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Numerical simulation of control ablation by transpiration cooling

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Abstract

A transient, one-dimensional numerical model is developed to describe the processes of transpiration cooling and ablation of the porous matrix used for the cooling. This model is based on the assumption of local thermal equilibrium. The problem of moving boundary due to ablation of the porous matrix is treated by the front-fixing method. This paper discusses the results of numerical simulations under different conditions and control parameters of ablation process. It was found that cooling effects and ablation processes are influenced by the coolant mass flow rate, the intensity of the heat flux, and the initial temperature at the start of transpiration cooling. In additional to the above three parameters, the Stefan number and the Biot number can also influence the transient cooling process, control ablative thickness of the porous plate by the reduction of ablative speed and duration, respectively.

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Abbreviations

a :

specific surface area of porous matrix

c :

specific heat capacity [J/(kg K)]

D :

hydraulic diameter of coolant channel (m)

k :

thermal conductivity [W/(m K)]

s 0 :

initial plate thickness (m)

d p :

characteristic size of porous matrix (m)

h :

heat transfer coefficient [W/(m2K)]

s :

ablation thickness (m)

\(\tilde{S}\) :

dimensionless thickness

T :

temperature (K)

θ:

dimensionless temperature

v :

velocity (m/s)

t :

time (s)

τ:

dimensionless time

y :

coordinate

Y :

dimensionless coordinate

\(\dot{q}\) :

heat flux (W/m2)

Q :

dimensionless heat flux

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

coolant mass flow rate [kg/(m2 s)]

M :

dimensionless coolant flow rate

L :

latent heat of solid material (J/kg)

Ste:

Stefan number

Pr:

Prandtl number

Bi:

Biot number

ɛ:

porosity

ρ:

density (kg/m3)

μ:

viscosity, (kg/m s)

α:

thermal diffusivity (m2/s)

0:

initial time

f:

coolant fluid

c:

constant/coolant at entry of channel

eff:

effective

s:

solid matrix

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Acknowledgements

The financial support provided by NSFC (No. 90305006) and EMNSFA (No. 2004kj365zd) is greatly appreciated. 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.

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Authors and Affiliations

  1. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, 230027, People’s Republic of China

    Jianhua Wang & Hainan Wang

  2. Beijing Aerospace Propulsion Institute, Beijing, 100076, People’s Republic China

    Jiguo Sun & Jue Wang

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  1. Jianhua Wang
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  2. Hainan Wang
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  3. Jiguo Sun
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  4. Jue Wang
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Correspondence to Jianhua Wang.

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Wang, J., Wang, H., Sun, J. et al. Numerical simulation of control ablation by transpiration cooling. Heat Mass Transfer 43, 471–478 (2007). https://doi.org/10.1007/s00231-006-0130-x

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