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Investigation of bubble parameters and interfacial heat transfer correlations based on radial void fraction profiles of R-134a subcooled boiling flows

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Abstract

The present study proposes the assessment of closure relations related to bubble parameters found in the wall heat flux partitioning model, as well as the assessment of interfacial heat transfer correlations, via CFD (computational fluid dynamics) simulation. The selection of these closure relations, most of the time, does not consider its applicability and scope, neglecting the effects that might affect the results obtained in two-phase flow simulations. In order to assess which relations can properly predict the boiling two-phase flow characteristics found in PWRs, an upward subcooled flow boiling in an annulus, with R-134a as the working fluid, was simulated based on the Eulerian two-fluid model. The void fraction radial profile of two-phase flow was attained, analyzed and compared to a benchmark study at different elevations. It can be concluded that the increase in pressure has a distinguishable impact on the predicting performance of the correlations. A trend of void fraction overprediction was observed at the inlet channel, whereas an underpredicting performance was found at the outlet channel. A crossed effect between bubble departure diameter, nucleate site density, and interfacial heat transfer coefficient on the void fraction profile was evidenced. Insightful considerations regarding the best models to be chosen for the simulation of subcooled boiling flows can be extracted from this investigation.

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Abbreviations

A :

Area, m2

A b :

Area of influence, –

C :

Coefficient, –

c p :

Specific heat, J/kg K

D :

Diameter, m

D w :

Bubble departure diameter, m

f :

Bubble departure frequency, 1/s

\(\vec{F}\) :

Force, N

g :

Gravity, m/s2

H :

Heat transfer coefficient

h :

Specific enthalpy, kJ/kg

\(h_{{{\text{lv}}}}\) :

Latent heat of evaporation, J/kg

Ja:

Jacob number, –

k :

Thermal conductivity, W/mK

L :

Specific latent heat, J/kg

\(\dot{m}\) :

Mass transfer, kg/m2 s

Nu:

Nusselt number, –

N w :

Nucleation site density, m2

P :

Pressure, Pa

Pr:

Prandtl number, –

\(\dot{q}\) :

Heat flux, kW/m2

Q :

Intensity of heat exchange, kW

r :

Radius, m

\(\vec{R}\) :

Interaction force, N

Re:

Reynolds number, –

T :

Temperature, K

\(\overline{\overline{t}}\) :

Stress–strain tensor, Pa

\(U_{b}\) :

Near wall bulk velocity, m/s

V :

Volume, m3

\(\vec{v}\) :

Velocity, m/s

α :

Phasic volume fraction, –

ρ :

Phase density, kg/m3

μ :

Shear viscosity, kg/s m

λ :

Bulk viscosity or diffusivity, kg/s m or m2/s

\(\theta\) :

Contact angle, degrees

\(\sigma\) :

Surface tension, N/m

ρ* :

Density ratio, –

\(\alpha^{*}\) :

Non-dimensional void fraction, –

\(\Delta\) :

Difference, –

b :

Covered by nucleating bubbles

c :

Critical

C :

Convective

cell:

Cell face

drag:

Drag

cm:

Coarse mesh

E :

Evaporative

exp:

Experimental

fm:

Fine mesh

ht:

Interfacial heat transfer

i :

Interfacial or inner

l :

Liquid

mesh:

Mesh

num:

Numerical

o :

Outer

q :

Phase q

Q :

Quenching

s :

Solid

sat:

Saturation

sub:

Subcooled

sup:

Superheat

td:

Turbulent dispersion

v :

Vapor

vm:

Virtual mass

W :

Wall

wl:

Wall lubrication

CFD:

Computational fluid dynamics

IHT:

Interfacial heat transfer

PWR:

Pressurized water reactor

WHFP:

Wall heat flux partitioning

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Acknowledgements

The authors are indebted to the Institute for Advanced Studies—IEAv and the Aerospace Science and Technology Department—DCTA for the technical support. The financial support of the National Council for Scientific and Technological Development—CNPq (Grant No. 427209/2018-8)—is also highly acknowledged.

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Authors and Affiliations

  1. Aeronautics Institute of Technology, São José dos Campos, Brazil

    Thaís P. A. Ferreira & Guilherme B. Ribeiro

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  1. Thaís P. A. Ferreira
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  2. Guilherme B. Ribeiro
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Correspondence to Guilherme B. Ribeiro.

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Ferreira, T.P.A., Ribeiro, G.B. Investigation of bubble parameters and interfacial heat transfer correlations based on radial void fraction profiles of R-134a subcooled boiling flows. J Braz. Soc. Mech. Sci. Eng. 43, 428 (2021). https://doi.org/10.1007/s40430-021-03154-7

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  • DOI: https://doi.org/10.1007/s40430-021-03154-7

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