Experimental Study on Ice Shedding Behaviors for Aero-Engine Fan Blade Icing during Ground Idle

Abstract

Fan blade icing can affect efficiency and aerodynamic stability, and the shed ice may be sucked into the core of the engine, causing adverse effects or even damage to the compressor components. Ice accretion and shedding are among the key issues in engine design and tests. But they have not been clearly understood. In this work, ice shedding from rotating aero-engine fan blades during continuous icing is experimentally investigated under the relevant airworthiness requirements. The phenomena of icing and ice shedding under different ambient temperatures and engine speeds are recorded to obtain the ice-shedding time and the characteristic length of the residual ice. Force analysis is used to understand the corresponding behavior. The degree of ice-shedding balance $D_b$ is defined to explore the symmetry of ice shedding. The results show that the shedding time is significantly affected by the rotational speed, and the characteristic length will first shorten and then grow as the ambient temperature decreases. When the ice shedding is completed instantaneously, $D_b$ will show a violent shock. There is a critical ambient temperature, below which the ice accretion will worsen significantly as temperature decreases. For aero-engine fan blade icing tests during ground idle, the critical ambient temperature ranges from −${5 }^{\circ }$C to −${9 }^{\circ }$C. In order for the ice to shed faster, the engine speed has to reach a threshold. This study can shed light on the preliminary characteristics of ice shedding from rotating components and provide guidance and a data basis for the numerical simulation of fan blade icing and the design of an aero-engine.

1. Introduction

There are supercooled water droplets in the atmospheric cloud environment. If an aircraft encounters such conditions during flight, ice can form on the different parts of the aircraft, such as the wing, the propeller, the engine, the various sensors, etc., resulting in a serious hazard to flight safety [1,2,3,4]. Engine icing under supercooled clouds will distort the air flow, reduce the air intake to cause an uncontrolled loss of thrust, and even cause flameout in serious cases [5,6,7,8]. Meanwhile, the accreted ice may be shed and sucked into the core of engine. This can result in structural damage to the compressor components, a decrease in compressor efficiency and aerodynamic stability, as well as combustion instability [9,10,11,12]. Therefore, it is particularly important to know the ice accretion and shedding behaviors in the engine induction system well.

To understand the ice accretion process in an engine in a supercooled cloud environment, the icing on the various parts of the the surfaces that are exposed to outside air and possibly impinged by the droplets have been studied experimentally and numerically. These components include nacelle [13,14], rotating spinner [11,15,16,17,18], rotating blades [6,19,20,21,22], inlet guide vanes [23], inlet strut [24], splitter [25], and so on. Additionally, various icing protection systems have been studied and developed to avoid icing. There are two commonly used methods at present, some using electrical heating and most relying on hot air bled from the engine compressor [24,26,27,28]. However, there is generally no special anti-/de-icing system for aero-engine fan blades; ice accumulated on them can only be shed during natural rotation [29]. Thus, it is especially necessary to investigate the ice accretion and shedding from the engine fan blade. In terms of rotor blade icing, more attention is paid to the wind turbine [30,31] or the helicopter [32,33], while relatively little attention is paid to the engine fan blade, and most of it consists of numerical studies [6,19,22,34,35,36]. For example, Das et al. [19] have conducted a numerical study to investigate ice accretion on a turbofan engine booster rotor with high bypass and found thicker ice shapes at the leading edge of the blade and more pressure surface coverage towards the hub. In addition, their results showed that ice formation will increase with engine speed reduction and is very sensitive to the change in inlet temperature. Hayashi and Yamamoto [34] have developed an icing simulation model that takes into account both ice growth and ice shedding in turbomachinery and can predict the time at which the ice shedding occurred. They also applied the model to a jet engine fan to study the effect of ice accretion and shedding on the flow field and found a drastic change in the engine performances due to ice growth or shedding in both the fan rotor and the fan exit guide vane [6]. Chen et al. [35] have developed a numerical ice-shedding model by taking into account the failure of ice itself and the failure of the interface between ice and the fan blade surface to predict ice shedding. They found that the ice shedding will occur at 73.6% design speed and vibration loading is an efficient way to de-ice under their given conditions. Zhou et al. [36] have performed a critical icing temperature analysis of aircraft engine fan during ground idle by using FENSAP-ICE and found the critical icing temperature by comparing the icing mass in different cases.

In terms of experiments, Tian et al. [22] have performed experiments by exposing a scaled aero-engine spinner-fan model in an icing research tunnel with typical wet glaze and dry rime icing conditions to reveal the characteristics of the ice growth process on the rotating fan blades and characterize the effects of ice accretion on the performance of the fan rotor. Their experimental results showed that the pressure increment of the air flow can reduce up to 60% after passing the ice fan rotor for 360 s under rime icing conditions and that the needle-shaped ice structure formed under glaze ice conditions can cause the airflow to depressurize after passing the ice fan rotor. However, almost none of these studies, whether experimental or numerical, have comprehensively considered the behaviors of ice shedding from the aero-engine fan blades under icing conditions, such as icing state, ice-shedding time and position, etc.

To study engine icing in atmospheric icing conditions, the engine icing test platform based on a refrigeration house has been developed [37]. The present work is to investigate and demonstrate the shedding behaviors of ice on aero-engine fan blades. The effects of engine speed and ambient temperature on the characteristics of ice shedding, mainly including ice-shedding time and the length of residual ice after shedding, are elaborated in detail. The phenomenon of periodic ice shedding for an engine in the ground idle state and the rule of ice shedding under various icing conditions are discovered. Then, a force analysis of ice shedding is performed to explain the changing trend in ice-shedding behavior. Finally, the symmetry of ice shedding by defining the degree of ice-shedding balance is investigated.

2. Experimental Method

2.1. Experimental Setup

A set of experimental simulation systems is designed, as shown in Figure 1. It mainly consists of four parts: a blowing system, a spray system, an engine simulator, and a refrigeration house. The blowing system can provide a maximum wind speed of 9 m/s, which meets the test requirements of the engine simulator during ground idle in the present work.

The spray system consists mainly of a spraying device, an air supply system, a water supply system, and a control system. The spray device with size of 1200 × 1200 mm is connected to the blowing system and installed at its outlet. It has 7 rows of spray bars, and each bar has 7 positions in which to arrange spray nozzles. Through the cooperation among the air supply system, the water supply system, and the control system, the parameters of the spray can be adjusted effectively.

The object of this test is a simple engine simulator. The rotating diameter of the fan blades is 500 mm. Due to the small diameter of the engine simulator and the large size of the motor required to meet the driving power demand, the motor cannot be installed inside the engine simulator. The simulator employs a commutator design with a variable-frequency motor installed in the back of the engine simulator. This motor is connected by the commutator and bearing to drive the fan of the engine simulator. The maximum speed can reach 4220 rpm. According to the cloud uniformity calibration results (cloud uniformity at a distance of 2 m meets the test requirements), the distance between the spray device and the nose cowls of the engine simulator is set to 1500 mm in the experiment.

The refrigeration house is commercial and the minimum refrigeration temperature can be as low as −${20 }^{\circ }$C. In the experiment, the temperature is monitored by a temperature controller (XMT-JK808, Yutaiyibiao, Ltd., Yuyao, China) with platinum resistor (PT100, Heraeus, Hanau, Germany). The measurement accuracy is within ±${0.5 }^{\circ }$C.

2.2. Spray Parameter Measurement and Calibration

The spray system must be calibrated before the experiment, which mainly includes the median volumetric diameter (MVD) of the drop and the liquid water content (LWC) of the spray. In addition, wind speed, cloud uniformity, and droplet temperature need to be determined or evaluated. Figure 2 shows the schematic diagram of the positions of each measuring instrument used to calibrate the spray system. The cross-sections selected to calibrate are 2 m and 2.5 m from the spray device.

Wind speed is measured with a hot-wire anemometer with measuring range 0.01 to 20 m/s and accuracy 0.5%. Because the ejected fluid from the spray system will affect the wind speed downstream, the wind speed is co-determined by the air pressure upstream in the spray system and the rotational speed of the fan in the blowing system. Therefore, a series of air pressures of the spray system used in the test is set in the process of calibration first, and then the rotational speed of the fan is adjusted to reach the required wind speed.

After the wind speed is determined, a uniform cloud has to be formed to determine the cloud characteristics of MVD and LWC. An icing grid is used to measure the uniformity of the spray. It is a 1200 × 1200 mm grid, and the grid mesh is 60 × 60 mm. Similarly to the method used by Ide and Oldenburg [38], the test is carried out at an environmental temperature of −${18 }^{\circ }$C to ensure that ice can form on the grid and that the face of the grid has a high collection efficiency. After continuous spraying for 15 min, the thickness of the icing is measured at each position on the grid to judge whether the spraying is uniform in the experimental section. Based on APR5905 [39], the LWC should not vary by more than ±20% from that of the test section centerline. According to the measurement, the area of the test section that meets the uniformity requirement is greater than 0.9 ${\mathrm{m}}^2$ at a distance of 2 m, which is much larger than the experimental requirement.

The LWC is measured by an icing blade, which is 400 mm long, 40 mm deep, and 3 mm thick. The test is also run at ambient air temperature of −${18 }^{\circ }$C and the spraying time is also 15 min. An industrial spray laser particle size analyzer (Winner319, Jinan Winner Particle, Ltd., Jinan, China) is used in the droplet size calibration. Its measuring range is 1 to 500 $\mathsf{\mu }$m and the error is within 3% in the range of 0 to 40 $\mathsf{\mu }$m. The measurement time is 5 min, and whether the droplet size can be kept within the fluctuation range of 3 $\mathsf{\mu }$m during the process is monitored to evaluate the stability of spray. After all the tests, it is obtained that the MVD ranges from 15 to 96 $\mathsf{\mu }$m and the LWC ranges from 0.05 to 7.7 ${\mathrm{g/m}}^3$.

The spray temperature cannot be measured, so it is roughly estimated through numerical simulation by Fluent. As shown in Figure 2, it is the change in the temperature difference $T_{diff}$ between water droplets (25 $\mathsf{\mu }$m diameter) and the environment with horizontal distance x under different ambient temperatures T. After a distance of 0.5 m, the water drop temperature is basically the same as the air flow temperature.

2.3. Experimental Measurement

In this work, since the shape of the ice on the blade and the mass of the shed ice could not be measured, two other key parameters are mainly measured: the time of ice shedding $t_s$, and the characteristic length of the residual ice $l_c$. During the experiments, a high-speed camera was used to record the ice-shedding phenomena, with 20 to 30 pictures per second, based on the requirements in different cases. By comparing the images, the time between the start of spraying and ice shedding can be obtained and considered as $t_s$. $l_c$ is defined as

$$l_c={\displaystyle \frac{l_r}{l_b}},$$

(1)

where $l_r$ is the length of residual ice on the blade after ice shedding and $l_b$ is the length of the fan blade, as shown in Figure 3. Each blade is numbered, so $t_s$ and $l_c$ can be measured and calculated for all blades. The measurement accuracy of $t_s$ is within 0.05 s, and the measurement error of $l_r$ is within 5%.

2.4. Experimental Conditions

The icing test is performed for the aircraft engine during ground idle. The environments should meet the conditions in Clause 33.68 (b), specified in the airworthiness regulations CCAR-33-R2 [40], including wind speed, cloud uniformity, LWC, MVD, and environmental temperature. In the test, the wind speed is fixed at 9 ± 0.2 m/s, the MVD is about 25 $\mathsf{\mu }$m, the LWC is approximately 0.954 g/m${\mathrm{g/m}}^3$, and the environmental temperature T varies from about −${1 }^{\circ }$C to −${9 }^{\circ }$C. The range of engine speed n is from 1800 to 3000 rpm. As a result, eight cases are carried out according to the test requirements, and

Table 1. The experimental cases and the mean temperature of air flow during the experiment.

Case	Set Temperature T (°C)	Engine Speed n (rpm)	Mean Temperature of Air Flow (°C)
1	−2	2400	−1.67
2	−3.5	2400	−3.48
3	−5	2400	−4.97
4	−7	1800	−7.08
5	−7	2400	−6.56
6	−7	2700	−6.53
7	−7	3000	−6.79
8	−9	2400	−8.89

gives the detailed parameters. The ejected water and air will affect the ambient temperature, so the measured air flow temperature is not necessarily equal to the set temperature and fluctuates over time. Table 1 gives the mean temperature of air flow for each case in the experiment. For convenience in the description, the set temperature for each case is used instead of the mean air flow temperature. The test time is 15 min, except for Case 4, for which the test time is longer than 1 h.

3. Results and Discussion

3.1. Effect of Environmental Temperature T

Figure 4 shows a series of images of ice accretion and shedding on fan blades with n = 2400 rpm when T is from −${2 }^{\circ }$C to −${9 }^{\circ }$C. When T = −${2 }^{\circ }$C, it is observed that ice does not form at the blade tip. The ice on blade 5 begins to break and partially shed at t = 149.10 s. Due to the small amount of ice on the leaves, it does not easily to fall off. During the recording time, the ice-shedding phenomenon occurs only on several blades. When T = −${3.5 }^{\circ }$C, there will be a more obvious phenomenon on ice shedding with an increasing amount of icing. Between t = 394.05 s and 397.55 s, ice on most blades appears to fall off. Ice on some blades falls off completely, as shown in Figure 4b t = 420 s. In the case of T = −${5 }^{\circ }$C, ice-shedding time is very concentrated, and a large amount of shed ice rotates along the inner surface of the fan cowl, as shown in Figure 4c t = 259.7 s. As the spraying continues, re-icing and ice shedding occur at the shedding site. In Figure 4d from t = 501.25 s to 590.05 s, a new phenomenon in ice shedding is found: ice on some blades sheds in small sections at T = −${7 }^{\circ }$C. As T drops to −${9 }^{\circ }$C, it takes a long time for the ice to break off. At t = 360.10 s, ice on blade 8 fractures in the middle and sheds. After 0.05 s, ice on about half of the blades sheds at the same time and a lot of crushed ice appears along the surface of the casing. At t = 361.95 s, the ice on all blades completes the first shedding. Compared with the blades on which ice shedding occurs when the environmental temperature is high, ice shedding in this case is not complete—there is still ice remaining, as shown in Figure 4e at t = 361.95 s. This is because, at lower temperature, stronger adhesion is formed between the ice and the blade surface, and the ice breaks rather than falling off the blade surface.

Figure 5 shows $t_s$ changing with T as n = 2400 rpm. The error bars indicate the mean absolute deviation (MAD). It should be noted that $t_s$ specifically refers to the time of first shedding of each blade. To show the characteristics of $t_s$ more comprehensively in different cases, four types of statistical time on ice shedding are given. The average shedding time $t_{sa}$ represents the average time of ice shedding from all fan blades that exhibited ice shedding during the test. The average time of intensive shedding $t_{si}$ is the average time of ice shedding in most fan blades, omitting the individually earlier or later shedding events. The other two times, $t_{se}$ and $t_{sl}$, represent the time of the earliest and the latest ice shedding, respectively. When T is higher than −${5 }^{\circ }$C, $t_{si}$ decreases with the decreasing temperature. It should be mentioned that the actual ice-shedding time is longer than the statistical ice-shedding time $t_s$ because most of the fan blades do not exhibit ice-shedding phenomena during the statistical time at T = −${2 }^{\circ }$C. When T is lower than −${5 }^{\circ }$C, $t_{si}$ will increase as T decreases. The reasons can be determined as, when T is close to ${0 }^{\circ }$C, although the ice adhesion strength is small, the ice builds up slowly and the amount of ice on the fan blades is small, making it difficult to shed. Both the ice adhesion strength and the rate of ice accretion increase with the decreasing temperature. As T decreases and progresses slightly away from ${0 }^{\circ }$C to about −${5 }^{\circ }$C, the latter is dominant. Thus, ice shedding occurs earlier. When T is sufficiently low, the former will be dominant, resulting in an increase in the time required to remove ice.

In addition, the occurrence of ice shedding may be too early if the ice adhesion strength is weak and too late if the ice adhesion strength is strong. At T = −${2 }^{\circ }$C, the MAD of $t_{sa}$ is great because the ice on most fan blades has not shed in the recording time and the ice on a few fan blades sheds too early. At −${3.5 }^{\circ }$C, only individual blades shed ice earlier and the MAD of $t_{sa}$ becomes much smaller. At −${5 }^{\circ }$C, the occurrence of ice shedding from all the blades is intensive and within 2 s. There is almost no difference between the four times. As T decreases to −${7 }^{\circ }$C, contrary to the case at −${3.5 }^{\circ }$C, the ice on individual fan blades sheds later and the MAD of $t_{sa}$ becomes larger again. T continuously decreases to −${9 }^{\circ }$C, ice shedding occurs intensively and within 2 s again. In summary, the phenomena on ice shedding change from no shedding on most fan blades, individual shedding earlier, intensive shedding, individual shedding later, to intensive shedding again from −${2 }^{\circ }$C to −${9 }^{\circ }$C.

The amount of residual ice after shedding is one of the key parameters for engine icing. Two characteristic lengths are calculated based on the lengths of residual ice on all fan blades measured. One is after the first shedding $l_{cf}$ and the other is after the end of the test $l_{ce}$. Figure 6 shows the two characteristic lengths at different environmental temperatures when n = 2400 rpm. The error bars also indicate MAD. From Figure 6, it can be found that $l_{cf}$ varies from 0.45 to 0.62 and is approximately equal to 0.6, except for T = −${5 }^{\circ }$C. Meanwhile, there are obvious differences among $l_{ce}$. At −${2 }^{\circ }$C, it is about 0.74. When T slightly drops to −${3.5 }^{\circ }$C, it dramatically decreases to about 0.39. Subsequently, $l_{ce}$ increases as the temperature decreases, and is about 0.9 at −${9 }^{\circ }$C. $l_{ce}$ is longer than $l_{cf}$ at −${2 }^{\circ }$C and −${9 }^{\circ }$C. For the former, it is because the amount of ice that accretes again after shedding is small at the higher temperature, which makes it not easy to shed. For the latter, it is because the ice adhesion strength is strong at the lower temperature. At −${3.5 }^{\circ }$C, $l_{ce}$ is obviously shorter than $l_{cf}$. This is because the amount of accumulated ice increases, but the ice adhesion strength is still relatively low. $l_{ce}$ and $l_{cf}$ are almost equal at −${5 }^{\circ }$C and −${7 }^{\circ }$C.

When n = 2400 rpm, from the amount of accreted ice (Figure 4), the ice-shedding time (Figure 5), and the characteristic length of the residual ice (Figure 6), it can be found that there is a critical temperature at about −${5 }^{\circ }$C, below which the amount of accreted ice obviously increases, $t_s$ prolongs, and $l_c$ increases. The icing temperature requires special attention ranges about from −${5 }^{\circ }$C to −${9 }^{\circ }$C, which basically agrees with the result that ranges from −${6 }^{\circ }$C to −${9 }^{\circ }$C by numerical simulation, evaluated based on the mass of accreted ice for an aircraft engine fan during ground idle [36].

After the test, the states of ice accretion on the fan blades experienced shedding in natural rotation at different environmental temperatures T at n = 2400 rpm are shown in Figure 7. The ice-formation rate will be higher and the ice will be firmer at a lower temperature. It can be seen that the height of residual ice on the blades increases as T decreases. This is due to the fact that, as T decreases, the frozen fraction increases, resulting in increasing the rate of ice growth. Although ice accretion on the spinner is not addressed in this paper, it can obviously be seen that needle-like ice is formed on the spinner when T is high, as shown in Figure 7 at T = −${2 }^{\circ }$C and −${3.5 }^{\circ }$C, which is basically consistent with the experimental results given by Li et al. [11] and Tian et al. [22].

3.2. Effect of Engine Speed n

The phenomenon of ice accretion and shedding on the fan blades at different engine speeds from 1800 rpm to 3000 rpm at T = −${7 }^{\circ }$C is shown in Figure 8. It should be noted that the same test conditions were used in the comparison, so Figure 4d and Figure 8b are the same. Because n = 1800 rpm is low, leading to a small centrifugal force, the ice is difficult to remove. As a result, icing on the blades is very serious, as shown in Figure 8a. For about the first 1 h and 10 min, there is a steady and continuous ice accumulating process on the blades. At t = 4400.47 s, ice on a few blades cracks and sheds. In the next 0.13 s, it can be seen that ice shedding occurs on almost all the blades. Although a small amount of ice still adheres on the edge of the blades, the shedding is relatively clean on the whole. Ice almost shed completely in a very short time. It is speculated that there may be two reasons: one is the large amount of ice accumulation, and the other is that the initial shedding causes the mechanical vibration of the fan or the engine. In the next few seconds, a huge amount of broken ice is driven by the fan to rotate along the surface of the casing. The smaller the broken ice, the easier it is to follow the air flow. At t = 4406.67 s, only a few large pieces of ice remain inside the fan housing.

As n increases to 2400 rpm, ice-shedding time decreases dramatically. Most of the ice shedding is completed around 272 s. When n = 2700 rpm, the time to complete the first round of ice shedding is approximately 207 s, and then re-icing and ice shedding occur in the blades, as illustrated in Figure 8c. The centrifugal acceleration will increase significantly with a rotational speed of 3000 rpm. Consequently, even a minimal accumulation of ice will be subjected to substantial centrifugal forces at such elevated rotational speeds, making ice near the blade tips relatively facile to dislodge. As a result, ice shedding occurs very early and the ice on blades 1, 4, and 7 has already shed before t = 120 s, as shown in Figure 8d. At t = 136.10 s, ice shedding occurs in half of the blades, and the ice on all blades has completed the first shedding before t = 157.30 s. At high rotation speeds, the period of ice accretion and shedding near the tip of the blades is short. Ice will accumulate and shed repeatedly. For example, blade 7 has twice experienced ice accreting and shedding processes within 270 s, as shown in Figure 8d, indicated by the arrows. However, ice near the root of the blades is still difficult to shed unless it accumulates in large amounts. Thus, icing on the root part is significantly more severe than on the tip part, as shown in Figure 8d, t = 360 s.

The force on the ice determines whether the ice will shed, and the rotational speed is a key factor affecting the force. $t_s$ under different engine speeds at T = −${7 }^{\circ }$C is shown in Figure 9. As n = 1800 rpm, $t_s$ is very long and the occurrence of ice shedding on all fan blades is very intensive in 1 s, as also shown in Figure 8a. Such a low rotational speed is not enough to cause ice to shed quickly. When n increases to 2400 rpm, although the ice on the individual fan blade sheds a little late, $t_s$ shortens dramatically to about 260 s on the whole. Next, $t_s$ stably decreases as n increases. In the meantime, ice shedding almost happens in a relatively concentrated time.

From Figure 5, it can be observed that $t_s$ mainly ranges from just over 200 s to over 400 s, with the maximum difference between different cases being about 200 s. From Figure 9, it can be observed that there is an order of magnitude difference in $t_s$ between low and high engine speeds. This indicates that, compared to T, n has a more significant effect on $t_s$.

Figure 10 shows $l_{cf}$ and $l_{ce}$ with different engine speeds when T = −${7 }^{\circ }$C. Except for n = 1800 rpm, both $l_{cf}$ and $l_{ce}$ gradually shorten as n increases from 2400 rpm to 3000 rpm. At n = 2400 rpm, the two lengths are substantially the same and equal to about 0.6. Because it is relatively easy to shed with the increasing amount of accreted ice, $l_{ce}$ is shorter than $l_{cf}$ at n = 2700 rpm and 3000 rpm. It should be noted that, when n = 1800 rpm, ice on fan blades almost completely shed, resulting in a large MAD, so the ranges of the two error bars both exceed the magnitude of the two lengths.

Similarly, when T = −${7 }^{\circ }$C, from the amount of accreted ice (Figure 8), the ice-shedding time (Figure 9), and the characteristic length of the residual ice (Figure 10), it can be found that there is a critical engine speed at about 2400 rpm, above which the amount of accreted ice reduces significantly, $t_s$ shortens remarkably, and $l_c$ gradually decreases.

Figure 11 shows the states of ice accretion after the test under different engine speeds n at T = −${7 }^{\circ }$C. At the same T, ice shedding is basically determined by n due to the same ice adhesion strength. For a lower n = 1800 rpm, ice is difficult to shed, resulting in a long icing time and a large amount of accreted ice. When a critical speed is reached, ice will shed as a whole. Therefore, although the amount of ice appears to be relatively small after the experiment (see Figure 11a), ice accretion is very serious during this process (see Figure 8a). From Figure 11b–d, for n = 2400 rpm to 3000 rpm, it can be found that the amount of residual ice decreases as n increases.

3.3. Ice Accumulation on the High-Pressure Side

Figure 12 shows the situations of ice accumulation on the high-pressure side of the blades after tests in different cases. From Figure 12a, it can be found that less ice is accumulated on the surface of the blade, while the ice mainly accretes on the leading edge of the blade. However, when T is relatively low, a large amount of ice accretes on the high-pressure side. In particular, in Figure 12c, it can be seen that the accreted ice has seriously blocked the flow channel at low engine speed for a long period of icing.

3.4. Explanation of Ice-Shedding Characteristics Based on Simplified Force Analysis

Ice shedding is a very complicated phenomenon, involving ice accumulating constantly, ice fracturing instantly, ice adhesion to the substrate, the vibration and deformation of components, etc. In addition, the force of ice under the action of airflow is complex, and, most importantly, many physical parameters of ice are still unclear. Here, a simple force analysis was used to explain the ice-shedding behavior. Figure 13 shows the schematic diagram of the force analysis, which only considers three main forces: the centrifugal force $F_c$, the ice adhesion force $F_a$, and the tensile failure force $F_t$.

Assuming that the shed ice is a whole body before shedding, the centrifugal force $F_c$ can be expressed as

$$F_c={\displaystyle \frac{1}{2}}m{\omega }^2(l+l_f),$$

(2)

where m is the mass of the shed ice, $\omega$ is the angular velocity, l is the distance between the tip of the rotating component and the axis of rotation, and $l_f$ is the distance between the fracture surface and the axis of rotation. After spray time $t_{spray}$, m can be estimated as

$$m={\int }_0^{t_{spray}}{\dot{m}}_i\left(t\right)dt,$$

(3)

where ${\dot{m}}_i=n_0{\beta }_{total}{V}_{\infty }{A}_{t}LWC$ is the rate of mass growth. $n_0$ is the frozen fraction, ${\beta }_{total}$ is the total collection efficiency, $V_{\infty }$ is the equivalent freestream velocity, and $A_t$ is the total frontal area of the rotating component or the accreted ice to the freestream direction at t.

The ice adhesion force $F_a$ can be expressed as

$$F_a=\tau (l-l_f)w,$$

(4)

where $\tau$ is the ice adhesion strength and w is the equivalent width of ice in contact with the surface.

The tensile failure force $F_t$ can be estimated as

$$F_t=\sigma A_f,$$

(5)

where $A_f$ is the area of fracture surface and $\sigma$ is the tensile failure stress.

In the moment before the appearance of ice shedding $t_s$, these three forces are in an instantaneous balance. Assuming that ${\beta }_{total}$ does not change over time and ${\dot{m}}_i$ is constant under the same conditions, ice-shedding time $t_s$ can be roughly predicted as

$$t_s={\displaystyle \frac{2\sigma A_f+2\tau w(l-l_f)}{{\dot{m}}_i(l+l_f)}}·{\displaystyle \frac{1}{{\omega }^2}},$$

(6)

and the characteristic length of residual ice $l_c\sim l_f/l$ can also be roughly predicted as

$${\displaystyle \frac{l_f}{l}}={\displaystyle \frac{2\sigma A_f/l+2\tau w-m{\omega }^2}{2\tau w+m{\omega }^2}},$$

(7)

From Equation (6), it can be seen that $t_s$ is mainly determined by $\omega$ when other icing parameters are the same. This is consistent with the experimental results (Figure 9). When $\omega$ is too low, the ice does not shed for a long time.

$\tau$ tends to increase steadily as temperature decreases [41], $\sigma$ is expected to increase approximately linearly at temperatures from −${5 }^{\circ }$C to −${45 }^{\circ }$C [42], and ${\dot{m}}_i$ would increase rapidly at first and then slow down until stable as temperature decreases [43] due to the influence of $n_0$. Combined with Equations (6) and (7), the possible reasons for $t_s$ and $l_c$ in Figure 5 and Figure 6 to show a trend of first decreasing and then increasing with decreasing temperature are analyzed as follows. Only slight ice accumulation would form on the blades when T is close to ${0 }^{\circ }$C, and less ice accretion will make it difficult to fall off, resulting in longer $t_s$ and larger $l_c$. As T decreases, ${\dot{m}}_i$ increases rapidly, causing a rapid increase in the mass of the accreted ice. However, since T is not too low at the moment, $\tau$ and $\sigma$ are not high. Therefore, $t_s$ and $l_c$ will decrease. While T drops to a certain level, the increasing rate of ${\dot{m}}_i$ starts to slow down. $\tau$ and $\sigma$ increase steadily yet. Thus, $t_s$ and $l_c$ will gradually reach a minimum at a critical temperature $T_c$. In the present experiment, $T_c$ is about −${5 }^{\circ }$C, as mentioned above. Next, $\tau$ and $\sigma$ continue to increase, and the increasing rate of ${\dot{m}}_i$ will gradually decrease with decreasing temperature. This will cause $t_s$ and $l_c$ to increase.

3.5. Degree of Ice-Shedding Balance

One of the issues with shedding is that only part of the ice on a blade falls off. The asymmetry of ice shedding can affect the rotational balance, causing unwanted vibration [8]. Figure 14 shows the schematic diagram on the state and symmetry of ice shedding with different numbers of blades. In the figure, b represents the blade and a represents the symmetry plane. To quantify ice-shedding symmetry, the degree of ice-shedding balance $D_b$ is defined. For two blades (Figure 14a),

$$D_b={\displaystyle \frac{\left|l_c\left(1\right)-l_c\left(2\right)\right|}{l_c\left(1\right)+l_c\left(2\right)}}\times 100\%,$$

(8)

$D_b$ = 0 corresponds to the complete symmetry of ice shedding and $D_b$ = 100% corresponds to complete asymmetry. For multiple blades, there will be multiple symmetric planes, and the balance degree for each symmetric plane should be calculated, where the maximum value is $D_b$. Thus, $D_b$ can be obtained for Figure 14b as

$$D_b=max(D_b\left(a1\right),D_b\left(a2\right),D_b\left(a3\right)),$$

(9)

where

$$D_b\left(a1\right)={\displaystyle \frac{\left|l_c{\left(1\right)}_{a1}-(l_c{\left(2\right)}_{a1}+l_c{\left(3\right)}_{a1})\right|}{l_c{\left(1\right)}_{a1}+(l_c{\left(2\right)}_{a1}+l_c{\left(3\right)}_{a1})}}\times 100\%,$$

(10)

where the subscript $a1$ represents the value of the component projected on the a1 axis. $D_b\left(a2\right)$ and $D_b\left(a3\right)$ can be obtained by the same calculation. Four four blades, there will be four planes of symmetry. Thus, $D_b=max(D_b\left(a1\right),D_b\left(a2\right),D_b\left(a3\right),D_b\left(a4\right))$ for Figure 14c. If there are m planes of symmetry, then

$$D_b=max(D_b\left(a1\right),D_b\left(a2\right),\cdots ,D_b\left(am\right))$$

(11)

Ice shedding does not occur simultaneously, so $D_b$ changes with ice shedding for each blade. Figure 15 shows the change of $D_b$ with time t in different cases. Before ice shedding occurs, it is considered that the icing on each blade is uniform and in equilibrium, that is, $D_b$ = 0. It can be seen that, in Case 3, although the residual ice after ice shedding is relatively small, $D_b$ is up to more than 30% in the ice-shedding process and changes significantly in a short period. This can cause sharp vibrations, making it dangerous. Except for Case 3, the maximum value of $D_b$ corresponding to other cases is about 15% and 20%. Among these cases, the ice-shedding time in Case 8 is the most concentrated, and, due to the low ambient temperature, large amount of icing, and large mass of shed ice, it is a harsh environment for icing safe operation and should be taken into account.

4. Conclusions

Ice shedding from the rotating fan blades of an aero-engine simulator is experimentally investigated during continuous icing in this paper. The effects of the environmental temperatures and the engine speeds on the ice-shedding time and the characteristic length of the residual ice are studied. Force analysis is performed to understand the behavior of ice shedding, and the degree of ice-shedding balance $D_b$ is defined to reflect the equilibrium in the ice-shedding process. The following conclusions can be drawn:

(1)

When the engine speed n is constant at 2400 rpm, the average of ice-shedding time $t_s$ is about 250 to 350 s and the characteristic length of the residual ice $l_c$ is about 0.4 to 0.6 in general. Both reduce first and then increase as the environmental temperature T decreases. Combined with experimental results and force analysis, it is indicated that there is a critical temperature $T_c$ at about −${5 }^{\circ }$C, below which the extent of ice accretion will be significantly aggravated, including the increase in the amount of accumulated ice, the prolongation in $t_s$, and the increase in $l_c$;

(2)

When the engine speed n is low, it can take hours for ice shedding, resulting in severe ice accretion. As n increases, $t_s$ decreases drastically and then slowly to one to two minutes or less, and $l_c$ gradually reduces. There is a critical engine speed $n_c$, above which the purpose of natural ice shedding under rotation can be achieved initially within minutes. $n_c$ is about 2400 rpm when T = −${7 }^{\circ }$C in the experiments;

(3)

The degree of ice-shedding balance $D_b$ can reach up to 30% in severe cases. The ice in Cases 3 (T = −${5 }^{\circ }$C, n = 2400 rpm) and 9 (T = −${9 }^{\circ }$C, n = 2400 rpm) falls off in a short period, resulting in sharp fluctuations in $D_b$, which are dangerous conditions that need attention for icing operation;

(4)

Combining the amount of ice accretion, the time of ice shedding, and the degree of ice-shedding balance, the range of critical ambient temperature is −${5 }^{\circ }$C to −${9 }^{\circ }$C for aero-engine fan blade icing tests during ground idle. Furthermore, the ice accreted at the roots of the blades is difficult to shed even at high engine speeds. Effective anti-/de-icing methods need to be developed.

The present work does not cover relevant studies on the effects of ice shedding and residual ice on fan performance, intake efficiency, vibration, etc., which are very important for engine design and safe operation. More relevant studies should be conducted in the future. In addition, to accurately predict the behavior of ice shedding, it is necessary to develop ice-shedding models on the basis of revealing the mechanism of ice shedding. Thus, for ice accumulation, ice shedding, the mass of ice shed, ice physical parameters, and other related factors, accurate experimental measurement technology needs to be developed next and quantitative mechanistic or engineering experimental research needs to be carried out.