^{1}

^{2}

^{1}

^{2}

^{1}

^{1}

^{2}

The sabot discard asymmetry caused by spinning affects the exterior ballistic characteristics and shooting accuracy of a gun with the rifled barrel. To gain a deeper understanding of the complex sabot discard performance for the armor-piercing, fin-stabilized discarding sabot (APFSDS), a numerical investigation is performed to assess the effects of the spin rate on the sabot discard characteristics. We obtain the calculation boundary by the interior ballistics and the firing conditions and carry out a numerical simulation under different spin rates using computational fluid dynamics (CFD) and a dynamic mesh technique. We analyze four aspects of sabot discard characteristics, namely, sabot separation, rod surface pressure, rod aerodynamic parameters, and discarding quantization parameters. Computational results show that the sabot separation nearly presents perfect symmetry at 0 rad/s, and when the initial rate of the sabot increases, there is more obvious separation asymmetry, and it contributes to the relative position variation among the sabots and the rod. The distinction of rod surface pressure indicates that the choked flow is the strongest flow source, and the spin rate has almost no effect on the pressure of the rod front part. When the monitoring point moves towards the fins, the pressure distribution and intensity change more dramatically. The initial spin rate and separation asymmetry produce a variation in the surface pressure, which further influences the rod aerodynamic characteristics. The discarding quantization parameters exhibit a certain variation rule with its spin rate. 2,000 rad/s has a significant influence on the rod aerodynamic coefficients during the weak coupling phase. When the spin rate is in the range of 0–900 rad/s, the discarding characteristics remain the same. However, when the spin rate exceeds 900 rad/s, the separation time and aerodynamic impulse have a quadratic polynomial relationship with the rate. Additionally, a spin rate of 1,000 rad/s is the optimal value for a rifled barrel gun.

The ultimate challenge of conventional weapons is the achievement of a longer firing range, higher muzzle velocity, and higher firing accuracy; therefore, the armor-piercing projectile comes into being and has a broad array of applications in tube-launched weapons [

We use high-speed photography to capture the APFSDS projectile attitude and provide a photo of the launching phenomenon in Figure

Launching phenomenon of a rifled barrel APFSDS.

Schematic diagram of the SDP. (a) Initial status of sabot separation. (b) Aerodynamic interference model.

Previous investigations have demonstrated that multiplex interference factors can result in a ballistic disturbance during the SDP [

Advances in computer technology and numerical algorithms have promoted the rapid development of CFD, which can be used to solve complex flow problems with supersonic characteristics [

Numerous scholars have conducted detailed studies on the SDP, but the impact of the sabot spin rate is a factor that cannot be ignored. The spin rate can affect the variation in sabot motion and rod aerodynamic, which further result in the difference of sabot discard characteristics. Against this background, a small-caliber APFSDS was chosen as a subcaliber representative configuration with three sabots in the simulation of a rifled barrel gun. We consider the Gatling gun launching peculiarity and the interior ballistic model to establish a simulation model under different spin rate cases. We then adopt the dynamic unstructured grid technology to solve the APFSDS separation and flow field. Subsequently, these analyses of sabot discard characteristics are conducted by sabot separation, rod surface pressure, rod aerodynamic forces, and discarding quantization parameters.

For the spin rate effect on the SDP, we make the following assumptions:

The influence of the propellant gas on the projectile is so small that the propellant gas action is not considered [

The total separation time of the SDP is in the millisecond scale; thus, we can neglect the velocity attenuation of the APFSDS.

The rod spin rate is very low; thus, its rotational motion is not considered.

There are several positioning grooves between the sabots and the rod, and the relative displacement between them is extremely small during cutting an obturator. Thus, we set the initial axial clearance as 1 mm between the rod and sabots.

We assumed that the inlet flow is a perfect gas.

The propellant type of the APFSDS is a single charge used to solve the simulation initial boundary, and the interior ballistic model can be written as follows [

State equation of the propellant gas:

Equation of energy conservation:

Kinetic equation of the projectile:

The numerical parameters (i.e., distance, time, velocity, and average pressure) are processed as dimensionless, and the fourth-order Runge–Kutta scheme is adopted to solve the internal ballistic equations.

For dynamic grids of cases, the general form of the control equation is obtained as follows:

Regarding equation (

Finite volume method [

For the interface

The turbulence model plays a key role in supersonic behavior, especially in dynamic separation with complex shock interactions. Chen et al. [

The dynamic equations and kinematics can describe the sabot separation motion and are derived using a Newtonian approach with inertial and flat earth assumptions. Therefore, the center of gravity (CG) translational motion and the rotational motion of CG are associated with the resulting forces and moments as follows:_{x}, _{y}, _{z}), _{x}, _{y}, _{z}), and _{xx}, _{yy}, _{zz}).

The inertial position kinematics and Euler angle kinematics are then determined:_{χ} = sin (_{χ} = cos (

Figure

Schematic of calculation.

The Army-Navy Basic Finned Missile (ANF) model discussed in Army Ballistic Research Lab Report 539 is usually utilized to verify the projectile aerodynamic, and we created its physical model with a 20 mm diameter [_{first} = 0.001 mm and _{L} = 10. The computed grid is shown in Figure

ANF verification model: (a) ANF parameters (mm) and (b) computed grid.

Comparison of DC between simulation and experiment.

Based on the SDP mechanism, APFSDS structure, and assumptions (1)–(4), we simplified the projectile as a model having a five-fin rod and three sabots [

Model definition. (a) Model configuration and dimension (D) and

Based on the APFSDS parameters and the estimated sabot motions, we established the outer flow zone with a hemisphere in the front and a cylinder in the back, and we optimized the outer field with _{O} = 46.3D and _{O} = 88.7D. The origin point of the zone is the hemisphere center. Subsequently, we performed a subtraction operation between the outer flow zone and the APFSDS to produce the simulation model, and we adopted the T-grid method to generate the unstructured tetrahedral mesh with ANSYS Corp.’s ICEM-CFD software. First, the shell grid was generated on the APFSDS surface and far field. Then, the prism grid was generated on the shell grid of sabots and rod, and the volume mesh finally grew from the prism grid to the shell grid as shown in Figure _{R} = 39D and _{R} = 22D covers the APFSDS in Figure _{first} = 0.015 mm and _{L} = 10 boundary layers, as shown in Figure

Computed grid. (a) Computational domain grid. (b) Refined zone grid. (c) Boundary layer grid.

After fulfilling the model discretization in space, we set the far field as the inlet pressure. Moreover, the wall of the APFSDS is assumed to be an adiabatic boundary. Considering the gravity effect and assumption (5), the incoming flow was a perfect gas with its parameter from state equations. Thus, the ambient conditions were 101325 Pa and 300 K. Combining assumptions (2) and (3) and the results from Section ^{−4} ms, respectively. For the initialization of parameters to solve aerodynamic coefficient, the reference in area and length was 91.61 mm^{2} and 170 mm, respectively. After solution initialization using the above model and various parameters for different spin rate cases, we monitored the pressure variation with separation time at the rod surface points and obtained the aerodynamic parameters of the rod and sabots and the motion history of the three-sabot system.

Spin rate of the sabot.

Case | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 |
---|---|---|---|---|---|---|

Spin rate (rad/s) | 0 | 750 | 900 | 1,050 | 1,500 | 2,000 |

Main properties of sabots.

Parameters | Expression | |||
---|---|---|---|---|

CG coordinate (mm) | _{(x, y, z)} | _{(0, 8.6, 0)} | _{(0, −4.3, −7.7)} | _{(0, −4.3, 7.7)} |

Euler angle (degree) | _{(x, y, z)} | _{(0, 0, 0)} | _{(0, −120, 0)} | _{(0, 120, 0)} |

Inertia moment (g·mm^{2}) | _{(Ixx, Iyy, Izz)} | _{(2305, 6852, 6359)} | _{(2305, 6852, 6359)} | _{(2305, 6852, 6359)} |

Inertia product (g·mm^{2}) | _{(Ixy, Ixz, Iyz)} | _{(60, 0, 0)} | _{(−30, −51.9, 42.8)} | _{(−30, 51.9, −42.8)} |

Mass (g) | _{20.3} | _{20.3} | _{20.3} |

As described in [

The dynamic characteristics of sabots are affected by the interaction of their initial states, the aerodynamic parameters, and gravity. Therefore, we investigated the boundary condition, aerodynamic characteristics, and kinematic parameters of the SDP under different spin rates. First, the initial state of the sabots is shown in Figure

Different spin rates can produce a difference in the movement and attitudes of sabots. Hence, we provide the sabots’ separation on the

Sabots’ motion of the

We plotted the aerodynamic coefficient curve for different spin rates. Figures

Aerodynamic force coefficients. Letters a–f stand for cases 1–6, respectively. DC is the drag coefficient, LIC is the lift coefficient, and LAC is the lateral force coefficient.

As the spin rate increases, the aerodynamic coefficients exhibit asymmetry. When the rate reaches 750 rad/s as compared with all forces in Figure

The following presents the CG motion in Figure

CG velocity of all sabots. Letters a, b, and c, respectively, stand for cases 1, 4, and 6. −

Therefore, the separation process shows near symmetry under 0 rad/s, which is the same conclusion about the tank gun in [

The separation asymmetry changes the relative position between the sabots and the rod, further affecting the intensity and action position of the shock wave. Therefore, the direct result is a variation in rod pressure and distribution. We established a series of monitoring points on the rod surface to explore the pressure intensity located at the rod axis section. As shown in Figure

Schematic of monitoring points.

Plane coordinates of the

Plane | ||||
---|---|---|---|---|

Value (mm) | 27.9 | 0 | −27.9 | 76.5 |

As mentioned in [

Peak values of points at 0 rad/s, and the unit is MPa.

Plane | Peak value | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | Average | |

2.074 | 3.225 | 2.701 | 3.171 | 2.312 | 3.345 | 2.805 | |

1.398 | 1.262 | 1.592 | 1.033 | 1.336 | 1.19 | 1.302 | |

0.631 | 0.189 | 0.635 | 0.190 | 0.636 | 0.187 | 0.411 | |

0.626 | 0.712 | 0.554 | 0.736 | 0.616 | 0.756 | 0.666 | |

1.689 | 1.208 | 1.917 | 1.144 | 1.400 | 1.265 | 1.437 | |

0.060 | 0.067 | 0.065 | 0.255 | 0.060 | 0.102 |

Pressure of different points under different cases: (a) case 1, (b) case 4, (c) case 5, and (d) case 6.

Figures

For the pressure intensity at 0 rad/s in Table

To further explore the pressure intensity at various rates, as shown in Figure

Pressure under different cases: (a)

The uneven pressure distribution mentioned in Section

Force coefficient: (a) DC, (b) LIC, and (c) LAC.

Moment coefficient: (a) RMC, (b) YMC, and (c) PMC.

During the time of 0-0.1 ms in Figure

Figures

Therefore, the 1,500 rad/s rate is the dividing point of the SDP. However, 2,000 rad/s has a significant influence on the rod aerodynamic coefficients during the weak coupling phase, which may result in the loss of flight stability.

The fundamental requirement for the SDP is rapid separation and interference reduction [

Combining the aerodynamic parameters with the surface pressure to analyze the separation time, we calculate the aerodynamic impulse from the separation time and aerodynamic forces. Table

Discarding characteristic under different spin rates.

Spin rate (rad/s) | 0 | 500 | 750 | 900 | 1000 | 1050 | 1500 | 1750 | 2000 |
---|---|---|---|---|---|---|---|---|---|

Discarding time (ms) | 1.780 | 1.781 | 1.785 | 1.786 | 1.85 | 1.865 | 2.000 | 2.091 | 2.251 |

Aerodynamic impulse (N·s) | 0.0743 | 0.0746 | 0.0751 | 0.0762 | 0.0794 | 0.0796 | 0.0855 | 0.0938 | 0.1049 |

As seen in Figures

Discarding characteristic. (a) Discarding time. (b) Aerodynamic impulse.

According to the interior ballistic parameters and launch conditions, the range of spin rate is approximately 1,000–2,000 rad/s, and the blue blocks of Figure

In this paper, we investigated the effect of the initial spin rate on the dynamic separation of the APFSDS using CFD and dynamic mesh approaches. This study explored the separation process at various spin rates. We also quantitatively analyzed the discarding characteristics against separation time and aerodynamic impulse. Special attention was given to understanding the separation of sabots, rod surface pressure, rod aerodynamic parameters, and quantization parameters of complex discarding characteristics. The following conclusions were drawn:

When the spin rate was 0 rad/s, the SDP exhibited near symmetry. As the initial spin rate of the sabot increased, there was more obvious separation asymmetry, and it contributed to the relative position variation among the sabots and the rod.

The distinction of the rod surface pressure indicates that the choked flow was the strongest flow source of the SDP. The spin rate had almost no effect on the pressure distribution of the front part of the rod. When the monitoring point moved towards the fins, the pressure distribution and intensity changed more dramatically. The initial spin rate and separation asymmetry produced a variation in surface pressure, which further influenced the rod aerodynamic characteristics.

For the aerodynamic coefficients, the 1,500 rad/s rate is the dividing point. However, 2,000 rad/s has a significant influence on the rod aerodynamic coefficients during the weak coupling phase, which may result in the loss of flight stability.

When the spin rate is in the range of 0–900 rad/s, the discarding characteristics remain the same. However, when the spin rate exceeds 900 rad/s, the discarding time and aerodynamic impulse have a quadratic polynomial relationship with the rate. Furthermore, a spin rate of 1,000 rad/s was found to be the optimal value for the APFSDS of the rifled barrel.

The results give a design reference for the APFSDS from a rifled barrel. Our future work is to calculate the dynamic separation process of the APFSDS considering the influence of gunpowder gas, making the APFSDS initial boundary agree with the firing condition.

Flux variable

General source term

_{D}:

Velocity of the dynamic mesh

Time step

_{1}:

Velocity vector

Sabot number

Inertia tensor

External moments

Angular velocity

Euler angles

Transformation matrix from inertial to body coordinates

_{p}:

Projectile base pressure

_{A}:

Equivalent length of the chamber

Burned ratio of the propellant

Gas constant

Energy capacity of the propellant

Muzzle velocity

Tangential velocity

_{p}:

Diameter of the projectile

_{First}:

Height of the first layer

_{O}:

Diameter of outer flow

_{R}:

Diameter of the refined zone

_{A}:

Aerodynamic impulse

Rod reference area

_{Γ}:

General diffusion coefficient

Flow velocity

Fluid density

Space step

Pressure flux

Sabot mass

External forces

Translational velocity

Absolute coordinates

_{p}:

Projectile base area

Transformation matrix from sabot Euler to attitude angles

Projectile displacement

_{g}:

Propellant mass

Coefficient of secondary work

Burning temperature of the propellant

_{p}:

Projectile mass

Specific heat

_{b}:

Rotational velocity of the barrel group

_{b}:

Rotation radius of the barrel group

_{L}:

Number of layers

_{O}:

Length of outer flow

_{R}:

Length of the refined zone

Incoming flow velocity

_{D}:

Discarding time

Armor-piercing fin-stabilized discarding sabot

Angle of attack

Advection upstream splitting method

User-defined functions

Drag coefficient

Lateral coefficient

Yaw moment coefficient

Calculated

Sabot discarding process

Computational fluid dynamics

Center of gravity

Army-navy basic finned missile

Lift coefficient

Roll moment coefficient

Pitch moment coefficient

Experimental.

The data used to support the findings of this study are included within this paper.

The authors declare that they have no conflicts of interest.