Effects of Different Materials and Structures on Mechanical Properties of Hail Used in Aviation Testing

Abstract

Hail absorption test of aeroengine is one of the important components of airworthiness certification. The accurate test data are closely related to the density and mechanical properties of the artificial hail used in airworthiness tests. Through experimental research, this study explores the impact of distilled water, carbonated water and deionized water on the density and mechanical properties of artificial hail. The study addresses the significant differences between the density and mechanical properties of artificial hail and natural hail in existing studies. Based on this, a new method for preparing airworthiness test hail is proposed. The results indicate that artificial hail samples with distilled water as the hail core and carbonated water as the hail shell have densities ranging from 0.87 cm³ to 0.89 cm³. Furthermore, the estimated average maximum compressive strength of samples is 6.538 MPa, with some samples as low as 3.681 MPa. The mechanical properties of this artificial hail are more similar to those of natural hail. This method can more realistically simulate natural hail environments and can be used for the fine design of airworthiness certification criteria.

1. Introduction

The successful delivery and maiden flight of the domestically produced C919 large aircraft demonstrate a significant breakthrough in China’s large aircraft manufacturing and production industry. This achievement is closely related to the continuous improvement of our airworthiness certification system. The enrichment of the system’s content and the enhancement of its standards have also played a crucial role in this success.

Hail ingestion testing is a critical method for verifying the overall safety and reliability of an engine. It is mandatory test content in airworthiness certification. The 2002 revised edition of China’s “Aircraft Engine Airworthiness Certification” includes Article 33.78. This article requires engines with an inlet area exceeding 0.64 m² to undergo hail ingestion testing. The regulation dictates that for every 0.0968 m² of inlet area or remaining area, 25 mm diameter hail and 50 mm diameter hail must be injected [1]. This requirement is in line with the regulations of the US FAA and EASA [2,3]. However, since natural hail is difficult to obtain and utilize in airworthiness certification testing, research on artificial hail has emerged as an alternative. In recent years, research on artificial hail has primarily focused on investigating the effects of different factors on the mechanical properties of artificial hailstones. Zhang et al. [4,5,6,7] explored the effects of freezing parameters and storage parameters on the mechanical properties of distilled water hail, expanding on existing knowledge. The study found that freezing temperature has the most significant effect on hail’s properties, with a reduction in freezing temperature from 0 °C to −40 °C resulting in a fourfold increase in compressive strength. Xu et al. [8,9,10] conducted an in-depth examination of the mechanical properties of hail under different strain rates. The study found that hail exhibited plastic characteristics at low strain rates, whereas it exhibits brittle characteristics at higher strain rates. Furthermore, Zhang et al. [11] observed that the compressive behavior of ice is strongly sensitive to the strain rate. Notably, the maximum stress that ice can withstand before failure increases as the strain rate increases. Apart from the strain rate, other factors such as the size, density, material, and structure of hail also play a significant role in influencing its mechanical behavior [12]. Research conducted by Aly et al. [13,14,15,16] showed that the maximum compressive strength of ice decreases dramatically as the hailstone size increases. Moreover, Tang et al. [17,18,19] explored the effects of cotton fiber type and content on the mechanical properties of hailstones, finding that the incorporation of cotton fibers has a substantial impact on the mechanical behavior of hail, including its maximum compressive strength. Li et al. [20] produced three types of hail samples with varying impurity contents by adding sodium-based expansive soil particles smaller than 45 μm and tested their properties. This study provides a new approach to investigating natural hailstones with impurities. Meanwhile, Uz et al. [21] fabricated artificial hail using 88% demineralized water and 12% liquid nitrogen. Through experiments, they verified that this artificial hail possesses good mechanical properties under high-speed impact conditions. Furthermore, Kim et al. [22,23,24] investigated the mechanical properties of single-layer, parallel-layer, and layered artificial hail. The result demonstrated the influence of artificial hail structure on its mechanical properties through high-speed impact testing.

While research on artificial hail has made significant progress [25], the existing studies still have limitations due to the disparity in application backgrounds. Taking artificial hail for aircraft airworthiness testing as an example, it is explicitly stipulated that the density of hail used in engine ingestion tests should be consistent with that of natural hail, ranging from 0.8 g/cm³ to 0.9 g/cm³ [1,26]. However, the density of hail samples used in the published studies on mechanical properties of artificial hail is almost all greater than 0.9 g/cm³. When the density of hail increases by about 3%, its compressive strength increases by about 1 fold. In addition, the average compressive strength of hail in the natural environment ranges from 0.22 to 1.64 MPa [27,28]. But the average compressive strength of artificial hail in existing studies is far beyond this range.

Therefore, based on a thorough understanding of the research background, this article identified three liquids with similar physical and chemical properties to natural water, and produced several hail samples, using them as raw materials to explore the changes in artificial hail density and mechanical properties under different materials. Finally, based on the obtained research results, a method for making artificial hail that is more similar to the mechanical properties of natural hail is proposed, which is to make the hail core with distilled water and the hail shell with bubbling water. The average density of hail with this structure is 0.871 g/cm³, and the estimated average maximum compressive strength is only 6.537 MPa. This type of hail may be able to simulate actual situations more realistically in airworthiness certification testing in the future, ensuring the authenticity and reliability of its related research laws, and providing assistance for more accurate airworthiness certification testing.

2. Preparation and Testing of Hail Samples

2.1. Preparation of Hail Samples

2.1.1. Materials for Hail Samples

Taking into account the economic feasibility and ease of acquisition of hailstone preparation materials, this experiment ultimately determined the preparation materials for hailstone samples to be the following three types: distilled water, carbonated water and deionized water. Distilled water was sourced at a price of 10 yuan per liter from Bkmam Biotechnology, located in Changsha, China. And deionized water was sourced at a cost of 66 yuan per liter from Hewei Medical Technology, located in Guangzhou, China. The conductivity of distilled water is generally between 1 to 5 μs/cm, while the conductivity of deionized water is typically between 0.05 to 0.1 μs/cm. But both of them are significantly lower than the conductivity of mineral water (over 1000 μs/cm). For carbonated water, Perrier brand sparkling mineral water is used, with a unit price of 16 yuan per liter. This particular bubble water consists mainly of water and carbon dioxide, with mineral content accounting for just 0.3%, a factor that can be disregarded.

2.1.2. Method for Preparing Hail Samples

In this experiment, all hail samples were created using molds. The mold consists of two parts that are connected by bolts. The upper half of the mold is composed of polycarbonate, while the lower half is composed of stainless steel, as shown in Figure 1. During the freezing process, the liquid in the lower half of the mold freezes first, because of the much higher thermal conductivity of stainless steel compared to polycarbonate. The volume of liquid will expand during the freezing process, causing excess liquid to be discharged from the drainage hole at the top of the mold. This prevents excessive compression and the formation of cracks in the hail, greatly improving the success rate of hail sample production.

2.1.3. Preparation Process of Hail Samples

There are many things to be aware of in the process of preparing a hail sample. First, the selected materials need to be injected into the mold cavity through the drainage hole using a syringe. At the same time, attention should be paid to positioning the syringe tip as close to the bottom of the cavity as possible to facilitate the escape of air along the drainage hole. After filling the cavity with liquid, check the mold’s sealing and place it in a liquid container corresponding to a depth of 0.5 m for half an hour. The aim is to ensure the removal of larger air bubbles from the cavity. Next, remove the mold from the liquid container and place it in a low-temperature constant temperature box for freezing at −20 °C for 24 h. Subsequently, remove the mold from the constant temperature box for demolding. Before the demolding process begins, allow the mold to sit in the air for 10–15 min. It will be easier to demold because of a complete separation between the surface of the hail sample and the inner surface of the mold. Lastly, inspect the demolded hail samples and pick those free of cracks and defects for experimentation. Before the experiment, reposition all hail samples in the −20 °C constant temperature chamber for storage until they reach the experimental temperature.

2.2. Testing of Hail Samples

2.2.1. Density Testing of Hail Samples

During the experiment, the mass of the hail samples was measured using a high-precision analytical balance. The electronic balance is the XPR204S/AC, selected from Shanghai Mettler-Toledo in China, as shown in Figure 2. The precision of the balance is 1 mg. The volume of hail samples was measured by the drainage method.

2.2.2. Mechanical Properties Testing of Hail Samples

Before the mechanical properties testing, it is necessary to open the low temperature box inside the universal testing machine first and cool the internal temperature of the testing machine to −20 °C in advance. This allows the temperature of the hail sample to remain unchanged during the test. Next, use a universal testing machine to determine the mechanical properties curve of the hail sample. At the same time, the data will be recorded by the computer, as illustrated in Figure 3a. The loading speed of the universal testing machine used in this experiment is fixed at 27 mm/min. According to Equation (1), the strain rate of the test is set at 0.018 s⁻¹. In the equation, ε, V and D represent the strain rate, the loading rate of the machine and the diameter of the hail sample, respectively.

$$\epsilon =\frac{V}{D}$$

(1)

The model of universal testing machine is the WDW-20 produced by Shanghai Song Dun Instrument Manufacturing in China. The load accuracy of the machine is ±0.01% and the measurement accuracy is within ±0.5% of the displayed value. Furthermore, its displacement resolution is up to 0.0001 mm and the maximum compression displacement rate is 500 mm/min (8.33 mm/s). The load was measured using a 0.01% F.S. dual-directional load sensor from HBM Germany, and the displacement was measured using a digital circuit to measure the absolute displacement between the upper and lower clamps, as shown in Figure 3b.

After obtaining the mechanical performance curve of the hail samples, it can be determined that the failure mode of the hail samples is brittle fracture. This conclusion is supported by existing research findings and experimental observations. Therefore, the complete brittle sphere compression strength analytical formula derived by Russell and Wood [29,30] can be used to estimate the maximum compressive strength of the hail samples, providing a more intuitive understanding of the variation pattern of their mechanical properties. The specific equation is as follows:

$${\sigma }_c\approx 0.44\frac{F}{\mathrm{\pi }{r}^2{\sin }^2\theta }$$

(2)

In the equation, F is the applied load, θ is the angle related to the contact area, r is the radius of the brittle sphere and σ_c is the estimated maximum compressive strength of the hail. The relationships between the parameters are shown in Figure 4a. As the universal testing machine measures the relationship between applied force F and displacement x, it is necessary to replace the contact angle θ in Equation (2) with the displacement x. As depicted in Figure 4b, when the universal testing machine applies a force F to the hail sample, the absolute displacement of the upper and lower clamps is x. At this moment, the top and bottom of the hail both undergo a displacement of x/2. Thus, Equation (1) can be transformed into the relationship between applied force F and displacement x, as demonstrated in Equation (3).

$${\sigma }_{\mathrm{c}}\approx 0.44\frac{F}{\mathrm{\pi }(rx-\frac{x^2}{4})}$$

(3)

3. Results and Analysis

3.1. Impact of Hail Materials on the Density and Mechanical Properties of Artificial Hail

This section details the preparation of hail samples with a 25 mm diameter using distilled water, carbonated water, and deionized water, as depicted in Figure 5. Specific parameters of some hail samples are listed in

Table 1. Parameters of artificial hail samples produced from different hail materials.

Sample (S)	Hail Species	m/g	v/cm3	ρ/g·cm−3	$\overline{\mathit{\rho }}$/g·cm−3
1	hail samples produced from distilled water	7.704	8.07	0.954	0.949
2		7.735	8.11	0.953
3		7.505	7.90	0.950
4		7.373	7.85	0.939
5	hail samples produced from carbonated water	6.882	8.00	0.860	0.849
6		6.351	7.50	0.847
7		6.518	7.80	0.835
8		6.810	7.90	0.861
9		6.495	7.80	0.832
10		6.800	7.90	0.860
11	hail samples produced from deionized water	7.227	8.10	0.892	0.897
12		6.247	7.10	0.880
13		7.338	8.10	0.905
14		7.275	8.00	0.909

. Among them, samples 1–4 are created from distilled water, samples 5–10 are created from carbonated water, and samples 11–14 are created from deionized water.

The artificial hail samples created from distilled water exhibit a clear and transparent exterior, with fine, cloudy opaque clusters appearing inside, as shown in the diagram. The opaque layer is primarily composed of a series of tiny cracks. In comparison, the hail samples produced from carbonated water are opaque overall, with numerous small bubbles inside. Finally, the hail samples produced from deionized water show no significant differences in appearance compared to those produced from distilled water.

From the table, it is evident that carbonated water hail and deionized water hail can significantly reduce the density of artificial hail compared to distilled water hail, while maintaining the hail volume nearly constant. This reduction in density is mainly due to the presence of numerous bubbles in carbonated water hail and the absence of positive and negative ions in deionized water. This absence further prevents the formation of hydrogen bonds. Overall, both carbonated water hail and deionized water hail are suitable for airworthiness certification testing.

Based on this, quasi-static compression tests were conducted on the above hail samples to investigate the differences in their mechanical properties. The results of the three types of hail are shown in Figure 6 and Figure 7.

In Figure 7a, it is evident that the estimated maximum compressive strength of distilled water hail samples is above 10 MPa. Among these samples, sample 1 (S1) exhibits the highest measured value at 19.121 MPa, while sample 6 (S6) shows the lowest measured value at 11.004 MPa. And the average estimated compressive strength of hail samples produced from distilled water is 14.105 MPa, approximately nine times that of natural hail. Figure 7c shows that, with a few exceptions, the estimated maximum compressive strength values of the majority of hail samples are approximately 10 MPa. Additionally, Figure 7b indicates that the estimated maximum compressive strength of carbonated water hail ranges from 12.766 MPa to 5.333 MPa. On the whole, the average estimated compressive strength values of carbonated water hail and deionized water hail are noticeably lower than distilled water hail. Hence, when compared to distilled water hail, bubble water hail and deionized water hail offer a more accurate reflection of the mechanical behavior of natural hail.

In this section, hail species whose mechanical properties are closer to those of natural hail were found, but the differences between them were still significant.

3.2. Impact of Hail Structure on the Density and Mechanical Properties of Artificial Hail

Based on the previous section, hail density produced from carbonated water falls between 0.83 g/cm³ and 0.86 cm³, and the mechanical properties of carbonated water hail closely resemble those of natural hail. Given the formation conditions and principles of natural hail, this section presents a new method for simulating natural hail production. It involves creating artificial hail cores using distilled water and carbonated water separately, and then using carbonated water and distilled water as the hail cores to form the shell.

As described in the subsequent text, the concrete approach includes preparing 25 mm hail from distilled water and carbonated water in molds. Prior to demolding, place the molds in a 30 °C constant temperature chamber for 1 h, then remove the melted water by opening the molds, leaving the hail core. Freezing must be conducted in two steps to ensure the core is located at the center of the hail sample. The first step involves cooling distilled water or carbonated water at 0 °C. Then, fill the lower half of the stainless-steel mold with the cooled water and the hail core. Next, freeze the mold at −20 °C in a constant temperature chamber for 0.5 h. The purpose of this procedure is to first freeze the ice core together with half of the ice shell into a whole. During this process, as the density of the ice core is lower, it will float on the surface of the liquid. So, a positioning plate in the constant temperature chamber can be used to secure the position of the ice core. Afterward, finalize the assembly of the mold and use distilled water or carbonated water to fill the remaining space in the mold. It is then placed in a −20 °C constant temperature chamber for the second freezing process and demolded after 10 h. The simulated hail obtained is displayed in Figure 8 and Figure 9.

The artificial hail samples prepared through the above method were subjected to mass and volume measurements, yielding the density of hail samples with different structures, as shown in

Table 2. Density of hail samples under different structures.

Sample (S)	Hail Species	m/g	v/cm3	ρ/g·cm−3	$\overline{\mathit{\rho }}$/g·cm−3
1	carbonated water cores and distilled water shells	7.440	8.50	0.875	0.873
2		7.526	8.45	0.891
3		7.167	8.50	0.843
4		7.305	8.30	0.880
5		7.440	8.50	0.875
6	distilled water cores and carbonated water shells	7.498	8.60	0.872	0.871
7		7.161	8.10	0.884
8		7.304	8.30	0.880
9		7.384	8.70	0.849

. Samples 1 to 5 have the carbonated water core and distilled water shell, while samples 6 to 9 have the distilled water core and carbonated water shell.

Static compression tests were conducted on the hail samples. They aim to obtain the mechanical performance curves of hail samples with two different structures, as shown in Figure 9 and Figure 10.

From Figure 9a, it can be observed that there is a significant difference in the load–displacement curves between hail samples with distilled water cores and carbonated water shells. Samples 1–2 (S1–S2) fractured with very little displacement of the universal testing machine and had a relatively low maximum load-bearing capacity. On the other hand, samples 3–4 (S3–S4) fractured only after a larger displacement of the universal testing machine, with a maximum load-bearing capacity more than twice that of the previous two samples. The primary reason for this phenomenon is attributed to manual handling and the influence of freezing equipment during the production process of the carbonated water shell. The carbonated water shell does not freeze immediately, leading to a significant upward movement of bubbles. The bubbles froze on the top of the hail eventually, resulting in differences in mechanical properties. Furthermore, both types of hailstones exhibit brittleness characteristics, as indicated by the curves above.

Figure 10 shows that, compared to the three types of hail mentioned in the previous section, the estimated average maximum compressive strength of hail with distilled water cores and carbonated water shells significantly decreased, especially for samples 3 (S3) and 4 (S4), with estimated maximum compressive strengths of 3.681 MPa and 3.739 MPa, respectively, which are similar to the mechanical performance of natural hail. On the other hand, the average estimated compressive strength of hail with carbonated water cores and distilled water shells was 9.358 MPa, showing similar mechanical performance to carbonated water hail.

4. Conclusions

Based on the relevant provisions of “Airworthiness Certification for Aircraft Engines”, this paper investigates the density and mechanical properties of 25 mm diameter hailstones for airworthiness testing under different materials and forming methods using experimental research. The conclusions of the study are as follows.

(1)

Both carbonated water hail and deionized water hail can partly reduce the density of artificial hail. The average density and estimated compressive strength of carbonated water hail are significantly lower than the other two types of hail. It is able to reflect the mechanical properties of natural hailstones.

(2)

The average density of hail with carbonated water cores and distilled water shells, as well as hail with distilled water cores and carbonated water shells, both meet the requirements of airworthiness certification testing. Hail with distilled water cores and carbonated water shells exhibit lower mechanical properties, with an average estimated maximum compressive strength of only 6.538 MPa, which is closest to the mechanical properties of natural hail.

(3)

This paper provides a new perspective and method for the preparation of hail for airworthiness testing. Furthermore, the paper also finds artificial hail that is closer to natural hail in terms of density and mechanical properties. Future investigations may reveal that this hail has the potential to compensate for the deficiencies of conventional hail in airworthiness certification testing. This could aid regulatory authorities in obtaining more precise airworthiness certification test data and revising airworthiness certification standards with increased detail.

All hail in this study was subjected to quasi-static compression tests, with strain rates much lower than actual impact tests. Therefore, the results of this experiment can serve as a reference within a certain range.