Mathematical Model of Fluids Motion in Poroelastic Snow-ice Cover

The dynamics of a snow-ice cover is considered within the theory of poroelasticity. The snow-ice cover is modeled by a three-phase medium consisting of water, air and ice. The governing equations are the equations of mass conservation for each phase with phase transitions, the equations of conservation of phase momentum in the form of Darcy’s law, the equation of conservation of momentum of the whole system, the rheological equation for porosity and the equation of heat balance of snow. In the full formulation the liquid and air pressures are functions of the temperature and the corresponding densities, and the viscosity and compressibility coefficients of ice are functions of the temperature. The problem of two-dimensional nonstationary filtration of water in a thin poroelastic ice plate is considered in the model case. The solution is obtained in quadratures

Exact regularized point particle method for multiphase flows in the two-way coupling regime

Particulate flows have mainly been studied under the simplifying assumption of a one-way coupling regime where the disperse phase does not modify the carrier fluid. A more complete view of multiphase flows can be gained calling into play two-way coupling effects, i.e. by accounting for the inter-phase momentum exchange, which is certainly relevant at increasing mass loading. In this paper we present a new methodology rigorously designed to capture the inter-phase momentum exchange for particles smaller than the smallest hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. The momentum coupling mechanism exploits the unsteady Stokes flow around a small rigid sphere, where the transient disturbance produced by each particle is evaluated in a closed form. The particles are described as lumped point masses, which would lead to the appearance of singularities. A rigorous regularization procedure is conceived to extract the physically relevant interactions between the particles and the fluid which avoids any ‘ad hoc’ assumption. The approach is suited for high-efficiency implementation on massively parallel machines since the transient disturbance produced by the particles is strongly localized in space. We will show that hundreds of thousands of particles can be handled at an affordable computational cost, as demonstrated by a preliminary application to a particle-laden turbulent shear flow.

Effect of Slip Velocity and Heat Transfer on the Condensed Phase Momentum Flux of Supersonic Nozzle Flows

One of the methods used for industrial cleansing applications employs a mixture of gaseous nitrogen and liquid water injected upstream of a converging-diverging nozzle located at the end of a straight wand assembly. The idea is to get the mixture to impact the surface at the maximum momentum flux possible in order to maximize the cleansing effectiveness. This paper presents an analysis geared towards this application in which the effects of slip and heat transfer between the gas and liquid phases are present. The model describes the liquid momentum flux (considered a figure of merit for cleansing) under a host of design conditions. While it is recognized that the emulsification mechanism responsible for cleansing is far more complicated than simply being solely dependent on the liquid momentum flux, the analysis presented here should prove useful in providing sufficiently accurate results for nozzle design purposes. [S0098-2202(00)01801-0]

Two-phase momentum flux in pipes and its application to incompressible flow in nozzles

The pressure drop produced when a single-phase gas or liquid flows through a nozzle can be reasonably well estimated from inviscid flow theory. A similarly based model, taking the slip with entrained liquid fraction approach, has been developed for two-phase gas—liquid flows. Fundamental to the model is the constraint that the nozzle flow depends on the entry conditions, particularly the momentum flux. At low qualities the tendency was for fractions of the liquid flow to be accelerated with the gas phase to maintain uniform momentum flux across the nozzle flow area. At higher qualities the gas core of the annular flow, along with its associated droplets, was found to contract with negligible interaction with the surrounding liquid film. The model has been compared with data sources and other models available in the literature and shown to perform well.