numerical simulation of interior ballistics

JOURNAL OF ENGINEERING AND APPLIED SCIENCE, VOL. 60, NO. 2, FACULTY OF ENGINEERING, CAIRO UNIVERSITY

2013, PP.163-176

NUMERICAL SIMULATION OF INTERIOR BALLISTICS FOR LARGE CALIBER GUIDED PROJECTILE NAVAL GUN

M. M. RASHAD１, X. B. ZHANG２ and H. ELSADEK３

ABSTRACT Interior ballistic numerical simulation for large caliber naval gun guided projectile system is carried out based on a predictive lumped parameter model for mixture of propellants, granular and black powder. Different propellant grain shapes, loading conditions and guided projectile masses are investigated in the simulations. The consequences of changing igniter propellant geometry and weight on the ignition time and the other interior ballistic parameters are also investigated. Simulation results revealed that changing grain geometry designs and loading conditions have a great impact on muzzle velocity, projectile acceleration and pressure history during interior ballistic cycle. The guided projectile mass investigations revealed that for firing heavy projectiles a relatively thick propellant grain size should be utilized. The simulation results are considered as a helpful guide for charge design considerations during launching guided munitions. The numerical results are validated with experimental data. The interior ballistics performance of a 130 mm naval guided projectile gun system is closely predicted using the proposed classical interior ballistic model and the numerical code.

KEY WORDS: Guided projectile, Simulation of Interior Ballistics, Lumped parameter model. 1. INTRODUCTION Guidance has two crucial benefits which it increases accuracy that guarantees

１

Phd candidate, [email protected] Corresponding author, Professor, School of Energy and Power Engineering, Nanjing University of Science and Technology, [email protected] 3 Phd candidate, [email protected] This work is supported by the Natural Science Foundation of Jiangsu Province (No. BK 20131348) 2

M. M. RASHAD, X. B. ZHANG and H. ELSADEK

target damage and far fewer rounds are needed to destroy the target. These advantages assure fewer guns for the same effect and an order-of-magnitude reduction in the logistics train behind the artillery unit. Modern munitions employ a variety of electronic and electromechanical devices for fusing, target detection, guidance and control. Consequently, these sensitive versions of munitions require more precise interior ballistic loading conditions and propelling charge designs in order to survive against harsh environment inside the gun. The propulsion system must get the projectile through the launch environment with consistent muzzle velocities, but without excessive stresses to the gun chamber or the projectile. During launch process projectile is exposed to extremely high rigid body acceleration, angular acceleration and rapid pressure decay at muzzle exit [1]. The rigid body acceleration is considered the major effective component on the performance and design of the guided projectile. In certain cases this acceleration can reach more than 10000 g [2-3]. Stresses induced into the guided projectile are chiefly due to the high acceleration that the propelling gases impart on it. This high acceleration can be returned to the high translational energy in medium and large calibers which is around 32% of the total propellant potential [4]. Therefore, accurate prediction of the interior ballistic parameters during firing process is a foremost problem. Many interior ballistic codes are of the zero-dimensional, lumped parameters, variety [5-6]. These codes are extremely useful for predictive applications because they run fast. One of the features of these codes which make them so useful is that we can easily include and track burn characteristics of multiple propellant types. This allows us to adapt the propellant burn characteristics so that a particular pressuredistance distribution is achieved while maintaining a particular muzzle velocity. In this study, lumped parameter mathematical model and numerical simulation for the large caliber naval gun guided projectile system (NGGP) are carried out using mixture of propellants, black powder of the igniter and multi-perforated (MP) granular propellant as a main charge. Different propellant grain shapes with different charging weights are used in the simulations in order to observe the effects of the geometry change and charging conditions on projectile acceleration, pressure history and muzzle

NUMERICAL SIMULATION OF INTERIOR BALLISTICS FOR LARGE CALIBER GUIDED PROJECTILE GUN SYSTEM

velocity. Projectiles which possess different masses are used in the simulations to investigate the mass change effect on the interior ballistic parameters. The numerical results are validated using the experimental measurements from firings of a real 130 mm NGGP system. 2. PHYSICAL PROCESS OF NGGP SYSTEM Design of innovative ammunition for certain tactical strategy requires a specific charge design to be used by the launching system. Due to its high charging density, Multi perforated granular propellant grains are known as the main charge for different propulsion systems [7]. Figure 1 illustrates schematically the configuration of a typical large caliber NGGP propelling charge. It is obvious from the figure that the charge consists of a large number of MP cylinders packed in random orientations around a bayonet igniter which include black powder propellant to start the ignition of the main propellant charge. The sequence of physical events may summarize as follows. When the NGGP system is activated, the base ignition black powder pad is ignited mechanically or electrically, then, the bayonet igniter is ignited. Hot gases from the igniter holes are injected into the propellant grains and the whole charge is ignited. The criterion of ignition, flame spreading and combustion of propellant grains can be referred to [8-9]. Consequently high pressurized gases accelerate the projectile down the bore until it expels out the gun muzzle.

1. Breech block; 2. MP propellant grains; 3. Igniter; 4. Guided projectile; 5. Barrel. Fig. 1. Schematic illustration of large caliber naval propelling charge


3. MATHEMATICAL MODEL OF THE INTERIOR BALLISTIC PROCESS Unlike the other lumped parameters models, an interior ballistic model for mixture of propellants is established taking into account the black powder in the igniter as the second propellant charge type. Constructing of this model of gun behavior is carried out based on considerations of the following areas, namely: 1. Noble-Abel equation of state. 2. Form function analysis. 3. Propellant burning rate equation. 4. Variable volume consideration of the gun- projectile system. 5. Pressure considerations. 6. Projectile motion. Some assumptions for simplification of the used classical interior ballistics model are discussed elsewhere [10-11]. In this study the general equations can be written as follows:  i   i Z i (1  i Z i  i Z i 2 )  u1i ni ( Z i  Z Ki ) dZi  p   e1i dt  ( Z i  Z Ki ) i  1, 2, ..., n 0 dv Sp  dt  m dl v dt n  Sp(l  l )   f ii  i   mv 2 2 i 1

                

(1)

Considering the separation point of slivers, the propellant grains form function equation  i can be presented as follows:  i Zi (1  i Zi  i Zi 2 ) ( Z  1) i    i    si Zi (1  si Zi ) (1  Zi  Z ) Ki  ( Zi  Z Ki )  1 n n  e  i 1 l  l0 [1   i   i (i  ) i ] ; Z Ki  1i  pi e1i i 1  pi i 1

(2)

(3)


Where,  i is the propellant's relative quantity of burnet powder, Zi is the relative burnet thickness of different propellants, n is the number of mixed charges kinds, χi, λi, μi and χsi are characteristic parameters of the propellants shape function, u1i is the burning rate coefficient, ni is the burning rate index, e1i is the half web thickness of the ith propellants, S is the cross-sectional area of bore, p is the chamber pressure, ϕ is the coefficient of secondary work, m is the projectile mass, v is the projectile velocity, ωi is the charges weight,  i is the co-volume of the propellant gas,  i is the loading density of the charges and fi is the propellant force. The model is solved using the fourth order Runge-Kutta technique which is considered as an important iterative approach for the approximation of solutions of ordinary differential equations with high accuracy [12-14]. 4. COMPUTATIONAL RESULTS AND DISCUSSION 4.1 Effect of Propellant Grain Shape on Interior Ballistic Parameters In this study, the MP propellant grain shape is changed to investigate its effect on the projectile acceleration performance, maximum chamber pressure and muzzle velocity of the NGGP system. Figure 2 shows the interior ballistics simulation results of (a) Pressure time history, (b) Projectile velocity, (c) Projectile acceleration and (d) Maximum and muzzle pressures versus half web thickness. It is revealed that decreasing the propellant half web thickness e11 has a great effect on the pressure history in the gun barrel in addition to the projectile acceleration. Figure 2a shows that the maximum pressure severely increases with decreasing the value of e11. Then, the period from ignition to the launch becomes larger than in case of using grains with large half web thickness. Consequently, these high chamber pressure values may affect the firing safety and may damage either gun chamber or the electronic and electromechanical devices suspended inside the projectile casing. On the other hand, in Figure 2b, muzzle velocity increases to reasonable values that are required in tactical purposes such as, increasing the projectile range. Figure 2c shows that the guided projectile acceleration increases with decreasing the half web thickness of the


propellant grains. Table 1 shows that increasing the half web thickness to a value of 0.93 mm, decreases the maximum projectile acceleration to a value of 9352 g, which is suitable value for launching a guided projectile. Conversely, decreasing e11 to a value of 0.75 mm, increases the acceleration to a higher value of 13822 g, which is a shocking conditions for performance of a guided projectile. Also, the value of maximum pressure and muzzle velocity increases to 404.056 MPa and 900 m/s, respectively, whereas the engraving time and the muzzle pressure decreases to 3.621 ms and 66.27 MPa, respectively. Comparing the maximum and muzzle pressures at lower values of half web thickness, Figure 2d, reveals high rapid pressure decay at muzzle exit which is the driver for the set forward (tension) loads of the guided projectile primary structure; it is also the principal contributor to the shock loading of internal components. So, it is preferred to choose e11 values to maintain moderate pressure decay at muzzle. Table 1 shows that increasing the half web thickness value e11 the engraving time is increased. For e11 values ranging from 0.75 mm to 0.93 mm, the engraving time increases from 3.621 ms to 4.417 ms, respectively, with a difference value about 0.9 ms. The role of the initial engraving process is to enable the gun system to build up a relatively large starting pressure. The engraving process would delay the projectile travel until the burning rate and gas pressure rate are at optimum values.

Table1. Effect of grain shape changes on different interior ballistics parameter. e11 (mm)

pm MPa

p muzzle MPa

vm (m/s)

0.75 0.79 0.83 0.85 0.87 0.91 0.93

404.05 365.59 333.59 319.57 306.63 283.64 273.36

66.27 67.64 69.20 70.36 71.40 73.04 73.69

900 884 867 858 849 829 819

Maximum Acceleration (g) 13822 12506 11412 10932 10490 9702 9352

engraving time (ms) 3.621 3.802 3.980 4.069 4.157 4.331 4.417


(a)

(c)

(b)

(d)

Fig. 2. (a) Pressure time history, (b) Projectile velocity, (c) Projectile acceleration and (d) Maximum and muzzle pressures versus half web thickness. 4.2 Effect of Major Propelling Charge Weight In this simulation different MP propellant charge weights are used to investigate its impact on the interior ballistic parameters, particularly the projectile acceleration. Figure 3 shows the simulation results of (a) Pressure time history, (b) Projectile velocity, (c) Projectile acceleration and (d) Maximum and muzzle pressures versus major propellant weight. As shown in Figs. 3a-b by increasing the seven perforated propellant charge weight, the maximum pressure and the muzzle velocity increase to


higher values. When the value of charge weight is equal to 11.4 kg the total interior ballistic cycle duration revealed its minimum and the chamber pressure reaches its maximum. This high pressure value affect on the guided projectile acceleration as shown in Fig. 3c. Increasing the charge weight, as shown in Fig. 3d, the maximum chamber pressure increases sharply, on the contrary the muzzle pressure slowly increases which will cause high rapid pressure decay at the muzzled exit. This rapid decay may disturb the performance of the guided projectile.

(a)

(c)

(b)

(d)

Fig. 3. (a) Pressure time history, (b) Projectile velocity, (c) Projectile acceleration and (d) Maximum pressure and muzzle pressure versus half web thickness, At different propellant weights.


It is obvious from Table 2 that the optimum working conditions for a safe performance of a guided projectile is at charge weight of 10.2 kg which assign an acceleration value of 9978 g. Also, increasing the charge weight leads to decreasing the engraving time consequently the whole interior ballistic cycle period is decreased. Table 2. Effect of MP propelling charge weight on the different interior ballistic parameters. ω1 (kg)

pm MPa

p muzzle MPa

vm (m/s)

Maximum Acceleration (g)

9.40 9.80 10.2 10.6 11.0 11.4

243.41 266.44 291.69 319.57 350.40 384.67

64.37 66.51 68.51 70.36 72.05 73.65

778.46 804.87 831.49 858.34 885.47 912.70

7327 9114 9978 10932 11986 13159

engraving time (ms) 5.037 4.691 4.368 4.069 3.790 3.529

4.3 Effect of Black Powder Geometry The effect of changing the black powder grain size on the interior ballistic parameters is shown in Fig. 4. The diameter of propellant spheres is changed from 1.4 mm up to 2.6 mm which reveals a very small effect on the ignition time for the whole propellant charge. Both increasing and decreasing regimes of the pressure curves reflect the same attitude for the different grain size diameter as shown in Fig. 4a. Consequently, the igniter performance and the value of the maximum pressure and muzzle velocity are not severely affected. Figure 4b shows that the guided projectile acceleration reveals a very slight change with changing the black powder propellant spheres diameter.


(a) (b) Fig. 4. (a) Pressure time history and (b) Projectile acceleration at different diameters of black powder spheres. 4.4

Effect of Black Powder Weight Figure 5 shows the effect of changing the igniter black powder charge weight

on (a) Pressure time history and (b) Projectile acceleration. As shown in Fig. 5a, the pressure curves are uniform with stable burning process for the propellant. Also, the maximum pressure posses a value of 319.5 MPa, about ±1.6 MPa, during different simulation runs taking into consideration that all other interior ballistic parameters are fixed. Accordingly, the projectile acceleration is changed to some extent that will not affect on the guided projectile performance.

(a)

(b)

Fig. 5. (a) Pressure time history and (b) Projectile acceleration at different weights of black powder.


4.5 Effect of Projectile Mass at Different Grain Shapes on Interior Ballistic Parameters Figure 6 shows the chamber pressure time histories, the projectile velocity and the projectile acceleration for three different projectile masses at different granular propellant grain shapes. As the propellant half web thickness acquire small values, the chamber pressure and the projectile velocity increases. So, the period from ignition time to the launch becomes shorter than that case of using big grain sizes. As sown in Fig. 6a, the peak pressure has low values in case of using light projectile mass compared to the other two cases and the muzzle velocity possess a high value which may reach to more than 1000 m/s. Then, the projectile acceleration increases to a value more than 13500 g as the grain half web thickness decreases as shown in Fig. 6d. As the projectile mass increases the chamber pressure has the opportunity to build up to higher values which may become out of safety conditions of launching process for a guided projectile as shown in Fig. 6c and d. Figure 6d shows that the change in the maximum projectile acceleration value becomes smaller in case of utilizing heavier projectiles in the simulation than of lighter ones. Figure 7 shows the time histories of the granular propellant burn up mass fraction. Figure 7a shows that, in case of lightest projectile condition and for all propellant grain sizes, the propellant keep on burning inside the chamber as the projectile ejected from the barrel. Due to this action of uncompleted burning of the propellant, some of its chemical energy is lost. On the contrary, Figs. 7b-c show the effect of the heavy projectiles on the burning process. As the projectile mass increases to some extent the propellant charge has the opportunity to develop a complete burning at which the relative quantity of burnet powder reaches to unity. This will affect on the kinetic energy and the performance of the guided projectile.


(a)

(b)

(c)

(d)

Fig. 6. Time histories of chamber pressure and the projectile velocity at (a) m=18.4 kg, (b) m=33.4 kg, (c) m=48.4 kg and (d) Projectile acceleration versus different propellant shapes.


(a)

(b)

(c) Fig. 7. Time histories of granular propellant relative burnt mass 1 at different propellant shapes for (a) m= 18.4 kg, (b) m= 33.4 kg, and (c) m= 48.4 kg. 5. EXPERMINTAL VALIDATION Many interior ballistic parameters can’t be measured experimentally except chamber pressure, projectile velocity at the muzzle and projectile acceleration. Table 3 represents the comparison between experimental and computational results for maximum chamber pressure, projectile muzzle velocity and projectile acceleration. All the practical firings for a real 130 mm NGGP system are carried out using 10.6 kg of MP propellant charge and 33.4 kg projectile. The correlation between numerical simulation and practical results shows a good agreement between them.


Table 3. Comparison between numerical and experimental results. Ballistic Parameter Maximum chamber pressure (MPa) Muzzle velocity (m/s) Projectile acceleration (g)

Experimental results 319.00

Simulation results 319.57

Error probability 0.17 %

855.00 10841.5

858.34 10932

0.39 % 0.83 %

6. CONCLUSIONS The major conclusions that arise from the previous discussions are:  The lumped parameters model for mixture of propellants is established and numerically simulated for the large caliber NGGP system. The model includes the effect of the igniter charge (Black powder) and the main propelling charge (seven perforated).  It is revealed that decreasing the granular propellant half web thickness e11 has a great power to influence the pressure history in the gun barrel in addition to the projectile acceleration which they both may severely increase.  Both half web thickness and granular propellant weight shows a great impact on the pressure decay at the gun muzzle exit.  There is a relation between projectile mass and granular propellant grain size where the projectile can acquire the most advantageous energy released from the propellant.  From the simulation results, it was concluded that for heavy projectiles a relatively big propellant grain size should be utilized to hold down the increase of the chamber pressure.  The numerical results were validated with experimental data and it was found that the proposed classical interior ballistic model is suitable for predicting the interior ballistic parameters.


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6.

7. 8. 9.

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12. 13. 14.

George Fotieo, “Gun launch dynamics of the navy 5-inch guided projectile”, NTIS, pp 371-375, 1982. Carlucci, Donald E., “Ballistics theory and design of guns and ammunition”, Taylor and Francis Group, 2007. Cordes J. A., Vega J., Carlucci D., Chaplin R. C., “Design Acceleration for the Army's Excalibur Projectile”, Armaments Engineering & Technology Center, Picatinny, New Jersey,OMB No. 0704-01-0188,2005. Herman Krier and Michael j. Adams, “An introduction to gun interior ballistics and a simplified ballistic code”, Interior ballistics of guns, Vol. 66, pp 1-36, 1979. Baer P.G. and Frankle J.M., “The Simulation of Interior Ballistic Performance of Guns by Digital Computer Program”, BRL Report No. 1183, USA ARDC, Ballistic Research Laboratories, Aberdeen Proving Ground, MD, 1962. Fredrick W. Robbins and Timothy S. Raab, “A Lumped-Parameter Interior Ballistic Computer Code Using the TTCP Model”, BRL Report No. 3710, USA ARDC, Ballistic Research Laboratories, Aberdeen Proving Ground, MD, 1988. Horst A.W., Conroy P. J., “Flame-Spreading Processes in a Small-Caliber Gun”, AD Report, ARL-TR-4181, Army Research Laboratory, Maryland, USA, 2007. Herman Krier, Rajan S., “Flame spreading and combustion in packed beds of propellant grains”, AIAA, Vol. 75, pp 1-11, 1975. Slobodan Jaramaz, “Flame spreading during Base Ignition of Propellant Charge: Theoretical and Experimental Studies”, Propellants, Explosives, Pyrotechnics, Vol. 22, PP 326-332, 1997. Jin Zhi Ming, “Interior ballistics in guns”, Publishing Company of Beijing institute of technology, Beijing, 2004. Yaun Y.X., Zhang X.B., “Multiphase hydrokinetic foundation of high temperature and high pressure”, Publishing Company of Harbin institute of technology, Harbin, (2005). Lapidus, L., and Seinfeld, J., “Numerical Solution of Ordinary Differential Equations”, NewYork, Academic Press, 1971. Acton, F.S., “Numerical Methods That Work”, Corrected Edition, Washington, Mathematical Association of America, Chapter 5, 1990. Gear, C.W., “Numerical Initial Value Problems in Ordinary Differential Equations”, Englewood Cliffs, NJ: Prentice-Hall, 1971.

‫‪M. M. RASHAD, X. B. ZHANG and H. ELSADEK‬‬

‫المحاكاة العددية للباليستيكا الداخلية لنظام المدفع البحرى كبير العيار ذو المقذوف الموجه‬ ‫ملخص‬ ‫تم تنفيذ محاكاة عمليات الباليستيكا الداخلية للمدفع البحرى كبير العيار ذو المقذوف الموجه‬ ‫باستخدام نموذج كالسيكى تنبؤى لمخلوط من نوعين من المواد القاذفة ‪ ،‬الحبيبات و البارود االسود‪ .‬وتم‬ ‫دراسة استخدام اشكال و اوزان مختلفة لشحنات حبيبات المادة القاذفة واوزان مختلفة للمقذوف الموجه‪.‬‬ ‫و قد اظهرت الدراسة ان تصميم شكل حبيبات المادة القاذفة و اوزان شحنات التعمير لها تأثير كبير على‬ ‫سرعة خروج المقذوف من فوهة ماسورة المدفع و على تسارعه وعلى تغير الضغط داخل ماسورة المدفع و‬ ‫ذلك فى حالة استخدام حبيبات المادة القاذفة ذات السبع ثقوب‪ .‬كما تم دراسة تاثير تصميم شكل و وزن‬ ‫المادة القاذفة للمشعل (البارود االسود) على زمن االشعال وباقى بارامترات الباليستسكا الداخلية‪ .‬كما تم‬ ‫التحقق من تاثير تصميم شكل حبيبات المادة القاذفة على زمن بداية دخول المقذوف للماسورة‪ .‬كما تم‬ ‫التحقق من نتائج النوذج الرياضى و المحاكاة العددية بمقارنة نتائجهم مع النتائج العملية لعمليات اطالق‬ ‫للمدفع البحرى ‪ 031‬مم وتعتبر نتائج المحاكاة مفيدة لتصميم الشحنات القاذفة للذخائر الحديثه الموجهة‪.‬‬