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Selected Aspects of Thermal-Hydraulics Modelling in Two-Phase Flows with Phase Change in Minichannels

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Frontiers and Progress in Multiphase Flow I

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Abstract

In the chapter some issues of thermal-hydraulics modeling of two-phase flows in minichannels with change of phase are presented. These encompass the common modeling of flow boiling and flow condensation using the same expression. Approaches to model these two respective cases show, however, that experimental data show different results to those obtained by methods of calculation of heat transfer coefficient for respective cases. Partially that can be devoted to the fact that there are non-adiabatic effects present in both types of phase change phenomena which modify the pressure drop due to friction, responsible for appropriate modelling. The modification of interface shear stresses between flow boiling and flow condensation in case of annular flow structure may be considered through incorporation of the so called blowing parameter, which differentiates between these two modes of heat transfer. On the other hand, in case of bubbly flows, the generation of bubbles also modifies the friction pressure drop by the influence of heat flux. Presented are also the results of a peculiar M-shape distribution of heat transfer coefficient specific to flow boiling in minichannels. Finally, some attention is devoted to mathematical modeling of dryout phenomena. A five equation model enabling determination of the dryout location is presented, where the mass balance equations for liquid film, droplets and gas are supplemented by momentum equations for liquid film and two-phase core.

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Abbreviations

B:

Blowing parameter, B = 2ϑ0/(cfu∞)

Bo:

Boiling number, Bo = q/(GhLG)

cf :

Friction factor

cp :

Specific heat, J/kg K

C:

Concentration

Con:

Constraint number, Con = (σ/g/(ρl − ρv))0.5/d

d:

Channel inner diameter, m

E:

Energy dissipation, W/m3

f:

Friction factor

f1, f1z :

Functions

F:

Enhancement factor, function

g:

Gravity, m/s2

G:

Mass flux, kg/m2 s

h:

Enthalpy, J/kg

hlv :

Latent heat of evaporation, J/kg

k:

Mass transfer coefficient, m/s2

l:

Bubble characteristic length, m

L:

Channel length, m

p:

Pressure, Pa

P:

Correction in Eq. (1.46)

Pr:

Prandtl number

q:

Heat flux, W/m2

R:

Two-phase flow multiplier

RMS :

Two-phase flow multiplier due to Müller-Steinhagen and Heck [17]

Re:

Reynolds number

S:

Suppression factor

x:

Quality

Xtt :

Martinelli parameter

T:

Temperature, K

u, w, ϑ0 :

Velocity, m/s

z:

Distance along the channel, m

α:

Heat transfer coefficient, W/m2 K

δ:

Thickness of liquid film, m

ξ:

Drag coefficient

λ:

Thermal conductivity, W/m K

μ:

Dynamic viscosity, Pa s

ρ:

Density, kg/m3

σ:

Surface tension, N/m

τ:

Shear stress, Pa

c:

Core

cb:

Convective boiling

D:

Deposition

E:

Entrainment

f:

Forced flow, liquid film

G:

Saturated vapour

i:

Interface

k:

Droplets

kr:

Critical

L:

Liquid

LO:

Liquid only

mt:

Mass transfer

PB:

Pool boiling

TP:

Two-phase flow

TPB:

Two-phase boiling

TPK:

Two-phase condensation

0:

Beginning of annular flow

∞:

Undisturbed flow

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Acknowledgments

The work presented in the paper was partially funded from the Polish Ministry for Science and Education research project No. N512 459036 in years 2009–2012.

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  1. Faculty of Mechanical Engineering, Department of Energy and Industrial Apparatus, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233, Gdansk, Poland

    Dariusz Mikielewicz

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    Lixin Cheng

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Mikielewicz, D. (2014). Selected Aspects of Thermal-Hydraulics Modelling in Two-Phase Flows with Phase Change in Minichannels. In: Cheng, L. (eds) Frontiers and Progress in Multiphase Flow I. Frontiers and Progress in Multiphase Flow. Springer, Cham. https://doi.org/10.1007/978-3-319-04358-6_1

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