Study on the Influence of Tip Clearance on Working Characteristics of High-Altitude Fan

Abstract

To study the influence of tip clearance on the working characteristics of high-altitude fans, this paper takes the MIX-140 high-altitude fan as the research object. Five different tip clearance (TC) models are selected. The CFD method is used to analyze the changes in the working characteristics of the fan under different flow rates and TCs in ground and high-altitude environments. The reliability of the numerical method is verified through a fan test bench. The results show that the tip leakage flow caused by the TC will continuously deteriorate the working characteristics of the fan. Under the rated flow rate in the ground environment, for every doubling of the blade’s TC, the static pressure difference will decrease by 5%, the efficiency will decrease by 2%, and the power will decrease by 3%. In a high-altitude environment, the flow rate corresponding to the maximum shaft power point of the fan will continuously increase with an increase in the tip clearance, which will bring about additional energy consumption. For high-altitude fans, the deformation caused by the high-speed rotation of the impeller needs to be taken into account. Undoubtedly, it is advantageous to choose the smallest possible tip clearance value. The results of the analysis and test methods in this paper will provide a basis for designing the tip clearance of high-altitude fans.

1. Introduction

Airships [1] and other aerostats with airbags, such as super-pressure balloons [2] and tethered balloons [3], require high-altitude fans to inflate the airbags and achieve functions such as adjusting their flight altitude [4] and maintaining their aerodynamic shape and pressure control [5]. With the continuous development of aerostat technology, the demand for high-performance and highly reliable high-altitude fans is increasing [6,7].

To ensure the impeller’s rotation, there is a certain gap between the impeller of a high-altitude fan and the static shell. This gap is called the tip clearance (TC) and is a key parameter in fan design and manufacturing [8]. Part of the fluid in the fan impeller flow passage flows through the TC under the pressure difference between the pressure side and the suction side of a blade, forming a tip leakage flow [9]. The TC not only generates the tip leakage flow but also has significant impact on the main flow and distribution in a blade, affecting the fan’s performance and operational stability. A change in the TC has a substantial impact on the pressure and efficiency of the fan [10,11]. Therefore, investigating the influence of TC on the performance and internal flow characteristics of a high-altitude fan and selecting an appropriate TC value has high scientific and engineering value for the development of high-altitude fans.

In the field of high-altitude fans for aerostats, Zhao et al. [12] considered the changes in air density, pressure, and temperature in high-altitude environments and proposed a numerical method for predicting the performance of centrifugal compressors in high-altitude environments. Wei et al. [13] proposed a method for selecting high-altitude fans for aerostats. Qu et al. [14] proposed a method for optimizing a mixed-flow fan suitable for stratospheric airships. Sun et al. [15] investigated the influence of different geometric parameters on the efficiency of high-altitude fans. Zhang et al. [16] proposed a series connection method for a super-pressure balloon fan, which helped in mitigating the impact of an insufficient fan capacity to some extent. The above-mentioned studies on high-altitude fans have mostly focused on performance prediction, structural design optimization, modified applications, and so on but have not investigated the TC. Presently, there are many studies on the influence of the TC on large-scale equipment, such as high-speed pumps [17,18], axial flow compressors [19,20], and aero-engines [21]. However, there are certain differences in their design structures and usage environments compared with those of high-altitude fans.

Based on this background, this study considered the MIX-140 high-altitude fan (Aerospace Information Research Institute, CHN, Beijing, China), which was developed independently [22], as the research object. Multiple models with different TCs were established, and the influence of changes in the TC on the working characteristics of high-altitude fans, both in ground and high-altitude environments, were analyzed. Combined with the influence of the centrifugal force, a reasonable TC value is proposed.

The rest of this paper is organized as follows: In Section 2, the fan model, which is the analysis object of this study, is established, and the numerical analysis method is clarified. In Section 3, different TC models are established. The numerical analysis method is used to investigate the influence of changes in the TC on the static pressure difference, efficiency, and shaft power of the fan in ground and high-altitude environments. In Section 4, the influence of the centrifugal force on the change in the TC is analyzed, and a reasonable TC value is provided. The rationality of the fan’s TC setting and the fan’s good environmental adaptability are verified through ground performance testing, high-altitude environment testing, and flight testing. Section 5 summarizes the findings of this study and suggests directions for future work.

2. The Analysis Model and Numerical Method

The analysis object of this study was the MIX-140 high-altitude fan, which is shown in Figure 1.

High-altitude fans are typically used in conjunction with valves to form the actuator of an aerostat pressure regulation system [23]. The main parameters of the fan are listed in

Table 1. Main parameters of MIX-140 high-altitude fan.

Description	Parameter	Value
Number of blades	Z	20
Blade thickness	T	1 mm
Impeller diameter	D1	φ140 mm
Fan inlet diameter	D2	φ84 mm
Fan outlet width	H	10 mm
Fan envelope size	D	φ220 × 150 mm
Blade wrap angle	φ	31–39°
Total weight	/	3.5 kg

.

The domain of the fan for fluid analysis was extracted based on the flow passage structure of the MIX-140 fan and consisted of three parts: the inlet domain, the impeller, and the diffuser. The fan consists of 20 blades, and the fan flow passage is designed in cyclic symmetry. During the numerical analysis, by setting cyclic symmetry boundaries, 1/20 of the flow passage was used for analysis, as shown in Figure 2.

Among these components, the impeller part was set as a rotating area with a certain rotational speed, and the inlet domain and the diffuser part were set as stationary areas. The “mixed plane” method was used for the connection between the rotating and stationary interfaces. This method transmits the parameters of the interface of the previous stage component to the interface of the next stage component after circumferential averaging [24]. In the whole analysis model, all wall surfaces were assumed to be subject to no-slip wall and smooth wall conditions.

In this study, the fluid mechanics analysis software ANSYS CFX18.0 was used for numerical analysis of the fan’s fluid characteristics. Because the flow inside the fan is mainly complex turbulent flow, to ensure an accurate simulation of the air flow inside the fan, a suitable turbulence solution method must be used [25]. According to the existing research, the shear stress transport model (SST) [26,27,28] is better suited to analysis under a low Reynolds number at a high altitude. Therefore, the SST model was selected to solve the three-dimensional time-averaged Navier–Stokes equation.

In the numerical analysis, the inlet was defined with environmental atmospheric pressure and environmental temperature boundary conditions, while the outlet was defined with the mass flow rate condition (converted from the volumetric flow rate). When the root mean square residual was less than 10⁻⁵, the calculation was considered to be convergent. The boundary conditions for the simulation analysis of the rated operating point of the fan in high-altitude and ground environments are listed in

Table 2. Boundary conditions for simulation analysis.

Boundary	Setting	Ground Values	High-Altitude Values
S1 Inlet	Total pressure	101,325 Pa	5500 Pa
S1 Inlet	Total temperature	300 K	216.65 K
S2 Outlet	Volume flow rate	1000 m3/h	400 m3/h
R1 Speed	/	10,000 r/min	25,000 r/min

.

In this study, ANSYS Mechanical was selected to mesh the fan’s inlet domain and diffuser and generate hexahedral meshes. The mesh structure of the fan impeller was generated using ANSYS TurboGrid 18.0. As shown in Figure 3, all the meshes are hexahedral meshes. The tip clearance is changed by changing the distance from the tip of the blade to the shroud. In order to predict the flow in the boundary layers at a high resolution, the minimum grid spacing on the solid wall was set to ensure y+ <3.

The number of elements directly affects the accuracy of the simulation results, and selecting a reasonable number of elements can reduce the computational burden. There-fore, it is important to perform mesh independence checks. This study selected six different element number sets for mesh independence testing.

The element distribution and the independence check results are presented in

Table 3. The pressure rise ${∆p}_i$ in each mesh and the efficiency η_i of each mesh.

Item	Mesh 1	Mesh 2	Mesh 3	Mesh 4	Mesh 5	Mesh 6
Inlet	8218	16,247	16,247	20,431	27,946	27,946
Impeller	118,490	238,417	302,828	365,321	414,260	556,986
Diffuser	1670	3521	13,680	25,412	59,064	59,064
Total mesh	128,378	258,185	332,755	411,164	501,270	643,996
${∆p}_i$$/{∆p}_1$	1	1.056	1.059	1.066	1.069	1.069
ηi/η1	1	1.028	1.029	1.040	1.043	1.043

.

${∆p}_i$ represents the static pressure difference in the fan with different numbers of elements;${\mathsf{\eta }}_{\mathrm{i}}$ represents the efficiency of the fan with different numbers of elements. The analysis results reveal that when the number of inlet elements was 27,946, the number of impeller elements was 414,260, and the number of diffuser elements was 59,064, the rate of the change in the fan’s efficiency and static pressure ratio was relatively low. Therefore, it was reasoned that the total number of elements should be controlled at 501,270 in the subsequent calculations and analyses. With this number of elements, the total number of nodes is 54,1394, and the average value of y+ in the blade area is 1.02.

3. Analysis of the Influence of the TC

Five different TC models with TCs of 0.3 mm, 0.6 mm, 0.9 mm, 1.2 mm, and 1.5 mm, respectively, were established. The influence of the TC on the working characteristics of the fan was analyzed from three aspects: the static pressure difference, efficiency, and shaft power. The tip leakage ratio was used to measure the relative size of the leakage at the tip.

The static pressure difference in the fan is expressed as follows:

$$∆p=p_{out}-p_{in}$$

(1)

where $p_{out}$ is the static pressure at the fan outlet, and $p_{in}$ is the static pressure at the fan inlet.

The total pressure difference in the fan is expressed as follows:

$$∆pt=p_{tout}-p_{tin}$$

(2)

where $p_{tout}$ is the total pressure at the fan outlet, and $p_{tin}$ is the total pressure at the fan inlet.

The fan efficiency is obtained as follows:

$$\eta =(Q·∆pt)/W$$

(3)

where Q is the flow rate of the fan, $∆pt$ is the total pressure difference, and $W$ is the shaft power.

The shaft power of the fan is expressed as follows:

$$W=(t·n)/9.55$$

(4)

where $t$ is the torque (n·m), and $n$ is the rotational speed (r/min).

The tip leakage ratio is defined as follows:

$$\gamma =Q_{tip}/Q$$

(5)

where $Q_{tip}$ is the flow rate through the TC area, and Q is the flow rate of the fan.

3.1. A Ground Environment

When the aerostat is on the ground awaiting take-off, a high-altitude fan is typically used to pre-fill the airbag with air. As the aerostat ascends, this part of the air gradually expands to fill the airbag. To ensure accuracy in calculating the amount of pre-filled air on the ground, it is necessary to analyze the ground working performance of the high-altitude fan.

The working characteristics of the fan were analyzed based on a flow rate range of 0.4 Q–1.6 Q. The working characteristic curves of the fan under different TCs were obtained based on the calculation method discussed in Section 2.

The static pressure difference in the fan was calculated using Equation (1), and a static pressure difference–flow rate change curve for the fan was drawn, as shown in Figure 4. As can be seen, under any TC, the static pressure difference in the fan decreased as the flow rate increased. The overall curve does not exhibit an obvious “saddle-shaped area”, which means that the fan has a wide range of applications. At any flow rate, the static pressure difference in the fan is significantly reduced, owing to the increase in the TC. Considering the rated flow point as an example, the static pressure in the fan is 2332 Pa when the TC is 0.3 mm. When the TC increases to 1.5 mm, the static pressure difference is only 1906 Pa. For every doubling of the TC, the static pressure difference is reduced by 5%.

The efficiency of the fan was calculated using Equation (3), and the efficiency–flow rate change curve for the fan was drawn, as shown in Figure 5. When the flow rate is Q, the fan reaches the highest efficiency point. If there is a flow offset, compared with a high flow, a low flow will cause a more obvious drop in efficiency. The TC has a very significant impact on the efficiency. When the TC is 0.3 mm, the maximum efficiency is 92%; when the TC increases to 1.5 mm, the maximum efficiency is reduced to 85%. For every doubling of the TC, the fan’s efficiency is reduced by 2%.

In an aerostat with a limited energy supply, the shaft power is a key parameter of the fan. The shaft power of the fan was calculated using Equation (4), and the shaft power–flow rate change curve for the fan is shown in Figure 6.

The results reveal that as the flow rate increases, the shaft power of the fan increases continuously, indicating that the fluid passing through the fan gains kinetic energy continuously under the action of the blades. The influence of the increase in the TC is obvious. At the rated flow, when the clearance is 0.3 mm, the shaft power of the fan is 344 W. When the clearance increases to 1.5 mm, the shaft power decreases to 315 W, marking a decrease of 8%.

Nephograms of the streamline and velocity distribution of the fan when the TC is 0.3 mm and 1.5 mm, respectively, are shown in Figure 7. The red arrow indicates the main direction of the flow. As can be seen, when the TC is 0.3 mm, the tip leakage flow is mainly radial flow from the pressure surface of the blade to the suction surface and flows out after converging with the mainstream. When the TC is 1.5 mm, the increase in the TC results in low kinetic energy in the fluid at the top of the TC, forming a flow that leaks circumferentially along the blade to the top of the adjacent blade. This part of the circumferential leakage flow exists in the TC area at the top of the blade and is ineffective. Therefore, the shaft power of the fan is significantly reduced.

Figure 8 shows nephograms of the streamline distribution inside the blade and the mass flow distribution at the TC when the TC is 0.6 mm and within the flow range of 0.4 Q–1.4 Q.

As shown in Figure 8a–c, when the flow rate is less than 0.8 Q, obvious flow separation and a vortex appear near the leading edge of the blade on the blade’s suction surface. This vortex consumes the kinetic energy of the fluid, thereby reducing the fan’s efficiency. However, as the flow rate increases, this effect diminishes. At the rated flow point Q, the flow separation phenomenon disappears, and the fan’s efficiency reaches the highest point.

Additionally, when the flow rate is less than 0.8 Q, an area with a large amount of tip leakage appears at the blade’s tail. Combined with the nephogram of the streamline distribution, it can be seen that unstable flow occurs at the leading edge of the blade at a low flow rate, and the overall flow velocity is low. When the flow develops to the tail of the blade, the flow tends to be stable, and the flow velocity increases, causing more tip leakage flow at the blade’s tail. When the flow rate increases, the flow separation phenomenon disappears, and the flow field tends to be smooth. Therefore, with a higher flow velocity, a relatively concentrated tip leakage flow appears at the blade’s leading edge.

3.2. A High-Altitude Environment

In a high-altitude environment, when the fan increases its rotational speed to 25,000 r/min, the rated flow rate Q can reach 1000 m³/h. Analysis of the working characteristics of high-altitude fans has important engineering significance for pressure control and energy consumption management during the flight of an aerostat. The fan’s working characteristics were analyzed based on the environmental conditions at an altitude of 20 km, where the aerostat is stationed. The flow rate range was 0.4 Q–1.6 Q. According to the calculation method presented in Section 2, “flow rate–static pressure” difference curves for the fan under different TCs were obtained, as shown in Figure 9.

As can be seen, the “flow rate–static pressure” difference curve for the fan at a high altitude is similar to that obtained in the ground environment. As the flow rate increases, the static pressure difference in the fan decreases continuously, and an obvious “hump area” is not observed. The influence of the TC on the static pressure difference is very important. Considering the rated flow point Q as an example, when the TC increases from 0.3 mm to 1.5 mm, the static pressure difference is reduced by 20%.

The efficiency curve for the fan is shown in Figure 10. The entire curve exhibits a trend of first increasing and then decreasing. The fan’s highest efficiency point appears at the rated flow rate. Considering a TC of 0.6 mm as an example, the fan’s highest aerodynamic efficiency is 86%.

The change in the TC has a strong effect on efficiency. Under different flow rates, the sensitivity of the efficiency to change is different. When the flow rate is 1.6 Q, the reduction in efficiency of the maximum clearance compared with the minimum clearance is 8%. When the flow rate is 0.4 Q, the fan’s efficiency is almost the same under different clearances. Calculated considering a TC of 0.6 mm, in a 20 km environment, the fan’s maximum static pressure is 1264 Pa. The flow rate at the rated operating point is 1000 m³/h, with a static pressure difference of 1000 Pa and efficiency of 86%, satisfying the usage requirements for conventional aerostats.

By using the shaft power when the TC is 1.5 mm as a reference and converting the ratio of the shaft power under another clearance, a shaft power ratio curve can be obtained, as shown in Figure 11. As can be seen, the sensitivity of the shaft power to the TC is obviously different. When the flow rate is less than Q, the curve values are all positive, and the shaft power increases as the clearance decreases. However, when the flow rate is greater than 0.8 Q, the ratio exhibits a downward trend. When the flow rate is 1.2 Q, the ratio is negative. This means that the shaft power increases with the TC. Hence, further analysis was carried out to investigate this phenomenon.

Nephograms of the streamlines through the TC and the velocity distribution at the blade outlet under different clearances when the flow rate is 0.8 Q and 1.2 Q are shown in Figure 12 and Figure 13, respectively.

As shown in Figure 12, when the flow rate is 0.8 Q, the leakage flow formed by the TC is divided into two parts. One part is radial leakage flow that converges with the mainstream in the flow channel and flows out from the outlet after being compressed by the blade; the other part is circumferential leakage flow that leaks to the TC at the top of the adjacent blade. This part of the fluid, which has not been compressed adequately by the blade, belongs to the internal flow of the impeller and has a low energy gain. By comparing the streamlines under different TCs, it can be found that as the TC increases, the circumferential leakage flow becomes increasingly obvious. Therefore, the shaft power decreases further as the TC increases.

As shown in Figure 13, when the flow rate is 1.2 Q, the flow velocity through the blade increases, and most of the leakage flow formed at the TC is radial leakage flow, without obvious circumferential leakage flow. The radial leakage flow converges with the mainstream in the flow channel and flows out from the outlet after being compressed by the blade. Therefore, the shaft power increases significantly compared with 0.8 Q. As the TC increases, the radial leakage flow through the TC also increases, resulting in an increase in shaft power. Additionally, by comparing the velocity distribution at the blade outlet under different clearances, it is evident that the leakage flow at the blade tip area increases with clearance. This interaction between the blade tip leakage flow and the mainstream flow enhances the mixing effect, leading to an expansion of the low-speed region. This causes a blocking effect in the impeller flow channel, causing a vortex and flow instability, thereby reducing the fan’s efficiency and static pressure difference.

Figure 14 shows the tendency of changes in the tip leakage ratio with the flow rate and TC.

As can be seen, under any flow rate, an increase in the TC leads to a simultaneous increase in leakage. When the flow rate of the fan is 0.4 Q, at a 1.5 mm TC, the tip leakage accounts for 44% of the total flow rate, which is the highest leakage ratio. This is because the flow rate in the flow channel is low when the flow rate is low, the flow is disorderly, and leakage mainly occurs in the circumferential direction of the blade tip, so the leakage ratio is large. When the TC is 0.3 mm and the flow rate is 1.4 Q, the tip leakage rate is only 2%, which is the lowest leakage rate. This is because when the flow rate is large, the flow rate inside the flow channel is high, the flow is stable, and most of the tip leakage flow is reunited with the mainstream, so the leakage ratio is reduced.

Under different flow rates, when the TC is 0.6 mm, the flow line at the TC and the flow velocity distribution cloud at the blade outlet are shown in Figure 15.

As shown in Figure 15a,b, when the flow rate is low, the flow velocity in the flow channel is low, and the flow is chaotic. Moreover, there is circumferential leakage flow at the adjacent blade top. When the flow rate increases and the flow tends to be stable, as shown in Figure 15c,d, most of the blade tip leakage flows converge with the mainstream in the flow channel and do not form circumferential secondary leakage flows. As can be seen in the nephogram of the velocity distribution at the outlet, as the flow rate increases, the area occupied by the low-velocity area caused by the circumferential secondary leakage flow decreases continuously, and the leakage ratio decreases accordingly.

The distributions of the average static pressure along the streamwise location in the fluid domain at flow rates of 0.6 Q, 0.8 Q, 1.0 Q, and 1.2 Q are shown in Figure 16. In the inlet domain, the increase in the air velocity causes a continuous decrease in static pressure; when air enters the impeller domain, it is compressed by the impeller, and the static pressure continues to increase. In the diffuser domain, as the flow space increases, the dynamic pressure of the fluid gradually transforms into static pressure, and the static pressure gradually increases. In the inlet domain, the static pressure values at different TCs and flow rates are almost the same, and as the flow rate increases, the static pressure decreases faster.

In the impeller domain, the static pressure distribution varies at different flow rates. As shown in Figure 16a, when the flow rate is 0.6 Q, the static pressure in the impeller domain decreases continuously with an increase in the TC along the streamwise location; in Figure 16b,c, it can be seen that the static pressure reverses with the change in the TC. The static pressure at a 0.3 mm TC is first lower than that at other TCs and then continuously increases to the highest pressure. This indicates that too small a gap can have a negative impact on the impeller; when the flow rate is 1.2 Q, as shown in Figure 16d, the static pressure at different clearances in the impeller domain is relatively close but still shows a continuous decrease in static pressure with the increase in the TC.

From the above analysis, it can be seen that an increase in the TC will lead to a continuous deterioration of the working characteristics of the fan. Therefore, it is necessary to choose an appropriate TC value to achieve higher-performance aerodynamic operating characteristics.

4. TC Settings and Testing

4.1. The Influence of Centrifugal Force on the TC

The impeller of the MIX-140 fan is made of high-strength aluminum. The impeller blade thickness is only 1 mm, with a total weight of only 260 g. When rotating at high speed, the deformation under the action of the centrifugal force cannot be ignored. As shown in Figure 17, owing to the small TC, there is friction between the top of the leading edge of the blade and the impeller cover (in the red box). Therefore, a suitable initial TC must be set.

Nephograms of the deformation of the impeller at an altitude of 20 km and on the ground at 0 km are shown in Figure 18a,b, respectively.

As can be seen, under the action of the centrifugal force, the deformation of the entire impeller is relatively small at the hub position, and the main deformation is concentrated at the blade. The maximum deformation is, respectively, 0.25 mm (under 26,000 r/min) and 0.037 mm (under 10,000 r/min). The position at which the maximum deformation occurs appears at the leading edge of the top of the blade. The deformation of the trailing edge of the blade is slightly lower than that of the leading edge, and the minimum deformation occurs at the middle of the blade. Therefore, the leading and trailing edges of the blade are most likely to rub against the impeller cover.

Nephograms of the equivalent stress of the impeller at different speeds are shown in Figure 19. At 26,000 r/min, the maximum stress of the impeller is 185 Mpa. At 10,000 r/min, the maximum stress of the impeller is 27 Mpa. The maximum stress occurs at the root of the leading edge and the trailing edge of the blade. Although the overall stress level in the impeller is low, it is far less than the yield strength of the impeller material itself, and if there is friction between the blade and the wheel cover, the stress value in the blade root may be too large and cause damage.

In Figure 20, curves of the maximum and minimum deformation at the top of the blade are drawn as a function of the impeller speed.

As can be seen, the amount of deformation of the blade exhibits a tendency to increase linearly with the rotational speed. Therefore, as the rotational speed increases, the amount of deformation increases faster. The amount of deformation corresponding to 10,000 r/min on the ground is approximately 0.04 mm, while the amount of deformation corresponding to 25,000 r/min at a high altitude is approximately 0.23 mm. Therefore, the margin of the static TC can be specified according to the maximum amount of deformation of the blade corresponding to the maximum rotational speed.

The axial distance of the MIX-140 fan can be changed by adjusting the gasket, thereby adjusting the TC value. In practice, considering uncertain factors such as the impeller’s vibration, assembly errors, and thermal deformation, the clearance value of the fan is set to no less than 0.9 mm.

4.2. Performance Testing and Experimentation

To validate the accuracy of the numerical analysis method described in Section 2 and establish a performance benchmark for the fan’s use, it is necessary to test the fan’s performance. The performance test for the MIX-140 fan was carried out on a fan test bench that complied with the specifications of the Air Movement and Control Association (AMCA). As shown in Figure 21a, this test bench was used to measure and record the fan’s performance curve. The test was carried out under the conditions of an ambient temperature of 300 K, an ambient pressure of 101,312 Pa, and relative humidity of 50%. Figure 21b shows the impeller of the MIX-140 fan.

During the test process, the fan speed was set to 10,000 r/min. The measured curve and the simulation curve for the fan are shown in Figure 22. As can be seen, the performance curve for the MIX-140 fan does not exhibit an obvious “saddle-shaped area”. As the flow rate of the fan increases, the static pressure difference in the fan gradually decreases. The measured maximum static pressure difference of the fan is 2632 Pa, and the maximum flow rate is 617 m³/h. By comparing the measured data curve with the simulation data curve, it is evident that when the flow rate is greater than 400 m³/h, the simulation data are slightly higher than the measured data. The reason for this is the existence of additional frictional resistance losses in the actual fan. When the flow rate is less than 400 m³/h, the difference between the simulation data and the measured data is small, and the error is approximately 2%. This verifies the accuracy of the simulation method discussed in Section 2.

To verify the operating conditions of the MIX-140 high-altitude fan in the near-ground flight state, a flight test was carried out on the Jimu No. 2 tethered balloon. Two fans were used in the flight test.

Figure 23 shows the Jimu No. 2 tethered balloon in flight with the MIX-140 high-altitude fan carried on its abdomen. Two fans were symmetrically installed on the belly of the tethered balloon, with a valve installed at the fan inlet and connected to the outside atmosphere and the fan outlet connected to the tethered balloon airbag. When the valve is opened, the fan can inflate the airbag as it runs.

Figure 24 shows the changes in flight altitude and balloon pressure during the descent of the tethered balloon. The green area in the picture indicates the activation of a single fan, while the yellow area indicates the activation of two fans simultaneously. When a single fan is turned on, the increase in pressure on the sphere is about 0.45 Pa/s. After turning on two fans, the balloon pressure increased at a rate of 0.95 Pa/s. Throughout the entire testing process, the fan operated normally. After the test, the fan impeller and impeller cover were inspected, and rubbing marks were not observed.

To verify the reliability of the MIX-140 fan for long-term operation in high-altitude, low-temperature, and low-pressure environments, a reliability test was conducted on the fan inside an environmental test chamber. The conditions inside the environmental test chamber were the same as those at an altitude of 20 km, and the fan was installed on a scaled-down capsule to simulate the actual usage conditions. The test bench [22] is shown in Figure 25.

Using the test bench shown in Figure 25, the static pressure values corresponding to different rotational speeds of the fan could be obtained, as shown in Figure 26. From the figure, it can be seen that as the rotational speed increases, the maximum static pressure value that the fan can provide increases. When the rotational speed of the fan reaches 25,000 r/min, the maximum static pressure value that the fan can provide is 1200 Pa, while the simulated numerical value obtained through the calculation method in Section 2 is 1214 Pa, with a small error between them. This verifies the accuracy of the simulation analysis and the effectiveness of the test.

After running stably in a low-temperature and low-pressure environment for about 550 h, the reliability test of the fan ended. The fan impeller and the impeller cover were inspected, and no friction marks were found. This demonstrates the rationality of the fan’s TC setting and the good environmental adaptability of the fan.

5. Conclusions

This study investigated the influence of changes in the TC on the working characteristics of the MIX-140 high-altitude fan. The changes in the static pressure difference, efficiency, and shaft power of the fan under five different TCs in ground and high-altitude environments were analyzed. Combined with the influence of the centrifugal force, a reasonable TC value is proposed. The rationality of the TC setting was verified through experiments.

The conclusions drawn from this study are as follows:

• An increase in TC will progressively degrade the fan’s performance characteristics. At the rated flow on the ground, for every doubling of the TC, the static pressure difference will be reduced by 5%, the efficiency will be reduced by 2%, and the shaft power will be reduced by 3%. To obtain excellent fan working characteristics, it is necessary to reduce the TC as much as possible.
• In a high-altitude environment, when the flow rate is less than the rated flow rate owing to the effect of the circumferential ineffective leakage at the blade tip, the fan’s shaft power will progressively decrease as the TC increases. When the flow rate increases and the tip leakage flow is mainly radial flow, the fan’s shaft power increases as the TC increases.
• Testing the fan with various types of test stands is an effective means to verify the performance and reliability of the high-altitude fan. The performance test bench, the scaled balloon test bench, the tethered balloon test platform, and the test method adopted in this paper can provide reference for the testing and use of high-altitude fans.
• The TC setting of 0.9 mm for the MIX-140 high-altitude fan is reasonable, without contact between the blade and the impeller cover. The TC setting considers both the fan’s working performance and its safe operation. The fan has good environmental adaptability, satisfying the usage requirements for aerostats.

In future work, the MIX-140 fan can be optimized for impeller design. Variable TC designs can be adopted, such as increasing the clearance at the leading edge and the trailing edge of the blade tip and reducing the clearance value in the middle of the blade. This will not only mitigate the reduction in the fan’s efficiency caused by the TC but will also minimizes the risk of blade friction.