# Numerical Simulation of the Hydrodynamic Performance and Self-Propulsion of a UUV near the Seabed
## 2 Studied Configuration
### Definition of Dimensionless Parameters  
In order to classify the computational cases and analyze the effects of \(Hd\) and \(Re_{L}\) on the rapidity and maneuverability of the UUV more conveniently, the dimensionless parameter \(Hd\), which is the ratio of the distance between the seabed and the axis of UUV to the maximum diameter of the UUV, is introduced in this paper. Additionally, the values of \(Hd\) are 1.5, 2, 2.5, 3, 5, 7, 9 and 10, which cover the extreme conditions of subsea exploration in practices. The oncoming velocity takes values in the range of 0.5 m/s, 1 m/s, 2 m/s, and 4 m/s, and the corresponding \(Re_{L}\) ranges from 9.97 \(\times\) 10\({}^{5}\) to 7.98 \(\times\) 10\({}^{6}\) depending on the length dimension of the vessel. The 3D dimensionless coefficients of drag, lift and pitch moment coefficients are used to describe the hydrodynamic characteristics of the UUV, respectively, which are calculated using following formula.  
\[Hd=H/D_{max} \tag{1}\]  
\[C_{d}=\frac{F_{x}}{\frac{1}{2}\rho S_{A}U^{2}} \tag{2}\]  
\[C_{l}=\frac{F_{z}}{\frac{1}{2}\rho S_{A}U^{2}} \tag{3}\]  
\[m_{y}=\frac{M_{y}}{\frac{1}{2}\rho S_{A}L_{A}U^{2}} \tag{4}\]  
\(C_{d}\), \(C_{l}\) and \(m_{y}\) describe the hydrodynamic characteristics of the UUV. The formulas \(F_{x}\), \(F_{z}\) and \(M_{y}\) the drag, lift and pitch moment of the UUV. \(S_{A}\) is the maximum cross-sectional area of the UUV. \(U\) is the speed of the vehicle. \(L_{A}\) is the total length of the UUV. \(\rho\) is the fluid density taken as 998 kg/m\({}^{3}\).  
\[J_{0}=\frac{V_{A}}{nD} \tag{5}\]  
\[K_{T}=\frac{T}{\rho n^{2}D^{4}} \tag{6}\]  
\[K_{Q}=\frac{Q}{\rho n^{2}D^{5}} \tag{7}\]  
\(J_{0}\), \(K_{T}\) and \(K_{Q}\) are the propeller open water performance parameters. \(J_{0}\) is an important parameter for propeller's performance, which is similar to the angle of attack in wing theory. \(V_{A}\) is the velocity at the propeller disc; \(n\) is the rotational speed of propeller in \(rps\); \(D\) is the propeller diameter. \(K_{T}\) and \(K_{Q}\) are the propeller thrust and torque coefficients, with \(T\) and \(Q\) being the propeller thrust and torque.  
\[t=\frac{R-R_{0}}{T} \tag{8}\]  
\[w=1-\frac{J_{0}}{J} \tag{9}\]  
\[\eta_{i}=\frac{K_{Q_{0}}}{K_{Q}} \tag{10}\]  
\[\eta_{H}=\frac{1-t}{1-w} \tag{11}\]  
The dimensionless parameters \(t\), \(w\), \(\eta_{i}\) and \(\eta_{H}\) depict the interaction between the hull and propeller. \(t\) describes the effects of the propeller on the drag characteristics of the hull. \(R\) is the drag of the self-propelled UUV. \(R_{0}\) is the drag of the bare UUV at the corresponding speed. Additionally, \(T\) is the thrust provided by the propeller on the aft of the UUV. In the absence of scaling effects, \(R\) and \(T\) are equal. \(w\) and \(\eta_{i}\) define the effects of the wake field of the self-propelled UUV on the propeller performance. \(J\) and \(K_{Q}\) are the feed ratios andtorque coefficients of the propeller of the self-propelled UUV. \(J_{\text{Q}}\) and \(K_{\text{Q}_{\text{0}}}\) are the feed ratios and torque coefficients of the propeller in open water condition derived by using the equal thrust method. \(\eta_{H}\) describes the hull efficiency and represents the combined effect of thrust reduction and wake fraction.  
The calculation cases in this paper are classified into two main categories, as shown in Table 3.