scholarly journals A Note on the Relaxation-Time Limit of the Isothermal Euler Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Jiang Xu ◽  
Daoyuan Fang
Keyword(s):  
Relaxation Time ◽  
Euler Equations ◽  
Time Limit ◽  
Isothermal Euler Equations

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.

Instability of a viscous coflowing jet in a radial electric field

2008 ◽  
Vol 596 ◽  
pp. 285-311 ◽  
Author(s):  
FANG LI ◽  
XIE-YUAN YIN ◽  
XIE-ZHEN YIN
Keyword(s):  
Relaxation Time ◽  
Electric Field ◽  
Thin Layer ◽  
Euler Number ◽  
Radial Electric Field ◽  
Dispersion Relations ◽  
Time Limit ◽  
Liquid Viscosity ◽  
Electrical Relaxation ◽  
Thin Layer Approximation

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

The relaxation-time limit in the compressible Euler–Maxwell equations

2011 ◽  
Vol 74 (18) ◽  
pp. 7005-7011 ◽  
Author(s):  
Jianwei Yang ◽  
Shu Wang ◽  
Juan Zhao
Keyword(s):  
Relaxation Time ◽  
Maxwell Equations ◽  
Time Limit ◽  
Compressible Euler
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