example involving the Stokes equations, and is then extended to the R13 equations. The results obtained from the generic MFS are validated against an analytical solution for the R13 equations. Following validation, the framework is applied to the case of thermally-induced flow between two non-coaxial cylinders. Since no analytical solution exists for this case, we compare the results obtained from the MFS with those obtained from the finite element method (FEM). To further assess computational efficiency, we analyze the runtimes of the FEM and MFS. The results indicate that the MFS converges faster than the FEM and serves as a promising alternative to conventional meshing-based techniques.
H-theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases
(AIP, 2023-12) Rana, Anirudh Singh
Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in nonequilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.
Modeling of rarefied gas flows in streamwise periodic channels: Application of coupled constitutive relations and the method of fundamental solutions
(Elsevier, 2025-03) Rana, Anirudh Singh
Periodic structures are ubiquitous in nature and engineering, offering unique properties that inspire a range of applications. This paper explores the mathematical modeling of periodic structures in rarefied gas flows using the coupled constitutive relations (CCR) model. The method of fundamental solutions (MFS), known for its meshfree nature and computational efficiency, is utilized as a numerical tool. The streamwise periodic boundary conditions are incorporated into the MFS for modeling two-dimensional flow in periodically patterned channels. We validate the developed CCR-MFS framework with analytical solutions for force-driven Poiseuille and Couette flow. The error analysis is also performed to determine the optimal singularity location. Furthermore, we simulate the flow in channels with periodic patterns by varying the accommodation coefficient. This allows us to analyze the effects of patterning and accommodation coefficients in the Maxwell model of boundary conditions. Effects of patterning on mass flux, energy flux, and average friction coefficients are also presented for the force-driven flow in patterned channels. Our simulations demonstrate the potential of the mathematical and computational techniques to enhance the performance and functionality of a range of technological applications.
A novel meshfree method for nonlinear equations in flow through porous media and electrohydrodynamic flows
(Taylor & Francis, 2024-05) Rana, Anirudh Singh
In this study, an efficient meshfree numerical method is introduced for solving the nonlinear boundary value problems. The method of fundamental solutions (MFS) is one of the most popular among meshfree methods. While traditionally limited to linear and homogeneous problems, this study extends the applicability of the MFS to include nonhomogeneous and nonlinear equations. To achieve this, an extended MFS is combined with a fixed-point iteration scheme. This developed framework is benchmarked to address two different flow problems. The first involves fluid flow through porous media in a channel governed by the nonlinear Brinkman-Forchheimer equation. The second problem pertains to electrohydrodynamic (EHD) flow in a circular conduit. The obtained solutions are compared with the finite element method and the solutions available in the existing literature.
Regularized Gaussian 11-moment equations for polyatomic gases: Derivation, linear analysis, and its applications
(Springer, 2025-09) Rana, Anirudh Singh
This article presents a macroscopic closure for rarefied polyatomic gas flows, focusing on a regularized Gaussian 11-moment (RG11) system. Our model uses a generalized Gaussian distribution-a product of Gaussian and Gamma functions-to capture both translational and internal energies of polyatomic molecules. The closure is achieved through a regularization technique, following Struchtrup & Torrilhon (Physics of Fluids, vol. 15, 2003) approach for R13 equations in monatomic gases. In addition, we use a Bhatnagar-Gross-Krook (BGK)-type relaxation model to evaluate the production terms in the moment equations. The proposed model incorporates three relaxation parameters, which can be tuned to match viscosity, bulk viscosity, and thermal conductivity accurately for the gas under consideration. By applying a Chapman-Enskog-like expansion and an order-of-magnitude analysis, we derive the RG11 equations, featuring non-zero constitutive relations for both internal and translational heat flux. This new formulation is linearly stable in one-dimensional case across all wavelengths and frequencies, aligns well with experimental data for sound wave propagation, and agrees with validated hydrodynamic theories that are known to match experimental results for Rayleigh-Brillouin scattering (RBS), outperforming the Navier-Stokes-Fourier (NSF) equations.
Stokes' paradox in rarefied gases: A perspective through the method of fundamental solutions
(2024-06) Rana, Anirudh Singh
In the realm of fluid dynamics, a curious and counterintuitive phenomenon is Stokes' paradox. While Stokes equations -- used for modeling slow and steady flows -- lead to a meaningful solution to the problem of slow and steady flow past a sphere, they fail to yield a non-trivial solution to the problem of slow and steady flow past an infinitely long cylinder (a two-dimensional problem essentially); this is referred to as Stokes' paradox. We revisit this paradox in the context of rarefied gas flows by means of the method of fundamental solutions (MFS). To this end, we adopt an extended hydrodynamic model, referred to as the CCR model, consisting of the balance equations for the mass, momentum and energy and closed with the coupled constitutive relations. We determine an analytic solution of the CCR model for the problem and compare it with the MFS-based numerical solution. Apart from addressing flow past a circular cylinder, we aim to showcase the capability of the MFS to predict the flow past other objects in two dimensions for which the analytic solutions do not exist. For that, we investigate the problem of rarefied gas flow past an infinitely long semicircular cylinder.
Temperature dependent Korteweg stress coefficient from the Enskog–Vlasov equation
(AIP, 2024) Rana, Anirudh Singh
Enskog–Vlasov equation—a nonlinear partial-integrodifferential equation, provides a robust framework for analyzing liquid dynamics and phase transition. The Vlasov force expanded using Taylor series yields Korteweg stress with two constant coefficients. The first coefficient yields the van der Waals like contribution to equilibrium pressure, while the second coefficient determines the interfacial stresses/surface tension. In this article, we express the second Korteweg constant coefficient as a function of temperature. The developed model effectively captures the liquid–vapor interfacial region in equilibrium, reproducing the sharp interfacial structure predicted by the full Enskog–Vlasov equation. Additionally, we compare our results with those obtained through a particle-based approach, as studied by Frezzotti et al. (2009) [“Direct simulation Monte Carlo applications to liquid–vapor flows,” Phys. Fluids 31, 062103 (2019)]. The proposed model balances simplicity with computational efficiency, comprehensively examined within the paper.
Thermodynamically admissible diffuse interface model for nanoscale transport of dense fluids
(2025-05) Rana, Anirudh Singh
We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to accurately capture transport phenomena across extremely thin interfaces due to underestimation of interface resistances. In this work, we improve the NSK model by adding a production term in the momentum equation based on higher-order corrections. To enhance interface resistances, viscosity and thermal conductivity are made dependent on the density gradient, increasing resistance only within the interface region. The gradient-based coefficients are determined by fitting to solutions of the Enskog-Vlasov equation for Couette flow (see Struchtrup and Frezzotti, 2022). Applying these fitted equations to pure heat conduction and planar evaporation problems shows that the model accurately captures interfacial transport, making it a useful tool for studying nanoscale evaporation, thermal management, and droplet dynamics on solid surfaces.
Thermophoresis and uniform flow in rarefied polyatomic gases: The role of constitutive relations and boundary conditions
(AIP, 2023) Rana, Anirudh Singh
Recently, Rana and Barve [“A second-order constitutive theory for polyatomic gases: Theory and applications,” J. Fluid Mech. 958, A23 (2023)] developed a second-order coupled constitutive relations (CCR) for polyatomic gases that include quadratic nonlinearities in the entropy flux and apply the second law. However, in that work, the boundary conditions were heuristically obtained to match the drag coefficient on a sphere and may not be accurate in situations where thermal transpiration and thermal stress are significant factors, as indicated by their asymptotic analysis. This article presents a systematic approach for deriving thermodynamically admissible boundary conditions for the CCR model. We also propose a set of higher-order boundary conditions based on an asymptotic analysis of the solutions for drag on flow past a sphere and thermophoretic drag. The goal of deriving these boundary conditions is to improve the accuracy of the CCR model when applied to external flows, such as slow flow past particles and thermophoretic motion of a spherical particle and doublet. The results of the study demonstrate that the combination of the newly derived boundary conditions in conjunction with the CCR equations shows excellent agreement with both theoretical predictions and experimental data over a wide range of Knudsen numbers. The study suggests that the approach presented in this article can be used to improve the accuracy of the CCR model in a variety of external flow applications.
A Viewpoint on Thermally-Induced Transport in Rarefied Gases through the Method of Fundamental Solutions
(Taylor & Francis, 2024-04) Rana, Anirudh Singh
Some phenomena pertaining to rarefied gases are beyond the reach of traditional fluid dynamics described, e.g., by the Euler or Navier–Stokes–Fourier equations. Therefore we adopt a recently developed model—referred to as the CCR model—to investigate thermally-induced transport in rarefied gases. To this end, the method of fundamental solutions is employed on the CCR model to investigate two problems: (i) a rarefied gas flow confined between two coaxial cylinders having different temperatures with the inner cylinder being circular while the outer being elliptical, and (ii) evaporation/condensation process in a rarefied vapor confined between two coaxial cylinders, again with the inner cylinder being circular and the outer being elliptical. Through a comprehensive analysis, the efficiency of the method of fundamental solutions is assessed. The work contributes toward a better understanding of thermally-induced confined rarefied gas flows.