*3.2. Test Verification*

The external characteristics of the pump system was calculated for the numerical model without cavitation. Figure 5 shows the comparison of test results and numerical simulation results. As shown in Figure 5, under the design flow condition, the difference between the numerical prediction result of the head and the experimental result is the smallest. At the design flow rate, the head difference between the test data and the numerical data is 1.2%. The comparison between numerical simulation results and experimental results shows the numerical results are relatively reliable.

**Figure 5.** Comparison of calculation and experiment result. \* *Qd* represents the design flow rate; and *Hd* represents the head of the waterjet propulsion pump system under the designed flow rate condition.

#### **4. Results and Discussion**

The most important factors affecting cavitation are pressure and velocity, so the cavitation number σ is used as a parameter to characterize the possibility of cavitation, σ, defined as:

$$
\sigma = \frac{P\_s - P\_V}{\frac{1}{2}\rho l I^2} \tag{8}
$$

where *Ps* is the reference static pressure, which is expressed as the pump inlet pressure in this study; *PV* is the vapor pressure; and *U* is the reference velocity, which is expressed as the inlet tip speed.

The net positive suction head (*NPSH)* is the difference between the total head of the liquid at the pump inlet and the pressure head when the liquid is vaporized. The net positive suction head-available (*NPSHa*) refers to the excess energy of the liquid at the pump inlet that exceeds the vaporization pressure at that temperature.

$$NPSH\_{\mathfrak{a}} = \frac{P\_{\mathfrak{s}}}{\rho \mathfrak{g}} + \frac{\upsilon\_{\mathfrak{s}}^2}{2\mathfrak{g}} - \frac{P\_{\text{cav}}}{\rho \mathfrak{g}} = \frac{P\_{\mathfrak{a}}}{\rho \mathfrak{g}} - H\_{\mathfrak{x}} - \sum h\_{\mathfrak{s}} - \frac{P\_{\text{cav}}}{\rho \mathfrak{g}} \tag{9}$$

where *Ps* <sup>ρ</sup>*<sup>g</sup>* is the pressure head of pump inlet section; *<sup>v</sup>*<sup>2</sup> *s* <sup>2</sup>*<sup>g</sup>* is the velocity head of pump inlet section; *Pcav* ρ*g* is the vaporization pressure value; *Pa* <sup>ρ</sup>*<sup>g</sup>* is the atmospheric pressure; *Hx* is the actual water suction head of the pump; and *hs* is the hydraulic loss from the intake surface to the pump inlet.

Since the calculation model is based on the center of the impeller, the installation height is 0. The *NPSHa* of the propulsion pump is calculated by the following formula:

$$NPSH\_d = (P\_{local} - P\_V) / \rho \text{g} \tag{10}$$

where *Plocal* is total pressure of inlet section.
