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Numerical investigation of transpiration and ablation cooling

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Abstract

To predict the integral performance of transpiration and ablation cooling during the reentry of hypersonic vehicles, an unsteady numerical model based on the assumption of thermal equilibrium is presented. The non-thermal equilibrium model and the thermal equilibrium model are coupled by the effective thermal properties of the porous matrix and the coolant. The calculation using the thermal equilibrium model shows the influence of the variation of the effective thermal properties on the numerical results by a comparison between constant and variable thermal properties. The comparison indicates that near the melting temperature of the porous matrix, the position of the moving boundary due to ablation is sensitive to the temperature, therefore, the variation of the thermal properties are considered in this paper. The process of ablation and transpiration cooling is simulated under different numerical conditions. The simulations demonstrate that the injection rate of coolant mass flow and initial temperature of cooling are important parameters for the control of the ablation process.

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Abbreviations

c :

Specific heat capacity [J/(kgK)]

d p :

Mean diameter of pore (m)

k :

Thermal conductivity [W/(mK)]

l :

Initial thickness of porous plate (m)

h s :

Interfacial heat transfer coefficient [W/(m2K)]

h v :

Volumetric heat transfer coefficient [W/(m3K)]

S :

Thickness (m)

T :

Temperature (K)

t :

Time (s)

v :

Velocity (m/s)

y :

Coordinate

Q 0 :

Heat flux (W/m2)

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

Coolant mass flow rate [kg/(m2s)]

\(\vec{V}\) :

Velocity vector (m/s)

α:

Thermal diffusivity (m2/s)

β:

Thermal polarizability

ɛ:

Porosity

ρ:

Density (kg/m2)

λ:

Latent heat of the solid matrix (J/kg)

0:

Initial time

c:

Constant/coolant

e:

Effective

m:

Ablation

p:

Porous material

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Acknowledgements

The project is supported by National Natural Science Foundation of China (No. 90305006) and Educational Administration Foundation of Anhui Province (No. 2004kj365zd). One of the authors (Jianhua Wang) is also grateful for the financial support provided by the Foundation of the Education Ministry of China for the Returned Overseas Scholars. We also thank Prof. Casey and Dr. Messner at the Institute of Thermal Fluid- Machinery and Laboratory of University Stuttgart for their helpful guidance and support. The first figure of this paper is taken from the paper of Choi et al. [7], we would like to express our appreciation to the authors.

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  1. 13th Department, University of Science and Technology of China, Jinzhai Road 96, Hefei, 230026, People’s Republic of China

    Jianhua Wang & Xingsi Han

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  1. Jianhua Wang
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  2. Xingsi Han
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Correspondence to Jianhua Wang.

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Wang, J., Han, X. Numerical investigation of transpiration and ablation cooling. Heat Mass Transfer 43, 275–284 (2007). https://doi.org/10.1007/s00231-005-0073-7

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