A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Advances in Aerodynamics

Table 2 Model details for numerical simulation setup in this work

Model No.	Mass flux injection / kg/(m²·s)	Coolant temperature / K	External pressure / Pa	Model type	Acceleration / m·s⁻²
1	0.05	300	50,000	2D	\(\vec a = - g\vec j\)
2	0.30
3	0.55
4	0.05		Linear changing pressure
5	0.05		50,000		\(\vec a = - g\vec j - 10g\vec i\)
6	0.05				\(\vec a = - g\vec j + 10g\vec i\)
7	0.05			3D	\(\vec a = - g\vec j\)

External heat flux (Unit: W/m²) distribution for all cases: \(\dot q(x,t) = \left\{ \begin{array}{ll} \frac{{t \times {{10}^5}}}{{3 \times (1 + \frac{x}{L})}}, & 0 \leq t < 30{\text{ s}} \\ {10^6}, & 30{\text{ s}} \leq t \leq 40{\text{ s}} \end{array} \right.\); L is the length of the porous plate
Linear changing pressure (Unit: Pa) for Model 4: \(p(t) = \left\{ \begin{array} {ll}(50 - 1.2t) \times {10^3},&0 \leq t < 30{\text{ s}} \\ 1.4 \times {10^4},&30{\text{ s}} \leq t \leq 40{\text{ s}} \end{array} \right.\)