Ice sensitivity analysis of different airfoils

When an aircraft passes through clouds containing supercooled water droplets, it condenses into ice on the surface of the wing. Wing icing will reduce the flight envelope of the aircraft as a whole, limit the flight range and speed, and threaten flight safety. The range and intensity of icing are not only determined by meteorological conditions but also closely related to the types of airfoils. In order to study the influence of airfoils on icing, GAW-2 high lift airfoil, NLF (1)-0215F natural laminar airfoil and SC (2)-0714 supercritical airfoil are selected as the representatives of the three mainstream airfoils. The Numerical simulation method is used to analyze the influence of icing parameters on the three airfoils, summarize the icing rules and analyze the differences.


Introduction
When an aircraft passes through clouds containing supercooled water droplets, it condenses into ice in some places, mainly by icing on the wings.The accumulation of ice on the wing will change the surface roughness and aerodynamic shape of the wing, and in severe cases, complex unsteady separation and reattachment will occur and form rich vortex structures and separation bubbles, and the flow characteristics of the whole wing will be fundamentally changed.as a result, the torque characteristics of the aircraft deteriorate, the control surface fails, and the plane is destroyed seriously.Wing icing has always been one of the most important aircraft design issues related to flight safety.With the continuous development of computational fluid dynamics and the continuous improvement of computer computing power, since the 1980s, icing numerical simulation began to appear and developed rapidly [1] , which has become an important reference and supplement outside physical experiments.
Wing icing is the result of the interaction of specific parameters, and the ice shape formed after icing is related to flight conditions, meteorological conditions and wing upwind area.However, most scholars have only studied the influence of different icing parameters on the ice shape of the same airfoil [1] [2] , and have not studied the ice shape difference caused by the difference of shape between different airfoils.To study the similarities and differences of icing of different kinds of airfoils, GAW-2, NLF (1)-0215F, SC (2)-0714 airfoils are selected as the typical representatives of high lift, laminar flow and supercritical airfoils respectively.FENSAP-ICE software is used to simulate the icing process of three kinds of airfoils and analyze the icing sensitivity.

Calculation principle of icing simulation
When FENSAP-ICE predicts the range, size and shape of icing on the wing surface, it includes three aspects: flow field calculation, droplet movement and impact characteristics, and icing calculation [3] .At present, there are two calculation strategies for numerical prediction of icing ice type: single-step method and multi-step method [4] [5] .The single-step method sequentially solves the air flow field, the impact characteristics of water droplets, the heat transfer and icing once, and directly outputs the final ice shape, which ignores the feedback effect of the wing shape and flow field on heat transfer and icing with time.When the simulation icing time is long, the error of the single-step method is larger.As a result, the multistep method arises at the historic moment, and the calculation process is shown in figure 1.The basic idea is multiple iterations and grid reconstruction, which divides the fixed simulation time into multiple segments, each of which is calculated by single-step method.The multi-step method takes into account the effects of ice accumulation on the air flow field and water droplet impact characteristics, and the simulation results are closer to the reality [6] .

Figure 1.
Calculation process of multi-step method for icing simulation.

Flow field calculation
The flow field in this study is mainly obtained by solving the fully turbulent steady compressible N-S equation with finite element method by FENSAP module, and the SST turbulence model is used for turbulence simulation.The specific transport equation is as follows: where K P is the generation term of turbulent kinetic energy, t  is the turbulent viscosity coefficient special for SST model, F is the mixed function, 3   are the model constant parameters which can be obtained by the mixed function.It should be noted that the SST turbulence model is not only very important in the flow field calculation, but also the most important convective heat transfer coefficient in the simulation of water droplet icing process is also calculated by the turbulence model.

Calculation of water droplet impact characteristics
Where ( , ) a x t  , ( , ) d u x t represents the volume fraction of water in the air and the velocity of the water droplets, the first term on the right side of the equation ( 4) represents the resistance term of the air flow acting on the droplets, the second term is the buoyancy and gravity terms of the droplets, and the dimensionless velocity is obtained in the previous step to solve the N-S equation.

Icing calculation
The final step of numerical simulation is ice formation calculation and ice shape generation, using the ICE3D module.The calculation of this module is based on the classic Messenger model [7] , which divides the icing surface into several control volumes, and establishes mass and energy conservation equations for each control volume to solve the icing amount.The mass conservation equation and energy conservation equation are as follows [8] : Where w  is the density of water, LWC ,  are the liquid water content in air and the droplet overall collision efficiency on the wall, f u , f h are the velocity and thickness of the water film, respectively.The three items on the right of the equal sign in equation ( 5) are respectively the collection amount of water drop impact, the evaporation amount of water and the total mass of ice.w is the physical property parameter of water and ice, the five items to the right of equation ( 6) are the heat of water droplets impacting on the wall, the latent heat of water evaporation and the heat of ice sublimation, the heat of freezing, the heat of radiation and the heat of convection.
In the icing calculation, the wing surface will become rough due to the influence of icing.Due to the disturbance effect of the surface rough structure on the air flow, the position of the flow transition will be greatly moved forward, and the convective heat transfer between the wall and the air flow will be greatly enhanced.Therefore, the effect of roughness on the wall convective heat transfer must be taken into account in the icing calculation.However, the mechanism of icing surface roughness is very complex, which is related to many factors, such as the flow stability of water film, the disturbance of water droplets and airflow, and so on.it is a coupled multi-scale problem, so it is difficult to simulate its characteristics by analytical method.therefore, it is generally not predicted in the icing numerical simulation, but calculated by the empirical formula obtained from the experiment.The equivalent sand roughness height model proposed by Shin et al. [9] is used to calculate the roughness, and the equivalent sand roughness height is related to the liquid water content, icing temperature and water droplet diameter in the icing meteorological conditions.0.6839 where

Characteristics of different airfoils
See figure 2 and figure 3 for the profile comparison of three different types of airfoils and the lift-drag pole curves of three airfoils at Reynolds number of 500,000.The chord length of all airfoils is c=1m.In icing calculation and analysis, the spanwise flow is highly similar, and the length is only 0.01c, which can be approximately regarded as a two-dimensional problem.

Selection of icing parameters
The selection of icing parameters needs to consider the scope of application of three different airfoils and the most likely icing conditions.The aerodynamic characteristics of the three airfoils are different, and the models used are also different.SC (2)-0714 airfoil is mainly suitable for medium and large transport aircraft, and the cruise Mach number is about 0.8, which is suitable for working in high subsonic conditions; GAW-2 airfoil is mainly used in general-purpose aircraft because of its excellent lift-drag ratio and maximum lift characteristics; NLF (1)-0215F airfoil has low drag coefficient both cruising and climbing at 9 million Reynolds number, which is used in high-performance single-engine general-purpose aircraft [10] .Due to the different design ideas and purposes of the three airfoils, it is necessary to select appropriate parameters to take into account the working conditions of the three airfoils as much as possible in order to compare the icing conditions and ice shapes of the three different airfoils.Since the icing phenomenon mainly occurs when the air pressure is low and passes through the clouds, taking into account the climatic conditions of different regions of the world, the altitude of the airport, the working height range of different aircraft, and the climbing and falling rates during take-off and landing, we choose the air pressure altitude of 3000 meters and the icing time of 10 minutes as the final simulation parameters.In order to make the simulation results closer to reality, the constraints of other atmospheric conditions are determined by the continuous maximum icing state in Appendix C of China Civil Aviation Regulations 25th Airworthiness Standard for Transport aircraft (CCAR-25-R4).
The maximum continuous intensity of atmospheric icing state (continuous maximum icing state) is determined by three variables: cloud liquid water content, average effective diameter of cloud water droplets and surrounding air temperature.The interrelationships of these three variables are listed in figure 4. The icing limit envelope expressed by height and temperature is listed in figure 5, The relationship between cloud liquid water content and droplet diameter and height can be determined in figure 4 and figure 5.The liquid water content of the cloud layer in the continuous maximum freezing state beyond the horizontal range of 17.4 nautical miles is determined by multiplying the liquid water content of figure 4 by the corresponding coefficient in figure 6 [11] .

Influence analysis of icing parameters
From the above, it can be seen that temperature, liquid water content and average droplet diameter are coupled with each other, and we select temperature and MVD as two atmospheric parameters and flight speed and angle of attack as two key variables to analyze the icing parameters of the airfoil.

Effect of icing temperature.
The influence of icing temperature on ice shape is studied.The calculated boundary conditions are shown in table 1    Comparing the same airfoil with different temperatures, it can be seen from the figure that the ice mass distribution is the most uniform when the temperature is -4.5 ℃.Due to the overflow of water droplets, a large amount of clear ice is formed at the edge of the water droplet capture zone of the upper and lower airfoils, but the ice shape is not thick and the transition is smooth, while when the temperature is -7 ℃, the upper and lower sheep horn ice is formed in the upper left position of all airfoils, and the total mass of ice accumulation reaches the maximum.And the length of the upper ice corner reaches the maximum.As the temperature rises further, the corner ice gradually moves downwards.When the temperature is below -15 ℃, the ice shape gradually degenerates into rime ice, and the ice shape covers the largest range at -30 ℃, when about 20% of the wing surface is already covered with ice.It can be seen that no matter what kind of airfoil, the effect of temperature on icing is the same as the change trend of ice shape when the temperature changes.
Compare the performance of different airfoils after icing at the same temperature.List the total ice accumulation and maximum horn ice length converted into 1C span for three types of airfoils at different temperatures, as shown in the table 2 below: According to the total ice mass, the ice mass of the three airfoils increases first and then decreases with the decrease of temperature, and reaches the maximum at -7℃.The maximum ice mass of supercritical airfoil is 1078g, and the minimum is 829.5 g of laminar airfoil.The total ice mass of supercritical airfoil is 29.96% more than that of laminar airfoil.The three airfoils have the lowest ice mass at -30℃, and the ice mass of the high lift airfoils is lower than that of the laminar airfoils.
From the comparison chart of ice shapes, it can be seen that the temperature at the maximum horn ice of the three types of airfoils is around -9℃.Therefore, a comparison table of the maximum horn ice length near this temperature is listed for further detailed analysis, as shown in the table 3.
Table 3 It can be seen that the laminar airfoil has grown the longest horn ice near -7℃, while the supercritical airfoil and high lift airfoil both have the longest horn ice length at -9℃.The horn ice length of supercritical airfoils is greater than that of high lift airfoils and greater than that of laminar airfoils.When the laminar flow airfoil reaches -10℃, the length of the horn ice formed on the lower wing surface is greater than that on the upper wing surface.However, when the horn ice length of the supercritical airfoil reaches its peak at -9℃, the ice shape will transition from clear ice to rime ice more quickly compared to other airfoils as the temperature decreases.Specifically, the total mass of ice and the decay rate of the horn ice length are faster.

Effect of average droplet diameter.
The effect of average droplet diameter on ice shape is studied.The selected boundary conditions are shown in table 4, and the specific ice shape is shown in figure 10, figure 11 and figure 12.As can be seen from the figure, the ice angle of each airfoil increases with the decrease of MVD, and the maximum thickness is about 24mm.With the increase of the diameter of water droplets, the coverage of ice increases, but the maximum thickness of ice decreases obviously, the maximum thickness of ice is not more than 6.5 mm at 40 μm, the ice thickness transition is smooth, and the amount of ice formation is minimum, all airfoil ice forms are characterized by relatively smooth frost and ice.The supercritical airfoil has the largest amount of ice mass captured, and its distribution is also the most dispersed.5, it is obvious that the laminar airfoil has the maximum ice mass and ice angle length at MVD = 20 μm, while the high lift airfoil and the supercritical airfoil have the maximum ice angle length at MVD = 15μm, when MVD = 20μm, the maximum amount of accumulated ice is obtained.Based on the NLF(1)-0215F laminar airfoil with the least ice accumulation, the ice accumulation of SC(2)-0714 supercritical airfoil is 11.7% higher than that of laminar airfoil, and the GAW-2 high lift airfoil is 6.7% higher than that of laminar airfoil.

Effect of speed.
In the course of flight, the aircraft generally only in the take-off and landing conditions will have a larger speed change.Therefore, the simulation is carried out in a relatively lowspeed environment, and the specific boundary conditions are shown in table 6.As can be seen from the figure13, figure14 and figure15, the horizontal contrast, regardless of the airfoil, with the increase of speed, ice coverage increases, the maximum thickness also increases, as can be seen in figure 16, the three airfoil ice accumulation with the speed of linear increase; For the GAW-2 airfoils and SC(2)-0714 airfoils, the longitudinal comparison shows that the airfoils with the velocity equal to 100 m/s have obvious ram-horn characteristics.However, NLF(1)-0215F could not form a sharp ice-type.The flow field characteristics of NLF(1)-0215F laminar airfoil make the velocity distribution near the leading edge wall more reasonable, and make it less easy to freeze during the acceleration of the aircraft take-off.As can be seen from figure 17, figure 18 and figure 19, with the increase of the angle of attack, the icing position moves to the lower wing, and the coverage of the ice shape increases, but the maximum thickness of the ice shape decreases slightly.The ice angle characteristic of GAW-2 high lift airfoil is the smallest when the angle of attack is 0 °, and the upper and lower ice angle expansion angle of NLF(1)-0215F laminar airfoil is the smallest.And when the angle of attack increases gradually, no matter which kind of airfoil, the expansion angle of the upper and lower ice angle remains basically unchanged.

Conclusion
Through a comprehensive comparison of the effects of the four parameters on the icing process, it can be seen that when the temperature, average droplet diameter, flight speed and angle of attack change, the ice profiles of three different airfoils have the same trend.Among the four parameters, the icing temperature and the average droplet diameter have an important influence on the types of ice shape.when the temperature is -7℃ and the average droplet diameter is about 20μm, it is generally clear ice. the total ice mass is also the largest, and the temperature has a greater influence on the ice type than the average droplet diameter.When the temperature or the average droplet diameter increases or decreases, the ice shape will gradually transition to mixed ice and eventually become frost ice with loose texture and round shape.In a certain range, the flight speed is proportional to the total mass of ice, and the increase of the flight speed will aggravate the formation of the ice angle, while the angle of attack directly determines the relative position of the ice angle and has a certain influence on the maximum thickness of the ice layer.
For different airfoils, the NLF(1)-0215F laminar flow airfoil exhibits the best overall performance.This airfoil exhibits excellent sensitivity to changes in average water droplet diameter and flight speed, with no particularly prominent ice angle characteristics observed when the parameters change.When the angle of attack changes, the change in the position of the ice depression is also minimal.Compared to the SC(2)-0714 supercritical airfoil, the overall performance is the worst.When various icing parameters change, the geometric characteristics of the ice shape change significantly, and it has the largest ice angle length, ice accumulation variation, and peak among the three airfoils.

Figure 3 .
Figure 3.Comparison of lift-drag pole curves of three airfoils.

Figure 4 .
Figure 4.The relationship between MVD and LWC in continuous maximum icing state.

Figure 5 .
Figure 5.The relationship between ambient temperature and air pressure height in continuous maximum icing state.

Figure 6 .
Figure 6.Relationship between LWC of continuous maximum icing state and horizontal distance of cloud layer.

Figure 16 .
Figure 16.Variation of ice accumulation of different airfoils with flight speed.

3. 3 . 4 .
Effect of angle of attack.Similar to the speed of flight, the angle of attack of the wing is usually changed only during take-off and landing.The parameters selected are shown in table7.

Table 1 .
. The boundary condition of temperature effect on icing.

Table 2 .
Variation of ice accumulation of different airfoils with temperature.
. Variation of maximum horn ice length of different airfoils with temperature.

Table 4 .
Boundary conditions of the effect of average droplet diameter on icing.

Table 5 .
Variation of ice accumulation of different airfoils with average droplet diameter.

Table 6 .
Boundary conditions of the effect of Flight Speed on icing.

Table 7 .
Boundary conditions for the effect of flight angle of attack on icing.