Research on icing scaling technology for large civil aircraft icing wind tunnel test

This article explores the icing scaling technology for large civil aircraft icing wind tunnel tests. Based on the typical critical icing conditions of large civil aircraft and the calibration of icing wind tunnel, and through the similarity analysis of water droplet trajectories, water collection, and energy balance, four similar parameters, namely modified inertia parameter, drop energy transfer parameter, stagnation freezing coefficient, and accumulation parameter, were selected as similarity criteria for icing scaling. Based on this criteria, icing scaling was conducted on the critical icing conditions of large civil aircraft, and the scaling results were evaluated by icing code. The results show that the water droplet collection and the ice shape before and after the scaling are in good agreement, and the similarity criteria used are appropriate. Finally, icing wind tunnel test was conducted in 3m × 2m test section using scaled icing conditions. The test results show that the main characteristics of the experimental ice shape are in good agreement with the calculated ice shape, and the calculated ice shape is more critical. The calculated ice shape can be used as a critical ice for aerodynamic wind tunnel tests and flight tests with simulated ice.


Introduction
Ice accumulation during flight poses a serious threat to flight safety [1][2][3][4].In order to be allowed to fly in icing conditions, the applicant must demonstrate the safety of the aircraft flying in icing conditions.Firstly, it is necessary to study the icing characteristics of aircraft, usually through a combination of numerical simulation, icing wind tunnel tests, natural icing flight tests, and other means [5].The icing wind tunnel is mainly used to confirm and validate the results of numerical simulations [6].In order to ensure that the results of the icing wind tunnel test are consistent with the actual icing, the ideal method is to use a full-size model for testing in desired icing conditions.However, due to the size of the icing wind tunnel and its ability to simulate flight and meteorological conditions, this method is often difficult to achieve [7].For example, when conducting icing wind tunnel tests on large civil aircraft, critical icing conditions in some scenarios are not within the well calibrated range of the icing wind tunnel.In addition, if the wind speed is too high, the ice shape may break and fall off under the action of aerodynamic forces, making it impossible to obtain a complete ice shape.Therefore, it is necessary to scale icing conditions and maintain consistent icing characteristics before and after the scaling.The research on icing similarity theory and similarity criteria has been ongoing since the 1950s and has formed a series of similarity criteria for different application scenarios [8][9][10].This article will determine applicable similarity criteria based on the calibration of the icing wind tunnel and the typical critical icing conditions of the large civil aircraft.Some reference conditions will be scaled, and the icing codes will be used to compare the water droplet impact characteristics and ice shape before and after the scaling.Finally, the criticality of the calculated ice shape was verified through icing wind tunnel tests.

Critical ice shape and critical icing conditions
Critical ice shape is the aircraft surface ice shape formed within required icing conditions, which results in the most adverse effects for specific flight safety requirements [11].For an aircraft surface, the critical ice shape may differ for different requirements (for example, stall speed, climb, aircraft controllability, control surface movement, control forces, air data system performance, dynamic pressure probes for control force "feel" adjustment, ingestion and structural damage from shed-ice, engine thrust, engine control, and aeroelastic stability).The icing conditions that generate critical ice shapes are called critical icing conditions.In order to obtain the critical icing conditions, it is necessary to develop criteria for determining the critical ice shape according to different requirements and conduct parameter sensitivity analysis within the flight envelope and meteorological envelope to determine the critical ice shape and corresponding critical icing conditions based on the criteria.The critical icing conditions for the wing and tail of a civil aircraft obtained through numerical simulation are shown in Table 1.This result needs to be verified through icing wind tunnel tests.This article will use the critical icing conditions in Table 1 as reference conditions for icing scaling research.

Icing scaling
The conditions that affect icing are mainly divided into two categories: flight conditions and meteorological conditions.Flight conditions include flight velocity, angle of attack, altitude (pressure), and flight time, while meteorological conditions include ambient temperature, liquid water content, and median volume diameter.Icing scaling generally does not involve angle of attack.When there is geometric scaling in the experimental model, the influence of geometric scaling should also be considered.The two experimental models involved in this article are both full-size and do not involve geometric scaling.Therefore, the icing scaling here mainly involves six parameters: flight velocity, altitude (pressure), flight time, ambient temperature, liquid water content, and median volume diameter.

Selection of similar parameters
3.1.1Droplet trajectory similarity.Using the modified inertia parameter K0 defined in formula (1) as a similar parameter for water droplet trajectories [8].In the formula: K is the dimensionless inertia parameter, and calculated according to formula (2); /  is the dimensionless droplet range parameter, calculated according to formula (3); MVD is the median volume diameter, and d is the diameter of the tangential circle at the leading edge of the airfoil,   is the density of water,   is air viscosity, Reδ is the dimensionless Reynolds number based on the median volume diameter.
In order to ensure similar water droplet trajectories, (K0)S=(K0)R should be met before and after scaling, where S represents the scaled state and R represents the reference state.

Water collection similarity.
Matching accumulation parameter   ensures that water collection is similar [8], which means (  )S= (  )R.The calculation of   is shown in formula (4),   is the ice density, LWC is the liquid water content,  is the icing duration time.
The calculation of  is shown in formula (5), and the calculation of n0 is shown in formula (6), where   is the freezing point temperature,  , is the specific heat of water,   is the latent heat of freezing, b is the relative heat factor.The air energy transfer parameter θ is calculated according to formula (7).In formula (7),   is the latent heat of evaporation,   is the water vapor pressure,   is the total pressure, ℎ  is the gas phase mass transfer coefficient, ℎ  is the convective heat transfer coefficient.The calculation of b is shown in formula (8), where  0 is the dimensionless stagnation collection coefficient and calculated according to formula (9).

Icing Scaling process
The scaling process is shown in Figure 1, where the determination of flight velocity and pressure is not in any particular order, as follows: a) Flight velocity V.The flight velocity is generally obtained by directly specifying.When selecting the flight velocity, it is necessary to consider the calibration of flow field and cloud field in the icing wind tunnel.Generally, the closer the velocity is to the reference velocity within the well calibrated range, the better.In addition, to prevent ice from falling off, the velocity should not be too high.b) Pressure (altitude) Pst.Considering the convenience of test and the insignificant impact of pressure on ice shape, the pressure (altitude) is also specified.Generally, the local pressure (altitude) of the icing wind tunnel is selected.c) Static temperature   .Scaling static temperature by matching droplet energy transfer parameter .d) Median volume diameter (MVD).Scaling MVD by matching modified inertia parameter.e) Liquid water content (LWC).Scaling LWC by matching the stagnation freezing coefficient n0.LWC needs to be determined through iteration, and in practical applications, an error of n0 before and after scaling within 10% is sufficient accurate.f) Icing duration time .Scaling duration time by matching the accumulation parameter   .

Evaluation of icing scaling results
The icing scaling results are shown in Table 2. Compare the droplet collection coefficient and ice shape before and after scaling using icing code.This code uses the panel method to calculate the air flow field, the Lagrange method to calculate the trajectory of water droplets, and the Messenger thermodynamic model to calculate the ice growth process.The comparison results of droplet collection coefficient and ice shape are shown in Figure 2 to Figure 5.It can be seen from the figure that the droplet collection coefficient before and after scaling is well matched, and the main characteristics such as ice horn height and angle are basically consistent.The ice shape in scaled icing conditions is more critical.

Icing wind tunnel test verification
Icing wind tunnel test was conducted in 3m × 2m test section using scaled icing conditions to obtain the ice shape.The experimental model adopts a vertical installation method and uses a rotary table to control the angle of attack, as shown in Figure 6.Perform pressure matching before the start of the experiment to ensure that the pressure distribution on the airfoil surface is consistent with theoretical calculations.The icing situation of the model in the wind tunnel is shown in Figure 7.The ice shape is obtained by thermal knife cutting and laser scanning, and three sampling points are set along the spanwise direction to obtain two-dimensional ice shapes [12].The comparison between the experimental ice shape and the calculated ice shape is shown in Figures 8 and 9. Figure 8 shows that the icing limit of the calculated and experimental ice shape is consistent, and the projection height of the calculated ice horn on the positive lift surface is greater than that of the experimental ice horn.Therefore, the calculated ice shape is more critical [13].The icing code used lacks enough ability to simulate the lower ice horn of supercritical airfoils.Figure 9 shows that the height and angle of the upper ice horn of the calculated ice shape are greater than those of the experimental ice shape, while the angle of the lower ice horn is consistent with the experimental ice shape, and the height is slightly smaller.

Conclusion and prospect
The comparison of icing characteristics in reference and scaled icing conditions using icing code shows that the water droplets collection characteristics and ice shape are in good agreement, and the scaling results are effective.The scaling process and similarity criteria used are appropriate.The experimental results of the icing wind tunnel indicate that the main characteristics of the experimental ice shape are in good agreement with the calculated ice shape, and according to the law for determining the critical ice shape [13], the calculated ice shape is more critical.The icing calculation program used lacks the ability to simulate the lower ice horn of supercritical airfoil, but it does not affect the judgment of the criticality of the ice shape.The calculated ice shape can be used as critical ice shape for aerodynamic wind tunnel tests and flight tests.
In this study, we focus on two-dimensional airfoil ice-accretion scaling.Future research about icing scaling needs to address applications such as swept-back wing, rotorcraft, ice protection system and supercooled large droplet (SLD).For example, for testing of ice-protection systems, the main objectives may be to match scale and reference non-dimensional impingement limits or water loading.For supercooled large droplet, the icing process of SLD includes the phenomena of fragmentation, collision, splashing, and secondary overflow, which makes the icing process and its impact more complicated than that of regular-sized droplets.The primary goal of scaling SLD is to reduce droplet diameter.

Figure 4 .Figure 5 .
Figure 4. Ice shape comparison results of case 1 Figure 5. Ice shape comparison results case 2

Table 2 .
Scaling results of critical icing conditions