Super-cooled droplet impact and ice accretion on an aircraft engine nacelle lip

This manuscript concentrated on the icing phenomenon on the lips of an engine nacelle. Numerical simulation was employed to establish the airflow, supercooled droplet impact, and engine nacelle ice accretion models. The study investigated the airflow field near the lip, the characteristics of supercooled droplet impact, and the ice accretion near the lip under different flight conditions. The computational results indicated that due to the effects of nozzle contraction and flow extraction, a low-pressure, high-velocity, and low-temperature region appeared on the inner side of the lip, leading to ice accretion on the nearby wall. The maximum collection efficiency on the lip surface at 20, 000 ft was slightly higher than that at 10, 000 ft, with a maximum value of approximately 0.6. In the computed conditions of this study, as the flight altitude and Mach number increased, the ice thickness on the lip surface increased and the ice spread inward, posing a significant risk of ingestion after detachment.


Introduction
Aircraft engines are the core power source for airplanes, and their performance determines flight safety.When the engine starts rotating at high speed, it may experience icing on components such as the lips of the engine nacelle, the inlet duct, and the struts due to the high-speed suction effect of the airflow in the intake duct.Once icing occurs, ice chunks may be ingested into the engine and damage the high-speed rotating fan blades and compressor blades, even causing engine damage or in-flight shutdown, posing a serious threat to aircraft safety [1][2].Therefore, in-depth research on engine icing and anti-icing is crucial for flight safety.
Chang et al. [3] carried out the design of a hot air anti-icing chamber and piping system for a type of engine air intake with manifold bulkhead, based on the calculation of water droplet impact characteristics of the air intake and the thermal calculation of the anti-icing system.Hu [4] conducted a numerical simulation study on the ice accumulation and growth process of aircraft engine inlet struts and fairings.The commercial software FENSAP-ICE and CANICE, which are specifically used for anti-icing calculations, have been developed abroad through a lot of research work carried out in the field of numerical simulation studies.For instance, Baruzzi et al. [5] simulated the ice accretion on the engine nacelle by using Fluent and FENSAP-ICE and then used ANSYS AUTODYN to simulate the impact of ice accumulation on the blades after activating the anti-icing system.Jung et al. [6] constructed a metamodel by using neural networks to evaluate the performance of the electric heating anti-icing system for a rotorcraft engine intake and validated the metamodel based on the performance of the electric heating anti-icing system.
Based on the research mentioned above, this manuscript focuses on the supercooled droplet impact and icing phenomenon on engine lips and establishes a mathematical model to simulate the supercooled droplet impact characteristics and ice accretion on the lips of a certain aircraft engine.Different flight conditions are considered to investigate the droplet collection characteristics on the lip surface and the ice growth process on the engine lip.

Computational model
Considering that the overall structure of the engine is relatively complex and this article does not involve complex processes such as internal combustion, mainly focusing on the impact of water droplets and icing at the engine lip, the model of the engine has been simplified in this article.Based on retaining the basic shape of the complete intake fairing and internal and external channels, the compressor, combustion chamber, turbine, and tail nozzle inside the engine have been removed, as shown in Figures 1 and 2.  To simulate the suction effect of the engine, the inlet, and outlet of the internal and external channels of the engine are treated as mass flow outlets and mass flow inlets in the model, respectively.
A half-model is used to generate unstructured grids for the geometric models, as shown in Figures 1  and 2. The surface and flow field grids of the engine nacelle are shown in Figure 3.In this study, three types of grids with nodes of 895, 364, 956, 524, and 998, 578 respectively, and the grid with 956, 524 nodes can meet the grid independence requirements through grid independence verification, as shown in Figures 3 and 4.  The design parameters of the inner and outer ducts at different heights according to the design requirements are shown in Table 1.
Table 1.Internal and external bypass design conditions.The controlling equations for the air flow field are as follows: (3) where ρ is the density (unit: kg/m 3 ); p is the pressure (unit: Pa); u  is the velocity (unit: m/s); is the shear stress (unit: Pa); H is the total enthalpy (unit: J); T is the static temperature (unit: K).
In the present research, it is assumed that there is no energy exchange occurs during the motion of the water droplets, so the control equations include only the continuity equation, and the momentum equation is shown as follows: (5) where w u  denotes the droplet vector velocity (unit: m/s); ρ w denotes the droplet density (unit: kg/m 3 ); where m  and q  represents mass flow and heat flow, respectively (unit: kg/s and W); the subscript 'imp' represents the impinging droplet term; 'in' represents the upstream inflow term; 'evp' represents the evaporation or sublimation term; 'ice' represents the icing term; 'out' represents the overflow to downstream outflow term; 'cnd' represents the anti-de-icing heating term; 'cnv' represents the convective heat transfer term.
The above numerical equations are solved by ANSYS FLUENT and FENASP ICE, and the airflow field, water droplet impact, and icing accretion under different working conditions can be predicted.

Results and analysis
Figures 5 and 6 show the pressure distribution on the lip surface and the velocity field near the outlet on the symmetry plane at altitudes of 10, 000 ft and 20, 000 ft, respectively.From Figure 5, it can be observed that due to the effects of nozzle contraction and flow extraction, a low-pressure region appears on the inner wall of the lip, resulting in high-velocity airflow near the lip surface.Due to the phenomenon of increasing air velocity and decreasing pressure, the temperature near the area may significantly decrease, ultimately leading to icing.Figure 7 illustrates the droplet collection efficiency on the lip surface at different flight altitudes.The maximum collection efficiency at 20, 000 ft is slightly higher than that at 10, 000 ft, with a maximum value of approximately 0.6.This indicates that more droplets are collected on the lip surface at higher altitudes, increasing the risk of ice accretion.
To investigate the icing process in the above low-pressure area, it is necessary to calculate the impact characteristics of super-cooled water drops on the lip surface first.Figure 7 shows the cloud pictures of the water drop collection coefficient on the engine nacelle lip at different heights, and Figure 8 illustrates the collection coefficient on the lip symmetry plane.Affected by the decrease of mass flow rate and the change of density of air in a culvert at 20, 000 ft height, the maximum collection coefficient on the lip surface at 20, 000 ft is slightly higher than that at 10, 000 ft, and the maximum value is approximately 0.6, as shown in Figure 7 and Figure 8 Based on the calculations of droplet impact characteristics, this study analyzed the ice accretion on the lips of the engine nacelle.Figure 9 presents the ice distribution and thickness contour maps on the lip surface after 5 minutes of icing at different flight altitudes.It can be observed that in the condition of H = 20, 000 ft and Ma = 0.651, the ice thickness on the lip surface is slightly higher than that in the condition of H = 10, 000 ft and Ma = 0.541, with the maximum thickness occurring at the leading edge of the lip, approximately 3.4 cm.To further compare the icing characteristics of the lip under different conditions, Figure 10 illustrates the ice shapes on the symmetry plane of the lip for two different conditions.It can be seen that as the flight altitude and the Ma number increase, the ice thickness on the lip surface increases, and the ice spreads inward.This poses a higher risk of ingestion after detachment.

Conclusion
This article established a flow and icing model of the engine nacelle by simulating the suction effect of internal and external ducts with flow rate.The airflow, super-cooled water droplet impact, and icing characteristics near the lip of the engine nacelle were investigated under different flight conditions, and the following conclusions were drawn: (1) Due to the effect of flow contraction and duct suction, a low-pressure area appears on the inside of the lip, and under the influence of increased velocity and reduced pressure, icing is more likely to occur in the vicinity of this area; (2) Due to the effect of decreased duct flow rate and changes in air density at 20, 000 ft altitude, the maximum collection coefficient on the lip surface at 20, 000 ft is slightly higher than that at 10, 000 ft, with a maximum value of about 0.6; (3) In the calculation conditions of this article, with the increase of flight altitude and Ma number, the thickness of ice on the lip surface increases, and the ice spreads inward towards the lip, posing a higher risk of being ingested after detachment.

Figure 1 .
Figure 1.Side view of the engine.

Figure 2 .
Figure 2. Completed geometric model of engine.

Figure 3 .
Figure 3. Grid of the engine.

Figure 4 .
Figure 4. Grid of the outflow field.

dwF
 is the air resistance to the droplet (unit: N); d is the average droplet diameter (unit: m); ,D sph Cis the drag coefficient of the spherical particle. 0

Figure 9 .
Figure 9. Cloud image of icing thickness on the surface of the lower lip in different states.

Figure 10 .
Figure 10.Ice shapes on the surface of the lower lip at 10,000 ft and 20,000 ft.