# Recoil Reduction Method of Gun with Side to Rear Jet Controlled by Piston Motion

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## Abstract

**:**

## 1. Introduction

## 2. Principle of the Piston-Controlled Gun

## 3. Theoretical Models

#### 3.1. Assumptions of the Model

- (1)
- Each phase is a continuum in line with the assumption of two-fluid model.
- (2)
- One-dimensional unsteady flow is considered in the barrel, the piston cavity, and the exhaust pipe.
- (3)
- The viscous dissipation of propellant gas and its heat loss to the wall are ignored.
- (4)
- The propellant gas flow is treated as an isentropic flow when the propellant gas flows through a bifurcated tube or elbow.

#### 3.2. The Governing Equations of the Two-Phase Flow in the Barrel

_{g}and ρ

_{p}are the gas and solid density, u

_{g}and u

_{p}are the gas and solid velocity, e

_{g}and e

_{p}are the gas and solid internal energy, φ is the porosity, p is the pressure, τ

_{p}and f

_{s}are the intergranular stress and interphase drag, Q

_{s}is the interphase heat transfer, m

_{c}is the gas generation rate of the solid propellant per unit volume, m

_{ign}is the gas generate rate of the ignition powder per unit volume, u

_{ign}is the velocity of the ignition powder, H

_{ign}is the enthalpy of the ignition powder, m

_{gb1}and m

_{pb1}are the mass flow rate of the gas and solid phase out of the barrel from the barrel vent per unit volume, u

_{gb1}and u

_{pb1}are the velocity of the gas and solid phase flowing through the barrel vent, ρ

_{gb}, p

_{b}, and e

_{gb}are the density, pressure, and internal energy of the gas phase flowing through the barrel vent.

#### 3.3. Dynamic Model of Gas–Solid Coupling in the Piston Cavity

_{h}, x

_{h}, and m

_{h}are the velocity, displacement, and mass of the piston, p

_{hd}is the pressure at the piston base, S

_{h}is the cross-section area of the piston cavity, F

_{0}is the spring preload, k

_{h}is the spring stiffness, F

_{v}is the friction force between the piston and the piston cavity.

**U**

_{h},

**F**

_{h},

**H**

_{h}, and

**J**

_{h}are similar to those in Equation (1).

#### 3.4. The Governing Equations of Two-Phase Flow in the Exhaust Pipe

#### 3.5. Gas Flow Model at the Barrel Vent and Rear Spray Channel

#### 3.6. Calculation of the Recoil Reduction Efficiency

_{o}is the recoil momentum of the gun without nozzle, I

_{r}is the recoil momentum of the gun with nozzle, I

_{p}is the momentum imparted to the gun system by the gas ejecting from the nozzle.

## 4. Numerical Method

#### 4.1. Difference Scheme

#### 4.2. Boundary Conditions

_{d}is the projectile displacement, L

_{b}and L

_{r}are the location of the barrel vent and the rear spray channel, p

_{d}is the projectile base pressure, Δx

_{2}is the length of the cell near the projectile base, t

_{s}is setting time, m

_{gb2}and m

_{pb2}are the mass flow rate of the gas and solid phase into the piston cavity from the barrel vent per unit volume, m

_{gr1}and m

_{pr1}are the mass flow rate of the gas and solid phase out of the piston cavity from the rear spray channel per unit volume, m

_{gr2}and m

_{pr2}are the mass flow rate of the gas and solid phase into the exhaust pipe from the rear spray channel per unit volume.

## 5. Results and Discussion

#### 5.1. Validation

#### 5.2. Decision of the Opening Time of the Rear Spray Channel

#### 5.3. Flow Field in the Piston Cavity

#### 5.4. Rarefaction Wave Front Propagation

#### 5.5. Flow Field in the Barrel

#### 5.6. Flow Field in the Exhaust Pipe

#### 5.7. Analysis of the Recoil Reduction Efficiency

## 6. Conclusions

- (1)
- The recoil reduction mechanism of the piston-controlled gun was revealed. By controlling the lateral ejecting of propellant gas with the piston, the rarefaction wave produced at the barrel vent just caught the projectile at the muzzle exit. Thus, the projectile base pressure did not reduce too much during the propulsion process, minimally reducing the muzzle velocity. Meanwhile, the recoil momentum was significantly reduced by venting high-pressure propellant gas from the barrel as much as possible.
- (2)
- The piston-controlled gun could be reset within the firing cycle, so the continuous firing mode is not affected. However, the rear spray channel will be closed during the piston reset motion, which is negative to the recoil reduction efficiency.
- (3)
- After the projectile reached the barrel vent, some high-pressure propellant gas flowed into the piston cavity, so the projectile base pressure dropped slightly. However, the piston cavity was closed before the rear spray channel was opened, so the velocity loss of the piston-controlled gun is similar to that of a traditional air-guided gun.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Structure diagram of the piston-controlled gun. (

**a**) Gas port in closed position; (

**b**) Gas port in opened position.

**Figure 3.**Simulation of the AGARD gun: (

**a**) pressure at projectile base and breech, (

**b**) projectile velocity.

Computed Value | Acceptable Range | Present |
---|---|---|

Maximum breech pressure (MPa) | 355–400 | 367 |

Maximum projectile base pressure (MPa) | 325–360 | 336 |

Muzzle velocity (m·s^{−1}) | 660–705 | 673 |

Exit time (ms) | 14.66–16.58 | 15.57 |

Parameter | Value |
---|---|

Barrel diameter (m) | 0.030 |

Length of barrel (m) | 2.457 |

Propellant mass (kg) | 0.119 |

Propellant density (kg·m^{−3}) | 1600 |

Projectile mass (kg) | 0.389 |

Parameter | Value |
---|---|

Position of barrel vent (m) | 0.45 |

Diameter of the piston cavity (m) | 0.021 |

Piston mass (kg) | 0.3588 |

Spring stiffness (N·m^{−1}) | 10000 |

Length of side nozzle (m) | 0.6 |

Sectional area of the barrel vent (mm^{2}) | 314 |

Sectional area of the rear spray channel (mm^{2}) | 346 |

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**MDPI and ACS Style**

Qiu, M.; Si, P.; Song, J.; Liao, Z.
Recoil Reduction Method of Gun with Side to Rear Jet Controlled by Piston Motion. *Symmetry* **2021**, *13*, 396.
https://doi.org/10.3390/sym13030396

**AMA Style**

Qiu M, Si P, Song J, Liao Z.
Recoil Reduction Method of Gun with Side to Rear Jet Controlled by Piston Motion. *Symmetry*. 2021; 13(3):396.
https://doi.org/10.3390/sym13030396

**Chicago/Turabian Style**

Qiu, Ming, Peng Si, Jie Song, and Zhenqiang Liao.
2021. "Recoil Reduction Method of Gun with Side to Rear Jet Controlled by Piston Motion" *Symmetry* 13, no. 3: 396.
https://doi.org/10.3390/sym13030396