The paper presents the parameters of the pressure wave incident on minehunter hull structure modeled on the simplified vessel hull of Kormoran II project

Grządziela Andrzej

Kiciński Radosław

Szturomski Bogdan

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCTOBER 2014. VOLUME 3. ISSN 2345-0533 357 
Analysis of the pressure wave parameters caused by 
TNT underwater explosion forced on the hull of 
minehunter 
Grządziela Andrzej1, Kiciński Radosław2, Szturomski Bogdan3 
Naval Academy in Gdynia, Gdynia, Poland 
1Corresponding author 
E-mail: 1a.grzadziela@amw.gdynia.pl, 2radoslaw.kicinski@o2.pl, 3b.szturomski@amw.gdynia.pl 
(Accepted 24 September 2014) 
Abstract. The paper presents the parameters of the pressure wave incident on minehunter hull 
structure modeled on the simplified vessel hull of Kormoran II project. 
Keywords: impact resistance of the structure, a model of the pressure wave, underwater  
explosion, short-term process, FEM, CAE, Kormoran II. 
In September 2013 Inspectorate of Polish Navy Armament signed a contract to build new ships 
for combating and setting mines codenamed “Kormoran II”. She has to be adapted to operate in 
the Polish economic zone, as well as in tactical operations in the Baltic and the North Sea. Basic 
assumptions tactical – technical shown below [1]: 
• Displacement: max: 850 tons;  
• Length: 58.00 m;  
• Width: 10.30 m;  
• Forecastle deck height: 6.40 m;  
• The height of the main deck, aft: 4.70 m;  
• Draft: 2.60 m;  
• Speed: not less than 15 kt;  
• Range: not less than 2,500 nautical miles. 
Due to the destination of the ship should be examined cases in which the ship may be exposed 
to the sea mine explosion. It is therefore necessary to distinguish underwater explosion (UNDEX) 
derived from the enemy charge and the explosion on board in case of a failure while setting up 
mine warfare. The effects of explosions are difficult to predict. In case of contact explosions which 
are explosions on board of the ship, it is possible to determine the pressure distribution derived 
from such an explosion by using the CONWEP procedure which is not described further. 
 
Fig. 1. The Kormoran II minehunter designed for the minefield setting 
Nowaday, many CAE programs uses CONWEP procedure to simple calculations for free 
explosions in the air. The value of pressure is determined by the program based on the weight of 
the load and then using TNT equivalents calculated for the respective loads. A similar situation 
can be applied to underwater explosions. In order to properly calculation of pressure wave incident 
on the structure shall be familiar with the phenomenon, analytical description of the pressure wave 
ANALYSIS OF THE PRESSURE WAVE PARAMETERS CAUSED BY TNT UNDERWATER EXPLOSION FORCED ON THE HULL OF MINEHUNTER.  
GRZĄDZIELA ANDRZEJ, KICIŃSKI RADOSŁAW, SZTUROMSKI BOGDAN 
358 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCTOBER 2014. VOLUME 3. ISSN 2345-0533  
used by the program and simplifying assumptions. 
Underwater explosion is a rapid equilibrium violation caused by detonation of explosive in 
water. During explosion the charge is converted from solid in to has product of volume equal to 
volume of explosive material, temperature range ܶ ≈ 3300 K and pressure ݌ ≈14000 MPa. With 
so much pressure gas bubble is formed which causes a spherical shock wave that propagates in 
the medium [3, 4]. The first of the researchers of this phenomenon was the R. H. Cole whose 
works are the basis for further research. The parameters of the shock wave and the gas bubble 
parameters are being investigated further. Currently the main of researchers are T. L. Geers,  
K. S. Hunter and C. K. Park. Most previous publications describes the behavior of gas bubbles, 
often omitting same shockwave. In this work, omit the description of the bubble in order to focus 
on the pressure wave from the detonation. This wave in the initial stage moves at a speed of the 
order of ݒ ≈ 5000-8000 m/s. Then, the water molecules act on the water layer adjacent losing 
speed and travel further the speed of sound in water, which is approximately ܿ଴ ≈ 1500 m/s. 
Pressure impulse was described by researchers in various ways. It is hard find a universal solution, 
however, due to the development of measuring instruments in this work decided that for the 
calculations related to underwater explosion the latest models, ie. model developed by Geers’a 
and Hunter will be best to use. The following figure shows the profiles described by researchers 
over the years [5]. 
 
Fig. 2. The pressure wave profiles described by researchers over the years [5] 
Cole formulas shown below. They were determined by the measurement of detonation of 
70-136 kg of TNT. Profile of the pressure wave is shown by the following formula: 
݌ሺݐሻ = 52.3 ቆ√݉
య
ݎ ቇ
ଵ,ଵଷ
∙ ݁ି
௧
ఏ, (1)
ߠ = 0.093√݉య  ቆ√
݉య
ݎ ቇ
ି଴,ଶଶ
, (2)
where: ݉ – charge mass, kg; ݎ – distance of epicenter, m; ݌௠௔௫ – peak pressure, MPa; ߠ – time 
constant, ms; ݐ – time, ms. 
Cole models were presented in 1948. Since that time was corrected by J. S Navagin,  
W. Stiepanow, and T. L. Geers and K. S. Hunter, the latter formulas are shown below: 
݌௠௔௫ = ௖ܲ ቀ
ܽ௖
ݎ ቁ
ଵା஺
∙ ݁ି
௧
ఏ, (3)
ߠ = ݒ௖ ቀ
ܽ௖
ݎ ቁ
஻
, (4)
ANALYSIS OF THE PRESSURE WAVE PARAMETERS CAUSED BY TNT UNDERWATER EXPLOSION FORCED ON THE HULL OF MINEHUNTER.  
GRZĄDZIELA ANDRZEJ, KICIŃSKI RADOSŁAW, SZTUROMSKI BOGDAN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCTOBER 2014. VOLUME 3. ISSN 2345-0533 359 
where: ܽ௖ – charge radius, m; ௖ܲ = 1.42; ݒ௖ = 0.992; ܣ = 0.13; ܤ = 0.18. 
In the case of explosions of any material other than TNT it is possible to use a TNT equivalent. 
The equivalent is very difficult to determine because of the multitude of comparative parameters. 
In practice the heat of explosion, detonation speed and pressure coming from the explosion at a 
test distance are compared. As the table shows the equivalents determined on the basis of various 
parameters differ significantly. A good solution is to use average values. 
Table 1. TNT equivalent for various explosives [2] 
Explosive Density ߩ (g/cm3) 
Heat of 
explosion ܳ 
(kJ/kg) 
Pressure 
݌ (MPa) 
Detonation 
speed ܦ (m/s) 
ܶܰ ௘ܶ 
(ܳ) 
ܶܰ ௘ܶ 
(݌) 
ܶܰ ௘ܶ 
(ܦ) 
TNT 1.64 5569 19.0 6950 1.00 1.00 1.00 
Hexogen 1.8 6334 34.7 8754 1.14 1.83 1.26 
Hexotol 90/10 1.61 6232 25.6 7910 1.12 1.35 1.14 
Hexotol 80/20 1.6 6150 24.2 7745 1.1 1.27 1.11 
Hexotol 70/30 1.59 6070 22.7 7580 1.09 1.19 1.09 
Octogen 1.9 6538 39.3 9100 1.17 2.07 1.31 
Octol 90/10 1.75 6438 30.3 8320 1.16 1.59 1.2 
Octol 80/20 1.71 6342 27.8 8050 1.14 1.46 1.16 
Octol 70/30 1.7 6242 26.7 7900 1.12 1.41 1.14 
Octol 60/40 1.7 6156 25.3 7680 1.11 1.33 1.11 
Pentryt 1.77 6400 33.5 8300 1.15 1.76 1.19 
Tetryl 1.68 5920 24.5 7560 1.06 1.29 1.09 
PBX-9011 1.77 6168 29.9 8700 1.11 1.57 1.25 
HMX/PU 80/20 1.43 5856 19.3 7334 1.05 1.02 1.06 
RDX/PU 80/20 1.57 5735 23.4 7778 1.03 1.23 1.12 
RDX/PU 70/30 1.38 5436 16.7 6961 0.98 0.88 1.00 
NM 1.13 6435 12.5 6523 1.16 0.66 0.94 
NGL 1.59 6606 24.6 7580 1.19 1.29 1.09 
DATB 1.79 5498 25.9 7520 0.99 1.36 1.08 
PETN/PU 90/10 1.65 6406 26.3 7950 1.15 1.38 1.14 
PETN/PU 80/20 1.5 6034 21.5 7465 1.08 1.13 1.07 
PETN/PU 70/30 1.39 5682 16.5 6957 1.02 0.87 1.00 
PEP (85/15) 1.5 6186 21.5 7600 1.11 1.13 1.09 
SEMTEX 1.4 6372 19.8 7220 1.14 1.04 1.04 
C-4 1.66 6650 25.7 8370 1.19 1.35 1.2 
COMP. B 1.72 6000 28.1 8052 1.08 1.48 1.16 
LX-17 1.91 4407 31.6 7630 0.79 1.66 1.1 
LX-14 1.83 6452 36.3 8958 1.16 1.91 1.29 
The task of explosions, should be regarded as an appropriate task described by the equation of 
motion. Recognition of this phenomenon using the finite element method requires the use of an 
appropriate equation in the form: 
ۻሺ܃ሻ܃ሷ + ۱܃ሶ + ۹ሺ܃, ઽሶ ሻ܃ = ۴ሺݐ, ܴ, ்݉ே்ሻ, (5) 
where: ۹ – stiffness matrix; ۻ – matrix of inertia (density matrix); ۱ = ߙۻ + ߚ۹ – damping 
matrix, where ߙ  and ߚ  are constant coefficients; ܃,  ܃ሶ ,  ܃ሷ  – displacement, velocity and 
acceleration vector; ۴ – load vector, ઽሶ  – strain rate vector; ݐ – time; ܴ – distance from epicenter; 
்݉ே் – TNT charge mass. 
In the task load vector ۴ have been set as a time-varying pressure wave in accordance with 
Eqs. (1), (2) or (3), (4). Other expressions of Eq. (5) in this work are omitted, because they describe 
the structure reaction while this work refers only to load. 
Polish Navy is currently using 4 types of sea mines. Among other, uses OS mine which 
ANALYSIS OF THE PRESSURE WAVE PARAMETERS CAUSED BY TNT UNDERWATER EXPLOSION FORCED ON THE HULL OF MINEHUNTER.  
GRZĄDZIELA ANDRZEJ, KICIŃSKI RADOSŁAW, SZTUROMSKI BOGDAN 
360 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCTOBER 2014. VOLUME 3. ISSN 2345-0533  
contains 110 kg TNT (Source: Laboratory of Underwater Weapons Polish Naval Academy). The 
paper examined a case in which such a charge detonates around the ship of Kormoran II project. 
Using CAD programs reflected outer shell of the ship, and then implements it into CAE program 
in which the relevant calculations were carried out.  
Charge was placed at a distance of 9 m below the keel of the ship. According to Eq. (3) the 
pressure on the front of the shock wave is 25.67 MPa. The pressure calculated by the program was 
29 MPa. The difference results from the strong relationship between the size and shape of mesh 
elements. In the paper [5] the effect of mesh size and shape on the propagation of the shock wave 
were analyzed. It was found that the 4 – nodal tetragonal of size of 0.5 m elements are best to use. 
 
 
Fig. 3. Pressure distribution of non-contact TNT explosion under the keel of the ship 
 
Fig. 4. Pressure distribution of non-contact TNT explosion under wet surface of the ship 
The pressure distribution of non-contact mine explosion in the acoustic medium in different 
time points were shown. The pressure wave reaches the ship’s hull and it is reflected resulting in 
ANALYSIS OF THE PRESSURE WAVE PARAMETERS CAUSED BY TNT UNDERWATER EXPLOSION FORCED ON THE HULL OF MINEHUNTER.  
GRZĄDZIELA ANDRZEJ, KICIŃSKI RADOSŁAW, SZTUROMSKI BOGDAN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCTOBER 2014. VOLUME 3. ISSN 2345-0533 361 
a negative pressure. The decrease of pressure can lead to cavitation under the keel of the ship. In 
this case, if the ship is treated as a beam supported continuously, due to cavitation a discontinuity 
of the support will appear and the ship would be load with the forces of gravity. In this work, this 
phenomenon is omitted. 
Study describes the phenomenon of underwater explosion. The model used in the study is the 
latest model of the shock wave in this type calculations. Problems that results from the application 
of the acoustic medium and its response for the given load. Also highlights the FEM equation that 
describes the dynamics task. The complexity of this task depends on the author and expected 
results. In case of underwater explosions weight loss, elements self – contact or hardening of the 
material due to the strain rate can be included. The influence of various parameters on the results 
will be examined in further publications. 
References 
[1] Remontowa Shipbuilding S.A., http://www.remontowa-rsb.pl/kormoran_ii/. 
[2] Jeremić Radun, Bajić Zoran An approach to determining the TNT equivalent of high explosives. 
Scientific-Technical Review, Vol. LVI, Issue 1, 2006. 
[3] Cudny K, Powierża Z. Selected issues impact resistance of ships. Gdynia, 1978, (in Polish). 
[4] Grządziela A. Model of impact underwater detonation. Journal of Kones, Vol. 18, Issue 2, p. 145-152, 
2011. 
[5] Kiciński R. Simulation of deformation of the hull of the submarine from the non-contact explosion of 
mines. Master’s thesis, Naval Academy in Gdynia, 2014, (in Polish). 


Analysis of the pressure wave parameters caused by TNT underwater explosion forced on the hull of minehunter

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Analysis of the pressure wave parameters caused by TNT underwater explosion forced on the hull of minehunter

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