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On a dryout point for a stationary incompressible thermal fluid with phase transition in a pipe

Yoshikazu Giga, Zhongyang Gu

Abstract

A dryout point is recognized as the position where the phase transition from liquid to vapor occurs. In the one-dimensional case, by solving the stationary incompressible Navier-Stokes-Fourier equations with phase transition, we derive a necessary and sufficient condition for a dryout point to exist when the temperature at the liquid-vapor interface is given. In addition, we show by considering thermodynamics that the temperature at the dryout point and the density of the vapor phase can be determined by given density and sufficiently small injected mass flux of the liquid phase.

On a dryout point for a stationary incompressible thermal fluid with phase transition in a pipe

Abstract

A dryout point is recognized as the position where the phase transition from liquid to vapor occurs. In the one-dimensional case, by solving the stationary incompressible Navier-Stokes-Fourier equations with phase transition, we derive a necessary and sufficient condition for a dryout point to exist when the temperature at the liquid-vapor interface is given. In addition, we show by considering thermodynamics that the temperature at the dryout point and the density of the vapor phase can be determined by given density and sufficiently small injected mass flux of the liquid phase.
Paper Structure (4 sections, 9 theorems, 116 equations, 12 figures)

This paper contains 4 sections, 9 theorems, 116 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Sharp interface model
  3. Interface temperature
  4. Stationary solutions to the Stefan problem

Key Result

Proposition 2.1

Assume the first relation of EI2. Then EI5 is equivalent to Here, $T_i^\nu=T_i\nu_\Gamma\cdot\nu_\Gamma$ ($i=1,2$) and $\rho_*$ is the harmonic mean of $\rho_i$ i.e., $1/\rho_*=(1/\rho_1+1/\rho_2)/2$.

Figures (12)

  • Figure 1: an annular flow with a dryout point
  • Figure 2: two phases and interface in a pipe
  • Figure 3: the graph of $\tilde{\psi}_u(\cdot,\theta)$ for $\theta<\theta_c$ and bitangent line
  • Figure 4: the graph of the pressure $\tilde{p}_u=-\partial_v\tilde{\psi}_u$ under $\theta_1<\theta_2$
  • Figure 5: condition \ref{['EENR']} under (M1)
  • ...and 7 more figures

Theorems & Definitions (13)

  • Proposition 2.1
  • proof
  • Proposition 2.2
  • Definition 2.3
  • Proposition 3.1
  • Theorem 3.2
  • Lemma 3.3
  • Theorem 3.4
  • Theorem 3.5
  • Theorem 4.1
  • ...and 3 more