# Experimental Study on the Effect of Different Parameters on Rotor Blade Icing in a Cold Chamber
## 2 Experimental Environment and Equipment
### Spray System  
Twin fluid nozzles were used to atomize water. The air and water were supplied to the nozzle through the compressor, and the internal structure of the nozzle could mix water and air evenly to produce fine droplet spray. The average diameter of water droplet is directly related to the water pressure and air pressure. By adjusting the pressure of air and water, the droplet diameter can be changed to meet the experimental requirements. A plurality of nozzles were installed on a spray rack, and the spray rack was placed in front of the rotor blades. The liquid water content (LWC) was affected by controlling the number of nozzles used. In the process of the experiment, rotor blades should be placed in the spray range of nozzles to ensure atomization uniformity. In the study of aircraft icing, the mean volume diameter of droplets (MVD) is usually used to represent the droplet diameter. In the experiment, a relatively simple and reliable statistical method was used to measure the droplet diameter. A thin layer of silicone oil was applied on the surface of glass slide, as shown in Figure 2. The glass slide coated with silicone oil was placed in the spray range of nozzles to collect a certain number of droplets. Due to the incompatibility between oil and water, the droplets were wrapped in silicone oil and keep original shapes for a short time. The droplets on the glass slide were observed and photographed under a high-power microscope; the observation results are shown in Figure 3. The MVD can be obtained by statistical calculation of droplet diameters. Figure 1: Environmental chamber and refrigeration system used in the experiment. Figure 2: Glass slide coated with silicone oil and high-power microscope. The measurement method of LWC in the cold chamber mainly used the ice thickness at the stagnation point of blade to calculate LWC. Its principle is that under the influence of aerodynamic force, the liquid water collected at the stagnation point only flows to both downstream sides, and no liquid water flows in. Therefore, the icing rate at the stagnation point can be calculated directly without iterative calculation. In this paper, the method in [15] was adopted. In the experiment, it was necessary to measure the ice thickness at the stagnation point for a certain icing time, and input parameters needed to be determined, including characteristic length, MVD, icing temperature, rotation speed, icing time, etc. According to the relevant calculation formula, we can calculate LWC in the cold chamber. On the basis of the MVD and rotation speed, we can obtain the droplet collection efficiency at the stagnation point of the rotor blade by using the calculation method of our research results in [19]. The droplet collection efficiency is a dimensionless parameter, and its calculation result does not depend on the LWC. The droplet collection efficiency at the stagnation point \(\beta_{0}\) can also be calculated by the following simplified formula:  
\[\beta_{0}=\left(\frac{1.40\times\left(K_{0}-0.125\right)^{0.84}}{1+1.40\times \left(K_{0}-0.125\right)^{0.84}}\right) \tag{1}\]  
where \(K_{0}\) is the modified inertia factor, which can be expressed as  
\[K_{0}=0.125+\frac{\lambda}{\lambda_{Stokes}}(K-0.125) \tag{2}\]  
\[K=\frac{\rho_{w}L^{2}V}{18d\mu_{a}} \tag{3}\]  
\[\frac{\lambda}{\lambda_{Stokes}}=(0.8388+0.001483\frac{VL\rho_{a}}{\mu_{a}}+0. 1847\sqrt{\frac{VL\rho_{a}}{\mu_{a}}})^{-1} \tag{4}\]  
where \(K\) is the inertia factor; \(\rho_{w}\) is the droplet density; \(d\) is the droplet diameter, which is equal to MVD; \(V\) is the far field velocity; \(L\) is the characteristic length; \(\mu_{a}\) is the dynamic viscosity; \(\rho_{a}\) is the air density; and \(\lambda/\lambda_{Stokes}\) is the dimensionless droplet range. When the droplet collection efficiency is obtained, it is necessary to determine the freezing coefficient at the stagnation point. The freezing coefficient \(f\) is the ratio of the amount of liquid water frozen into ice and the total amount of liquid water.