*3.2. Effect of Beam Power on Heat Transfer*

The influence of beam power increase on the heat transfer characteristics of liquid hydrogen is characterized by the change of temperature. The temperature distribution with large beam power from 100 kW to 500 kW is shown in Figure 7. As is evident from Figure 7, the temperature of liquid hydrogen in the cavity tends to be symmetrically distributed at different beam power. On the contrary, the temperature at different wall positions of the external aluminum container is quite different, which is manifested in the relatively high temperature values in four corners. The maximum value appears at the lower left corner of the hydrogen container at 500 kW, which is specifically 33 K. And as power increases, the difference becomes more pronounced, due to the irregular heat source of the moderator itself. As shown in Figure 6, the temperature at the wall position corresponding to the high heat deposition is also higher, and the increase of power further highlights this phenomenon. In addition, it can be seen that the liquid hydrogen temperature in the cavity has a partial fluctuation under the power of 300~400 kW, which is thanks to the increase of the overall heat source affecting the physical properties of liquid hydrogen. The overall temperature increases from about 18 K to 20 K corresponding to 500 kW in this range, which is in a transition state, so the liquid hydrogen temperature is unevenly distributed.

Considering the neutron performance and hydrogen system safety, the wall temperature of the container is forbidden to exceed the vaporization temperature of the working fluid; thus, the maximum temperature value is the focus of attention and ensures that it is within the safe range. The specific relationship between maximum temperature of container, poisoned plate and hydrogen with beam power is studied in Figure 8; it is found that there is an approximate linear growth relation between them. For the local thermal deposition of DPHM, due to the increase of the Footprint size of the beam, the growth multiple will be smaller than that of the increase of beam power. The latent heat in steady flow is negligible, so the heat change in DPHM is mainly caused by the scattering reaction, which means that the energy generated by per unit volume is proportional to the temperature difference. In this case, the heat deposition increases linearly, resulting in a linear increase in maximum temperature.

**Figure 7.** The temperature distribution of DPHM with various beam power (*q* = 60 g/s, *x* = 0 mm): (**a**) 100 kW; (**b**) 200 kW; (**c**) 300 kW; (**d**) 400 kW; (**e**) 500 kW.

**Figure 8.** The variation of maximum temperature with different beam power.

#### *3.3. Effect of Mass Flow on Heat Transfer*

The analysis of flowing process mainly includes the selection of flow range and the analysis of pressure loss. The higher the mass flow, the smaller overall temperature rise of liquid hydrogen, and the temperature distribution inside the container is relatively uniform, which is also beneficial to the neutron moderating effect. At the cross section of *x* = 0 mm, it can be observed, from Figure 9, that the average temperature of the side with lower liquid hydrogen flow is higher due to the uneven segmentation of the cross-sectional area of the import pipeline by the poisoned plate. The velocity contours under different mass flow are also listed, and it can be seen that the temperature distribution is basically unchanged but that the overall temperature decreases gradually with the increase of flow rate.

**Figure 9.** Temperature distribution of DPHM (beam power = 500 kW): (**a**) *x* = 0 mm (60 g/s); (**b**) *y* = 0 mm (30, 60, 90, 120, 150 g/s).

Correspondingly, Figure 10 presents the detailed flow of liquid hydrogen inside the cavity under the 60 g/s mass flow when the turbulence viscosity ratio is about 5, which is also one of the important factors affecting heat transfer. There are two distinct symmetrical vortices on both sides of the bottom of the container according to Figure 10a; part of the liquid hydrogen from the exit is involved in the vortex, and the other part is gathered up at the neck by the inertial force. Moreover, it can be seen that due to the separation of the poisoned plate, the size and position of the vortex generated by different flow rates are different but all located near the inner wall of the container, where the intensity of vortex dominates the heat transfer.

**Figure 10.** The streamline in the DPHM: (**a**) *x* = 0 mm; (**b**) *y* = 0 mm.

The effect of mass flow on maximum temperature under 500 kW beam power is shown in Figure 11. Specifically, the heat transfer effect is significantly improved by distinct increment of turbulence effect in the flow range of 30~60 g/s, while the slope decreases with the increase of mass flow, which proves that the cooling effect reduces gently. It also should be noted that the increase of mass flow is accompanied by the increase of pressure loss, which will be detrimental to the stability of the flow. The intersection point between the temperature curve of liquid hydrogen and the corresponding pressure drop curve is noted, which is in the range of 60~90 g/s, indicating that the cooling effect is the best and the flow is relatively stable.

The liquid hydrogen carries out jet impact on the bottom surface, which was taken as the research object result of its good heat transfer effect, after flowing out of the hydrogen intake pipe with a vertical distance of 5 mm, as shown in Figure 12. For a smooth surface, with the flow of liquid hydrogen reaching the wall, the pressure forces the jet to flow axially along the wall. Combined with the pressure distribution, it can be seen that the target surface located in the impact zone is under the maximum pressure, and then diffuses and decreases along the periphery, leading to a gradual decrease in velocity. The temperature

in the center area of the target surface increases slowly with a similar regularity. This is because the viscous boundary layer on the wall gradually thickens and the surface heat transfer coefficient decreases when the liquid hydrogen flows in the radial direction.

**Figure 11.** The variation of maximum temperature with different mass flow.

**Figure 12.** Physical parameters distribution of target surface: (**a**) Pressure; (**b**) Velocity; (**c**) Temperature.

The local heat transfer coefficient is obtained by the following equations,

$$h = \frac{q\_w}{T\_w - T\_b} \tag{18}$$

$$T\_b = f(H\_{b\prime}P) \tag{19}$$

$$H\_b = \frac{\int\_A \rho w H dA}{\int\_A \rho w dA} \tag{20}$$

where *qw*, *Tw*, *Tb*, *w* and *H* are the local heat flux of wall, averaging temperature of wall, bulk fluid temperature, bulk fluid axial velocity and bulk fluid enthalpy.

Figure 13 shows the distribution of the flow heat transfer coefficient *h* at the bottom target face along the *x*-axis, corresponding to the temperature distribution. It reaches the maximum value at the position of poisoned plate and then gradually decreases, which is due to the poor heat transfer at this place due to the flow dead zone generated by the shunting phenomenon. After that, the heat transfer coefficient increases gradually with the flow recovery.

**Figure 13.** The distribution of the heat transfer coefficient of the target surface along the x axis.
