*3.4. Effect of Pressure on Heat Transfer*

To explore the influence of law of pressure change in a pseudo-critical region, the inlet temperature of hydrogen is set to 30 K. Figure 14 shows the influence of changing mass flow on the axial distribution of the wall temperature, *Tw*, of the hydrogen intake tube and the bulk temperature, *Tb*, of liquid hydrogen inside the tube. The results show that the temperature of both the wall and the liquid hydrogen increases gradually with the deepening of the flow distance. This is because there is no heat source around when the liquid hydrogen flows into the pipeline at the beginning, so the temperature change is not obvious. After that, due to the influence of thermal deposition of the poisoned plate and container, the two kinds of temperature increase significantly, and the temperature rise range of the wall surface is about 3 K. When the pressure is 15 bar, the temperature value will change at the mutation position corresponding to the physical property of liquid hydrogen in Figure 4, while the temperature will not change at a distance from the critical value. Moreover, different pressures have little effect on the average temperature of the fluid in the tube. It can be concluded that under supercritical pressure, the drastic change of physical properties in the critical region will have a great impact on turbulent heat transfer, resulting in the deterioration of convective heat transfer.

The basic formula of jet impingement heat transfer is the Newton cooling Equation,

$$q = h(T\_w - T\_j) \tag{21}$$

where *Tj* is jet temperature and *h* is local impact convective heat transfer coefficient. In order to obtain the average *h* of the whole target surface, the local *h* curve of the target surface must be obtained, and then the *h* of each point can be calculated through a surface integral along the radius [39]. The local Nusselt number can be expressed as

$$Nu = \frac{h\_j d}{\lambda\_j} \tag{22}$$

where *hj*, *d* and *λ<sup>j</sup>* are local impact convective heat transfer coefficient, diameter of nozzle and thermal conductivity of jet.

**Figure 14.** Variations of temperature along axial direction under different pressures: (**a**) *x* = 0 mm; (**b**) *y* = 0 mm.

In order to more specifically reflect the heat flow characteristics of liquid hydrogen inside the vessel, the relationship between the average Nusselt number on the target surface and the resistance *f* along the hydrogen inlet pipe and the jet Reynolds number *Re* was explored under different pressure conditions. As can be seen from Figure 15, *Nu* increases significantly with the increase of *Re* and tends to change linearly. Simultaneously, the flow boundary layer in the inlet pipe segment gradually becomes thinner, the flow resistance decreases, the resistance coefficient decreases, and the pressure on the target surface also increases. The intersection point of *Nu* and f represents the inlet flow of liquid hydrogen corresponding to different pressures when the optimal cooling effect is achieved under the premise of considering the comprehensive characteristics of flow resistance and heat transfer characteristics. On the other hand, with the continuous increase of *Re*, the variation trend of *Nu* corresponding to different pressures is the same. At the pressure of 15 bar, the corresponding overall curve of *Nu* moves down and the heat transfer capacity decreases, which further proves that near the critical region, while the physical property variation caused by the pressure change worsens the turbulent heat transfer.

**Figure 15.** The variation of *Nu* with *Re* at the target surface.
