# Experimental Study on the Effect of Different Parameters on Rotor Blade Icing in a Cold Chamber
## 2 Experimental Environment and Equipment
### Spray System
When \(f=0\), there is no water freezing into ice. When \(f=1\), it means that the droplets collected are immediately frozen into ice; when \(0<f<1\), it means that part of the water is frozen and the other part remains liquid. Figure 3: Droplet diameter distribution observed under high-power microscope. According to the energy balance of liquid water, the expression of freezing coefficient can be given as follows:  
\[f=(\frac{C_{p,ws}}{L_{f}})(\phi+\frac{\theta}{b}) \tag{5}\]  
Figure 3.0  
Figure 3.1  
where \(C_{p,ws}\) is the specific heat capacity of water, \(L_{f}\) is the latent heat of freezing of water, \(\phi\) is the energy exchange coefficient of droplets, \(\theta\) is the energy exchange coefficient of air, \(t_{f}\) is the freezing temperature of water, \(t_{st}\) is the surface temperature of water, \(C_{p,a}\) is the specific heat capacity of air, \(h_{G}\) is the heat conduction coefficient of air, \(p_{ww}\) is the vapor pressure of water at the frozen surface, \(p_{w}\) is the vapor pressure of water in the atmosphere, \(p_{st}\) is the static pressure, \(L_{v}\) is the latent heat of evaporation of water, and \(h_{c}\) is convective heat transfer coefficient. The relative thermal coefficient \(b\) can be calculated as follows:  
Figure 3.2  
The convective heat transfer coefficient \(h_{c}\) can be obtained by Nusselt number \(Nu\):  
Figure 3.3  
where \(\lambda_{a}\) is the thermal conductivity of the air and \(d\) is the droplet diameter. When \(Re>10^{5}\), \(Nu\) has the following approximate formula:  
Figure 3.4  
When \(Re\leq 10^{5}\), \(Nu\) can be expressed as  
Figure 3.5  
According to [PERSON] and [PERSON]'s suggestion [20], the freezing coefficient in the experiment and the calculated freezing coefficient can be modified by a linear relationship:  
Figure 3.6  
where \(f_{e}\) is the modified value, and \(f_{a}\) is the theoretical analysis value of freezing coefficient. After obtaining the droplet collection efficiency and freezing coefficient at the stagnation point, we can calculate the LWC on the basis of the ice thickness. It was assumed that the droplet collection efficiency and ice density at the stagnation point remained unchanged with the change of ice shape, and thus the mass flux of liquid water collected can be calculated as follows:  
Figure 3.7  
The ice thickness at the stagnation point can be expressed as  
Figure 3.8By integrating the above formulas, the following relation can be obtained:  
Figure 3.9  
where the ice density \(\rho_{ice}\) is constant, the ice thickness \(H\) and icing time \(t\) can be measured in the experiment, and the far field velocity \(V\) can be calculated by rotation speed and blade radius. It can be seen that the relationship between ice thickness and LWC is monotonic, and the average LWC in the icing process can be obtained by programming. According to [15; 16; 20], the measurement results of LWC and MVD have uncertainty, and the error is less than 15% in most cases. In the current situation, this uncertainty is difficult to solve effectively.