Extraction of the translational Eucken factor from light scattering by molecular gas

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh-Brillouin scattering (RBS) experimental data. From the numerical simulation of the \cite{LeiJFM2015} model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas-surface interactions do not affect the measurements. For the first time, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of N2, CO2 and SF6 are simultaneously extracted from RBS experiments

Extraction of the translational Eucken factor from light scattering by molecular gas

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet, this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh–Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas–surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of N2 , CO2 and SF6 are simultaneously extracted from RBS experiments

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g.~D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as that used in simulating hydrodynamics (i.e.~D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. {In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature can not describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows.} Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries

A lattice Boltzmann method for axisymmetric thermocapillary flows

In this work, we develop a two-phase lattice Boltzmann method (LBM) to simulate axisymmetric thermocapil- lary flows. This method simulates the immiscible axisymmetric two-phase flow by an improved color-gradient model, in which the single-phase collision, perturbation and recoloring operators are all presented with the axisymmetric effect taken into account in a simple and computational consistent manner. An additional lattice Boltzmann equation is introduced to describe the evolution of the axisymmetric temperature field, which is coupled to the hydrodynamic equations through an equation of state. This method is first validated by simulations of Rayleigh-B ́enard convection in a vertical cylinder and thermocapillary migration of a de- formable droplet at various Marangoni numbers. It is then used to simulate the thermocapillary migration of two spherical droplets in a constant applied temperature gradient along their line of centers, and the influence of the Marangoni number (Ca), initial distance between droplets (S0), and the radius ratio of the leading to trailing droplets (Λ) on the migration process is systematically studied. As Ma increases, the thermal wake behind the leading droplet strengthens, resulting in the transition of the droplet migration from coalescence to non-coalescence; and also, the final distance between droplets increases with Ma for the non-coalescence cases. The variation of S0 does not change the final state of the droplets although it has a direct impact on the migration process. In contrast, Λ can significantly influence the migration process of both droplets and their final state: at low Ma, decreasing Λ favors the coalescence of both droplets; at high Ma, the two droplets do not coalesce eventually but migrate with the same velocity for the small values of Λ, and decreasing Λ leads to a shorter equilibrium time and a faster migration velocity

Influence of intermolecular potentials on rarefied gas flows: fast spectral solutions of the Boltzmann equation

The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coefficients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, differences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, differences in other quantities such as density, temperature, and velocity can be very large

A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio

A color-gradient lattice Boltzmann method (LBM) is proposed to simulate ax- isymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision op- erator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly re- covered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method’s numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time mod- el is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LB- M. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios

Accurate and efficient computation of the Boltzmann equation for Couette flow : influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient

The Couette flow is one of the fundamental problems of rarefied gas dynamics, which has been investigated extensively based on the linearized Boltzmann equation (LBE) of hard-sphere molecules and simplified kinetic model equations. However, how the different intermolecular potentials affect the viscous slip coefficient and the structure of Knudsen layer remains unclear. Here, a novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions of Couette flow accurately and efficiently: the velocity distribution function is first solved by the conventional iterative scheme, then it is modified such that in each iteration i) the flow velocity is guided by an ordinary differential equation that is asymptotic-preserving at the Navier–Stokes limit and ii) the shear stress is equal to the average shear stress. Based on the Bhatnagar–Gross–Krook model, the SIS is assessed to be efficient and accurate. Then we investigate the Knudsen layer function for gases interacting through the inverse power-law, shielded Coulomb, and Lennard-Jones potentials, subject to diffuse-specular and Cercignani–Lampis gas-surface boundary conditions. When the tangential momentum accommodation coefficient (TMAC) is not larger than one, the Knudsen layer function is strongly affected by the potential, where its value and width increase with the effective viscosity index of gas molecules. Moreover, the Knudsen layer function exhibits similarities among different values of TMAC when the intermolecular potential is fixed. For Cercignani–Lampis boundary condition with TMAC larger than one, both the viscous slip coefficient and Knudsen layer function are affected by the intermolecular potential, especially when the “backward” scattering limit is approached. With the asymptotic theory by Jiang and Luo (2016) [14] for the singular behavior of the velocity gradient in the vicinity of solid surfaces, we find that the whole Knudsen layer function can be well fitted by the power series ∑ n=0 2∑ m=0 2c n,mx n(xln⁡x) m, where x is the distance to the solid surface. Finally, the experimental data of the Knudsen layer profile are explained by the LBE solution with proper values of the viscosity index and TMAC

Case report: Sarcomatoid urothelial carcinoma of the renal pelvis masquerading as a renal abscess

Sarcomatoid urothelial carcinoma (SUC), a rare tumor of the urinary tract epithelium, exhibits a high degree of malignancy and therefore a poor prognosis. Due to the absence of specific clinical presentations and imaging findings, SUC of the renal pelvis masquerades as a renal abscess is frequently under-recognized or misdiagnosed as benign inflammatory disease, resulting in delayed or erroneous treatment. Here, we report a patient with SUC of the renal pelvis who presented with a renal abscess. Repeated anti-inflammatory treatment was ineffective. Unexpectedly, cancerous cells were detected in subsequent exfoliative cytology of nephrostomy drainage fluid. In accordance with this, radical surgery and postoperative chemotherapy were conducted. Fortunately, neither recurrence nor metastasis occurred during a one-year follow-up