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METHOD OF TEMPERATURE CONTROL AND FORCED COOLING OF THE BARREL OF AN ARTILLERY GUN USING A THERMOELECTRIC GENERATOR
Shabatura Yu.
Professor, PhD
Head of the chair of electro mechanics and electronics
Seredyuk B. Associate professor, PhD Chair of electro mechanics and electronics
Balandin M. Doctoral Student
Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine,
Abstract
A method of controlling the temperature of an artillery barrel and, if necessary, its forced cooling due to the reverse operation of a thermoelectric generator based on the use of Peltier elements, which is mounted on the barrel of an artillery gun, is proposed.
Keywords: artillery gun, thermoelectric module, thermoelectric generator, barrel temperature, thermal conductivity.
Introduction
An important feature of technical progress is that in the process of designing and developing technical devices, designers and scientists have always tried to make them the most effective in terms of their functional purpose. This principle was used to create modern models of weapons, including guns.
The nature of modern armed conflicts has shown their transience and increasing requirements for the combat effectiveness of weapons - range, accuracy and rate of fire. Increasing the rate of fire leads to the operation of weapons in extreme conditions, which negatively affects their survivability. So, modern artillery systems (AS), such as, for example, 155-mm self-propelled gun (SG) PzH 2000, are equipped with digital fire control systems (FCS), automatic guidance in two planes and automatic charging system allowing to fire in the so-called "pseudo-volley". This allows to simultaneously hit the target with several shells fired from a single gun, which fly through various trajectories, by automatically changing the angles of elevation and the amount of powder charge [1]. The capabilities of this SG allow hitting the target with five shells at the same time, which significantly increases its firepower. However, firing in this mode leads to rapid heating of the barrel, which severely affects the accuracy of fire and survivability of the barrel. As a result, modern SGs with high firepower are equipped with systems for monitoring the temperature of the barrel and its forced cooling.
Currently, SG with forced cooling of the barrel are not available neither in Ukraine nor in most countries of the world, therefore, control of the barrel temperature must be carried out to increase the rate of fire during long firing of most AS. In order to be able to conduct fire for one hour, the rate of fire of such guns should not exceed 2 shots per minute. At a higher rate of fire, after 20 minutes the barrel temperature reaches a critical value of + 160°C and there is a need for forced cooling of the barrel [2].
Thus, the low efficiency of modern AS as heat engines in terms of estimating the value of the conversion of thermal energy of combustion of gunpowder charge into kinetic energy of the projectile has led to a reasonable search for additional ways to use thermal energy dissipated during firing. In [3], the use of a semiconductor thermoelectric generator (TEG) on Peltier elements was proposed for this purpose. The peculiarity of such generators is that they can operate both in "direct" mode, converting heat flow into electrical energy, and in "reverse" mode, carrying out intensive cooling of the barrel by consuming electrical energy. The above allows the use of TEGs, which are mounted on the artillery gun (AG) barrel to generate electricity during intense firing while simultaneously controlling the barrel temperature. When this temperature reaches certain critical value TEG is switched to reverse mode actively cooling the barrel, dissipating the previously accumulated electrical energy in the battery devices.
The purpose of the article
The purpose of the article is to assess the possibility of using the TEG installed on the barrel of the AG, as a means of controlling the temperature of the barrel and, if necessary, as a means of forced cooling of the barrel due to the operation of the specified TEG in reverse mode.
Results and Discussions The authors, in [3], proposed a method of converting the dissipated heating energy of the AG barrel into electrical energy by installing a TEG on the barrel, the principle of operation of which is based on the use of the Seebeck effect. This TEG generates electricity due to the temperature difference of its working surfaces. The power of this generator depends on the difference between these temperatures and is calculated according to the formula:
(
P - I2
PTEM - 1
■ R, -
2N a AT R+R,
>2
R.
, ' (1)
where, N - the number of pairs of thermoelectric elements in the module;
TEM is thermoelectric module;
a - Seebeck coefficient (thermoEMF);
I - the strength of the current generated by the
TEG;
Rj - resistance to external load;
R - internal resistance of TEG;
AT = Tb — Ta - the difference between the temperature of the barrel and the ambient temperature.
Based on the known parameters of the TEG and the value of the ambient temperature, the measurement of the generated current allows calculating the surface temperature of the barrel.
The temperature of the barrel is determined by the formula:
Tb -
I ■ (R + Ri )
+ T a.
(2)
2 N -a
Upon reaching the maximum allowable values of both the temperature of the outer surface of the barrel and the electric current TEG switches to reverse mode, in which it is supplied with voltage, and accordingly begins cooling of the thermoelectric modules (TEMs) that are part of it, thereby a forced cooling of the outside trunk AG occurs.
Heat transfer energy heated in the process of intensive firing of the barrel Qb determined by the equation [4]:
Qb - Se ■ao ■ S
(It.)4 _ (I±.)4 100 100
(3)
where, - degree of blackness of the material;
(Jq - Stefan-Boltzmann coefficient, W/m2K4; S - the surface area of the radiation, m2;
T
ambient temperature, K.
The amount of heat that accumulates in the barrel metal Qi is determined by the formula:
Q = cs • mb - AT, (4)
where, Cs - specific heat of the barrel material,
J/ kg-K.
The duration of the heat radiation process is defined as the ratio of the amount of heat to the radiation
Se Go • S
AT = -
(IL)4 _ ilaL)4 100 100
• tr
energy
Qu!Qb :
tr =
Cs • mb • AT
Se •Go • S
(_ZL )4 _ (la. )4
• (5)
100 100 From the previous formula, based on the known tr , one can calculate the temperature difference
AT in the process of radiation, which will be installed at the end of tr:
cs ■ mb
(6)When installing the TEG on the part of the barrel,
*
the mass of this part m b is calculated in accordance with the formula:
m*b = S -X'Pb, (7) where, X - the wall thickness of the heated barrel,
m;
Pb - the density of the steel from which the barrel is made, kg/m3.
The proposed model of TEG, which was installed on the barrel of an artillery gun is shown in Fig. 1. It consists of an aluminum bandage 2, thermoelectric modules (Peltier elements) 3 and a ribbed radiator 4.
Figure 1. General view of a cylindrical TEG mounted on the barrel of an artillery cannon.
The thermal model of the TEG placed on the barrel Figure 2:
of the artillery gun is shown on
Figure 2 - Thermal model of a TEG placed on the barrel of an artillery cannon.
The following notations are used in the figure: Pb - heat flow from the barrel of an artillery can-
resistance of TEM, K/W; Rtr - thermal resistance between the Peltier element and the cooling radiator,
non, W; Rbb - thermal resistance between the barrel and K/W; Rr - thermal resistance of the radiator, K/W; RB
the bandage, K/W; Rb - thermal resistance of the TEG bandage, K/W; - thermal resistance between the
bandage and the Peltier element, К/Вт; RTEM - thermal
- thermal resistance between the cooling radiator and the external environment, K/W; PTEO - power of electric energy generated by TEG, W; Tc - the temperature
of the cold side of the TEM, K; T - the temperature of the hot side of the TEM, K; Tm - the mean temperature of the cooling radiator, K.
Because high-quality heat-conducting adhesive was used to improve heat transfer between all components of the TEG, the layer thickness of which was incomparably smaller than in other structures, so the resistances Rjj , RJr£M, Rtr can be neglected.
When installing a gun on the barrel, a thermoelectric generator, will change the nature of heat transfer from the radiant heat exchange system of the barrel-environment which is described by formula 3 to a more complex - convective heat exchange between the barrel, TEG layers and radiant heat exchange between the radiator and the environment.
Heat flux during convective exchange of multilayer structures, in this case between the barrel and TEG layers is described by equations [5]:
q -
M ■ (tb _ ta )
1 , d2 1 , d3
--ln — +--ln —
2X1 d1 2X2 d2
(8)
where, tb, ta - gun barrel temperature and ambient temperature;
X - thermal conductivity coefficients of TEG;
d - diameters of cylindrical structures of TEG.
The surface temperature of the aluminum bandage, which is the hot side of the TEM, is determined by the equation:
ln
dal
tal
q
2m
dbou
Xai
(9)
In thermoelectric modules, part of the heat flux is converted into electrical energy, the amount of which depends on the number of thermoelectric modules (Peltier elements) N1 and the power of each module, which in turn depends on the temperature difference of its hot and cold surfaces. Thus, heat flow qi passing through the TEM is equal to:
q1 - q _ qe - q _ N1- Ptem ■
(10)
In addition, it should be noted that the magnitude of the heat flux converted into electrical energy qe with decreasing barrel temperature will also decrease and will be zero when the barrel cools to ambient temperature.
The temperature of the outer surface of the TEM, which is the basis of the cooling radiator, is determined by the equation:
. dtem
ttem - tai -
ln-
q1 da,
2k Xtem
(11)
The power of the cooling radiator is calculated by the formula:
Wr = at- Qr-Sr, (12) where, Qr = tTEM - ta - the magnitude of overheating of the heat transfer surface, °C.; S r - radiator surface area, m2; a, - total heat transfer coefficient, which includes convective ak and radial coefficients ap.
las:
at =ak +ap. (13)
Coefficient ak is calculated by simplified formu-
■ for a vertically oriented plate of a height l:
ak = ki( Q-
(14)
- for a horizontally oriented surface which has the smallest side of length a:
ak =Wt-ki((Q- (15)
a
where, k1 - coefficient that depends on the arithmetic mean temperature of the radiator:
k = po-Tm +1,41, (16)
where, Tm - arithmetic mean temperature, Tm = 0,5(tr + ta );
p0 =-1,8-10-3,i/°C, coefficient =1,3 for a surface with a hot side facing upwards and =0,7 for a surface with a hot side facing down.
Radiant heat transfer coefficient ap is determined by the formula:
ap - 5,67 ■ se
tr + 273 100
ta + 273 100
(tr + 273) _ (ta + 273)
(17)
where, tr - the average temperature of the radiator, which is determined by the formula:
tr = k2[tTEM — ta 1 (18)
where, fe - coefficient that takes into account the uneven thermal field of the radiator. For natural convection of the air it is taken fe = 0,96, while with a forced cooling fe = 0,93.
Hence, the total cooling time of the AG barrel with integrated TEG in the passive cooling mode (electric power generation mode) will be determined by the formula:
cs-m *b - ATm
'rTEG
Wr
(19)
Thus, due to the increase of the cooling surface area and due to the lower degree of blackness of the radiator surface than the degree of blackness of the barrel, the total cooling time will decrease by 1208s -which is 32% of the duration of the cooling process in normal mode.
In addition, for faster cooling of the barrel during long firing and thus heating of the barrel to the maximum allowable temperatures, the proposed TEG model can be used in "active" mode, for which the TEG with the reversed pole is supplied with direct current, resulting in the TEM side plane facing opposite direction to the barrel to be cooled, and the heat flow to be transferred to the radiator and dissipated into the atmosphere.
The maximum refrigeration capacity of modern TEM is determined by their technical characteristics and can reach up to 200 Watts. Under the condition of forced cooling of the artillery barrel through the surface of the TEG bandage, which has a high thermal conductivity and insignificant thickness, the amount of heat
4
4
flux absorbed by the TEM increases up to 20 times, which will significantly reduce the cooling time of the barrel. In addition, the mode of forced cooling is stable and does not depend on changes in barrel temperature. When using TEG as an active source of forced cooling of the barrel surface, the total cooling time will decrease by 1726s - which is 46.8% of the cooling process in normal mode.
According to the results of mathematical modeling of cooling processes of the barrel under normal conditions, under conditions of cooling the barrel with TEG in passive cooling mode, and under conditions of cooling the barrel with TEG in active cooling mode, computer modeling of cooling processes of AG barrel in each of these processes is carried out. The results of computer simulation are shown in Figure 3 :
JS
a
È if
ai
5
£
l-H
6
0
01 M H
¡L X1
a -
200
170
£ Ü
^ O l-H
S -
■o a
® S
-5 S
140
110
s a so — «
a a
iL
50
20
4 \ \ * * * *» X
. \ t s • \
4 + t 4 \ \ S V \
\ \ * * \ % 2 \ \
* 3 *. 4 t % * * \ \
0
700
1400 2100 2800 3500 4200
Barrel cooling time, s
Figure 3 - Results of computer simulation of artillery barrel cooling processes.
The figure uses the following notation: 1- cooling in normal mode; 2- with TEG, in the mode of passive cooling; 3 - with TEG, in the mode of active cooling.
From the given computer simulation data it is clear that with the installation of TEG on the AG barrel, the cooling time of the barrel is significantly reduced compared to the usual cooling process in the barrel-environment system, both in passive and active mode of its use.
Conclusions:
1. The proposed TEG model, which is installed on the barrel of an artillery gun can be used not only as a source of energy, but also as a means of controlling the temperature of the barrel, and if necessary as a means of active cooling of the barrel.
2. When operating in energy generation mode, the proposed TEG in addition to the main function performs the function of additional "passive cooling" of the barrel by converting part of the heat flow into electricity, and increasing the intensity of radiant heat transfer by installing a ribbed cooling radiator with a larger area and smaller degree of blackness .
3. In intense fire modes, at barrel heating temperatures close to critical, TEG can forcibly cool the outer surface of the barrel due to the Seebeck effect, which can achieve a significant reduction in cooling time of the barrel, and therefore conventional artillery systems
will able to conduct intense fire which is not possible at a given time.
References
1. A.A. Vakal, G.O. Boyko, Trends in the development of self-propelled artillery systems of the world's leading countries. №1 / 2014. Weapons and military equipment. Pp. 19-24.
2. M.I. Belyaev, O.M. Tolmachev. Monitoring the state of self-propelled artillery of the land forces of the Armed Forces of Ukraine and determining the directions of its development. Weapons systems and military equipment. Military and technical problems. 2015 №3 (43). Pp. 11-15
3. Shabatura Yu.V., Balandin M.V. System of conversion of thermal energy of a gun barrel into electric on the basis of application of Peltier elements. Military-technical collection of the National Academy of Land Forces. Lviv, 2018. Issue 20. P. 55-64.
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