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A Numerical Investigation of Transpiration Cooling with Liquid Coolant Phase Change

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Abstract

This article presents a numerical approach to investigate the transpiration cooling problems with coolant phase change within porous matrix. A new model is based on the coupling of the two-phase mixture model (TPMM) with the local thermal non- equilibrium (LTNE), and used to describe the liquid coolant phase change and heat exchange processes in this article. The effects of thermal conductivity, porosity, and sphere diameter of the porous matrix on the temperature and saturation distributions within the matrix are studied. The results indicate that an increase in the porosity or sphere diameter can lead to an area dilation of two-phase region and a rise of liquid temperature; whereas an increase in the thermal conductivity of the porous matrix results only in a rise of liquid temperature, but drops of solid temperature and temperature gradient on the hot surface. The influence of hot surface pressure on cooling effect is discussed by numerical simulations, and numerical results show that the effect of the transpiration cooling will be worse under higher pressure. The investigation also discovers an inverse phenomenon to the past investigations on the transpiration cooling without coolant phase change, namely in two-phase region, coolant temperature may be higher than solid temperature. This inversion can be captured only by the new LTNE–TPMM.

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Abbreviations

y :

Coordinate

L :

Thickness of solid matrix

T :

Temperature

k :

Thermal conductivity

m :

Coolant mass flow rate

d p :

Characteristic size of porous matrix

c f :

Coolant specific heat capacity

f (s):

Hindrance function

g :

Gravitational constant

h c :

Interfacial convective coefficient

h :

Enthalpy

h fg :

Latent heat

J (s):

Capillary J-function

K :

Permeability

k r :

Relative permeability

P :

Pressure

Q :

Heat flux

s :

Liquid saturation

u :

Velocity

\({\varepsilon }\) :

Porosity

γ :

Two-phase advection correlation

Γ :

Effective diffusion coefficient

α sf :

Specific surface of porous media

μ :

Viscosity

λ:

Relative mobilities

β :

Fluid expansion coefficient

ν :

Kinetic viscosity

σ :

Surface tension

ρ :

Density

f:

Fluid

c:

Coolant

l:

Liquid

v:

Vapor

sat:

Saturated state

s:

Solid

sf:

Solid-fluid

eff:

Effective

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Authors and Affiliations

  1. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96, Hefei, 230027, Anhui, People’s Republic of China

    J. X. Shi & J. H. Wang

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  1. J. X. Shi
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  2. J. H. Wang
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Correspondence to J. H. Wang.

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Shi, J.X., Wang, J.H. A Numerical Investigation of Transpiration Cooling with Liquid Coolant Phase Change. Transp Porous Med 87, 703–716 (2011). https://doi.org/10.1007/s11242-010-9710-9

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  • DOI: https://doi.org/10.1007/s11242-010-9710-9

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