Analysis of the Propulsion Performance and Internal Flow Field of an Underwater Launcher

Abstract

The gas-curtain launch is designed to address the shortcomings of conventional underwater launchers, such as poor dependability and low muzzle velocity. In this paper, the influence of jet structures on the propulsion performance and internal flow field of an underwater gas-curtain launcher is investigated. To conduct the experiment on a small-aperture underwater launcher, three projectiles with different jet structures were designed. The experimental results show that a projectile with a central nozzle is more conducive to gas-curtain formation than one with four sidewall grooves. Additionally, the central nozzle can reduce launch resistance and improve propulsion performance more effectively. Furthermore, increasing the diameter of the central nozzle aids in gas-curtain formation and propulsion performance. Following the experiment, a numerical model of the internal flow field for gas-curtain launch is built in order to develop numerical simulations under three jet structures. The calculation results show that the three gas-curtain projectiles can likewise acquire good propulsion performance. Different jet structures have significant impacts on the launching resistance of a gas-curtain launcher, thereby affecting its propulsion performance. The launch resistance is lower when the central nozzle jet structure is utilized; however, the muzzle velocity is also lower because more gas is consumed for drag reduction and the projectile force area is smaller. This study reveals the effect of jet structure on the propulsion performance and flow field evolution of a gas-curtain launcher.

1. Introduction

Tremendous resistance makes it difficult for underwater vehicles to navigate at high speeds. To address this vexing issue, supercavitation technology was developed, which can greatly lower the navigation resistance of underwater vehicles [1,2,3,4,5]. However, supercavitation technology is only applicable to vehicles that have been fully submerged in water, and it is incapable of reducing resistance during the vehicles’ underwater launching processes. As a result, finding a way to reduce resistance in the launching process is critical. The most ideal method for underwater launchers is to keep the barrel free of water to ensure that the projectile always moves in a low-resistance gas environment, achieving propulsion performance similar to that of an air launcher.

To achieve this goal, previous researchers preferred to add additional devices to keep water out of the barrel. Stace [6] proposed sealing the muzzle using a baffle and a member and then rotating the baffle to realize continuous sealing during the firing interval. Another two sealing methods were put forward by Kirschner and his team. One makes sure the pressure of gas inside the barrel is higher than the pressure of external water by an external gas source with a pressure regulator, thus preventing water from entering the barrel [7]. The other seals the barrel with a coaxial inner barrel and an outer barrel [8]. In addition to the above sealing devices, Fu [9] designed a plurality of movable baffles which involves magnetic and waterproof properties to realize sealing the muzzle. By pushing the baffle to transition between the sealing and firing positions, a continuous waterproof effect is achieved. Although the above sealing devices help the purpose of muzzle sealing, they also make the underwater launcher more complex. Obviously, the complex structure will reduce the reliability of the underwater launcher and make it unable to meet the complex underwater continuous shooting environment. Therefore, researchers are looking for more suitable solutions. Cipolla [10] proposed firing a blank ammunition firstly to generate gas and steam to replace water in the barrel, resulting in a low-resistance launching environment for succeeding projectiles. However, serious accidents may happen if water gets into the barrel before live ammunitions are shot.

To solve the shortcomings of existing underwater launching methods, such as poor reliability or low muzzle velocity [11], the gas-curtain launch for underwater launchers is proposed. By introducing a portion of the chamber gas to the projectile front, water within the barrel will be forced out. Then, in the barrel, a low-resistance gas route is created for the projectile, resulting in higher propulsion performance than that of usual fully submerged launchers without increasing structural complexity [12,13,14]. For the gas-curtain launch, predecessors conducted some mechanistic research, focusing mainly on the gas–water interaction mechanism in a confined circular tube. Hu [15] conducted experiments to investigate the impact of nozzle size and number on the expansion properties of a high-temperature and high-pressure gas jet in water after developing three different rectangular sidewall grooves. The numerical model and simulation analyses were conducted on this foundation. Zhao [16] investigated the effect of nozzle size and injection direction on the expansion characteristics of a gas jet in water and examined the distribution law of characteristic parameters using conical spray nozzles. By opening 4–8 strands of grooves in the inner wall of a circular tube, Hu studied the interaction features of numerous gas jets with water [17]. Zhou [18] conducted gas-curtain simulated launching experiments to further clarify the mechanism of the gas–water interaction within the barrel, as other research had not included projectile motion. However, a transparent plexiglass tube was utilized to examine the gas–liquid interaction process, resulting in a simulated projectile velocity of no more than 20 m/s.

Although prior studies have disclosed the mechanism of the gas–water interaction with a static- or low-speed gas-curtain projectile, there has been minimal study on the gas–water interaction in the high-speed launching process, which involves the final application of the gas-curtain launcher. Based on this, three gas-curtain projectiles with varied jet structures are constructed for shooting experimental study on a 12.7 mm underwater launcher, and a numerical model for computation is established. The influence of jet structures on the propulsion performance and gas–liquid flow field of a gas-curtain launch is reflected in both experiments and calculations.

2. Experimental Research

2.1. Experimental Device

The experimental system is depicted schematically in Figure 1, which comprises primarily a launching platform, a water tank, a high-speed video recorder, a pressure tracking system, and an ignition source.

The structural diagram and dimensions of three gas-curtain projectiles with varying jet structures are illustrated in Figure 2 and

Table 1. Structure and dimension of gas-curtain projectiles.

No.	Type	Characteristics	Jet Structure and Size/mm	Mass m/g
1	A	Central nozzle	Φ3	45
2	B	Central nozzle	Φ4	45
3	C	Sidewall groove	4 × Φ2	45

, respectively.

It can be found that the jet structure and size of projectile A is a central nozzle with a diameter of 3 mm, whereas the jet structure of projectile B is a 4 mm diameter central nozzle. The jet structure of projectile C is relatively complex, consisting of a central nozzle, four lateral nozzles, and four sidewall grooves. The head construction of the three projectiles is consistent, and their mass is equalized by slightly extending the projectile’s length. All three projectiles use the same ammunition belt.

2.2. Experimental Results and Discussions

To conduct the experiment, mixed charge is used. One of the propellants has a fast burning rate, which is utilized to swiftly create gas to form a gas-curtain. The other has a slow burning rate and is utilized to continuously burn to maintain the gas-curtain and promote the projectile. Figure 3 depicts the chamber pressure for the three launching conditions.

Table 2. Interior ballistics results.

No.	Projectile Type	Barrel Length x/m	Projectile Weight m/g	Charge Weight ω/g	Maximum Pressure pm/MPa	Muzzle Velocity v0/m·s−1
1	A	1.028	45	8.5	53.4	159.8
2	B	1.028	45	8.5	41.8	177.5
3	C	1.028	45	8.5	70.9	150.1

displays the interior ballistics results for the matching launching conditions.

According to Figure 3 and Table 2, the propulsion performance of projectile B is the best with maximum pressure and muzzle velocity of 41.8 MPa and 177.5 m/s, respectively. The propulsion performance of projectile A and projectile C deteriorates in turn. The results demonstrate that the central nozzle promotes the creation of the gas-curtain, lowering launching resistance and achieving greater propulsion performance than the sidewall grooves. Furthermore, increasing the diameter of the central nozzle improves the propulsion performance.

Compared with the experimental results of a fully submerged launch in Reference [19] (116.0 MPa/172.8 m·s⁻¹), it can be found that the three jet structures suggested in this paper can provide a good drag reduction effect.

3. Numerical Analysis

3.1. The Modeling and Verification

The modeling and verification of the gas-curtain launch are briefly introduced as follows [19].

3.1.1. Physical Model

(1)

The burning of propellant satisfies the law of exponential burning rate.

(2)

The impetus f, residual capacity α, and specific heat ratio k are considered to be constant; ϕ is taken as the coefficient of other minor work.

(3)

The composition of the gas jet is not taken into account, and its volumetric force is neglected.

(4)

Ignoring the influence of liquid water evaporation due to heat absorption.

3.1.2. Mathematical Model

(1)

Form function of the propellant:

$$\psi =\{\begin{array}{ll}{\chi }_{0}Z(1+{\lambda }_{0}Z+{\mu }_0{Z}^2),& 0\le Z\le 1\\ {\chi }_{\mathrm{s}}Z(1+{\lambda }_{\mathrm{s}}Z),& 1<Z<Z_{\mathrm{k}}\\ 1,& Z=Z_{\mathrm{k}}\end{array}$$

(1)

where ψ is the mass fraction of burnt propellant, Z is the relative thickness of burnt propellant, and χ₀, λ₀, μ₀, χ_s, and λ_s are form characteristic quantities of the propellant.

(2)

Burning law of the propellant:

$$\frac{dZ}{dt}=\frac{u_1{p}^n}{e_1}$$

(2)

where e₁ is half of the web thickness of the propellant, u₁ is the burning coefficient, n is the burning exponent, and p is the mean pressure in the chamber.

(3)

Momentum equation of projectile:

$${\displaystyle {\int }_0^A(p_{\mathrm{b}}-p_{\mathrm{h}}})\mathrm{d}A=\phi m\frac{dv}{dt}$$

(3)

where A is the sectional area of the projectile, p_d is the pressure at the projectile base, p_h is the pressure at the projectile head, m is the mass of the projectile, v is the velocity of the projectile, and φ is the minor work coefficient.

(4)

Orifice flow equation:

$$\dot{m}={\phi }_2{S}_{\mathrm{n}}{p}_{\mathrm{b}}{K}_0$$

(4)

where

$$K_0=\{\begin{array}{l}\sqrt{\frac{2k_{\mathrm{p}}}{\left(k_{\mathrm{p}}+1\right)f_{\mathrm{p}}}\left[{\left(\frac{p_{\mathrm{h}}}{p_{\mathrm{b}}}\right)}^{\frac{2}{k_{\mathrm{p}}}}-{\left(\frac{p_{\mathrm{h}}}{p_{\mathrm{b}}}\right)}^{\frac{k_{\mathrm{p}}+1}{k_{\mathrm{p}}}}\right]},\frac{p_{\mathrm{h}}}{p_{\mathrm{b}}}>{\left(\frac{2}{k_{\mathrm{p}}+1}\right)}^{\frac{k_{\mathrm{p}}}{k_{\mathrm{p}}-1}}\\ \sqrt{\frac{k_{\mathrm{p}}}{f_{\mathrm{p}}}{\left(\frac{2}{k_{\mathrm{p}}+1}\right)}^{\frac{k_{\mathrm{p}}+1}{k_{\mathrm{p}}-1}}},\frac{p_{\mathrm{h}}}{p_{\mathrm{b}}}\le {\left(\frac{2}{k_{\mathrm{p}}+1}\right)}^{\frac{k_{\mathrm{p}}}{k_{\mathrm{p}}-1}}\end{array}$$

$p_{\mathrm{b}}=p/\left(1+\frac{\omega }{3{\phi }_{1}m}\right)$ is the pressure on the projectile base, ϕ₂ is the flow correction factor, S_n is the cross-sectional area of the nozzle, f_p is the impetus, and k_p is the adiabatic exponent. ${\rho }_i$ and $v_i$ are the density and velocity of the combustion gas passing through the nozzle entrance, respectively.

(5)

Energy equation of interior ballistics:

$$\frac{Ap(l_{\psi }+l)}{\theta }=\frac{f\omega \psi }{\theta }-[\frac{\phi }{2}m{v}^2+C_p{\displaystyle {\int }_0^t\dot{m}Tdt}+{\displaystyle {\int }_0^x{\displaystyle {\int }_0^A{p}_{\mathrm{h}}}\mathrm{d}A}\mathrm{d}l]$$

(5)

where ω is the charge weight, θ = k₀–1, l is the projectile displacement, v_g is the average velocity of the propellant gas flowing through the center nozzle inside the projectile, C_p is the constant-pressure specific heat capacity, and T is the gas temperature. l_ψ is the diameter-shrunk length of the free volume and is given by

$$l_{\psi }=l_0[1-\frac{\Delta }{{\rho }_{\mathrm{p}}}(1-\psi )-{\alpha }_{\mathrm{p}}\Delta (\psi -\frac{{\displaystyle {\int }_0^t\dot{m}dt}}{\omega })]$$

where l₀ is the diameter-shrunk length of the chamber, Δ is the charge density, ρ_p is the solid propellant density, and α_p is the covolume.

(6)

State equation of the gas inside the chamber:

$$Ap\left(l+l_{\psi }\right)=R\left(\omega \psi T-{\displaystyle {\int }_0^t\dot{m}T\mathrm{d}t}\right)$$

(6)

where R is the gas constant and T is the temperature.

(7)

Motion equation:

$$\frac{dl}{dt}=v$$

(7)

The base pressure and the head pressure calculated by the above jet equations are fed back to the User-Defined Functions (UDF), which are adopted to calculate the projectile velocity, displacement, and pressure. These quantities allow us to realize the coupling of the jet equations and the interior ballistics equations.

The continuity, momentum, energy conservation, state, and turbulence equations for unsteady combustion-gas jet flows are as follows.

(8)

Mass conservation equations:

$$\begin{array}{l}\frac{\partial \left({\alpha }_g{\rho }_g\right)}{\partial t}+\nabla \cdot \left({\alpha }_g{\rho }_g\mathit{\upsilon }\right)=0\\ \frac{\partial \left({\alpha }_l{\rho }_l\right)}{\partial t}+\nabla \cdot \left({\alpha }_l{\rho }_l\mathit{\upsilon }\right)=0\end{array}$$

(8)

These mass conservation equations are for each phase. Here, ρ_g and ρ_l denote the density of the gas and liquid, respectively. The volume fractions of each phase satisfy α_g + α_l = 1, where α_g is the volume fraction of the gas phase and α_l is the volume fraction of the liquid phase. v is the velocity vector.

(9)

Mixture momentum conservation equation:

$$\frac{\partial }{\partial t}\left(\rho \mathit{\upsilon }\right)+\nabla \cdot \left(\rho \mathit{\upsilon }\mathit{\upsilon }\right)=-\nabla p+\nabla \cdot \left[\mu \left(\nabla \mathit{\upsilon }+\nabla {\mathit{\upsilon }}^{{\rm T}}\right)\right]$$

(9)

The momentum conservation equation is for the two-phase mixture. The density and viscosity of this two-phase mixture are given by ρ = α_gρ_g + α_lρ_l and μ = α_gμ_g + α_lμ_l. p is the fluid pressure in the flow field.

(10)

Mixture energy conservation equation:

$$\frac{\partial }{\partial t}\left(\rho E\right)+\nabla \cdot \left[\mathit{\upsilon }\left(\rho E+p\right)\right]=\nabla \cdot \left(k_{\mathrm{eff}}\nabla T\right)$$

(10)

The energy conservation equation is for the two-phase mixture. The volume-of-fluid model treats energy E and temperature T as mass-averaged variables:$E=\left({\alpha }_g{\rho }_g{E}_g+{\alpha }_l{\rho }_l{E}_l\right)/\left({\alpha }_g{\rho }_g+{\alpha }_l{\rho }_l\right)$, $T=\left({\alpha }_g{\rho }_g{T}_g+{\alpha }_l{\rho }_l{T}_l\right)/\left({\alpha }_g{\rho }_g+{\alpha }_l{\rho }_l\right)$. k_eff is the effective thermal conductivity.

(11)

Turbulence equation:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\frac{\partial u_j}{\partial x_i}-\rho \epsilon$$

(11)

$$\frac{\partial }{\partial t}\left(\rho \epsilon \right)+\frac{\partial }{\partial x_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x_j}\right]-C_{\epsilon 2}\rho \frac{{\epsilon }^2}{k}+C_{\epsilon 1}\frac{\epsilon }{k}\rho \overline{u_i^{\prime }{u}_j^{\prime }}\frac{\partial u_j}{\partial x_i}$$

(12)

where k and ε are the kinetic energy and dissipation rate, respectively. The constants ${\sigma }_k=1.0$ and ${\sigma }_{\epsilon }=1.3$ are the Prandtl numbers corresponding to the turbulent kinetic energy and the dissipation rate, respectively. ${\mu }_t=C_{\mu }{k}^2/\epsilon$ is the turbulent viscosity. The constants $C_{\epsilon 1}=1.44$, $C_{\epsilon 2}=1.92$, and $C_{\mu }=0.08$ are empirical coefficients.

3.1.3. Numerical Verification

Based on the theoretical model presented above, numerical verification was performed. Figure 4 shows that the interior ballistics pressure–time curve calculated by the theoretical model is in good agreement with the experimental results. The mean error is less than 5.6%, which verifies the rationality of the theoretical model.

3.2. Analysis of Propulsion Performance

The influence of jet structure on the propulsion characteristics is currently being investigated.

Table 3. Charging parameters.

Parameters	Values	Units
ω	17	g
m	45	g
ρp	1600	kg·m−3
fp	950	kJ·kg−1
θp	0.25
lg	1.028	m
V0	2.175 × 10−5	m3
pb0	1.0	MPa
ps	45.0	MPa

shows the charging parameters adopted in the calculations.

The interior ballistics results with three different jet structures are shown in

Table 4. Interior ballistics results with three jet structures.

Condition	Projectile Type	x/m	ω/g	pm/MPa	v/m·s−1	t/ms
1	A	1.028	17	338.9	729.6	2.37
2	B	1.028	17	325.0	688.2	2.42
3	C	1.028	17	353.2	775.1	2.28

. It can be seen that when projectile A is utilized, the maximum pressure is 338.9 MPa and the muzzle velocity is 729.6 m/s. The maximum pressure and muzzle velocity are reduced to 325.0 MPa and 688.2 m/s, respectively, when the diameter of the central nozzle is enlarged (projectile B). The overall nozzle area of projectile C is the same as that of projectile B. While projectile C is adopted, the maximum pressure and muzzle velocity are 353.2 MPa and 775.1 m/s, respectively.

Figure 5 shows the distribution curves of the characteristic parameters of interior ballistics (chamber pressure, projectile velocity, and warhead pressure) under the above calculation conditions. As can be observed from Figure 5a,b, when projectile C is used, the rise rate of chamber pressure is the largest, and when projectiles A and B are used, the chamber pressure rise rate decreases in turn. This is because the propellant gas behind the projectile is continuously ejected to the projectile front through the jet structure. Compared with projectiles A and C, projectile B is more unfavorable to the storage of propellant gas behind the projectile. From Figure 5c,d, it can be found that the ascending rates of projectile velocity from large to small are in the following order: projectile C, projectile A, and projectile B. On the one hand, this is due to the influence of chamber pressure. On the other hand, the force areas of the three gas-curtain projectiles are different. From large to small, projectile C has the largest force area, the second is projectile A, and the smallest is projectile B. From Figure 5e,f, it can be found that projectile B can obtain the lowest head pressure, then projectile A, and finally projectile C. This is also because compared with projectiles A and C, projectile B is more conducive to the expansion of the propellant gas jet near the nozzle exit. It should be noticed that when projectile B is employed, the pressure at the projectile head rises dramatically later in the propulsion phase, which is due to the insufficient expansion of the gas-curtain.

It is obvious that jet structure within a gas-curtain projectile has an important influence on the drag reduction and propulsion performance of an underwater launcher.

3.3. Gas-Curtain Evolution Characteristics

The influence of jet structure on drag reduction effect and interior ballistics characteristics is mainly reflected in the evolution characteristics of the gas-curtain. Therefore, the evolution characteristics of the gas-curtain before projectile start-up are analyzed. Moreover, the gas-curtain can be separated into three stages according to its evolution process, namely, the Taylor cavity expansion stage (the first stage), the gas-curtain formation stage (the second stage), and the gas-curtain steady growth stage (the third stage).

Figure 6 corresponds to the expansion process of the gas-curtain before projectile A starts to move. Similarly, Figure 7 and Figure 8, respectively, correspond to those of projectiles B and C. It should be noted here that in order to obtain the best propulsion performance under the corresponding jet structure, the charge burning rate used is slightly different, while other initial loading conditions are the same.

It can be found in Figure 6 and Figure 7 that the evolution process of the gas-curtain is similar when projectiles A and B are used. In the first stage, the gas passes directly through the central nozzle, forming a bubble cavity at the outlet of the nozzle. The Taylor cavity progressively grows as gas is continuously injected, and the head of the cavity remains relatively smooth. Although the jet tail begins necking, the droplets have not been sucked into the cavity. In the following stage, the continuous injection of gas and the increase in injection pressure bring a strong Taylor–Helmholtz instability effect, resulting in great changes in gas–liquid entrainment and Taylor cavity shape. The specific manifestations are as follows: the surface of the Taylor cavity becomes extremely irregular, many droplets are entrained in the cavity, and the necking phenomenon of jet tail is more obvious. It is at this stage that the gas-curtain is initially formed, but there is still water near the projectile surface and within the gas-curtain. A depression arises at the head of the gas-curtain at the same time. The chamber gas continues to inject into the gas-curtain along the jet structure inside the projectile in the third stage. The water at the projectile head and in the gas-curtain gradually travels downstream due to the turbulence in gas–liquid mixing. Simultaneously, the gas-curtain keeps growing near the muzzle.

It is clear from Figure 8 that the sidewall jet firstly forms a small cylindrical Taylor cavity between the projectile and the barrel at 2 ms. Then, the sidewall jet expands axially and radially at the same time. At 5 ms, the four sidewall jets gradually begin to contact each other, and axial displacement of the Taylor cavity also increases rapidly. Until 6.5 ms, the sidewall jets converge near the projectile head, so it can be determined that the gas-curtain is initially formed. During the third stage (13.0~30.3 ms), with the injection of gas, the gas-curtain continues to grow, but there is still a gap at the gas-curtain head. With the entrainment of gas and liquid, the gap decreases gradually.

Comparing Figure 6, Figure 7 and Figure 8, it can be found that the gas-curtain formation process of projectile C is quite different from that of a projectile with a central nozzle. The primary cause is that the jet structure of projectile C makes the process of gas entering the barrel from the combustion chamber more complex. That is, after flowing into the projectile through the central nozzle, the gas firstly turns 90 degrees to enter the side nozzle and then 90 degrees again to get into the sidewall grooves. Finally, the sidewall gas jets converge in the barrel, forming a gas-curtain immediately. At the same time, it is found that a projectile with sidewall grooves is more conducive to draining off water near the projectile head than a projectile with a central nozzle.

3.4. Analysis of Pressure Distribution

The corresponding pressure cloud maps of the internal flow field under the above three conditions are given in Figure 9, Figure 10 and Figure 11 to further understand the influence of jet structure.

As can be seen in Figure 9, due to less chamber gas being injected into the front of projectile A through the central nozzle (the diameter is 3 mm) at 1.0 ms, the pressure field is relatively straightforward, with the pressure decreasing down the axis. At 3.7 ms, the gas expands rapidly after exiting the nozzle outlet, causing the Taylor cavity’s continuous expanding. Next, compression waves are then generated at the head of the Taylor cavity, producing several expansion-compression waves within the gas-curtain. Moreover, upstream of the Taylor cavity lies a high-pressure area with a maximum pressure of roughly 6.2 MPa. At 5.0 ms, the pressure is nearly 9.0 MPa at the nozzle exit. Afterward, the gas expands quickly, causing the pressure to rapidly fall to below 2.0 MPa. The pressure fluctuates at roughly 5.0 MPa due to the increasing expansion-compression effect within the Taylor cavity. The compression-expansion effect within the Taylor cavity reduced with the creation of the gas-curtain at 9.0 ms, despite the fact that the injection pressure continues to grow. Pressure decreases rapidly with certain oscillation after the nozzle outlet and fluctuates around 4.1 MPa downstream. At 15.0 ms, the gas-curtain further expands, and gas goes through two continuous compression-expansion processes after exiting the nozzle. The pressure downstream is kept within 4.0 MPa. The internal pressure is mildly more than 4.0 MPa, and there is a minor compression wave at the surface of the gas–liquid interface. The pressure is low overall at 29.3 ms, and it varies at the nozzle and drops along the way.

In Figure 10, while projectile B is used (the diameter of the central nozzle is 4 mm), maximum pressure at the Taylor cavity head reaches about 8 MPa and 14.3 MPa, respectively, at 1 ms and 2.5 ms. Pressure in the tube decreases along the way as a whole. From 4 to 7 ms, with the formation of Taylor cavity, there are multiple pressure waves reflected back and forth between the projectile head and the gas–liquid interface, which makes the pressure in the Taylor cavity fluctuate along the way. At 12 ms, the multiple pressure waves in the Taylor cavity are more obvious. At 17.8 ms, the gas expands and depressurizes rapidly after exiting the nozzle, forming a Mach plate structure downstream, and the pressure in the gas-curtain is within 5.7 MPa.

In Figure 11, at 2 ms, the gas sprays to the projectile front are less while projectile C (with four 2 × 2 mm sidewall grooves) is used. Pressure near the projectile head is about 3.7 MPa and then decreases along the way. At 3.5 ms, the pressure in the central nozzle fluctuates at a high level and decreases after passing through the side nozzle, while pressure near the projectile head rises to about 5.6 MPa and then decreases along the way. From 5 ms to 6.5 ms, with the formation of the gas-curtain, the gas in the tube expands further, making pressure at the projectile head decrease to less than 5 MPa. At 13 ms, pressure at the projectile head decreases to about 3.3 MPa due to the further expansion of the gas-curtain. At 30.3 ms, pressure in most areas near the projectile head further decreases to less than 2.4 MPa, but the mean pressure on the surface begins to rise because the pressure at the bottom of sidewall grooves exceeds 9.9 MPa.

It should be noted that there are great differences in the pressure field evolution process when the above three projectiles are used, which further explains the distribution characteristics of the interior ballistics characteristic parameters in Figure 5. That is, the larger cross-sectional area of projectile C is more conducive to acceleration. However, it is difficult to obtain the same low head pressure as projectiles A and B because there is always a high-pressure area at the bottom of sidewall grooves, which are not conducive to drag reduction and projectile acceleration. In general, compared with the drag reduction effect brought by the jet structure, the effective cross-sectional area has a greater impact on the propulsion performance of an underwater gas-curtain launcher, so the muzzle velocity of projectile C is the highest.

4. Conclusions

The influence of jet structure on the propulsion characteristics of an underwater gas-curtain launcher was discussed experimentally and numerically in this research. The following are the conclusions that have been reached.

(1)

The experimental results show that under the same charge condition, the maximum pressure and muzzle velocity of projectile A are 53.4 MPa and 159.8 m·s⁻¹, respectively. For projectiles B and C, the maximum pressure and muzzle velocity are 41.8 MPa/177.5 m·s⁻¹ and 70.9 MPa/150.1 m·s⁻¹, respectively. This demonstrates that the interior ballistics characteristics of a gas-curtain launcher are heavily influenced by jet structures.

(2)

The calculation results reveal that the three jet structures have good drag reduction effects and interior ballistics performance, but there are still some variances in the propulsion performance and flow field. In general, the central nozzle is more conductive to drag reduction than the sidewall grooves, but it also loses the effective cross-sectional area of the projectile. However, the effective cross-sectional area has a higher impact on the propulsion performance of an underwater gas-curtain launcher.

(3)

The nozzle construction of projectiles A and B is identical, as are the gas-curtain evolution and pressure distribution characteristics. While projectile C has a more complicated sidewall groove jet structure than the first two, its gas-curtain evolution and flow field pressure distribution characteristics are more complicated.