Effect of poloidal equilibrium flow and pressure gradient on the m/n = 2/1 tearing mode

The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of ≠0 ( is plasma pressure), the radial part of motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equation (Whittaker equation) containing second order singularity, the tearing mode stability index Δ′ is obtained. It is shown that, the effect of equilibrium poloidal flow and pressure gradient has the adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of instability region of the poloidal flow with pressure perturbation.

Instability of the Non-Isothermal Inclined Film Flow of a Power-Law Fluid With Temperature Dependent Consistency

In this thesis we undertake a theoretical study of the flow stability of a liquid film with power-law rheology down a heated incline. We develop and implement a mathematical model for the flow that captures the variation with temperature of the rheological aspect of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infintesimal perturbations imposed on the equilibrium flow. We obtain asymptotic solutions based on the assumption of perturbations of long wavelength and small variation in viscosity with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian reheology and the dependence of the fluid properties on temperature

Instability of the Non-Isothermal Inclined Film Flow of a Power-Law Fluid With Temperature Dependent Consistency

In this thesis we undertake a theoretical study of the flow stability of a liquid film with power-law rheology down a heated incline. We develop and implement a mathematical model for the flow that captures the variation with temperature of the rheological aspect of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infintesimal perturbations imposed on the equilibrium flow. We obtain asymptotic solutions based on the assumption of perturbations of long wavelength and small variation in viscosity with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian reheology and the dependence of the fluid properties on temperature

HESS Opinions: Unsaturated infiltration – the need for a reconsideration of historical misconceptions

Briggs (1897) deduced capillary flow from deviation of the equilibrium between capillarity and gravity. Richards (1931) raised capillary flow to an unproven soil hydrological dogma. Attempts to correct the dogma led to concepts of non-equilibrium flow, macropore flow, and preferential flow during infiltration. Viscous film flow is proposed as an alternative approach to capillarity-driven flow during unsaturated infiltration.

HESS Opinions: Unsaturated infiltration: from unproven capillary flow to viscous flow

Briggs (1897) deduced capillary flow from deviation of the equilibrium between capillarity and gravity. Richards (1931) raised capillary flow to an unproven soil hydrological dogma. Apparent corrections of the dogma led to non-equilibrium flow, macropore flow, and preferential flow during infiltration. Viscous flow is proposed as alternative to capillary flow during unsaturated infiltration.

The thermochemical non-equilibrium expansion effects of the high enthalpy nozzle

The high enthalpy shock tunnel can simulate the free-flow speed above 3km/s. The characteristic of the flow is that the kinetic energy of the high enthalpy stagnation gas is high enough to effectuate high-temperature effects such as dissociation even ionization of fluid molecules. The stagnation gas is converted into the hypervelocity free flow through the high enthalpy nozzle. The flow of high enthalpy flow in the high enthalpy nozzle can be divided into three regions: an equilibrium region, a non-equilibrium region and a frozen region. The equilibrium flow region is upstream of the throat, the non-equilibrium flow region is near the throat, and the frozen flow region is not far downstream of the throat. The study focuses on the conical nozzle, testing thermochemical non-equilibrium expansion effects under the different expansion angle of the expansion section, the curvature radius of the throat, the throat radius, and the convergence angle of the convergent section. A multi-block solver for axisymmetric compressible Navier-Stokes equations is applied to simulate the thermochemical non-equilibrium flow in several high enthalpy conical nozzles. The significant conclusions of this study contain tripartite. Firstly, the thermochemical non-equilibrium effects are sensitive to the maximum expansion angle and throat radius, but not to the radius of throat curvature and the contraction angle. Secondly, as the maximum expansion angle decreases and the throat radius increases, the flow approaches equilibrium. Finally, the maximum expansion angle and the throat radius not only affect the position of the freezing point but also impacts the flow field parameters, such as temperature, Mach number, and species mass concentration.