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Numerical analysis on thermal characteristics of transpiration cooling with coolant phase change

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Abstract

A numerical investigation of phase change transpiration cooling has been conducted in this work using the modified separate flow model, in which the effects of capillarity, non-isothermal characteristics in two-phase region and the local thermal non-equilibrium characteristics between the coolant and the matrix have been considered to describe the liquid coolant phase change and heat exchange process. The influences of thermal conductivity, porosity and sphere diameter of the porous matrix, main flow temperature and heat transfer coefficient at the hot surface on temperature and saturation distributions and temperature difference within the matrix have been investigated numerically. The results indicate that a higher coolant mass flow rate can delay liquid evaporation, increase the temperature gradient in superheated vapor region and decrease the solid temperature at the hot surface, but with an increase in main flow temperature or heat transfer coefficient at hot surface, the coolant temperature increases in liquid region and especially in superheated vapor region, and the solid temperature at the hot surface increases dramatically. The results also indicate that a higher solid conductivity corresponds to a higher temperature in liquid region and in nearly the whole superheated vapor region, but a slightly lower temperature at the hot surface. A special result has been obtained that with an increase in the porosity and sphere diameter the corresponding interface of liquid region moves leftwards with the two-phase region extended, and the coolant temperature decreases in two-phase region and superheated vapor region, while in liquid region firstly it decreases and then increases, as may be determined by both heat transfer and especially pressure drop which varies dramatically with porosity and sphere diameter. The thermal non-equilibrium characteristics have been analyzed, and the results show that it is obvious at the cold surface, at the hot surface and at the beginning and the ending of two-phase region, and it is most obvious near the ending of two-phase region, and the coolant temperature is higher than the solid temperature at the beginning of two-phase region.

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Abbreviations

ε :

Porosity

s :

Liquid saturation

ρ :

Density (kg m−3)

c p :

Specific heat capacity (J kg−1 K−1)

u :

Velocity (m s−1)

t :

Time (s)

h :

Specific enthalpy (J kg−1)

Q sf :

Convection or boiling heat flow (J m−3 s−1)

Q boil :

Boiling heat flow (J m−3 s−1)

Q :

Volumetric heat source (J m−3 s−1)

T :

Temperature (K)

σ :

Interfacial tension (N m−1)

J :

Capillary J-function

K r :

Relative permecapacity

μ :

Dynamic viscosity (kg m−1 s−1)

K :

Permecapacity

k :

Heat conductivity (W m−1 K−1)

Nu :

Nusselt number

Re p :

Reynolds number in porous media

Pr :

Prandtl number

d p :

Hydraulic diameter (m)

α sf :

Aspect ratio

q :

Heat flux (J m−2 s−1)

h lg :

Latent heat (J kg−1)

h sv :

Heat transfer coefficient of vapor (W m−2 K−1)

h sl :

Heat transfer coefficient of liquid (W m−2 K−1)

g :

Acceleration of gravity (m s−2)

h c :

Heat transfer coefficient at the cool surface (W m−2 K−1)

h hot :

Heat transfer coefficient at the hot surface (W m−2 K−1)

T hot :

Main fluid temperature at the hot surface (K)

s :

Solid

r :

Relative

f :

Fluid

l :

Liquid

v :

Vapor

p :

Pressure

sat:

Saturated

eff:

Effective

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Acknowledgements

The work was supported by the Fundamental Research Funds for the Central Universities (China University of Mining and Technology) (No: 2014QNA25), Natural Science Foundation of Jiangsu Province (No: BK20140193).

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  1. School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Chengyun Xin, Lang Lu & Xinyu Liu

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  1. Chengyun Xin
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Correspondence to Chengyun Xin.

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Xin, C., Lu, L. & Liu, X. Numerical analysis on thermal characteristics of transpiration cooling with coolant phase change. J Therm Anal Calorim 131, 1747–1755 (2018). https://doi.org/10.1007/s10973-017-6562-3

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