scholarly journals On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1039
Author(s):  
Maren Hantke ◽  
Ferdinand Thein
Keyword(s):  
Euler Equations ◽  
Single Phase ◽  
Two Phase Flows ◽  
Two Phase ◽  
First Order ◽  
Engineering Sciences ◽  
The One ◽  
First Order Phase ◽  
Isothermal Euler Equations ◽  
Appl Math

Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.

scholarly journals A general existence result for isothermal two-phase flows with phase transition

2019 ◽  
Vol 16 (04) ◽  
pp. 595-637
Author(s):  
Maren Hantke ◽  
Ferdinand Thein
Keyword(s):  
Phase Transition ◽  
Euler Equations ◽  
Equations Of State ◽  
Linear Equations ◽  
Two Phase Flows ◽  
Kinetic Relation ◽  
Two Phase ◽  
Uniqueness Results ◽  
Wide Range ◽  
Isothermal Euler Equations

Liquid–vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in [M. Hantke, W. Dreyer and G. Warnecke, Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition, Quart. Appl. Math. 71(3) (2013) 509–540]. This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of this work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and cavitation are discussed.

Friction Factor Equations Accuracy for Single and Two-Phase Flows

2020 ◽  
Author(s):  
Germano Scarabeli Custódio Assunção ◽  
Dykenlove Marcelin ◽  
João Carlos Von Hohendorff Filho ◽  
Denis José Schiozer ◽  
Marcelo Souza De Castro
Keyword(s):  
Pressure Drop ◽  
Friction Factor ◽  
Single Phase ◽  
Computational Cost ◽  
Two Phase Flows ◽  
Two Phase ◽  
Explicit Equation ◽  
Implicit Equation ◽  
Lower Accuracy ◽  
Statistical Metrics

Abstract Estimate pressure drop throughout petroleum production and transport system has an important role to properly sizing the various parameters involved in those complex facilities. One of the most challenging variables used to calculate the pressure drop is the friction factor, also known as Darcy–Weisbach’s friction factor. In this context, Colebrook’ s equation is recognized by many engineers and scientists as the most accurate equation to estimate it. However, due to its computational cost, since it is an implicit equation, several explicit equations have been developed over the decades to accurately estimate friction factor in a straightforward way. This paper aims to investigate accuracy of 46 of those explicit equations and Colebrook implicit equation against 2397 experimental points from single-phase and two-phase flows, with Reynolds number between 3000 and 735000 and relative roughness between 0 and 1.40 × 10−3. Applying three different statistical metrics, we concluded that the best explicit equation, proposed by Achour et al. (2002), presented better accuracy to estimate friction factor than Colebrook’s equation. On the other hand, we also showed that equations developed by Wood (1966), Rao and Kumar (2007) and Brkić (2016) must be used in specifics conditions which were developed, otherwise can produce highly inaccurate results. The remaining equations presented good accuracy and can be applied, however, presented similar or lower accuracy than Colebrook’s equation.

scholarly journals Riemann solver with internal reconstruction (RSIR) for compressible single-phase and non-equilibrium two-phase flows

2020 ◽  
Vol 408 ◽  
pp. 109176
Author(s):  
Quentin Carmouze ◽  
Richard Saurel ◽  
Alexandre Chiapolino ◽  
Emmanuel Lapebie
Keyword(s):  
Single Phase ◽  
Riemann Solver ◽  
Two Phase Flows ◽  
Two Phase ◽  
Non Equilibrium

FIRST ORDER PHASE TRANSITIONS, WHEN AND FROM WHERE DO THEY EMERGE? —THE CASE OF GELS

1995 ◽  
Vol 09 (07) ◽  
pp. 737-749 ◽  
Author(s):  
KEN SEKIMOTO
Keyword(s):  
Phase Transition ◽  
Transition Temperature ◽  
Transition Point ◽  
The Other ◽  
Basic Fact ◽  
Theoretical Understanding ◽  
First Order ◽  
First Order Phase Transition ◽  
The One ◽  
First Order Phase

We briefly review the recent theoretical understanding of the first order phase transition undergone by gels with an emphasis on physical concepts, deliberately excluding details of modeling and analytic methods. The density of a gel changes discontinuously at the transition point. A variety of features of the transition result from the basic fact that the inhomogeneity of the density of the gel inevitably causes shear deformation. This deformation, on the one hand, reflects the geometry of the sample and, on the other hand, may alter the transition temperature.

Single-phase and two-phase flows through helical rectangular channels in single screw expander prototype

2014 ◽  
Vol 26 (1) ◽  
pp. 114-121 ◽  
Author(s):  
Guo-dong Xia ◽  
Xian-fei Liu ◽  
Yu-ling Zhai ◽  
Zhen-zhen Cui
Keyword(s):  
Single Phase ◽  
Two Phase Flows ◽  
Two Phase ◽  
Single Screw ◽  
Rectangular Channels
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