# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 2 Numerical Simulation Basics
### Determination of Self-Propulsion Point  
Based on the submarine hull resistance and propeller open-water performance curves, a numerical simulation study of the self-propulsion hydrodynamic performance of the submarine model was conducted. The process of determining the self-propulsion point is shown in Figure 3. Additionally, when using a deep diving test system, the effect of surface wave-making can be neglected. Experimental data from submarine tests indicate that in the coercive force calculation Formula (6), the value of \(C_{fs}+\Delta C_{T}\) often lies between \(C_{fm}\) and \(C_{fm}+C_{fw}\), with the difference between the two being less than \(2\times 10^{-4}\). Assuming that slight variations in the propeller load during model testing have minimal impact on the self-propulsion factor, it can be approximated that \(F_{D}\approx 0\) represents the self-propulsion point during underwater submarine tests. This self-propulsion point is achieved when the propeller thrust equals the submarine resistance [12; 13].  
\[F_{D}=1/2\rho V^{2}S_{m}\Big{(}C_{fm}-C_{fs}-\Delta C_{T}\Big{)} \tag{6}\]  
where \(V\) is the inflow velocity, \(C_{fm}\) is the friction resistance coefficient of the ship model, \(C_{fs}\) is the friction resistance coefficient of the full-scale ship, \(\Delta C_{T}\) is the roughness allowance coefficient, and \(C_{fw}\) is the wave resistance coefficient of the ship model; other definitions are as above.  
The specific process is as follows: 1. Determine the advance coefficient based on the velocity, propeller diameter, and propeller rotational speed, and use the advance coefficient to find the propeller thrust from the propeller open-water performance curve. Compare it with the submarine hull resistance to determine the initial propeller rotational speed \(n_{0}\). 2. Conduct a numerical calculation of the submarine model's self-propulsion hydrodynamic performance under the fixed velocity and propeller rotational speed \(n_{0}\). After the data converge, compare the propeller thrust \(T\) with the submarine hull resistance \(R\). If \(T=R\), then \(n_{0}\) is the propeller rotational speed at the self-propulsion point. If \(T\
eq R\), determine the relative magnitude of \(T\) and \(R\). If \(T>R\), reduce the propeller rotational speed; if \(T<R\), increase the propeller rotational speed. 3. To better obtain the propeller rotational speed at the self-propulsion point, select two sets of propeller rotational speeds where \(T>R\) and two sets where \(T<R\), and determine the propeller rotational speed corresponding to the intersection point where \(T\) equals \(R\) by plotting the \(T\)-\(n\) and \(R\)-\(n\) curves. The intersection point is the propeller rotational speed corresponding to the self-propulsion point. 4. Conduct a numerical simulation study of the submarine model's self-propulsion hydrodynamic performance at the self-propulsion point, and analyze the self-propulsion characteristics and the unsteady force load characteristics of the propeller.  
Figure 2: SUBOFF submarine, E1619 propeller, and self-propulsion geometric model.