scholarly journals Modelling phase transition in metastable liquids: application to cavitating and flashing flows

2008 ◽  
Vol 607 ◽  
pp. 313-350 ◽  
Author(s):  
RICHARD SAUREL ◽  
FABIEN PETITPAS ◽  
REMI ABGRALL
Keyword(s):  
Present Model ◽  
Chemical Potential ◽  
Equations Of State ◽  
Normal Velocity ◽  
Two Phase ◽  
Chemical Relaxation ◽  
Order Of Magnitude ◽  
Two Temperatures ◽  
Simple Contact ◽  
Transition Fronts

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

scholarly journals An experimental and theoretical investigation of diffusion in a two-phase alloy

1948 ◽  
Vol 192 (1031) ◽  
pp. 575-592 ◽  
Keyword(s):  
Free Energy ◽  
Single Phase ◽  
Phase State ◽  
Theoretical Treatment ◽  
Research Association ◽  
Essential Difference ◽  
Two Phase ◽  
Two Factors ◽  
Order Of Magnitude ◽  
The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

Effect of Precursory Cooling on Falling-Film Rewetting

1975 ◽  
Vol 97 (3) ◽  
pp. 360-365 ◽  
Author(s):  
K. H. Sun ◽  
G. E. Dix ◽  
C. L. Tien
Keyword(s):  
Atmospheric Pressure ◽  
Present Model ◽  
Front Velocity ◽  
Falling Film ◽  
Vapor Mixture ◽  
Thin Slab ◽  
Flow Rates ◽  
Variable Flow ◽  
Order Of Magnitude ◽  
Hot Surface

An analytical model for falling-film wetting of a hot surface has been developed to account for the effect of cooling by droplet-vapor mixture in the region immediately ahead of the wet front. The effect of precursory cooling is characterized by a heat transfer coefficient decaying exponentially from the wet front. Based on the present model, the wet front velocity, as well as the temperature profile along a thin slab, can be calculated. It is demonstrated that the precursory cooling can increase the wet front velocity by an order of magnitude. Existing experimental data with variable flow rates at atmospheric pressure are shown to be successfully correlated by the present model.

Study on C–S and P–R EOS in pseudo-potential lattice Boltzmann model for two-phase flows

2017 ◽  
Vol 28 (09) ◽  
pp. 1750120 ◽  
Author(s):  
Yong Peng ◽  
Yun Fei Mao ◽  
Bo Wang ◽  
Bo Xie
Keyword(s):  
Surface Tension ◽  
Lattice Boltzmann ◽  
Equations Of State ◽  
Density Ratio ◽  
Maximum Density ◽  
Lattice Boltzmann Model ◽  
Two Phase Flows ◽  
Two Phase ◽  
Spurious Currents ◽  
Pseudo Potential

Equations of State (EOS) is crucial in simulating multiphase flows by the pseudo-potential lattice Boltzmann method (LBM). In the present study, the Peng and Robinson (P–R) and Carnahan and Starling (C–S) EOS in the pseudo-potential LBM with Exact Difference Method (EDM) scheme for two-phase flows have been compared. Both of P–R and C–S EOS have been used to study the two-phase separation, surface tension, the maximum two-phase density ratio and spurious currents. The study shows that both of P–R and C–S EOS agree with the analytical solutions although P–R EOS may perform better. The prediction of liquid phase by P–R EOS is more accurate than that of air phase and the contrary is true for C–S EOS. Predictions by both of EOS conform with the Laplace’s law. Besides, adjustment of surface tension is achieved by adjusting [Formula: see text]. The P–R EOS can achieve larger maximum density ratio than C–S EOS under the same [Formula: see text]. Besides, no matter the C–S EOS or the P–R EOS, if [Formula: see text] tends to 0.5, the computation is prone to numerical instability. The maximum spurious current for P–R is larger than that of C–S. The multiple-relaxation-time LBM still can improve obviously the numerical stability and can achieve larger maximum density ratio.

scholarly journals Are cosmological gas accretion streams multiphase and turbulent?

2018 ◽  
Vol 610 ◽  
pp. A75 ◽  
Author(s):  
Nicolas Cornuault ◽  
Matthew D. Lehnert ◽  
François Boulanger ◽  
Pierre Guillard
Keyword(s):  
Galaxy Formation ◽  
Direct Interaction ◽  
Mass Range ◽  
Initial Kinetic Energy ◽  
Two Phase ◽  
Dynamical Time ◽  
Order Of Magnitude ◽  
Post Shock ◽  
Gas Accretion ◽  
Halo Gas

Simulations of cosmological filamentary accretion reveal flows (“streams”) of warm gas, T ~ 104 K, which bring gas into galaxies efficiently. We present a phenomenological scenario in which gas in such flows, if it is shocked as it enters the halo as we assume and depending on the post-shock temperature, stream radius, its relative overdensity, and other factors, becomes biphasic and turbulent. We consider a collimated stream of warm gas that flows into a halo from an overdense filament of the cosmic web. The post-shock streaming gas expands because it has a higher pressure than the ambient halo gas and fragments as it cools. The fragmented stream forms a two phase medium: a warm cloudy phase embedded in hot post-shock gas. We argue that the hot phase sustains the accretion shock. During fragmentation, a fraction of the initial kinetic energy of the infalling gas is converted into turbulence among and within the warm clouds. The thermodynamic evolution of the post-shock gas is largely determined by the relative timescales of several processes. These competing timescales characterize the cooling, expansion of the post-shock gas, amount of turbulence in the clouds, and dynamical time of the halo. We expect the gas to become multiphase when the gas cooling and dynamical times are of the same order of magnitude. In this framework, we show that this mainly occurs in the mass range, Mhalo ~ 1011 to 1013 M⊙, where the bulk of stars have formed in galaxies. Because of the expansion of the stream and turbulence, gas accreting along cosmic web filaments may eventually lose coherence and mix with the ambient halo gas. Through both the phase separation and “disruption” of the stream, the accretion efficiency onto a galaxy in a halo dynamical time is lowered. Decollimating flows make the direct interaction between galaxy feedback and accretion streams more likely, thereby further reducing the overall accretion efficiency. As we discuss in this work, moderating the gas accretion efficiency through these mechanisms may help to alleviate a number of significant challenges in theoretical galaxy formation.

scholarly journals The single phase and two-phase equations of state for aluminum

2012 ◽  
Author(s):  
Haifeng Liu ◽  
Haifeng Song ◽  
Gongmu Zhang
Keyword(s):  
Single Phase ◽  
Equations Of State ◽  
Two Phase

scholarly journals Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars

Universe ◽  
2019 ◽  
Vol 5 (8) ◽  
pp. 186 ◽  
Author(s):  
Mateusz Cierniak ◽  
Tobias Fischer ◽  
Niels-Uwe Bastian ◽  
Thomas Klähn ◽  
Marc Salinas
Keyword(s):  
Equations Of State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Type Model ◽  
Two Phase ◽  
Relativistic Mean Field ◽  
Nuclear Equation Of State ◽  
Hot Matter ◽  
The Stability ◽  
Quark Phase

We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag–type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non–trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass–radius relations.

Liquid and Gas Phase Velocity Measurements for Two Phase Flow in a Branching Microchannel Network

2007 ◽  
Author(s):  
Younghoon Kwak ◽  
Deborah Pence ◽  
James Liburdy ◽  
Vinod Narayanan
Keyword(s):  
Liquid Velocity ◽  
Leading Edge ◽  
Velocity Measurements ◽  
Trailing Edge ◽  
Two Phase ◽  
Order Of Magnitude ◽  
Image Pairs ◽  
Superficial Gas Velocity ◽  
Liquid Flows ◽  
Velocity Deficits

This is a work in progress. The objective of the present work is to develop techniques for assessing velocity deficits in branching microchannel networks. Liquid velocity distributions were acquired using μPIV in gas-liquid flows through the initial branch in a fractal-like branching microchannel flow network. Gas interface velocities were determined along the centerline of the channel. The flow rate of air and water were 0.0016 g/min and 20 g/min, respectively. The primary observed flow regime was elongated bubbles. Experimental liquid velocities well matched the 0.20 m/s superficial liquid velocity. Experimental interface velocities were approximately an order of magnitude higher than the superficial gas velocity of 0.01 m/s. Velocity deficits based on measurements are on the order of 0.065 m/s. Using interfacial velocities at the channel centerline, the trailing edge velocity was observed to be 15% percent faster, on average, than the leading edge velocity. This could be attributed to bubbles expanding into the bifurcation. Twenty percent standard deviations in average interface velocities were attributed to insufficient samples as well as projected to be a consequence of changing shape of the interface between consecutive image pairs. Changes in bubble shape may also be responsible for the observed differences between leading and trailing edge velocities.

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