Theoretical and experimental studies on the interior ballistic of large UAV ejection based on trifluoromethane phase transition

Abstract

Unmanned aerial vehicles (UAVs) have demonstrated immense value in the military sector. This research proposes the use of Trifluoromethane as a novel cold ejection medium. Trifluoromethane, being easily compressible, exhibiting high safety and low infrared characteristics, is well-suited for small-volume high-pressure chambers. The feasibility of Trifluoromethane for UAV ejection has been confirmed through experiment. Furthermore, a thermodynamic numerical model has been established for the ejection medium to investigate the effects of key parameters on ballistic performance. The study’s findings demonstrate that as the volume of the high-pressure chamber increases, the ejection velocity of the UAV is enhanced, but the improvement slows down. Meeting the ejection velocity specifications for the UAV, reducing the volume of the high-pressure chamber can lower the peak pressure within the low-pressure chamber. An increase in the release pressure of the high-pressure chamber can enhance the ejection velocity, but the improvement slows down. Lowering this pressure can effectively reduce the UAV’s acceleration. There is a maximum valve diameter beyond which the ejection velocity remains constant, however, the peak acceleration can still increase. Enlarging the volume of the low-pressure chamber can effectively reduce the UAV’s peak acceleration. This study provides a safe and efficient technical solution for the cold ejection of large UAVs.

Introduction

In the recent conflicts between Russia and Ukraine, as well as between Palestine and Israel, unmanned aerial vehicles (UAVs) have demonstrated significant military application value with their capabilities for intelligence.

reconnaissance, positioning and tracking, communication, missile strike guidance, and rapid penetration and attack, becoming a key force in determining the outcome of battles. UAVs, with their sophisticated structure, ease of use, flexibility, and maintainability, have received widespread recognition from both military and civilian sectors world wide^1,2,3,4,5_.

Successful launch of UAVs is a prerequisite for their successful mission execution, with ejection methods including pneumatic launch^6,7, electromagnetic launch^8,9,10,11, rocket-assisted launch¹², and hand toss launch¹³. Electromagnetic launch systems are complex and costly, while solid rocket exhaust is characterized by high temperatures, high infrared signatures, and the emission of harmful gases. Compared to other launch methods, pneumatic ejection offers greater energy, fewer geographical limitations, and convenient transportation, providing a more significant operational advantage^14,15. Compressed air is the most common method for pneumatic ejection, and extensive research has been conducted on compressed gas ejection, indicating that the main structures of the ejection system—the high-pressure gas storage chamber, valve, and low-pressure chamber—significantly influence the ballistic performance of the launch system. Wang et al¹⁶. studied the impact of valve opening methods, full-open time, and full-open area on launch performance. Skews et al¹⁷. have conducted studies on the impact of high-pressure chamber pressure on the actuation of driven objects. Ruleva and Solodovnikov¹⁸demonstrated that the opening time of the valve has a dependency on both the high-pressure chamber and the low-pressure chamber. They employed numerical simulation methods to analyze the flow field at the outlet when the valve is opened. Zhang et al¹⁹. conducted research on a novel gas gun and optimized structural parameters such as membrane thickness, cylinder length, and the mass of the explosive charge. Gao et al²⁰. established an internal ballistic mathematical model and, combined with experiments, investigated the effects of UAV weight and high-pressure chamber release pressure on internal ballistic parameters. Sung et al²¹. established a numerical model and investigated the influence of pressure changes at the front end of the projectile within the launch tube, as well as the effect of constant pressure on the projectile’s velocity. They demonstrated that considering the pressure at the front end of the projectile as variable leads to a decrease in the projectile’s velocity.

Although compressed air ejection has found numerous applications^22,23, it has distinct disadvantages: In certain specific systems, the installation space for compressed air cylinders is limited, resulting in smaller cylinder volumes. To compress the air to a relatively high pressure, the compression system must expend a considerable amount of energy, leading to significant energy consumption. Moreover, to maintain this pressure over a certain period, there is a high demand for the pressure resistance of the compressed air cylinders, which substantially increase the weight of these cylinders. If the compressor’s capacity is limited, it can only compress air to lower pressures. To achieve the same launch specifications, the volume of the compressed air cylinder would have to increase multiple times, thereby impacting the spatial arrangement of the entire system. Therefore, there is a need to identify a gas that is more readily compressible than air and through heating or other measures, can rapidly increase the pressure within a high-pressure chamber under lower storage conditions to achieve the ejection of UAVs and meet the specified launch criteria.

Trifluoromethane, a widely used environmental refrigerant also known as R23, has a critical pressure of 4.832 MPa, a critical temperature of 26.14 °C, and a critical density of 570 kg/m³. With its low critical pressure, it is easily compressible into a liquid state by pumps to achieve high-density storage. Consequently, the requirements for the pressure resistance and weight of the high-pressure chamber are not stringent. Furthermore, as shown in Fig. 1, it has a low critical temperature, which can be rapidly transformed from storage state at room temperature to a high-temperature, high-pressure state by heating, thereby rapid release and expand to work. Figure 1was created using 3ds Max software (version 2020) and Adobe Photoshop software (version 2023)^24,25.Therefore, it possesses good engineering usability and is prone to thermal phase transitions that lead to expansion and work, making it an ideal medium for cold-launch applications.

Fig. 1

Schematic diagram of R23 performing work after being heated.

In this work, we propose a novel ejection method for UAVs that employs Trifluoromethane as the medium for cold gas ejection. The feasibility of using Trifluoromethane for UAV ejection was first verified through a ejection tests. Subsequently, we developed a numerical model of aerodynamic ejection thermodynamics with Trifluoromethane as the ejection medium, which was grounded in the principles of mass and energy conservation and described by the real gas state equation. This model was then rigorously validated against experimental data from the ejection tests. Furthermore, we utilized the model to explore the impact of key parameters within the ejection system on the internal ballistic performance of UAVs ejected using Trifluoromethane. Specifically, we investigated the effects of the high-pressure chamber volume, the high-pressure chamber release pressure, the valve diameter, the low-pressure chamber volume, and the launch cylinder length.

UAV ejection experiments using trifluoromethane

Experimental setup and parameters

As shown in Fig. 2, to validate the feasibility of using Trifluoromethane for the ejection of UAVs, a cylinder-type UAV ejection system was designed, comprising several components including a high-pressure chamber, a rupture disc valve, a low-pressure chamber, a counterweight of the UAV, and an ejection cylinder. Figure 2was created using PowerPoint software (version 2023)²⁶.The rupture disc valve was engineered to fully open in less than 0.2 ms, enabling an instantaneous opening and depressurization action^27,28. Prior to the ejection, liquid Trifluoromethane was stored in the high-pressure chamber. A ignition material was placed within the high-pressure gas storage chamber. Upon receiving an activation signal, the ignition material rapidly released heat. The liquid Trifluoromethane quickly underwent a phase change upon heating, causing a sharp increase in pressure. When the pressure within the high-pressure chamber reached the burst pressure of the rupture disc, the disc fully opened in less than 1 ms. The high-temperature, high-pressure gas from the high-pressure chamber was then instantaneously sprayed into the low-pressure chamber. Once the pressure in the low-pressure chamber exceeded the combined weight and resistance of the piston and the UAV, the UAV was accelerated forward and ejected from the ejection cylinder, completing the ejection process.

Fig. 2

Schematic diagram of the experimental system.

The experimental setup, as depicted in Fig. 3, utilized counterweight to substitute for actual UAVs. The ejection velocity of the counterweight was calculated using high-velocity camera. Pressure changes within the low-pressure chamber were measured with a pressure sensor, with a sampling frequency of 10, kHz. The data acquisition system employed was model DH5922D. The parameters related to the experiment were set as shown in Table 1. In this experiment, black powder was utilized as the ignition material, with the corresponding data depicted in Table 2.

Fig. 3

Testing apparatus.

Table 1 Parameter Settings of Test.

Table 2 Parameter Settings of Ignition Material.

Experimental results and analysis.

Markers were affixed to the counterweights, with each small square on the marker paper measuring 3.0 cm in length. The end marker on the counterweight was selected as the reference point for length, with a length of 3.0 cm, which served as the basis for velocity calculations. The high-velocity photography of the counterweight exiting the launch cylinder is depicted in Fig. 4.

Fig. 4

Pre- and Post-Egress images of the marker point exiting the launch cylinder.

In the high-velocity camera footage, the time at which the marker point began to emerge from the cylinder was 0.0564 s. The time at which the marker point was completely clear of the cylinder was recorded as 0.05712 s. The egress velocity of the marker point was determined to be 41.6 m/s.

Figure 5 presents the pressure curve obtained from the low-pressure chamber tests. It is observable that the pressure within the low-pressure chamber rose sharply, and subsequently, the counterweight was propelled. Within 30 ms, the pressure in the low-pressure chamber decreased to ambient atmospheric pressure. From the experiment, it was evident that Trifluoromethane was capable of rapidly ejecting the UAV counterweight from the cylinder. This demonstrates the feasibility of using Trifluoromethane as a propellant medium for the ejection of UAVs.

Fig. 5

Pressure test curve of low pressure chamber.

Parameter uncertainties

We utilized pressure sensors to measure the pressure within the low-pressure chamber, with a maximum test pressure of 10 MPa and an accuracy of 0.2%. The weight of the UAV and the ignition materials was determined using an electronic scale, which has a maximum weighing capacity of 10 kg and an accuracy of 0.05%. The volumes of the high and low-pressure chambers were tested using the water displacement method. We filled the high and low-pressure chambers with water using a measuring cup, and after the chambers were filled to the brim, we weighed the water to determine the volume of the high and low-pressure chambers. The measuring cup had a maximum volume of 50 ml and an accuracy of 0.05%. The diameters of the valves, the internal diameter of the launch tube, the diameter of the ignition material filling, and the filling length were measured using a vernier caliper with a maximum range of 150 mm and an accuracy of 0.01%. The effective acceleration length was tested with a ruler, which had a maximum range of 1 m and an accuracy of 0.05%. The length of the marking point used to test the egress velocity of the UAV from the launch tube is 3.0 cm, and measured using a vernier caliper with a range of 150 mm and an accuracy of 0.01%. The process of the UAV exiting the launch tube was captured using high-speed camera with a frame rate of 10,000 Fps and an accuracy of 0.01%.

The density of trifluoromethane, the density of ignition materials, and the egress velocity of the UAV from the launch tube are indirect measurements. According to the error propagation theory proposed by Moffat²⁹, for an indirectly measured quantity, assuming it is synthesized from a number of directly measured quantities, i.e., assuming R = f(x₁, …, x_i, …, x_N), the uncertainty of a single measurement is propagated through Eq. (1), and the uncertainty of the derived quantity R is also calculated through Eq. (1). The uncertainties of the experimental targets, pressure and velocity, are 0.2% and 0.014%, respectively. The uncertainties of all parameters are shown in Table 3.

$$R = \left[ {\sum\limits_{i = 1}^{N} {\left( {\frac{\partial R}{{\partial x_{i} }}\partial x_{i} } \right)^{2} } } \right]^{1/2}$$

(1)

Table 3 Parameter Measurements and Uncertainties.

Establishment and validation of the trifluoromethane ejection thermodynamic model

Ejection model

The ejection model, referring to literature^30,31, was based on the principles of mass and energy conservation, and the description of Trifluoromethane as a real gas. A thermodynamic numerical model for aerodynamic ejection, which considers the combustion process of ignition materials, has been established, utilizing Trifluoromethane as the ejection medium. The ejection system model is composed of several components, including a high-pressure chamber, a valve, a low-pressure chamber, a piston, an UAV, and an ejection cylinder, as depicted in Fig. 6.

Fig. 6

Schematic Diagram of the Ejection Model.

The ejection process involves complex phenomena such as convective heat transfer, non-uniform phase change, and multiphase mixing. To simplify the research process, the following assumptions were made:

• (1) The high-pressure chamber and the low-pressure chamber are considered to be perfectly rigid, without taking into account volume changes due to factors such as pressure or temperature.

• (2) It is assumed that the fluid in the high-pressure chamber is uniformly distributed and in a state of complete thermodynamic equilibrium throughout the process.

• (3) Before the UAV is ejected from the cylinder, the ejection medium does not undergo heat exchange with the high-pressure chamber, the low-pressure chamber, or the tray.

The thermodynamic parameters of fluid within the high-pressure chamber are denoted as pressure P₀, temperature T₀, internal energy U₀, specific enthalpy h₀, density ρ₀, and volume V₀. The initial fluid in the high-pressure chamber is trifluoromethane, which, upon the combustion of the ignition material, transitions into a mixture of trifluoromethane and the gases produced by the combustion of the ignition material.

The parameters of the ignition material are: mass m_ex, burn rate v_ex, specific energy E_ex, filling diameter D_ex, filling density $\rho_{{{\text{ex}}}}$, and length L_ex.

The mass flow rate of fluid within the high-pressure chamber is given by Eq. (2),

$$\frac{{{\text{d}}m_{{0}}^{{}} }}{{{\text{d}}t}} = - q_{m} + m_{{{\text{exout}}}}^{{}}$$

(2)

where $m_{0}$ is the mass of fluid in the high-pressure chamber, kg. $q_{m}$ is the mass flow rate through the valve, kg/s.$m_{{{\text{exout}}}}^{{}}$ is the mass of gases released by the ignition material per unit time, kg/s.

$$m_{exout}^{{}} = \gamma \cdot v_{ex}^{{}} {\kern 1pt} (\frac{{D_{ex} }}{2})^{2} {\kern 1pt} \rho_{ex} (\int_{0}^{t} {v_{ex}^{{}} dt} \le L_{ex} )$$

(3)

$$m_{exout}^{{}} = 0{\kern 1pt} (\int_{0}^{t} {v_{ex}^{{}} dt}> L_{ex} )$$

(4)

where $\gamma$ is the ratio of the mass of gases generated by the ignition material to the mass of the ignition material, %. v_exis the burn rate in meters per second, m/s. In practical applications within the high-pressure chamber, the burn rate is typically calculated using an exponential formula as referenced³², as shown in Eq. (5).

$$v_{{{\text{ex}}}}^{{}} = aP_{0}^{n}$$

(5)

where a is the combustion coefficient, and n is the combustion index.

The rate of change of internal energy of fluid in the high-pressure chamber is given by Eq. (6),

$$\frac{{{\text{d}}U_{0}^{{}} }}{{{\text{d}}t}} = - q_{m} \cdot h_{{{\text{out}}}}^{{}} + E_{{{\text{exout}}}}^{{}}$$

(6)

where $h_{{{\text{out}}}}$ is the specific enthalpy of fluid at the outlet to the high-pressure chamber. E_exout is the heat released by the ignition material per unit time, J/s.

Assuming a uniform distribution of the fluid and a state of complete thermodynamic equilibrium throughout the process, so,

$$h_{out} = h_{{0}}$$

(7)

where, h₀ is defined as follows:

$$h_{0} = f(\rho_{0} ,u_{0} {)}$$

(8)

where,

$$\rho_{0} = \frac{{m_{0} }}{{V_{0} }}$$

(9)

$$u_{0} = \frac{{U_{0} }}{{m_{0} }}$$

(10)

where,

$$V_{0} = \int_{0}^{t} {v_{ex}^{{}} dt} \cdot \left( {\frac{{D_{ex} }}{2}} \right)^{2} + V_{0}^{1} {\kern 1pt} (\int_{0}^{t} {v_{ex}^{{}} dt} \le L_{ex} )$$

(11)

$$V_{0}^{{}} = V_{0}^{1} + \frac{{m_{ex} }}{{\rho_{ex} }}{\kern 1pt} (\int_{0}^{t} {v_{ex}^{{}} dt}> L_{ex} )$$

(12)

$$E_{exout}^{{}} = E_{ex} \cdot v_{ex}^{{}} \cdot (\frac{{D_{ex} }}{2})^{2} \cdot \rho_{ex} {\kern 1pt} \int_{0}^{t} {v_{ex}^{{}} dt} \le L_{ex}$$

(13)

$$E_{exout}^{{}} = 0{\kern 1pt} \int_{0}^{t} {v_{ex}^{{}} dt}> L_{ex}$$

(14)

where $V_{0}^{1}$ is the initial volume of fluid within the high-pressure chamber, m³.

The temperature T₀ and pressure P₀ of fluid in the high-pressure chamber are defined by Eq. (15) and Eq. (16),

$$T_{0} = f(\rho_{0} ,u_{0} {)}$$

(15)

$$P_{0} = f(\rho_{0} ,u_{0} {)}$$

(16)

For fluid in the low-pressure chamber, the thermodynamic parameters are pressure P, temperature T, internal energy U, specific enthalpy h, density ρ, and volume V. The mass flow rate of fluid in the low-pressure chamber is given by Eq. (17),

$$\frac{{{\text{d}}m}}{{{\text{d}}t}} = q_{m}$$

(17)

where $m$ is the mass of fluid in the low-pressure chamber.

When the force created by the pressure is less than the combined weight and resistance of the piston and the aircraft, the rate of change of internal energy of fluid in the low-pressure chamber is given by Eq. (18),

$$\frac{{{\text{d}}U}}{{{\text{d}}t}} = q_{m} \cdot h_{in}$$

(18)

where $h_{{{\text{in}}}}$ is the specific enthalpy of fluid at the outlet of the valve.

$$h_{{{\text{out}}}} = h_{in}$$

(19)

Upon the force created by the pressure exceeding the combined weight and resistance of the piston and the aircraft, the piston and the aircraft are propelled. At this point, the rate of change of internal energy of fluid in the low-pressure chamber is given by Eq. (20),

$$\frac{{{\text{d}}U}}{{{\text{d}}t}} = q_{m} \cdot h_{in} - \Delta E_{{\text{g}}} - \Delta E_{k}$$

(20)

where $\Delta E_{g}$ is the sum of the gravitational and frictional work done on the piston and the aircraft, as well as air resistance, kJ. $\Delta E_{k}$ is the incremental kinetic energy of the piston and the aircraft, kJ.

$$\Delta E_{g} = m_{UAV} \cdot g \cdot \sin (\theta ) \cdot \Delta x + \beta \cdot m_{UAV} \cdot g \cdot {\text{cos}}(\theta ) \cdot \Delta x + P_{atm} \cdot S \cdot \Delta x$$

(21)

where S is the area of the piston force, m². m_UAV is the combined mass of the piston and the UAV, kg. β is the coefficient of friction, which typically ranges from 0.1 to 0.2, we take it as 0.15. θ is the ejection angle, °. P_atm is atmospheric pressure. $\Delta x$ is the displacement of the piston and the aircraft along the launch tube, m.

The temperature T and pressure P of fluid in the low-pressure chamber are defined by Eq. (22) and Eq. (23), respectively.

$$T = f(\rho ,u{)}$$

(22)

$$P = f(\rho ,u{)}$$

(23)

where,

$$\rho = \frac{m}{V}$$

(24)

$$u = \frac{U}{m}$$

(25)

The motion of the piston and the UAV is calculated by Eq. (26),

$$m_{UAV} \cdot a = (P - P_{{{\text{atm}}}} ) \cdot S - m_{UAV} \cdot g \cdot \sin (\theta ) - \beta \cdot m_{UAV} \cdot g \cdot {\text{cos}}(\theta )$$

(26)

The mass flow rate q_m through the valve, which dynamically changes with the pressures in the high-pressure and low-pressure chambers, is related to the critical pressure ratio Pr²⁹ and can be calculated by Eq. (27),

$$p_{r} = (\frac{2}{{{\text{k}} + 1}})^{{\frac{{\text{k}}}{{{\text{k}} - {1}}}}}$$

(27)

When the ratio of the low-pressure chamber pressure to the high-pressure chamber pressure P/P₀ equals Pr, the flow within the valve reaches a critical state. The mass flow rate through the valve will be at its maximum, and further reduction in the low-pressure chamber pressure will not increase the flow rate, resulting in choked flow. This maximum value can be calculated by Eq. (28),

$$q_{\max } = \mu S_{t} \sqrt {{\text{k}}(\frac{2}{{{\text{k}} + 1}})^{{\frac{{{\text{k}} + 1}}{{{\text{k}} - 1}}}} P_{0} \rho_{0} }$$

(28)

When the ratio P/P₀ is greater than Pr , the mass flow rate of the medium through the valve can be calculated by Eq. (29),

$$q_{m} = \mu S_{t} \sqrt {\left( {\frac{{2{\text{k}}}}{{{\text{k}} - {1}}}} \right)P_{0} \rho_{0} \left[ {\left( {\frac{P}{{P_{0} }}} \right)^{{{2 \mathord{\left/ {\vphantom {2 {\text{k}}}} \right. \kern-0pt} {\text{k}}}}} - \left( {\frac{P}{{P_{0} }}} \right)^{{{{{\text{k}} + 1} \mathord{\left/ {\vphantom {{{\text{k}} + 1} {\text{k}}}} \right. \kern-0pt} {\text{k}}}}} } \right]}$$

(29)

where μ is a flow coefficient related to the valve structure, which can be selected between 0.85 and 0.95 based on experimental results or experience. S_t is the valve area. k= 1.25 is the isentropic coefficient for Trifluoromethane³³.

The fis the real thermophysical state equation of Trifluoromethane, which is used to calculate the thermophysical parameters. The NIST database contains a vast amount of thermophysical state parameters for fluid substances, and its updated accuracy has been widely recognized by scholars and engineering professionals^34,35 Therefore, this work employs the real thermophysical state equation for Trifluoromethane as calculated from the NIST database.

Model validation

The pneumatic ejection thermodynamic numerical model was programmed and computed using the Matlab software. The accuracy of the model was then verified against the ejection experiments conducted as described in the experimental section. The parameters for the validation model were set according to the parameters of the ejection experiments detailed in the experimental section. The simulated velocity and displacement curves for the UAV are depicted in Fig. 7. A comparison of the simulated and actual test results for the pressure in the low-pressure chamber is shown in Fig. 8, and the simulated temperature in the low-pressure chamber is illustrated in Fig. 9.

Fig. 7

Simulated velocity and displacement curves.

Fig. 8

Comparison of curves between simulated pressure and actual test in low pressure chamber.

Fig. 9

Simulation curve of low-pressure chamber temperature.

As depicted in Fig. 7, the simulated ejection velocity of the UAV upon exiting the cylinder is 42.3 m/s, whereas the actual test velocity is 41.6 m/s, resulting in a deviation of 1.78%. Figure 8 shows the comparison between the simulated and actual pressure curves in the low-pressure chamber. The total time for pressure increases and decreases is consistent between the two, however, there is a discrepancy in the peak values. This discrepancy can be attributed to the model’s one-dimensional assumption, which considers the pressure in the entire low-pressure chamber to be uniformly distributed. In the actual test, the pressure sensor is in close proximity to the valve, leading to higher measured pressures during the pressure rise compared to other locations in the low-pressure chamber and lower pressures during the pressure drop. Additionally, the presence of reflected waves during the ejection process contributes to the deviation between the actual and simulated curves, which aligns with practical law. As shown in Fig. 9, the temperature inside the cylinder at the time of UAV ejection is 196.5 K, significantly lower than the ambient temperature, confirming that the ejection was indeed a true cold gas ejection.

The comparison between the test results and the simulation results indicates that the pneumatic ejection thermodynamic numerical model is relatively accurate and can be applied to predict the internal ballistic parameters for UAVs of greater mass.

Influence of design parameters on internal ballistic parameters

This study employs a pneumatic ejection thermodynamic numerical model to investigate the influence of key structural components of the ejection system on the ballistic parameters of Trifluoromethane-propelled UAVs. Specifically, the effects of the high-pressure chamber volume, the release pressure of the high-pressure chamber, the valve diameter, the volume of the low-pressure chamber, and the length of the launch cylinder are examined. To concurrently validate the feasibility of using Trifluoromethane for the ejection of larger UAVs, this work selects a total mass of 550 kg for the UAV and the piston. The other basic reference conditions are as follows: the volume of the high-pressure chamber is 4 L, with a liquid density of 1100 kg/m³, the diameter of the valve is 40 mm, the valve opening pressure is 50 MPa, the volume of the low-pressure chamber is 50 L, the internal diameter of the launch cylinder is 430 mm, the length of the ejection cylinder is 4.5 m, the launching angle is 85°.The subsequent computational scenarios disregard the heating process of liquid Trifluoromethane by the ignition material, concentrating instead on the state following the complete attainment of the high-pressure chamber’s release pressure, thereby facilitating a clearer investigation of the underlying principles.

Impact of High-pressure chamber volume

Under the condition of constant density, the volume of the high-pressure gas storage chamber determines the mass of Trifluoromethane utilized. To analyze the impact of the high-pressure gas storage chamber volume on the internal ballistics of the UAV, calculations were performed for three different initial volumes 4 L, 6 L, and 8 L, with all other parameters remaining constant.

Figure 10 presents the pressure variation curves for the high-pressure chamber and the low-pressure chamber corresponding to different high-pressure chamber volumes prior to the UAV’s egress from the cylinder. It can be observed that regardless of the high-pressure chamber’s volume, the pressure within the high-pressure chamber gradually decreases upon valve opening. Initially, the pressure in the low-pressure chamber increases, and then it gradually decreases as the UAV begins to move. As the volume of the high-pressure chamber increases, the time taken for the pressure to decrease to its minimum value becomes longer, and the peak pressure in the low-pressure chamber is higher, with a faster rate of increase and a slower rate of decrease. Figure 11 can explain this phenomenon. With a larger high-pressure chamber volume, and density being constant, more Trifluoromethane is stored within it. Over time, a high-volume high-pressure chamber releases a greater mass flow rate compared to a low-volume chamber. Consequently, a larger quantity of Trifluoromethane is released into the low-pressure chamber per unit time, leading to a rapid and substantial increase in pressure and temperature within the low-pressure chamber. The larger the volume of the high-pressure chamber, the more trifluoromethane it can contain. Despite the relatively large mass flow rate per unit time, it is insufficient to ensure the rapid completion of the internal Trifluoromethane release. This results in an extended duration for the pressure and temperature within the high-pressure chamber to decrease to their minimum values.

Fig. 10

Different pressure curves for different volumes of high-pressure chamber.

Fig. 11

Different valve output mass flow for different volumes of high-pressure chamber.

Figure 12 illustrates the temperature variation curves for the high-pressure chamber and the low-pressure chamber prior to the UAV’s egress from the cylinder, corresponding to different high-pressure chamber volumes. It can be observed that regardless of the high-pressure chamber’s volume, the temperature within the high-pressure chamber gradually decreases upon valve opening. The temperature in the low-pressure chamber exhibits an initial rapid decrease, followed by an increase, and then a subsequent decrease. This trend in the low-pressure chamber’s temperature is attributed to the instant when the high-pressure chamber is opened, and a small amount of Trifluoromethane is sprayed into the low-pressure chamber, causing an instantaneous decrease in density and a corresponding drop in temperature. As more Trifluoromethane is progressively sprayed in, the density and pressure within the low-pressure chamber gradually increase, leading to a gradual rise in temperature. Once the pressure in the low-pressure chamber reaches a certain level and the UAV begins to move, the density and pressure of the Trifluoromethane within the low-pressure chamber gradually decrease, causing the temperature to decrease as well. When the high-pressure chamber volume is 4 L, the minimum temperature in the low-pressure chamber is 188 K, which is lower than that observed when the high-pressure chamber volumes are 6 L and 8 L. As shown in Fig. 13, although the phase state of Trifluoromethane in the low-pressure chamber approaches a gas–liquid two-phase state towards the end of the ejection process in all three scenarios, it remains in the gaseous state and has no impact on the ejection of the UAV.

Fig. 12

Different temperature curves for different volumes of high pressure chamber.

Fig. 13

Phase diagrams of low pressure chambers corresponding to different high pressure chamber.

Figure 14 demonstrates that as the volume of the high-pressure chamber increases, the peak acceleration of the UAV within the low-pressure chamber becomes higher, and correspondingly, the ejection velocity of the UAV exiting the cylinder also increases. When the volume of the high-pressure chamber is increased from 4 to 6 L, the maximum acceleration increases from 136.4 m/s² to 158.0 m/s², and the corresponding maximum velocity increases from 13.7 m/s to 18.4 m/s, resulting in a 34.3% increase. Upon further increasing the volume from 6 to 8 L, the maximum acceleration rises from 158.0 m/s² to 177.7 m/s², and the corresponding maximum velocity increases from 18.4 m/s to 22.3 m/s, indicating a 21.1% increase.

Fig. 14

Different velocity and acceleration curves of the aircraft for different volumes of high-pressure chamber.

The results indicate that Trifluoromethane can be effectively utilized for the ejection of large UAVs. As the volume of the high-pressure chamber increases, the ejection velocity of the UAV upon exiting the cylinder also increases, but the rate of increase diminishes over time. As can be seen from Fig. 15, in the computational example of this work, when the volume of the high-pressure gas storage tank is increased to 1000 L, the increase in the ejection velocity of the UAV from the launch cylinder is almost negligible. Furthermore, if the ejection velocity is meeting the minimum ejection velocity requirements, selecting a smaller high-pressure chamber volume can reduce the peak pressure and temperature within the low-pressure chamber. It can enhances the structural safety of the low-pressure chamber and ensures the safety of the ejection process. Additionally, it can reduce the launch overload experienced by the UAV, preventing damage to the UAV’s airframe and engine components from excessive instantaneous impact.

Fig. 15

The velocity of the UAV flying out of the launcher varies with the volume of the high-pressure chamber.

Impact of high-pressure chamber release pressure

To analyze the impact of the high-pressure chamber release pressure on the internal ballistics of UAV ejection, the release pressure of the high-pressure chamber was varied while keeping all other parameters of the base case constant. Calculations were conducted for three scenarios with high-pressure chamber release pressures of 50 MPa, 60 MPa, and 70 MPa, respectively.

Figure 16 illustrates the pressure change curves for the high-pressure gas storage chamber and the low-pressure chamber prior to the egress of the UAV from the cylinder under different high-pressure chamber release pressures. As the valve was opened, the pressure within the high-pressure chamber gradually decreased. The pressure in the low-pressure chamber initially increased, and then, as the UAV commenced movement, the pressure in the low-pressure chamber gradually decreased. For the high-pressure chamber, an increase in the release pressure implies an increase in the peak pressure within the chamber. Similarly, for the low-pressure chamber, the peak pressure increases from 0.66 MPa to 0.75 MPa, and then to 0.85 MPa, with increments of 13.6% and 13.3%, respectively. This indicates that increasing the release pressure has a significant impact on the peak pressures in both the high-pressure and low-pressure chambers.

Fig. 16

Different pressure curves corresponding to different releases pressure of high-pressure chamber.

Figure 17 displays the temperature variation curves for the high-pressure chamber and the low-pressure chamber before the UAV exits the cylinder, under different release pressures of the high-pressure chamber. It is evident that upon the opening of the valve, the temperature within the high-pressure chamber gradually decreased in all instances. For the low-pressure chamber, the temperature consistently exhibited an initial rapid decrease, followed by an increase, and then a subsequent decrease. For the low-pressure chamber, as the release pressure of the high-pressure chamber increased, the initial temperature drop in the low-pressure chamber’s temperature curve became progressively less pronounced. This was due to the fact that with an increase in the release pressure of the high-pressure chamber, the release temperature of the Trifluoromethane also increased. Consequently, the temperature decrease of the Trifluoromethane sprayed into the low-pressure chamber at the moment the high-pressure chamber was opened was reduced, causing the curve to tend towards a consistently decreasing form. With the increase in the release pressure of the high-pressure chamber, the minimum temperature in the low-pressure chamber rose slightly from 188 to 191 K. As can be seen from Fig. 18, the phase state of Trifluoromethane within the low-pressure chamber remained consistently in the gaseous state, which had no impact on the ejection of the UAV.

Fig. 17

Different temperature curves corresponding to different releases pressure of high-pressure chamber.

Fig. 18

Phase diagrams of low pressure chambers corresponding to different releases pressure of high-pressure chamber.

From Fig. 19, it can be observed that as the release pressure of the high-pressure chamber increases, the peak acceleration of the UAV within the low-pressure chamber becomes higher, and correspondingly, the ejection velocity of the UAV as it exits the cylinder also increases. When the release pressure of the high-pressure chamber was increased from 50 to 60 MPa, the maximum acceleration rose from 136.4 m/s² to 159.35 m/s², and the corresponding maximum velocity increased from 13.7 m/s to 15.5 m/s, representing a 13.1% increase for maximum velocity. Upon further increasing the release pressure from 60 to 70 MPa, the maximum acceleration increased from 159.35 m/s² to 185.14 m/s², and the corresponding maximum velocity increased from 15.5 m/s to 17.2 m/s, resulting in an 11.0% increase for maximum velocity.

Fig. 19

Different velocity and acceleration curves of the aircraft corresponding to different releases pressure of high-pressure chamber.

The results indicate that the greater the release pressure of the high-pressure chamber, the higher the ejection velocity of the UAV upon exiting the cylinder. However, the rate of increase in ejection velocity diminishes over time, suggesting the existence of a threshold release pressure beyond which the increase in ejection velocity is almost negligible, approaching 0%. If the UAV ejection does not excessively pursue ejection velocity and satisfies the minimum ejection velocity requirements, opting for a lower release pressure of the high-pressure chamber can reduce the peak pressures and temperatures within both the high-pressure and low-pressure chambers. This approach enhances the structural safety of the chambers and ensures the safety of the ejection process. Additionally, it can reduce the launch overload experienced by the UAV, preventing damage to the UAV’s airframe, engine, and other components from excessive instantaneous impact.

Influence of valve diameter

To analyze the impact of valve diameter on the internal ballistics of UAV ejection, the diameter of the valve released was altered while maintaining all other parameters of the base case constant. Calculations were performed for three scenarios with valve diameters of 30 mm, 40 mm, and 50 mm, respectively.

Figure 20 illustrates the pressure change curves for the high-pressure gas storage chamber and the low-pressure chamber prior to the egress of the UAV from the cylinder under different valve diameters. It is observed that regardless of the valve diameter size, the pressure within the high-pressure chamber gradually decreases upon valve release. Initially, the pressure in the low-pressure chamber increases, and then it gradually decreases as the UAV begins to move. With an increase in valve diameter, the time it takes for the pressure in the high-pressure chamber to decrease to its minimum value becomes shorter, and the peak pressure in the low-pressure chamber becomes higher, with a faster rate of increase and decrease. Figure 21 can explain this phenomenon because as the valve diameter increases, the mass flow rate released during the initial phase of depressurization from the high-pressure chamber is greater. Consequently, the amount of Trifluoromethane released into the low-pressure chamber per unit time is higher, leading to a rapid and significant increase in pressure. When the release reaches a certain duration, the density of Trifluoromethane within the high-pressure chamber corresponding to the larger valve diameter decreases to a point where its effect surpasses the impact of the valve diameter alone. After this point, the mass flow rate corresponding to the system with a larger valve diameter becomes less than that of the system with a smaller valve diameter. Therefore, the amount of Trifluoromethane released into the low-pressure chamber per unit time gradually decreases, resulting in a more rapid decline in both the pressure and temperature within the low-pressure chamber.

Fig. 20

Different pressure curves for different valve diameter.

Fig. 21

Different valve output mass flow for different valve diameter.

Figure 22 displays the temperature variation curves for the high-pressure chamber and the low-pressure chamber before the UAV exits the cylinder, under different valve diameters. It is observed that as the valve is opened, the temperature within the high-pressure chamber gradually decreases. The temperature in the low-pressure chamber consistently exhibits an initial rapid decline, followed by an increase, and then a subsequent decrease. For the low-pressure chamber, with an increase in valve diameter, the initial drop in the temperature curve becomes less pronounced. This is because, with an increase in valve diameter, the mass of Trifluoromethane that is sprayed into the low-pressure chamber at the moment the high-pressure chamber is opened increases, resulting in a smaller temperature drop. The curve as a whole tends to develop into a continuously decreasing form. The temperature in the low-pressure chamber experiences a sharp decline, followed by an increase and then a subsequent decrease. This fluctuation is also caused by changes in the mass flow rate, as shown in Fig. 21. It can be inferred from Fig. 23 that the phase state of Trifluoromethane within the low-pressure chamber has been consistently gaseous, which does not affect the ejection of the UAV.

Fig. 22

Different temperature curves for different valve diameter.

Fig. 23

Phase diagram of low pressure chamber corresponding to different valve diameter.

As shown in Fig. 24, under the condition of a larger release diameter, the peak acceleration inside the UAV cylinder is high. When the valve diameter is increased from 30 to 40 mm, the maximum acceleration of the UAV inside the low-pressure chamber increases from 105.4 m/s² to 136.3 m/s², an increase of 29.3%. The exit velocity of the UAV from the cylinder increases from 11.7 m/s to 13.7 m/s, an increase of 17.1%. When the valve diameter is further increased from 40 to 50 mm, the maximum acceleration of the UAV inside the low-pressure chamber increases from 136.3 m/s² to 164.7 m/s², an increase of 20.8%. The exit velocity of the UAV from the cylinder increases from 13.7 m/s to 14.6 m/s, an increase of 6.6%. It can be observed that as the valve diameter increases, the increase in peak acceleration is greater than the increase in velocity. When the diameter is increased to a certain extent, there will be a situation where increasing the valve diameter only increases the peak acceleration, with the velocity increasing almost negligibly.

Fig. 24

Different velocity and acceleration curves of the aircraft for different valve diameter.

From the results presented above, it can be inferred that for a specific catapult system, there exists a critical release diameter. Beyond this diameter, the ejection velocity of the UAV will no longer increase, instead, only the peak acceleration will increase. If the objective is to maximize the ejection velocity of the UAV upon exiting the cylinder, one could opt for this critical diameter. However, if the ejection velocity is not the primary concern for the UAV launch, and provided that the minimum ejection velocity is met, selecting a valve with a smaller diameter can reduce the peak pressure inside the low-pressure chamber, ensuring the safety of the launch.

The influence of the low-pressure chamber volume

To analyze the influence of the low-pressure chamber volume on the internal ballistics of UAVs, the volume of the low-pressure chamber was altered while keeping other parameters of the basic operational condition constant. Calculations were performed for three scenarios with chamber volumes of 30 L, 50 L, and 70 L, respectively.

Figure 25 presents the pressure variation curves within the high-pressure chamber and the low-pressure chamber corresponding to different low-pressure chamber volume conditions before the UAV exits the cylinder. It can be observed that as the volume of the low-pressure chamber increases, the rate of pressure decrease in the high-pressure chamber during the initial phase of release remains consistent, while at the end of the release phase, the pressure decreases more rapidly under conditions with a smaller low-pressure chamber volume. The pressure within the low-pressure chamber also exhibits a pattern of initial increase followed by a decrease. As the volume of the low-pressure chamber increases, the peak pressure and temperature within the chamber become lower, and both the rate of increase and decrease slow down. This phenomenon can be explained from the perspective of mass flow rate, as shown in Figs. 26 and 27. Since the high-pressure chamber pressure and valve release diameter are consistent across the three conditions, the mass flow rate for each condition directly reaches its maximum (i.e., calculated according to the maximum flow rate formula (28) during the initial phase of release. Consequently, the rate of pressure decrease in the high-pressure chamber is consistent during the initial phase. At this time, the larger the volume of the low-pressure chamber, the smaller the peak pressure within it, and the slower the rates of both increase and decrease. When the release time reaches 160 ms, the mass flow rate for each condition begins to be calculated according to formula (29), as depicted in Fig. 27. Under conditions with a smaller low-pressure chamber volume, the mass flow rate is higher before 192 ms, resulting in a more rapid decrease in the high-pressure chamber pressure and temperature. After 259 ms, although the mass flow rate under conditions with a smaller low-pressure chamber volume decreases, its impact has become negligible.

Fig. 25

Different pressure curves for different volumes of low pressure chamber.

Fig. 26

Comparison of mass flow rate for low pressure chamber with 70L volume.

Fig. 27

Different valve output mass flow for different volumes of low pressure chamber.

Figure 28 displays the temperature variation curves within the high-pressure chamber and the low-pressure chamber corresponding to different low-pressure chamber volume conditions before the UAV exits the cylinder. It can be observed that as the valve opens, the temperature within the high-pressure chamber gradually decreases, and the temperature within the low-pressure chamber exhibits a trend of rapid decrease followed by an increase and then a subsequent decrease. For the low-pressure chamber, as the volume increases, the first descending waveform of the low-pressure chamber temperature curve has a larger drop. This is because, at the instant the high-pressure chamber is opened, under the same mass flow rate, the density of Trifluoromethane within the larger volume low-pressure chamber is momentarily lower, resulting in a lower instantaneous temperature. Figure 29 indicates that the phase state of Trifluoromethane within the low-pressure chamber remains consistently in the gaseous state, which has no impact on the ejection of the UAV.

Fig. 28

Different temperature curves for different volumes of low pressure chamber.

Fig. 29

Phase diagram of low pressure chamber corresponding to different volumes of low pressure chamber.

As depicted in Fig. 30, the peak acceleration of the UAV is higher under conditions with a smaller low-pressure chamber volume. When the volume of the low-pressure chamber is increased from 30 to 50 L, the maximum acceleration of the UAV within the chamber decreases from 183.2 m/s² to 136.4 m/s², a reduction of 25.5%. The exit velocity of the UAV from the cylinder decreases from 14.7 m/s to 13.7 m/s, a reduction of 6.8%. When the volume of the low-pressure chamber is further increased from 50 to 70 L, the maximum acceleration of the UAV within the chamber decreases from 136.4 m/s² to 111.2 m/s², a reduction of 18.5%. The exit velocity of the UAV from the cylinder decreases from 13.7 m/s to 12.8 m/s, a reduction of 6.6%. It is evident that as the volume of the low-pressure chamber increases, the reduction in peak acceleration is significantly greater than the reduction in velocity.

Fig. 30

Different velocity and acceleration curves of the aircraft for different volumes of low pressure chamber.

The influence of the launch cylinder length

To investigate the impact of launch cylinder length on the internal ballistics of UAVs, the length of the launch cylinder was varied while keeping other parameters of the basic operational condition constant. Calculations were conducted for three scenarios with launch cylinder lengths of 3.5 m, 4.5 m, and 5.5 m, respectively.

As illustrated in Fig. 31, altering the length of the launch cylinder does not change the developmental trend or the values of the pressure curves in the high-pressure and low-pressure chambers, it only affects their final end times and final pressures, without impacting the peak pressures or the peak acceleration of the UAV. As shown in Table 4, the longer the launch cylinder, the lower the final pressure in the low-pressure chamber, which is also equivalent to the nozzle pressure. When the launch cylinder length is 3.5 m, the nozzle pressure is 0.11 MPa. When the launch cylinder length is 4.5 m, the nozzle pressure is 0.087 MPa, and when the launch cylinder length is 5.5 m, the nozzle pressure is 0.071 MPa. From Fig. 29 and Table 2, it can be observed that the effect of launch cylinder length on the ejection velocity of the UAV follows a parabolic form, meaning that as the launch cylinder length increases, the ejection velocity of the UAV first increases and then decreases. When the basic operational conditions are set with a high-pressure chamber volume of 4 L, a high-pressure chamber liquid density of 1100 kg/m³, a valve diameter of 40 mm, a valve opening pressure of 50 MPa, a low-pressure chamber volume of 50 L, and an inner diameter of the launch cylinder of 430 mm, the optimal launch cylinder length for maximum UAV ejection velocity is 2.46 m.

Fig. 31

Displacement, velocity and pressure curves of low pressure chamber.

Table 4 Simulation result.

The analysis results indicate that for a specific catapult system, there exists an optimal launch cylinder length that maximizes the UAV ejection velocity without affecting acceleration. If the UAV ejection does not overly pursue ejection velocity, and provided that the minimum ejection velocity is met and the overall structure of the UAV ejection system allows, using a longer launch cylinder can reduce the launch cylinder nozzle pressure, as well as the noise at the moment of UAV ejection and the design strength required at the launch cylinder nozzle.

Conclusions

This work introduces Trifluoromethane as a novel working medium for the cold gas catapult of UAVs. The feasibility of using Trifluoromethane for catapulting UAVs was validated through ejection experiments. Additionally, a thermodynamic numerical model for pneumatic ejection was established, further confirming the method’s feasibility. The influence of the high-pressure chamber volume, valve diameter, and low-pressure chamber volume on the ballistic parameters of Trifluoromethane-propelled UAVs was discussed.

(1) Trifluoromethane can be utilized for catapult launching UAVs, ensuring that the temperature within the launch cylinder remains below 200 K upon ejection, thereby enabling a cold launch capability.

(2) Under conditions of constant liquid density, as the high-pressure chamber volume increases, the pressure within the low-pressure chamber, the UAV’s acceleration, and the ejection velocity from the cylinder all gradually increase, although the rate of velocity increase diminishes. In the computational example presented in this work, increasing the volume of the high-pressure gas storage tank to 1000 L results in an almost negligible increase in the UAV’s ejection velocity from the launch cylinder. Ensuring the minimum ejection velocity, a smaller high-pressure chamber volume can reduce peak pressures and temperatures within the low-pressure chamber, thereby ensuring launch safety.

(3) The higher the release pressure from the high-pressure chamber, the greater the ejection velocity of the UAV from the cylinder, yet the rate of increase in velocity diminishes. Provided that the minimum ejection velocity is met, a lower release pressure from the high-pressure chamber can reduce the peak pressure and temperature within both the high-pressure and low-pressure chambers, as well as the UAV acceleration, thereby ensuring the safety of the launch.

(4) For a specific catapult system, there is a threshold release diameter for the valve beyond which the UAV’s ejection velocity will no longer increase, only the peak acceleration will increase. With other parameters held constant, appropriately increasing the low-pressure chamber volume can effectively reduce the UAV’s peak acceleration within the launch cylinder, with a negligible reduction in the UAV’s egress velocity.

(5) For a given catapult system, an optimal launch cylinder length exists that maximizes the UAV’s ejection velocity without affecting its acceleration. When the minimum ejection velocity is met, using a longer launch cylinder can reduce the pressure at the nozzle of the launch cylinder.