Phase appearance or disappearance in two-phase flows

This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. After an asymptotic study of the model, this paper proposes accurate and robust numerical methods adapted to the simulation of phase appearance or disappearance. Polynomial solvers are developed to avoid the use of eigenvectors which are needed in usual shock capturing schemes, and a method based on an adaptive numerical diffusion is designed to treat the positivity problems. An alternate method, based on the use of the hyperbolic tangent function instead of a polynomial, is also considered. Numerical results are presented which demonstrate the efficiency of the proposed solutions

A diffuse interface model for two-phase ferrofluid flows

We develop a model describing the behavior of two-phase ferrofluid flows using phase field-techniques and present an energy-stable numerical scheme for it. For a simplified, yet physically realistic, version of this model and the corresponding numerical scheme we prove, in addition to stability, convergence and as by-product existence of solutions. With a series of numerical experiments we illustrate the potential of these simple models and their ability to capture basic phenomenological features of ferrofluids such as the Rosensweig instability

Two-Phase Cooling Flows with Magnetic Reconnection

Motivated by the observations of high Faraday rotation measures measured in cooling flow clusters we propose a model relevant to plasmas with comparable thermal and magnetic pressures. Magnetic field reconnection may play a major role in changing the topology of the magnetic field in the central cooling flow regions. The effect of the topology change is that cool flux loops can reconnect to hot flux loops that are connected to the overall thermal reservoir of the cluster. There can be a rapid recycling of mass between hot and cold phases on a time scale of 3 x 10^8-10^9 yr which may reduce the inferred inflow and mass condensation rates by at least an order of magnitude. A central multiphase medium is a direct consequence of such a model. Throughout the cooling flow the filling factor of the hot loops (T > 2 x 10^7 K) is of order unity. The filling factor of the cool loops (T < 2 x 10^7 K) is 0.1-1% with a corresponding mass fraction of cold phase of 1-10%. A crucial parameter is the coherence length of the field relative to the cooling radius and the distribution of field energy with scale. When the cooling radius is greater than the field coherence length then cooling flows proceed as usual. When the coherence length is greater than the central cooling radius, however, the thermal energy of the reservoir can be tapped and the mass condensation rates may be very significantly reduced. Three additional conditions must be satisfied: I. Cold loops must be able to fall at least as far as the mean distance between hot loops in a cooling time; II. Loops must enter an evaporative phase on reconnecting; and III. A sufficient number of hot loops penetrate the cold phase region to power the radiative losses.Comment: 16 pages, uses AAS macro aasm

Two-phase discharge flow prediction in safety valves

Safety Relief Valves (SRV) are necessary elements in the protection of any pressurised system and the prediction of the expected discharge flows is an important consideration for the valve sizing to ensure that rupture pressures do not occur. The high speed flows that occur inside the SRV are complex particularly when a two-phase flow is involved and lead to a less capable protection device which result in larger valves compared to single phase flows. In this paper the ability of a CFD based two phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼” inlet bore size has been tested experimentally over a pressure range of 6-15 barg and air mass qualities from 0.1-1 when discharging to near atmospheric conditions for a fully open condition. A two-dimensional mixture model consisting of mixture mass, momentum, and energy equations, combined with a liquid mass equation and the standard k- ε turbulence model for mixture turbulent transport has been used to predict the two phase flows through the valve. The mixture model results have been compared with the Homogenous Equilibrium Model (HEM) commonly used for in valve sizing in non flashing two phase flow conditions. The accuracy of the models over the two phase flow range are quantified and discussed

A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier-Stokes equations with additional stress term, Cahn-Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary convections in a two-layer fluid system and thermocapillary migration of a drop are computed using a continuous finite element method. The results are compared to the corresponding analytical solutions and the existing numerical results as validations for our model