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A study of nucleate boiling and critical heat flux with EHD enhancement

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Abstract

The paper describes results from an experimental and theoretical study of the effect of an electric field on nucleate boiling and the critical heat flux (CHF) in pool boiling of R123 at atmospheric pressure on a horizontal wall with a smooth surface. Two designs of electrode (parallel rods and wire mesh) were used. The experimental data exhibit some differences from the data obtained by other researchers in similar experiments on a wall with a different surface finish and with a slightly different design of wire mesh electrode. The hydrodynamic model for EHD enhancement of CHF cannot reconcile the differences. A theoretical model has been developed for the growth of a single vapour bubble on a superheated wall in an electric field, leading to a numerical simulation based on the level-set method. The model includes matching of sub-models for the micro- and macro-regions, conduction in the wall, distortion of the electric field by the bubble, the temperature dependence of electrical properties and free-charge generation. In the present form of the model, some of these effects are realised in an approximate form. The capability to investigate dry-spot formation and wall temperature changes that might lead to CHF has been demonstrated.

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Abbreviations

\(\bar{A}\) :

Hamaker constant, J

A :

empirical constant

B :

empirical constant

c P :

specific heat at constant pressure (J/(kg K))

d :

characteristic length (m)

E :

electric field strength (V/m)

El :

electric influence number

E l′:

electric influence number

El * :

electric influence number

f l :

fugacity

g :

gravitational vector (m/s2)

H :

Heaviside step function

h :

grid spacing (m)

h 0 :

heat transfer coefficient without electric field

h E :

heat transfer coefficient with electric field

\(h_{{ev}} = 2{\sqrt {\frac{M}{{2\pi \bar{R}T_{v}}}}}\frac{{\rho_{v} h^{2}_{{fg}}}}{{T_{v}}}\) :

evaporation heat transfer coefficient (W/(m2 K))

h fg :

latent heat of evaporation (J/kg)

HV :

applied high voltage (kV)

k :

thermal conductivity (W/(m K))

M :

molecular weight (kg/mol)

m :

mass flux vector (kg/(m2 s))

\(\dot{m}_{{\rm mic}} \) :

evaporation rate from the microlayer (kg/s)

Nu :

Nusselt number

Pr :

Prandtl number

p :

pressure (N/m2)

\(\bar{p}\) :

empirical constant

Q :

integrated heat flux (W/m)

q :

heat flux (W/m2)

q cr (E) = q E :

critical heat flux with electric field (kW/m2)

q cr (0) = q 0 :

critical heat flux without electric field, (kW/m2)

r :

radial coordinate (m)

r c :

half-width of zone in (48) (m)

R :

radius of computational domain (m)

\(\bar{R}\) :

universal gas constant

R o :

radius of dry region beneath a bubble (m)

R 1 :

radial location of the interface at y = h/2 (m)

t :

time (s)

T :

temperature (K)

ΔT = T w − T sat :

wall superheat (K)

u :

velocity vector (u,v)

u :

r-directional velocity (m/s)

v :

y-directional velocity (m/s)

V :

bubble volume (m3)

V c :

control volume (m3)

V l :

molar volume (m3/mol)

y :

vertical coordinate (m)

Y :

height of computational domain (m)

α K :

coefficient of thermal increase of electric conductivity R123 (1/K)

β T :

coefficient of thermal expansion (1/K)

Γ:

mass flow rate in the microlayer (kg/s)

δ:

thickness (m)

δ0 :

initial thickness (m)

δɛ (ϕ):

delta function

δ T :

thermal boundary layer thickness (m)

ɛ:

electric permittivity (F/m)

ɛ0 :

electric permittivity vacuum (F/m)

ɛ r :

relative electric permittivity

κ:

interface curvature (1/m)

λ d :

wavelength (m)

μ:

dynamic viscosity (N s/m2)

ρ:

mass density (kg/m3)

ρ e :

electric charge density (C/m3)

σ:

surface tension (N/m)

τ:

charge relaxation time (s)

σ e :

electric conductivity (S)

ϕ:

level set function

Φ:

electric potential (V)

φ:

apparent contact angle (deg)

ψ:

initial bubble shape profile

int:

interface

l:

liquid

sat:

saturation

v:

vapour

w:

wall interface

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Acknowledgments

This work was supported by the Engineering and Physical Sciences Research Council Grants GRS41814 and GR. R37129.

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Authors and Affiliations

  1. School of Engineering and Electronics, The University of Edinburgh, Edinburgh, EH9 3JL, UK

    Y. Hristov & K. Sefiane

  2. School of Engineering and Design, Brunel University, West London, Uxbridge, Middlesex, UB8 3PH, UK

    D. Zhao, D. B. R. Kenning & T. G. Karayiannis

Authors
  1. Y. Hristov
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  2. D. Zhao
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  3. D. B. R. Kenning
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  4. K. Sefiane
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  5. T. G. Karayiannis
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Corresponding author

Correspondence to K. Sefiane.

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Hristov, Y., Zhao, D., Kenning, D.B.R. et al. A study of nucleate boiling and critical heat flux with EHD enhancement. Heat Mass Transfer 45, 999–1017 (2009). https://doi.org/10.1007/s00231-007-0286-z

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