VHS Model Research Articles

Numerical investigation into the low-pressure detection sensor performance of hydrogen gas with variable soft sphere molecular model

Direct Simulation Monte Carlo (DSMC) method is used to simulate the hydrogen detection process with Microscale In-Plane Knudsen Radiometric Actuator (MIKRA). The variable soft sphere (VSS) model is applied to depict molecular diffusion in the gas mixtures that its results are compared with variable soft sphere (VSS) in literature. On the right side of the shuttle arm, the influence of molecular model (VSS and VHS) on the simulation results is small. And the temperature ratio, heat transfer ratio and pressure ratio are highly close to 1. But on the left side of the shuttle arm, the differences are significant resulting from molecular models. Especially, for the heat transfer on the left side of the shuttle arm, heat transfer ratio of VHS model to VSS model is maximally about 4.3. The influence of gas pressures and hydrogen concentrations on the detection performance of MIKRA is also discussed. The decrease of hydrogen concentration and the increase of gas pressure cause the center of the main vortex to move towards the heater arm, and the influence of the gas pressure is more significant. On the other hand, Knudsen force increases with the increase of the hydrogen concentration and its peak value is obtained in a higher gas pressure. For example, the peak value of Knudsen force can be attained for the gas pressure of about 387 Pa in the pure hydrogen domain while in the pure nitrogen domain, the gas pressure of about 260 Pa. Simultaneously, the relation of the linear dependence of Knudsen force on the hydrogen concentration is proposed to detect hydrogen concentration in N2–H2 mixtures.

Ground thermal response to heat conduction in a power transmission tower foundation

An analytical formulation is developed to predict transient heat conduction in a semi-infinite medium with a vertical finite line heat source, which represents a buried tower of a power transmission line foundation. Unlike past studies with a constant line heat source, the current model develops a time-dependent variable heating strength, as well as a time varying surface temperature of the ground. An approximate VHS model (variable heating strength) is developed for sinusoidal variations of the line source strength and surface temperature, in order to simulate seasonal variations of ground temperatures. The VHS model reduces computational time and exhibits good accuracy, when compared against a full exact solution. The model is applied to heat conduction in a tower foundation, with time-varying ground surface temperatures. Effects of ground thermal conductivity and diffusivity, as well as variations of the line source strength, are investigated in this article.

Transient heat conduction from a vertical rod buried in a semi-infinite medium with variable heating strength

In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground, due to a power transmission tower installed in a region of initially frozen ground.

Modified Generalized Hard Sphere Collision Model for Direct Simulation Monte Carlo Calculations

The generalised hard sphere collision model (GHS) was introduced by Hassan and Hash [Physics of Fluids A, v5(3), 738-744 (1993)] and is a generalization of the Sutherland collision model suggested by Kuscer [Physica, v158, 784-800 (1989)]. Despite its superior modelling of realistic gas viscosities, compared to the Variable Hard Sphere collision model, the GHS model is rarely used because of its great computational expense compared to the VHS model. We show here how a slight modification of the GHS model makes it no more than 15% more computationally expensive than the VHS model, while retaining its superior viscosity modelling. All that is required is that the collision probability be limited for collision speeds approaching zero, rather than increase to infinity as it does for the original GHS model. A particularly simple modification is to use a Maxwell collision cross-section (equal probabilities) for collision energies less than the attractive energy of a realistic molecular model (characteristic temperature T* approximate 90 - 150 K). For temperatures above T*, the GHS viscosity is retained, while for temperatures less than T* the viscosity is slightly different from the GHS viscosity, but arguably more realistic.

The van Hove singularity in the cuprate superconductors: A reassessment

Recent theoretical advances in the superconductivity of the cuprates have found that (1) Fermi surface nesting is enhanced in Luttinger liquids over conventional Fermi liquids, and (2) nesting associated with the van Hove singularity (vHS) is considerably stronger than conventional nesting. Meanwhile, angle-resolved photoemission experiments have unambiguously demonstrated that the vHS is present at the Fermi level of optimum T c in all of the highest- T c materials studied: YBa 2Cu 3O 7, YBa 2Cu 4O 8, and Bi 2Sr 2CaCu 2O 8. Some implications of these results are discussed. In particular, this paper stresses the close connection between the ID Hubbard model and the 2D vHS model. The origin of the “ghost” Fermi surfaces is shown to be the same in both models: a large density of low energy 2 k F electron-hole pairs. (In a doped antiferromagnet, these electron-hole pairs can be identified with spinons.) The insulating state of the one-dimensional Hubbard model can be described as a “correlation-induced vHS”. It is shown that correlation effects are essential for restoring the Mott picture of the insulator instability in the 2D vHS model.

Definition of mean free path for real gases

Attention is drawn to the inconsistency in the conventional procedure for the definition of a mean free path in a real gas through the classical hard sphere result. It is shown that the variable cross-section hard sphere, or VHS, model can be used to define a mean free path that properly accounts for the temperature exponent of the coefficient of viscosity of the gas. In addition, the VHS model is shown to have advantages over the classical inverse power law models for numerical and analytical studies.