Shockwave Overpressure of Propellant Gases Around the Mortar

This paper is a result of many years of research in the field of the powder gases shockwave overpressure, which occurs during firing from the mortar. The cause of these occurences is a sudden flow of powder gases from the weapon barrel and its expansion in the undisturbed environment. In this paper, an influence of a propellant charge on the overpressure intensity of the shockwave produced by powder gases nearby mortar is shown. The research comprised modelling and computation of the overpressure field around the weapon, in order to determine its intensity and distribution in space and time. With the aim of the real description of the mentioned occurences, the theoretical part was given, and then the numerical modelling of the instantaneous flow of the powder gases from the motrar barrel has been conducted. Experimental results are obtained from the firing experiments with the 120mm mortar. Computation and experimental results are given in the form of a chart of the barrel pressure change and overpressure of powder gases, at the characteristic measuring points around mortar.


Introduction
HE need for the increase in the maximum range, which is mostly achieved by improving aerodynamic characteristics of the missile, and by the construction changes of the weapon, also leads to the use of greater, and actually more powerful powder charges.A more powerful powder gases, as a consequence, have an increase in the operation pressure in the weapon barrel, and the greater production of the powder gases, which leads to the increase in the overpressure around the weapon.As a consequence there is the occurrence of the greater overpressure around the weapon, which is particularly emphasized at the mortar, where the firing operator (gunner) is in the vicinity of the weapon during the procedure of loading and firing [1].Everything mentioned imposes the need of defining an influence of the weight increase of a propellant charge on overpressure intensity of a nearby mortar's shockwave.
Theoretical basis is set up and mathematical modelling is done, as well as computation of characteristic gas dynamic values [3].
For the verification of the applied numerical model [4], the experimental measuring method was used.

Theoretical basis
With the aim of resolving complex gas dynamics phenomena, Computational fluid dynamics (CFD) with finite volume method (FVM) is used, in order to enable the use of the unstructured mash and simple use of Neumann's boundary condition.
In theory, the following equations are used: Conservation of mass: Conservation of momentum: , , , 0 Conservation of energy: , ., , Where ρ is the fluid density, v i -components of the velocity vector components, е -internal energy per unit mass, F i -components of body force vector volume, p -pressure, τ iј -viscous stress tensor, Т -temperature, q i -heat flux and rheat supply per unit mass.
Navier-Stokes set of equations in the so-called conservation form [5], [6]: Where: U is conservative flow variables vector per unit volume, F is convective flux variable vector, G is diffusion flux variable vector, and B is a source term (mass, momentum and energy).
In the process of numerical simulation, in the exit cross section, on the muzzle, an equation of pressure change with time defined as in Eq. ( 5) is used: Where K is coefficient for barrel, p is pressure, p p is the initial pressure and t is time.

Gas dynamics calculations
Numerical simulations provide preconditions which, by computation, enable reaching the characteristic values of the gas flow, which sets free in the firing process.The belonging physical appearances are simulated in the proposed mathematical model, and the condition of the gas phase of the combustion products and the surrounding air may be monitored in space and time.This way the shock wave front, which moves through the space, causing the change of the condition in the undisturbed environment, is clearly noticed.
Numerical computation was conducted on the basis of the proposed mathematical model and realized by software ANSYS FLUENT, where the averaged Navier-Stokes equations are solved [9].
Used dynamic mesh adaption [11] is based on the pressure gradient, because of its very high value near the shock.
In Fig. 1 a scheme with characteristic measuring places that correspond with an actual position of crew members is given.

Interior ballistics calculations
Interior ballistics calculations are done for the case of firing 120 mm lightweight high explosive shell (LTF), propellant charges O+6 (ignition charge + 6 increment charges), O+7 (ignition charge + 7 increment charges) and new extended range 120 mm mortar shell with propellant charge O+10 (ignition charge + 10 increment charges).Interior ballistics calculations are done for the three presented cases, using the software which performs calculations by simplified Serebryakov method.Pressure versus time curves (p -t), i.e. pressure calculations for the three presented examples are given in Fig. 4.
For lightweight shell 120 mm LTF, a standard propellant charge (O+6) and a charge for safety check at extreme barrel pressure (O+7), with double based propellant was used.For extended range mortar shell 120 mm XM95, a new propellant charge, which is also double based, but with different characteristics was used.
Input data for interior ballistics calculations are given in Table 1.The results of the experiment, measured during the process of firing several groups of shells are given in the Table 2.

Result analyses
Generally, the results obtained with a gas dynamic computation (2D), are fully satisfying, as confirmed by the experimental results that are measured during firing and presented in Fig. 8.In the available literature [14], there is a fact stated that the model of gas dynamic computation (2D) with the cylindrical shockwave is of a the greater overpressure value in comparison with the sphere shockwave which has been confirmed in this case.

Conclusion
On the basis of the conducted analysis, the computational results, and experimental testing with the 120 mm mortar system with applied construction solutions following conclusions were made: -gas dynamics computations, with 2D numerical simulation, showed that the proposed mathematical model, with the applied software that used the adaptively generated mesh, determines the position and shockwave strength accurately and precisely enough, as shown in Fig. 8, -proposed mathematical model and applied numerical simulation gives 3D presentation of gaseous dynamics parameters of gas flow (velocity, density, pressure and concentration) which can be observed in different time intervals and different points in space around the weapon, -with propellant charge O+10, which provides maximum velocity of 400 m/s, the overpressure at the gunner's position is Δp = 0,32 bar, which requires the use of protective equipment and imposes the need of reducing the overpressure, because the overpressure of 0,30 bar and more is considered to be the one that may cause issues and disturbance of mortar crew.

Figure 1 .
Figure 1.Measuring point's scheme The results of the numerical calculations of the overpressure versus time, calculated for characteristic measuring points MM1, MM2 and MM3, for 120 mm mortar firing are given in Fig.2.

Figure 2 .Figure 3 .
Figure 2. Gas dynamic computation (2D), In Fig.3 visualized results of the numerical calculations for the gas flow characteristics captured in characteristic moment are shown.

Figure 4 .
Figure 4. Comparative overview of pressure versus barrel length for firing 120 mm

Tabe 1 .
Input data for interior ballistics calculations kg 0,040 kg Weight of increment charge 0,456 kg 0,532 kg 0,810 kgExperimental resultsExperiment was realized by firing from the 120 mm mortar.The overpressure values at the characteristic measuring points around the weapon barrel were measured with the PCB sensors, as shown in Fig.5.Used sensors are PCB Piezotronics mod.137A24, with measuring range of up to 17.27 bars and sensitivity of 20mV/psi.