## 3 Test Method  
### Similarity Criteria  
From the point of view of the model test, the simulation of ice-water-propeller interaction must meet the similarity criteria. This model test considers the similarity relationship based on the geometric similarity, motion similarity, viscous force similarity, cavitation similarity, and similarity with the mechanical properties of ice.  
1. Geometric similarity The propeller model, constructed according to the scale ratio of 1:16.46, ensures geometric similarity between the full-scale propeller and the model.
2. Motion similarity The dimensionless advance coefficient \(J\) is the same for the model and full-scale propeller, which ensures that the motion of the model is similar to that of the full-scale propeller. The dimensionless coefficients of the thrust and torque of the propeller and a single blade are defined as follows: \[J=\frac{V}{nD}\] (1) \[K_{T}=\frac{T}{\rho n^{2}D^{4}}\] (2) \[K_{Q}=\frac{Q}{\rho n^{2}D^{5}}\] (3) \[K_{TA\_BLADE}=\frac{T_{A}}{\rho n^{2}D^{4}}\] (4) \[K_{TT\_BLADE}=\frac{T_{T}}{\rho n^{2}D^{4}}\] (5) \[K_{QX\_BLADE}=\frac{Q_{X}}{\rho n^{2}D^{5}}\] (6) \[K_{QY\_BLADE}=\frac{Q_{Y}}{\rho n^{2}D^{5}}\] (7) \[K_{QZ\_BLADE}=\frac{Q_{Z}}{\rho n^{2}D^{5}}\] (8)  
where \(V\) is the inflow velocity, \(n\) is the propeller rotational speed, \(D\) is the propeller diameter, \(\rho\) is the density of water, and \(T\) and \(K_{T}\) are the propeller thrust and thrust coefficient, respectively; \(Q\) and \(K_{Q}\) are the propeller torque and torque coefficient, respectively; \(T_{X}\) and \(K_{TX\_BLADE}\) are the thrust and thrust coefficient of a single blade in the \(X\) direction, respectively; \(T_{T}\) and \(K_{TT\_BLADE}\) are the tangential force and tangential force coefficient of a single blade, respectively; \(Q_{X}\), \(Q_{Y}\), \(Q_{Z}\), and \(K_{QX\_BLADE}\), \(K_{QY\_BLADE}\), and \(K_{QZ\_BLADE}\) are the torque and torque coefficients, respectively, of a single blade in three directions.
3. Viscous force similarity Due to the fact that the condition of equality of the Reynolds number cannot be satisfied in the model test, the Reynolds number \(Re_{(0.75R)}\) of the chord length of the blade section at \(0.75R\) is required to exceed the critical Reynolds number: \[Re_{(0.75R)}=\frac{L_{0.75R}\sqrt{\
u^{2}+\left(0.75\pi nD\right)^{2}}}{\
u}>3.0\times 10^{5}\] (9) where \(L_{0.75R}\) is the chord length of the blade section at \(0.75R\), and \(\
u\) is the coefficient of kinematic viscosity of water.  
(4) Cavitation similarity  
The cavitation number of the rotational speed of the flow passing through the propeller disk at a radius of \(0.8R\) directly above the propeller axis is equal to that of the full-scale ship:  
\[\text{Full}-\text{scale}: \sigma_{ns(0.8R)}=\frac{p_{a}+\rho_{s}g(h_{s}-0.4D_{s})-p_{v}}{0.5 \rho_{s}{(0.8\pi n_{s}D_{s})}^{2}}\] (10) Model \[: \sigma_{nm(0.8R)}=\frac{p_{0(0.8R)}-p_{v}}{0.5\rho_{m}{(0.8\pi n_{m}D_{m})} ^{2}} \tag{11}\] \[\sigma_{ns(0.8R)}=\sigma_{nm(0.8R)} \tag{12}\]  
where \(\sigma\) is the cavitation number, \(P_{a}\) is the atmospheric pressure, \(P_{v}\) is the vaporization pressure of water, \(h_{s}\) is the center depth of the full-scale propeller shaft, and \(P_{0(0.8R)}\) is the static pressure of the \(0.8R\) radial blade section at the 12 o'clock position; the subscripts \(s\) and \(m\) represent the full-scale propeller and model, respectively.  
(5) Similarity with the mechanical properties of ice  
The milling test of the ice propeller follows the Cauchy number similarity criterion, which for maintaining the elastic force similarity between the model ice and sea ice:  
\[\frac{\rho_{s}{(n_{s}D_{s})}^{2}}{E_{s}}=\frac{\rho_{m}{(n_{m}D_{m})}^{2}}{E_ {m}} \tag{13}\]  
where \(E_{s}\) is the elastic modulus of sea ice, and \(E_{m}\) is the elastic modulus of model ice. Other definitions are shown above.