Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

In the present paper, we provide an analytical expression for the first- and second-order thermal slip coefficients, σ1,T and σ2,T, by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules. The Cercignani-Lampis scattering kernel of the gas-surface interaction has been considered in order to take into account the influence of the accommodation coefficients (αt, αn) on the slip parameters. Comparing our theoretical results with recent experimental data on the mass flow rate and the slip coefficient for five noble gases (helium, neon, argon, krypton, and xenon), we found out that there is a continuous set of values for the pair (αt, αn) which leads to the same thermal slip parameters. To uniquely determine the accommodation coefficients, we took into account a further series of measurements carried out with the same experimental apparatus, where the thermal molecular pressure exponent γ has been also evaluated. Therefore, the new method proposed in the present work for extracting the accommodation coefficients relies on two steps. First of all, since γ mainly depends on αt, we fix the tangential momentum accommodation coefficient in such a way as to obtain a fair agreement between theoretical and experimental results. Then, among the multiple pairs of variational solutions for (αt, αn), giving the same thermal slip coefficients (chosen to closely approximate the measurements), we select the unique pair with the previously determined value of αt. The analysis carried out in the present work confirms that both accommodation coefficients increase by increasing the molecular weight of the considered gases, as already highlighted in the literature.

On the mechanism of droplet rolling and spinning in inclined hydrophobic plates in wedge with different wetting states

A water droplet rolling and spinning in an inclined hydrophobic wedge with different wetting states of wedge plates is examined pertinent to self-cleaning applications. The droplet motion in the hydrophobic wedge is simulated in 3D space incorporating the experimental data. A high-speed recording system is used to store the motion of droplets in 3D space and a tracker program is utilized to quantify the recorded data in terms of droplet translational, rotational, spinning, and slipping velocities. The predictions of flow velocity in the droplet fluid are compared with those of experimental results. The findings revealed that velocity predictions agree with those of the experimental results. Tangential momentum generated, via droplet adhesion along the three-phase contact line on the hydrophobic plate surfaces, creates the spinning motion on the rolling droplet in the wedge. The flow field generated in the droplet fluid is considerably influenced by the shear rate created at the interface between the droplet fluid and hydrophobic plate surfaces. Besides, droplet wobbling under the influence of gravity contributes to the flow inside the rolling and spinning droplet. The parallel-sided droplet path is resulted for droplet emerging from the wedge over the dusty surface.

Does Balance Dynamics Well Capture the Secondary Circulation and Spinup of a Simulated Hurricane?

This study investigates a claim made by Heng et al. in an article published in 2017 and intimated soon after in their article published in 2018 that axisymmetric “balanced dynamics can well capture the secondary circulation in the full-physics model” during hurricane spinup. Using output from a new, convection-permitting, three-dimensional numerical simulation of an intensifying hurricane, azimuthally averaged forcings of tangential momentum and heat are diagnosed to force an axisymmetric Eliassen balance model under strict balance conditions. The balance solutions are found, inter alia, to poorly represent the peak inflow velocity in the boundary layer and present a layer of relatively deep inflow extending well above the boundary layer in the high-wind-speed region of the vortex. Such a deep inflow layer, a hallmark of the classical spinup mechanism for tropical cyclones comprising the radial convergence of absolute angular momentum above the boundary layer, is not found in the numerical simulation during the period of peak intensification. These deficiencies are traced to the inability of the balance model to represent the nonlinear boundary layer spinup mechanism. These results are contrasted with a pseudobalance Eliassen formulation that improves the solution in some respects while sacrificing strict thermal wind balance. Overall, the quantitative results refute the Heng et al. claim and implicate the general necessity of the nonlinear boundary layer spinup mechanism to explain the spinup of a hurricane in realistic model configurations and in reality.

How Much Does the Upward Advection of the Supergradient Component of Boundary Layer Wind Contribute to Tropical Cyclone Intensification and Maximum Intensity?

Although the development of supergradient winds is well understood, the importance of supergradient winds in tropical cyclone (TC) intensification is still under debate. One view is that the spinup of the eyewall occurs by the upward advection of high tangential momentum associated with supergradient winds from the boundary layer. The other view argues that the upward advection of supergradient winds by eyewall updrafts results in an outward agradient force, leading to the formation of a shallow outflow layer immediately above the inflow boundary layer. As a result, the spinup of tangential wind in the eyewall by the upward advection of supergradient wind from the boundary layer is largely offset by the spindown of tangential wind due to the outflow resulting from the agradient force. In this study, the net contribution by the upward advection of the supergradient wind component from the boundary layer to the intensification rate and final intensity of a TC are quantified through ensemble sensitivity numerical experiments using an axisymmetric TC model. Results show that consistent with the second view above, the positive upward advection of the supergradient wind component from the boundary layer by eyewall updrafts is largely offset by the negative radial advection due to the outflow resulting from the outward agradient force. As a result, the upward advection of the supergradient wind component contributes little (often less than 4%) to the intensification rate and but it contributes about 10%–15% to the final intensity of the simulated TC due to the enhanced inner-core air–sea thermodynamic disequilibrium.

Comments on “On a Continuum Model for Avalanche Flow and Its Simplified Variants” by S. S. Grigorian and A. V. Ostroumov

This note first summarizes the history of the manuscript “On a Continuum Model for Avalanche Flow and Its Simplified Variants” by Grigorian and Ostroumov—published in this Special Issue—since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor’s personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian’s stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian–Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment.

Research on Fluid Flow and Permeability in Low Porous Rock Sample Using Laboratory and Computational Techniques

The paper presents results of fluid flow simulation in tight rock being potentially gas-bearing formation. Core samples are under careful investigation because of the high cost of production from the well. Numerical simulations allow determining absolute permeability based on computed X-ray tomography images of the rock sample. Computational fluid dynamics (CFD) give the opportunity to use the partial slip Maxwell model for permeability calculations. A detailed 3D geometrical model of the pore space was the input data. These 3D models of the pore space were extracted from the rock sample using highly specialized software poROSE (poROus materials examination SoftwarE, AGH University of Science and Technology, Kraków, Poland), which is the product of close cooperation of petroleum science and industry. The changes in mass flow depended on the pressure difference, and the tangential momentum accommodation coefficient was delivered and used in further quantitative analysis. The results of fluid flow simulations were combined with laboratory measurement results using a gas permeameter. It appeared that for the established parameters and proper fluid flow model (partial slip model, Tangential Momentum Accommodation Coefficient (TMAC), volumetric flow rate values), the obtained absolute permeability was similar to the permeability from the core test analysis.