# Numerical Simulation of the Hydrodynamic Performance and Self-Propulsion of a UUV near the Seabed
## 3 Numerical Methods
### Verification of Numerical Method  
Due to the lack of experimental data for the self-propelled model, the articles adopt the same validation strategy as the others [1; 2; 3; 4]. Numerical simulations of the UUV and propeller from the available experimental study data are carried out separately to verify the feasibility of the numerical method used in the paper.  
The SUBOFF is an axisymmetric vehicle and the hydrodynamic test is carried out by David Taylor Research Center. It is aimed at providing a data base for CFD validation  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid Cell (M)** & \(C_{I}\) & \(m_{y}\) & \(K_{T}\) & \(K_{Q}\) \\ \hline
3.2 & 0.0255 & 0.0089 & 0.1087 & 0.0248 \\
6 & 0.0248 & 0.0085 & 0.1070 & 0.0234 \\
8.4 & 0.0246 & 0.0084 & 0.1061 & 0.0236 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Grid-independence verification.  
Figure 3: Grid settings. (**a**) The longitudinal profile grid of the domain with \(HD\) of 1.5; (**b**) UUV nose grid; (**c**) UUV tail grid; (**d**) propeller grid.  
and other flow field analysis related to submarines. A large number of academics adopt SUBOFF as a research object for UUV. The AFF-3 model in SUBOFF is chosen in this paper to verify the feasibility of the numerical method. [PERSON] et al. [16] experimentally studied the hydrodynamic performance of the AFF-8 model at a \(Re_{L}\) of 12 \(\times\) 10\({}^{6}\). The wake characteristics of the AFF-2 model at \(Re_{L}\) 1.1 \(\times\) 10\({}^{6}\) were investigated by [PERSON] et al. [17] through wind tunnel tests. [PERSON] et al. [18] investigated the turbulent boundary layer on the surface of the AFF-8 model with a Re of 1.2 \(\times\) 10\({}^{6}\) by CFD method.  
The distribution of pressure coefficient (\(C_{p}\)) with \(Re_{L}\) of 1.2 \(\times\) 10\({}^{6}\) is obtained by CFD method. \(C_{p}\) is calculated by Equation (17). The comparison of the numerical results is given in Figure 4. It can be seen that the distribution of \(C_{p}\) on the hull surface agrees well with the results of other researchers, except that field near the fin plate of the model. The main reason for the phenomenon is the absence of a bridge in the AFF-3 model. The differences in the geometric models lead to the divergence in the flow field distribution at the leading edge of the stern appendages.  
There are two reasons for the discrepancy.  
1. The geometric profile of the model used in the article is different from that of [16; 17; 18]. The geometric model in the article contains the stern appendages, but not the fair-water, while [16; 18] contain both the stern appendages and the fair-water, and [17] has neither the stern appendages nor the fair-water.
2. The most significant reason is that the cross section of [16; 17; 18] from which the \(C_{p}\) is obtained did not pass through the stern appendages, while the cross section of this paper passed through it.  
The DTMB 4119 propeller has been used to verify the reliability of numerical methods and has been widely applied to research the cavitation performance of the propeller. The open water characteristics of this propeller were obtained by CFD method and compared with the experimental results. As shown in Figure 5, the numerical results agree well with the experimental results. The largest discrepancy appears in the efficiency variable with J of 0.833, with a relative error of 2.57%, which can be accepted. The experimental results for this propeller were obtained from reference [19].