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High breaking capacity fuses with improved cooling
International Journal of Thermal Sciences 70 (2013) 144e153
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
High breaking capacity fuses with improved cooling Adrian Ples¸ca* Gheorghe Asachi Technical University of Ias¸i, Blvd. Dimitrie Mangeron, 21-23, Ias¸i 700050, Romania
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 April 2012 Received in revised form 20 March 2013 Accepted 21 March 2013 Available online 24 April 2013
This paper describes a high breaking capacity fuse with improved cooling. The fuse is equipped with only heat sinks or heat sink and fan, an idea derived from the power semiconductor devices field. Some 3D thermal models are proposed for every analysed case of natural and forced cooling. The best solution was the fuse with three aluminium identical heat sinks mounted on the ceramic body. The influence of the fin length, base plate thickness of the heat sink, number of fins and the shape of the fin cross-section, has been investigated. There is a good correlation between experimental and simulation results. Ó 2013 Elsevier Masson SAS. All rights reserved.
Keywords: 3D thermal model High breaking capacity fuses Heat sinks
1. Introduction In its simplest form, the fuse consists of a piece of metal wire connected between two terminals on a suitable support; and in its complex form it is made up of a cartridge fuse link mounted in a carrier and fuse base. Modern cartridge fuse links contain fusible elements mounted in rigid housings of insulating material. The housings are filled with suitable exothermal and arc-quenching powders, such as silica, and they are sealed by metal endcaps which carry the conducting tags or end connections. The metal parts, other than the fusible elements, are invariably of copper, brass, steel or composites and they must be capable of operating under the exacting thermal, mechanical and electrical conditions which may arise in service. A fuse must be able to carry normal load currents and even transient overloads (and the thermal cycling which accompanies them) for a service life of at least 20 years, without any change of state that might affect its electrical performance [1]. To carry out versatile studies in this field without having to resort to real tests through prototypes, it is desirable to have mathematical models that adequately simulate their real behaviour. Nowadays, to obtain a better characteristic curve, the fuse link has evolved towards more complicated geometric shapes, presenting restrictions at regular intervals along their length. Due to this complicated geometry and to the fact that, as a rule, parameters such as electrical resistivity, thermal conductivity and specific heat vary with temperature, it is not possible to undertake the study
* Tel.: þ40 723055173; fax: þ40 232 237627. E-mail address: [email protected]. 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2013.03.023
using simple analytical techniques and it is necessary to resort to numerical calculations to obtain a theoretically valid model of fuse link behaviour. In previous research studies, because of limited computer capabilities, the authors had to concentrate on partial problems or on parts of the fuse geometry. The progress in computer technology enables the modelling and simulation of more and more complex structures in less time. Hence, a thermal model of the fast fuse operating at high frequencies is reported in Ref. [2]. There are several mathematical approaches to model the operation of a fuse link with different geometric shapes [3,4] and to study the transient heating process of current limiting fuses [5]. Also, in Refs. [6,7] some mathematical models adequate to analyse the thermal transfer in the porous medium of high breaking capacity fuses, have been developed. Numerical methods to study the prearcing times at high breaking capacity fuses and thermal behaviour of fuses for power semiconductors protection, are reported in Refs. [8e10]. In Ref. [11] a commercial finite element method package has been used to model heating of relatively simple fuse geometries without notches and with one single notch, respectively. The finite element method has been used to compute the prearcing times [12], to obtain timeecurrent characteristics [13], or to study the thermal behaviour of film substrate fuses [14]. Other models based on finite element method have been reported in Refs. [15,16]. In Ref. [17] a program code for modelling fuses including M-effect using the finite volume method, has been developed. This study attempts to model the thermal behaviour of high breaking capacity fuses, especially in the case of steady-state conditions. A three-dimensional model of the fuse has been developed using the Pro-ENGINEER software. In the next section, there are
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Nomenclature b c Is j k kair L Nu P Pr Ps Re Rn
gap between the fins specific heat over current current density convection coefficient heat transfer coefficient in the case of forced cooling heat sink length in the flow direction Nusselt number rated power loss Prandtl number supplementary power loss Reynolds number rated resistance of the fuse
Rth S vair
thermal resistance cross-section air speed
Greek symbols Dq Laplace operator for the temperature g material density gair density of air l thermal conductivity lair thermal conductivity of air r electric resistivity q temperature at nodes qa ambient temperature qfmax maximum fuse link element temperature mair dynamic viscosity of air
presented some solutions to improve the fuse cooling on the basis of aluminium heat sinks and heat sink with fan. All solutions are analysed from thermal point of view. The 3D finite elements ProMECHANICA software has been used to perform steady-state thermal simulations. In the case of fuse with forced cooling, the heat transfer coefficient has been computed. For the fuse with improved cooling, an over current coefficient can be defined. In the case of fuse equipped with three same aluminium heat sinks, a thermal analysis from geometrical point of veiw, has been done. The goal was to obtain the minimum temperature in the middle of the fuse links. Finally, to validate the 3D thermal models, some experimental tests have been made.
qjt¼0 ¼ qa
2. Thermal model
qjt¼0 ¼ qa
The aim of this study is to develop a 3D model of a high breaking capacity fuse with heat sinks mounted on the ceramic body. The fuse is not a homogeneous body. It includes different type of materials with different physical and thermal properties. In order to define the mathematical model, the fuse area is divided into subareas which represent the main components of the high breaking capacity fuse, as shown in Fig. 1. For each sub-area of the fuse, the heat transport equation, initial and boundary conditions can be written [18,19], as follows: Sub-area 1: fuse links
vq gc ¼ lDq þ rðqÞj2 vt
(1)
Boundary conditions (between solids from sub-area 1 and subarea 2 and sub-area 4):
l1 grad q1 j1e2 ¼ l2 grad q2 j1e2 ; l1 grad q1 j1e4 ¼ l4 grad q4 j1e4
(2)
Initial conditions:
qjt¼0 ¼ qa
145
(6)
Sub-area 3: ceramic body
gc
vq l ¼ lDq k ðq qa Þ vt S
(7)
Boundary conditions (between solids from sub-area 3 and subarea 2; convection condition to the outside sub-area 5 e air):
l3 grad q3 j3e2 ¼ l2 grad q2 j3e2 ;
lgrad qj3e5 ¼ kðq qa Þ (8)
Initial conditions:
(9)
Sub-area 4: knife contacts
gc
vq l ¼ lDq k ðq qa Þ S vt
(10)
Boundary conditions (between solids from sub-area 4 and subarea 1; convection condition to the outside sub-area 5 e air):
l4 grad q4 j4e1 ¼ l1 grad q1 j4e1 ; lgrad qj4e5 ¼ kðq qa Þ (11) Initial conditions:
qjt¼0 ¼ qa
(12)
A 3D model for a high breaking capacity fuse has been developed using a specific software, the Pro-ENGINEER, an integrated thermal design tool for all type of accurate thermal analysis on devices. The subject was a fuse type gG, size 2, with rated current by 160 A, rated voltage about 550 V, rated power losses of 12.8 W and rated breaking capacity of 120 kA. The 3D model had taken into consideration all the component parts of a high breaking capacity
(3)
Sub-area 2: granular quartz
gc
vq l ¼ lDq k ðq qa Þ vt S
(4)
Boundary conditions (between solids from sub-area 2 and subarea 3; convection condition to the outside sub-area 5 e air):
l2 grad q2 j2e3 ¼ l3 grad q3 j2e3 ; Initial conditions:
lgrad qj2e5 ¼ kðq qa Þ (5)
Fig. 1. Simplified model of the fuse with sub-areas (1 e fuse links; 2 e granular quartz; 3 e ceramic body; 4 e knife contacts; 5 e air).
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Fig. 2. Thermal model of the high breaking capacity fuse (1 e end tag (knife type); 2 e rivet; 3 e ceramic body; 4 e inner cap; 5 e outer cap; 6 e fuse link; 7 e alloy M-effect; 8 e granular quartz).
fuse: outer cap, end tag, rivets, inner cap, ceramic body, fuse links, special alloy for M-effect and granular quartz, as shown in Fig. 2. It was considered a simplified geometry for the rivets. There is high purity quartz sand of 99.65% and the average granular size about 0.45 mm. At the proposed fuse model, taking into account the small dimensions of the fuse link, especially its thickness (0.2 mm), the skin effect is neglected.
3. Thermal simulations It was considered a typical application when this type of fuse is used to protect against over currents a three-phase power electrical installation. The current which flows through the fuse is about 160 A, the rated one. In this case, because the fuse has two fuse link elements and assuming an equal distribution of the current flow, each fuse link will dissipate 6.4 W from a total power loss of 12.8 W. For all thermal simulations 3D finite elements Pro-MECHANICA software has been used. The material properties of every component part of the fuse are described in Table 1 [20,21] according to Fig. 2. The heat load has been applied on surfaces of the fuse link elements, 6.4 W on each one. There is a uniform spatial distribution on surfaces with constant cross-sections. Because of the notches, the fuse links have a variable cross-section and therefore, the thermal load around the notches has a not homogeneous distribution. The mesh of this 3D fuse thermal model has been done using tetrahedron solid elements. The single pass adaptive convergence method to solve the thermal steady-state simulation has been used. The analyzed fuse has the following overall dimensions: length of the ceramic body: 61 mm, square cross-section: 50 mm 50 mm, total length including the knife type contacts: 150 mm. The fuse link has a length of 55 mm, width about 10 mm and thickness of 0.2 mm. The ambient temperature was about 23 C.
Fig. 3. High breaking capacity fuse with three heat sinks mounted with wires on the lateral surfaces (1 e heat sinks; 2 e fuse; 3 e fuse-holder; 4 e wires).
From experimental tests, it was computed k ¼ 15.5 W/m2 C, for this type of high breaking capacity fuse [22]. Hence, it was considered the convection condition like boundary condition for the outer boundaries such as outer caps, end tags, rivets, ceramic body, and it has been applied on surfaces with an uniform spatial variation and a bulk temperature of 23 C. With the aim to improve the cooling of the fuse link elements, and therefore of the whole fuse, an idea derived from the power semiconductor devices technology has been used. Hence, on the lateral surfaces of the ceramic body of the fuse, one or more heat sinks have been mounted. Also from experimental tests, it was obtained the value of 17.55 W/m2 C for the convection coefficient of aluminium heat sinks. They are pressed on the external side of the ceramic body of the fuse using stressed stainless or copper wires which are mounted through the fins of the heat sink and the opposite side of the ceramic body of the electric fuse. An example of three heat sinks mounted on lateral surfaces of the fuse, is presented in Fig. 3. In order to improve the thermal transfer from the fuse to the heat sink, thermal grease has been used. The following cases have been analysed: a. fuse without heat sinks, Fig. 2 b. fuse with one heat sink mounted on upper side of the ceramic body, Fig. 4.1 c. fuse with two heat sinks mounted on the lateral sides of the ceramic body, Fig. 4.2 d. fuse with three heat sinks mounted on the upper and lateral sides of the ceramic body, Fig. 4.3 e. fuse with one heat sink mounted on upper side of the ceramic body and fan, Fig. 4.4 For every thermal simulation, the initial model of the high breaking capacity fuse was the same and also the load on each fuse
Table 1 Material data at 20 C in correlation with component parts from Fig. 2. Parameter
g (kg/m3) c (J/kg C) l (W/m C)
Material Ceramic body e Steatite C221 (3)
Copper (6)
Iron FE40 (2)
Brass (1)
Aluminium (5)
Alloy SnCu1 (7)
Insulation material/pressed carton (4)
Granular quartz (8)
2700 900 2.6
8900 385 385
7190 420.27 52.028
8550 386 115
2700 890 220
7310 217 67
1400 0.099 0.063
830 1201 1
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link and environment temperature has been considered at the same values. The only difference was the type of the heat sink mounted on the fuse ceramic body. The final structured mesh has 14,477 elements for the basic fuse without heat sinks, 36,778 elements in the case of the use with only one heat sink, 37,556 elements in the situation with the fuse together with two heat sinks mounted on the lateral sides of the ceramic body, 19,041 elements in the case of the fuse with three simple heat sinks and 21,286 elements for the fuse with heat sink and forced cooling. In the last case, the fuse with forced cooling, the used fan is similar as PC cooler with the aim to cool the microprocessor. Here, the fan is mounted on the top of the heat sink with four small screws through those four corners of the fan case. To obtain the heat transfer coefficient acting upon the fins, an equation developed in Ref. [23] has been used. The Reynolds number used is a modified channel Reynolds number defined as,
Re ¼
gair vair b b $ mair L
(13)
It has to be considered for the analysed heat sink the following parameters values: L ¼ 51 mm and b ¼ 3 mm. The physical parameters of air used in computations are: lair ¼ 0.0257 W/m C, gair ¼ 1.205 kg/m3, mair ¼ 18.63 106 kg/ms, Pr ¼ 0.713, [20]. The Nusselt number is given by the equation,
1
Nu ¼ 2 6 6 6 6 4
1 Re
Pr 2
3 þ
30:33
(14)
7 7 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!3 7 7 pffiffiffiffiffiffi 3:65 5 0:664 RePr0:33 1 þ pffiffiffiffiffiffi Re 1
Finally, the heat transfer coefficient has the relation,
kair ¼
Nulair b
(15)
The variation of the heat transfer coefficient for different air speed values is shown in the graphic from Fig. 5. Also, on the same graphic, the experimental values are presented. It observes a good correlation between computed (kair_calc) and experimental (kair_exp) values till approximate an air speed of 3 m/s. The differences can be explained because of the complex heat sink geometry (Fig. 4.4), the approximations for the parameters L and b used in equations (13) and (15) and because actually, there is a nonuniform spatial distribution of the thermal transfer coefficient on the surfaces of the heat sink. Further on, some steady state thermal simulations have been done. The temperature distribution inside the fuse and through a fuse link element is shown from Fig. 6.1e6.5. Also, the fuse link lengthwise temperature distribution is presented in Figs. 7 and 8, according to above analysed cases. 4. Discussion of the results As it can be seen in the pictures, Fig. 6.1e6.5, the maximum temperature is obtained in the middle of the fuse link elements. This is explained because of notches made on the fuse links in order to clear the fault current as soon as possible and to interrupt the electric circuit without high over voltages. It was assumed that every
Fig. 4. 1. Thermal model of the high breaking capacity fuse with one heat sink mounted on the upper side of the ceramic body (M e measurement point). 2. Thermal model of the high breaking capacity fuse with two heat sinks mounted on the lateral
sides of the ceramic body (M e measurement point). 3. Thermal model of the high breaking capacity fuse with three heat sinks mounted on the upper and lateral sides of the ceramic body. 4. Thermal model of the high breaking capacity fuse with heat sink and fan mounted on the top of the heat sink.
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70 60
kair[W/m 2°C]
50 40 30 20 10 0 0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
v[m/s] kair_exp
kair_calc
Fig. 5. Thermal transfer coefficient variation against air speed. Comparison between experimental (kair_exp) and computing (kair_calc) values.
fuse link element has to dissipate the same quantity of heat; hence the maximum temperature is the same for any of these. The maximum temperature value is 80.12 C for the fuse without heat sinks (Fig. 6.1), 74.18 C in the case when the fuse has mounted a heat sink on the upper side of the ceramic body (Fig. 6.2), 71.3 C when the fuse has on both lateral sides mounted two heat sinks (Fig. 6.3) and 68.12 C in the last case when the fuse has mounted three heat sinks on upper and lateral sides of the ceramic body (Fig. 6.4). In the case of fuse with forced cooling, the maximum temperatures are: 76.16 C for no air speed, 71.38 C when air speed is 2 m/s, 70.37 C for an air speed about 3.6 m/s and 69.56 C when air speed has 5 m/s (Fig. 6.5). It observes approximately the same temperature decrease when the fuse is equipped with three similar heat sinks and only one heat sink but with forced cooling. Hence, there is a maximum temperature decrease of 12 C, when the fuse is equipped with three same aluminium heat sinks with respect to the case when the fuse has not any type of heat sink mounted on the ceramic body. Therefore, there is the possibility to overload the fuses which are equipped with heat sinks. The maximum temperature in the middle of the fuse links will be the same but the power loss can be increased. Consequently, the operating current for the fuse with heat sinks will be higher with respect to the fuse without heat sinks. It may define an over current coefficient ks with the formula:
Is 1 ks ¼ ¼ In In
sffiffiffiffiffiffi Ps Rn
(16)
In the case of the analysed fuse with rated current of 160 A and rated power loss of 12.8 W, results a rated resistance of the fuse about 0.5 mU. For every analysed case of fuse with different types of heat sinks and forced cooling, the supplementary power loss Ps has been established from steady-state thermal simulations in order to obtain the same maximum temperature in the middle of the fuse link elements as in the case of fuse without mounted heat sinks. The values for supplementary power loss and over current coefficient are concluded in Table 2. As expected, the highest value of the over current coefficient is outlined in the case of fuse with three same heat sinks mounted on the ceramic body. Hence, the fuse can operate at an over current of 160 A 1.125 ¼ 180 A, with 20 A more than the rated current of the fuse without heat sink. Of course, the over current value will be
higher at fuses with higher rated current. In the case of fuse with forced cooling, the best over current coefficient (1.109) has been obtained for an air speed of 5 m/s. A better coefficient means higher air speed values or an optimal geometry for the heat sink used at forced cooling. Also, the steady-state thermal simulations provide the fuse link lengthwise temperature distribution, Figs. 7 and 8. As expected, the maximum temperatures are in the middle of the fuse links. There is a decrease with 12 C for the situation when the fuse has mounted three same heat sinks (3heatsink) compared to the case of fuse without heat sink (0heatsink). In the situation of forced cooling, Fig. 8, there is a decrease of 6.6 C from the case when the fuse is equipped with only one heat sink and no air speed (v ¼ 0) to the case when the fuse has the same heat sink but the air speed is about 5 m/s (v ¼ 5). The end terminals of the fuse link have lower temperature values because of the influence of the knife contacts which act as real heat sinks for the fuse link elements. As can be noticed from the diagrams, actually there is a translation of the curve for fuse link lengthwise temperature distribution in the case of fuse without heat sink to lower temperatures in correspondence with the cases with one, two and three heat sinks mounted on the fuse. The same translation can be noticed in the case of forced cooling, from fuse with heat sink but no air speed (v ¼ 0) to lower temperatures in correspondence with air speed up to 5 m/s, Fig. 8. Therefore, the effects of the heat sinks and forced cooling on the fuse, is like ambient temperature has been decreased with the same values. From steady-state thermal simulations, results that show the most important decrease of the maximum temperature of the fuse link element occurs in the case of fuse with three same aluminium heat sinks mounted on upper and both lateral sides of the ceramic body. Of course, if the heat sinks will be equipped with fans mounted on the top side, the decrease of the maximum temperature of the fuse links will be higher. Further on, this type of heat sink has been analysed from geometrical point of view in order to obtain the minimum temperature in the middle of the fuse link elements at the rated current. First, the length of the fins has been varied. The power loss was constant, 12.8 W and a value of 23 C for the ambient temperature has been considered during all steadystate thermal simulations. To analyse the influence of different geometric parameters of the heat sink, the thermal resistance fuse link to environment has been computed. Hence, Fig. 9 presents the
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149
Fig. 6. 1. Temperature distribution of fuse without heat sinks. 2. Temperature distribution of fuse with one heat sink. 3. Temperature distribution of fuse with two heat sinks. 4. Temperature distribution of fuse with three heat sinks. 5. Temperature distribution of fuse with forced cooling (air speed about 5 m/s).
variation of the thermal resistance at different length of the fins, thickness of the base plate and number of the fins. It is to be observed the decrease of the thermal resistance when the length of the fins increases. This length cannot be increased too much because of technological and economical reasons. The thickness of the base plate was another geometrical parameter which has been varied. In this case, the thermal resistance decrease is not so important when the base plate thickness is increased. At a thickness variation from 1 to 10 mm, results a thermal resistance decreasing only by 0.04375 C/W. Unlike previous parameter, the number of the fins leads to an important variation of the thermal resistance fuse link to environment. Obviously, the more fins, the lower thermal resistance. On the other hand, the number of fins cannot be increased too much because of technological problems which occur when this type of heat sink has to be manufactured. The shape of the crosssection fin was the last parameter which has been analysed. It was considered a rectangular 1.5 mm 3.2 mm cross-section, a circular one with the diameter of 3 mm and an ellipse cross-section with the greater focus of 3.2 mm and the small axis of 1.5 mm. The lower value for the thermal resistance is in the case of circular
cross-section of the fin, 3.478 C/W, then the value in the case of rectangular cross-section, 3.518 C/W, and finally the case of ellipse cross-section with a value for thermal resistance of 3.564 C/W. It can be noticed slightly differences among these thermal resistances; the highest difference is only 0.086 C/W. Apart from the fact that the circular cross-section of fins has the lowest thermal resistance (3.478 C/W), this configuration is easily constructed from technologically point of view and more suitable to be mounted on the fuse in order to get a minimum value for the fuse link temperature. In the case where the fuse together with the heat sinks, is placed within fuseboards or close the different electrical devices or busbars, there is the risk that the overvoltage operation surge finds path for the electric arc through the fins of the mounted heat sinks. To reduce the risk of electric arc discharges, the fins of the heat sinks or the whole heat sinks can be covered with a thin layer of insulating varnish in order to increase the electrical insulation of the heat sink and to avoid electric arc occurrence between fins of the heat sinks. To validate the 3D thermal models, some experimental tests have been made in the same conditions as in the case of thermal
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Fig. 6. (continued).
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151
90 80
θ[°C]
70 60 50 40 30 0
10
20
30
40
50
x[mm] 2h_sim
1h_sim
0h_sim
3h_sim
2h_exp
1h_exp
0h_exp
3h_exp
Fig. 7. Fuse link lengthwise temperature distribution. Comparison between experimental results (0 h_exp e fuse without heat sinks; 1 h_exp e fuse with one heat sink; 2 h_exp e fuse with two heat sinks; 3 h_exp e fuse with three heat sinks) and simulations (0 h_sim e fuse without heat sinks; 1 h_sim e fuse with one heat sink; 2 h_sim e fuse with two heat sinks; 3 h_sim e fuse with three heat sinks).
80 75 70
θ[°C]
65 60 55 50 45 40 0
10
20
30
40
50
x[mm] v0_sim
v2_sim
v3.6_sim
v5_sim
v0_exp
v2_exp
v3.6_exp
v5_exp
Fig. 8. Fuse link lengthwise temperature distribution in the case of forced cooling. Comparison between experimental results (v0_exp e no air speed; v2_exp e air speed of 2 m/s; v3.6_exp e air speed of 3.6 m/s; v5_exp e air speed of 5 m/s) and simulations (v0_sim e no air speed; v2_sim e air speed of 2 m/s; v3.6_sim e air speed of 3.6 m/s; v5_sim e air speed of 5 m/s).
simulations. An electric circuit diagram used for experimental tests is shown in Fig. 10. The main switch K, allows supplying with low-voltage the autotransformer ATR, which adjusts the input voltage for the current supply CS. This is an electromagnetic power device built on the transformer principle. It has an adjustable primary voltage and on the secondary side, high value current can be obtained. The high current from CS, flows through the high breaking capacity fuse F, and will warm it. The current value is measured by an ammeter A, through a current transformer CT. Using proper thermocouples Th, type K, the temperatures in the middle of the fuse link, in the middle of the upper and/or lateral surface of the external surface of the ceramic body and the extreme point of the external end surface of the heat sink, have been acquired. The thermocouples have been
bonded on the fuse links and ceramic body using a special adhesive paste which withstand at high temperatures. This paste sticked the thermocouple on a very small surface very close to the hot junction in order to provide the necessary contact force for the hot junction on the fuse elements or ceramic body. The hot junction of the thermocouples has not been covered with adhesive paste, so there is a good contact of the hot junction with the surfaces to be measured. After the fitting was done, some experimental tests have been made in order to measure the temperatures both with thermocouples and an infrared camera type FLIR E40. The difference between temperatures measured with thermocouples and with infrared camera was less than 2.3 C, within a range of 100 C. Thus, the error because of temperature measurement using thermocouples is about 2.3%. The measurement points are the same
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100
12
90 10
80
8
60 50
6
40
g[mm]
l[mm], N
70
4
30 20
2
10 0
0 3,2
3,3
3,4
3,5
3,6
3,7
3,8
3,9
Rthfa[°C/W] l[mm]
N
g[mm]
Fig. 9. Comparison among thermal resistance fuse link to environment variation against length of the fins l[mm], thickness of the heat sink base plate g[mm] and number of the fins (N) in the case of fuse with three identical heat sinks.
A K
PC/DAQ ATR CS Th
CT
~
F
Fig. 10. Experimental main circuit.
as in the thermal simulations. The small voltage signals provided by thermocouples have been amplified using a signal conditioning board type AT2F-16 with the error of 0.5%. The amplified signal was the input for a data acquisition board type PC-LPM-16 which can be programmed with LabVIEW software. The sampling rate was 50 kS/s and the analogue inputs have a resolution on 12 bits. The comparisons between simulation and experimental results are presented in Figs. 7 and 8. The experimental temperature values are smaller than the simulation ones. This is because during the experimental tests the high breaking capacity fuse was mounted on its fuse-carrier and there are busbars to connect the fuse with protected device. Because of their volume and thermal capacity, these entire external components act like real heat sinks for the fuse link, resulting in an important heat dissipation rate. Thus, the experimental values are placed under the thermal simulation ones. On the other hand, the differences between the temperature values resulting from experimental tests and those obtained during simulations are due to various factors: measurement errors, Table 2 Supplementary power loss and overload coefficient. Analysed case
Ps [W]
ks
Fuse Fuse Fuse Fuse Fuse Fuse
14.3 15.2 16.2 15.1 15.48 15.76
1.056 1.089 1.125 1.086 1.099 1.109
with with with with with with
one heat sink two heat sinks three heat sinks forced cooling, air speed of 2 m/s forced cooling, air speed of 3.6 m/s forced cooling, air speed of 5 m/s
thermal model simplifications, unbalanced current distribution through fuse links and mounting test conditions. The thermal model has not included different types of current busbars from the fuse to other devices to be protected like motors or other type of loads. Nevertheless, the maximum difference between the experimental and simulation results is less than 3.5 C.
5. Conclusion Understanding and optimizing the operating mechanisms of high breaking capacity fuses, the thermal behaviour of the fuse itself and its application are of major interest. Further on, the main conclusions of the simulation study and experimental results are presented: the 3D thermal model has been included all the necessary components for a high breaking capacity fuse such as outer caps, end tags, rivets, inner caps, ceramic body, fuse link elements, special alloy for M-effect and granular quartz; the simulations have been considered the whole thermal model, not parts of it or cross-sections; in steady-state conditions there is a maximum temperature in the middle of fuse links and the minimum values at the endterminals; in order to improve the fuse link cooling, which leads to whole fuse cooling, on the lateral surfaces of the ceramic body of the fuse, one or more heat sinks have been mounted. The case of
A. Ples¸ca / International Journal of Thermal Sciences 70 (2013) 144e153
fuse with three aluminium simple heat sinks mounted on the upper and lateral sides of the ceramic body, leads to the best cooling of the fuse. Another solution, is to mount a fan on the upper side of the heat sink. This solution can be applied to one, two or three heat sinks mounted on the lateral sides of the fuse ceramic body. An optimal designing for the heat sink together with a fan may offer the best solution for fuse cooling; there is the possibility to overload the new type of fuses equipped with heat sinks and fan; depending on the heat sink type and/or forced cooling, the timeecurrent characteristics for the new situation will be translated to the right side of the timeecurrent plane and will influence the discrimination possibilities within overload range, between fuses and/or between fuses and circuit breakers; besides power supply issues, the fan placed on the heat sink only slightly improves the fuse cooling, thus it is not recommended to use a fan for the exploitation; there is a good correlation between experimental and simulation temperature values; using the 3D simulation software package it can improve the high breaking capacity fuse designing from thermal point of view, also having the possibility to get new solutions for a better protection of power electrical devices.
Acknowledgements This work was supported by CNCSIS e UEFISCDI, project number 610 PNII e CAPACITATI 2013. References [1] A. Wright, P.G. Newbery, Electric Fuses, IEE, London, 2004. [2] J. Gelet, D. Tournier, M. Ruggiero, Evaluation of thermal and electrical behaviour of fuses in case of paralleling and/or high frequencies, in: Proc. of the 6th Int. Conf. on Electric Fuses and their Applications, Torino, 1999, pp. 49e53. [3] C. Garrido, J. Cidrás, Study of fuse links with different t-I curves using a mathematical model, in: Proc. of the 6th Int. Conf. on Electric Fuses and their Applications, Torino, 1999, pp. 21e24. [4] C.S. Psomopoulos, C.G. Karagiannopoulos, Temperature distribution of fuse elements during the pre-arcing period, Electric Power Systems Research 61 (2002) 161e167. Elsevier. [5] E. Torres, A.J. Mazón, E. Fernández, I. Zamora, J.C. Pérez, Thermal performance of back-up current-limiting fuses, Electric Power Systems Research 80 (2010) 1469e1476. Elsevier.
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[6] D. Rochette, S. Clain, Mathematical model and simulation of gas flow through a porous medium in high breaking capacity fuses, International Journal of Heat and Fluid Flow 25 (2004) 115e126. Elsevier. [7] D. Rochette, S. Clain, W. Bussière, Mathematical model using macroscopic and microscopic scales of an electrical arc discharge through a porous medium in HBC fuses, in: Proc. of the 7th Int. Conf. on Electric Fuses and their Applications, Gdansk, 2003, pp. 188e193. [8] D. Rochette, R. Touzani, W. Bussière, Numerical study of the short pre-arcing time in high breaking capacity fuses via an enthalpy formulation, Journal of Physics D: Applied Physics 40 (2007) 4544e4551. [9] S. Memiaghe, W. Bussière, D. Rochette, Numerical method for pre-arcing times: application in HBC fuses with heavy fault-currents, in: Proc. of the 8th International Conference on Electric Fuses and their Applications, Clermont-Ferrand, IEEE Catalog Number 07EX1870, 2007, pp. 127e132. [10] A. Plesca, Numerical thermal analysis of fuses for power semiconductors, Electric Power Systems Research 83 (2012) 144e150. [11] D.A. Beaujean, P.G. Newbery, M.G. Jayne, Modelling fuse elements using a C.A.D. software package, in: Proc. of the 5th Int. Conf. on Electric Fuses and their Applications, Ilmenau, 1995, pp. 133e142. [12] H. Kürschner, A. Ehrhardt, G. Nutsch, Calculation of prearcing times using the finite element method, in: Proc. of the 5th Int. Conf. on Electric Fuses and their Applications, Ilmenau, 1995, pp. 156e161. [13] C. Cañas, L. Fernández, R. González, Minimum breaking current obtaining in fuses, in: Proc. of the 6th Int. Conf. on Electric Fuses and their Applications, Torino, 1999, pp. 69e74. [14] M. Wilniewczyc, P.M. McEwan, D. Crellin, Finite-element analysis of thermally-induced film de-bonding in single and two-layer thick-film substrate fuses, in: Proc. of the 6th Int. Conf. on Electric Fuses and their Applications, Torino, 1999, pp. 29e33. [15] K. Jakubiuk, W. Aftyka, Heating of fuse-elements in transient and steady-state, in: Proc. of the 7th Int. Conf. on Electric Fuses and their Applications, Gdansk, 2003, pp. 181e187. [16] A. Hamler, S. Gril, J.P. Cukovic, Thermal analysis and temperature calculation for the NV melting fuse, in: Proc. of the 9th International Conference on Electric Fuses and their Applications, Maribor, 2011, pp. 219e224. [17] M. Lindmayer, 3D simulation of fusing characteristics including the M-effect, in: Proc. of the 6th Int. Conf. on Electric Fuses and their Applications, Torino, 1999, pp. 13e20. [18] N. Wakil, N.C. Chereches, J. Padet, Numerical study of heat transfer and fluid flow in a power transformer, International Journal of Thermal Sciences 45 (2006) 615e626. Elsevier. [19] N.C. Chereches, M. Chereches, C. Popovici, Mixed convection flow inside a vertical channel of a double-skin envelope, International Review of Mechanical Engineering 3 (2009) 739e745. [20] G. Hortopan, Aparate Electrice de Comutatie, Technical Publishing House, Bucharest, 1993. [21] I. Barbu, Sigurante Electrice de Joasa Tensiune, Technical Publishing House, Bucharest, 1983. [22] A.A. Minea, An experimental method to decrease heating time in a commercial furnace, in: Experimental Heat Transfer, vol. 23, Taylor and Francis, 2010, pp. 175e184. [23] R.E. Simons, Estimating parallel plate-fin heat sink thermal resistance, Electronics Cooling 9 (2003) 8e9.
Contents lists available at SciVerse ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
High breaking capacity fuses with improved cooling Adrian Ples¸ca* Gheorghe Asachi Technical University of Ias¸i, Blvd. Dimitrie Mangeron, 21-23, Ias¸i 700050, Romania
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 April 2012 Received in revised form 20 March 2013 Accepted 21 March 2013 Available online 24 April 2013
This paper describes a high breaking capacity fuse with improved cooling. The fuse is equipped with only heat sinks or heat sink and fan, an idea derived from the power semiconductor devices field. Some 3D thermal models are proposed for every analysed case of natural and forced cooling. The best solution was the fuse with three aluminium identical heat sinks mounted on the ceramic body. The influence of the fin length, base plate thickness of the heat sink, number of fins and the shape of the fin cross-section, has been investigated. There is a good correlation between experimental and simulation results. Ó 2013 Elsevier Masson SAS. All rights reserved.
Keywords: 3D thermal model High breaking capacity fuses Heat sinks
1. Introduction In its simplest form, the fuse consists of a piece of metal wire connected between two terminals on a suitable support; and in its complex form it is made up of a cartridge fuse link mounted in a carrier and fuse base. Modern cartridge fuse links contain fusible elements mounted in rigid housings of insulating material. The housings are filled with suitable exothermal and arc-quenching powders, such as silica, and they are sealed by metal endcaps which carry the conducting tags or end connections. The metal parts, other than the fusible elements, are invariably of copper, brass, steel or composites and they must be capable of operating under the exacting thermal, mechanical and electrical conditions which may arise in service. A fuse must be able to carry normal load currents and even transient overloads (and the thermal cycling which accompanies them) for a service life of at least 20 years, without any change of state that might affect its electrical performance [1]. To carry out versatile studies in this field without having to resort to real tests through prototypes, it is desirable to have mathematical models that adequately simulate their real behaviour. Nowadays, to obtain a better characteristic curve, the fuse link has evolved towards more complicated geometric shapes, presenting restrictions at regular intervals along their length. Due to this complicated geometry and to the fact that, as a rule, parameters such as electrical resistivity, thermal conductivity and specific heat vary with temperature, it is not possible to undertake the study
* Tel.: þ40 723055173; fax: þ40 232 237627. E-mail address: [email protected]. 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2013.03.023
using simple analytical techniques and it is necessary to resort to numerical calculations to obtain a theoretically valid model of fuse link behaviour. In previous research studies, because of limited computer capabilities, the authors had to concentrate on partial problems or on parts of the fuse geometry. The progress in computer technology enables the modelling and simulation of more and more complex structures in less time. Hence, a thermal model of the fast fuse operating at high frequencies is reported in Ref. [2]. There are several mathematical approaches to model the operation of a fuse link with different geometric shapes [3,4] and to study the transient heating process of current limiting fuses [5]. Also, in Refs. [6,7] some mathematical models adequate to analyse the thermal transfer in the porous medium of high breaking capacity fuses, have been developed. Numerical methods to study the prearcing times at high breaking capacity fuses and thermal behaviour of fuses for power semiconductors protection, are reported in Refs. [8e10]. In Ref. [11] a commercial finite element method package has been used to model heating of relatively simple fuse geometries without notches and with one single notch, respectively. The finite element method has been used to compute the prearcing times [12], to obtain timeecurrent characteristics [13], or to study the thermal behaviour of film substrate fuses [14]. Other models based on finite element method have been reported in Refs. [15,16]. In Ref. [17] a program code for modelling fuses including M-effect using the finite volume method, has been developed. This study attempts to model the thermal behaviour of high breaking capacity fuses, especially in the case of steady-state conditions. A three-dimensional model of the fuse has been developed using the Pro-ENGINEER software. In the next section, there are
A. Ples¸ca / International Journal of Thermal Sciences 70 (2013) 144e153
Nomenclature b c Is j k kair L Nu P Pr Ps Re Rn
gap between the fins specific heat over current current density convection coefficient heat transfer coefficient in the case of forced cooling heat sink length in the flow direction Nusselt number rated power loss Prandtl number supplementary power loss Reynolds number rated resistance of the fuse
Rth S vair
thermal resistance cross-section air speed
Greek symbols Dq Laplace operator for the temperature g material density gair density of air l thermal conductivity lair thermal conductivity of air r electric resistivity q temperature at nodes qa ambient temperature qfmax maximum fuse link element temperature mair dynamic viscosity of air
presented some solutions to improve the fuse cooling on the basis of aluminium heat sinks and heat sink with fan. All solutions are analysed from thermal point of view. The 3D finite elements ProMECHANICA software has been used to perform steady-state thermal simulations. In the case of fuse with forced cooling, the heat transfer coefficient has been computed. For the fuse with improved cooling, an over current coefficient can be defined. In the case of fuse equipped with three same aluminium heat sinks, a thermal analysis from geometrical point of veiw, has been done. The goal was to obtain the minimum temperature in the middle of the fuse links. Finally, to validate the 3D thermal models, some experimental tests have been made.
qjt¼0 ¼ qa
2. Thermal model
qjt¼0 ¼ qa
The aim of this study is to develop a 3D model of a high breaking capacity fuse with heat sinks mounted on the ceramic body. The fuse is not a homogeneous body. It includes different type of materials with different physical and thermal properties. In order to define the mathematical model, the fuse area is divided into subareas which represent the main components of the high breaking capacity fuse, as shown in Fig. 1. For each sub-area of the fuse, the heat transport equation, initial and boundary conditions can be written [18,19], as follows: Sub-area 1: fuse links
vq gc ¼ lDq þ rðqÞj2 vt
(1)
Boundary conditions (between solids from sub-area 1 and subarea 2 and sub-area 4):
l1 grad q1 j1e2 ¼ l2 grad q2 j1e2 ; l1 grad q1 j1e4 ¼ l4 grad q4 j1e4
(2)
Initial conditions:
qjt¼0 ¼ qa
145
(6)
Sub-area 3: ceramic body
gc
vq l ¼ lDq k ðq qa Þ vt S
(7)
Boundary conditions (between solids from sub-area 3 and subarea 2; convection condition to the outside sub-area 5 e air):
l3 grad q3 j3e2 ¼ l2 grad q2 j3e2 ;
lgrad qj3e5 ¼ kðq qa Þ (8)
Initial conditions:
(9)
Sub-area 4: knife contacts
gc
vq l ¼ lDq k ðq qa Þ S vt
(10)
Boundary conditions (between solids from sub-area 4 and subarea 1; convection condition to the outside sub-area 5 e air):
l4 grad q4 j4e1 ¼ l1 grad q1 j4e1 ; lgrad qj4e5 ¼ kðq qa Þ (11) Initial conditions:
qjt¼0 ¼ qa
(12)
A 3D model for a high breaking capacity fuse has been developed using a specific software, the Pro-ENGINEER, an integrated thermal design tool for all type of accurate thermal analysis on devices. The subject was a fuse type gG, size 2, with rated current by 160 A, rated voltage about 550 V, rated power losses of 12.8 W and rated breaking capacity of 120 kA. The 3D model had taken into consideration all the component parts of a high breaking capacity
(3)
Sub-area 2: granular quartz
gc
vq l ¼ lDq k ðq qa Þ vt S
(4)
Boundary conditions (between solids from sub-area 2 and subarea 3; convection condition to the outside sub-area 5 e air):
l2 grad q2 j2e3 ¼ l3 grad q3 j2e3 ; Initial conditions:
lgrad qj2e5 ¼ kðq qa Þ (5)
Fig. 1. Simplified model of the fuse with sub-areas (1 e fuse links; 2 e granular quartz; 3 e ceramic body; 4 e knife contacts; 5 e air).
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Fig. 2. Thermal model of the high breaking capacity fuse (1 e end tag (knife type); 2 e rivet; 3 e ceramic body; 4 e inner cap; 5 e outer cap; 6 e fuse link; 7 e alloy M-effect; 8 e granular quartz).
fuse: outer cap, end tag, rivets, inner cap, ceramic body, fuse links, special alloy for M-effect and granular quartz, as shown in Fig. 2. It was considered a simplified geometry for the rivets. There is high purity quartz sand of 99.65% and the average granular size about 0.45 mm. At the proposed fuse model, taking into account the small dimensions of the fuse link, especially its thickness (0.2 mm), the skin effect is neglected.
3. Thermal simulations It was considered a typical application when this type of fuse is used to protect against over currents a three-phase power electrical installation. The current which flows through the fuse is about 160 A, the rated one. In this case, because the fuse has two fuse link elements and assuming an equal distribution of the current flow, each fuse link will dissipate 6.4 W from a total power loss of 12.8 W. For all thermal simulations 3D finite elements Pro-MECHANICA software has been used. The material properties of every component part of the fuse are described in Table 1 [20,21] according to Fig. 2. The heat load has been applied on surfaces of the fuse link elements, 6.4 W on each one. There is a uniform spatial distribution on surfaces with constant cross-sections. Because of the notches, the fuse links have a variable cross-section and therefore, the thermal load around the notches has a not homogeneous distribution. The mesh of this 3D fuse thermal model has been done using tetrahedron solid elements. The single pass adaptive convergence method to solve the thermal steady-state simulation has been used. The analyzed fuse has the following overall dimensions: length of the ceramic body: 61 mm, square cross-section: 50 mm 50 mm, total length including the knife type contacts: 150 mm. The fuse link has a length of 55 mm, width about 10 mm and thickness of 0.2 mm. The ambient temperature was about 23 C.
Fig. 3. High breaking capacity fuse with three heat sinks mounted with wires on the lateral surfaces (1 e heat sinks; 2 e fuse; 3 e fuse-holder; 4 e wires).
From experimental tests, it was computed k ¼ 15.5 W/m2 C, for this type of high breaking capacity fuse [22]. Hence, it was considered the convection condition like boundary condition for the outer boundaries such as outer caps, end tags, rivets, ceramic body, and it has been applied on surfaces with an uniform spatial variation and a bulk temperature of 23 C. With the aim to improve the cooling of the fuse link elements, and therefore of the whole fuse, an idea derived from the power semiconductor devices technology has been used. Hence, on the lateral surfaces of the ceramic body of the fuse, one or more heat sinks have been mounted. Also from experimental tests, it was obtained the value of 17.55 W/m2 C for the convection coefficient of aluminium heat sinks. They are pressed on the external side of the ceramic body of the fuse using stressed stainless or copper wires which are mounted through the fins of the heat sink and the opposite side of the ceramic body of the electric fuse. An example of three heat sinks mounted on lateral surfaces of the fuse, is presented in Fig. 3. In order to improve the thermal transfer from the fuse to the heat sink, thermal grease has been used. The following cases have been analysed: a. fuse without heat sinks, Fig. 2 b. fuse with one heat sink mounted on upper side of the ceramic body, Fig. 4.1 c. fuse with two heat sinks mounted on the lateral sides of the ceramic body, Fig. 4.2 d. fuse with three heat sinks mounted on the upper and lateral sides of the ceramic body, Fig. 4.3 e. fuse with one heat sink mounted on upper side of the ceramic body and fan, Fig. 4.4 For every thermal simulation, the initial model of the high breaking capacity fuse was the same and also the load on each fuse
Table 1 Material data at 20 C in correlation with component parts from Fig. 2. Parameter
g (kg/m3) c (J/kg C) l (W/m C)
Material Ceramic body e Steatite C221 (3)
Copper (6)
Iron FE40 (2)
Brass (1)
Aluminium (5)
Alloy SnCu1 (7)
Insulation material/pressed carton (4)
Granular quartz (8)
2700 900 2.6
8900 385 385
7190 420.27 52.028
8550 386 115
2700 890 220
7310 217 67
1400 0.099 0.063
830 1201 1
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147
link and environment temperature has been considered at the same values. The only difference was the type of the heat sink mounted on the fuse ceramic body. The final structured mesh has 14,477 elements for the basic fuse without heat sinks, 36,778 elements in the case of the use with only one heat sink, 37,556 elements in the situation with the fuse together with two heat sinks mounted on the lateral sides of the ceramic body, 19,041 elements in the case of the fuse with three simple heat sinks and 21,286 elements for the fuse with heat sink and forced cooling. In the last case, the fuse with forced cooling, the used fan is similar as PC cooler with the aim to cool the microprocessor. Here, the fan is mounted on the top of the heat sink with four small screws through those four corners of the fan case. To obtain the heat transfer coefficient acting upon the fins, an equation developed in Ref. [23] has been used. The Reynolds number used is a modified channel Reynolds number defined as,
Re ¼
gair vair b b $ mair L
(13)
It has to be considered for the analysed heat sink the following parameters values: L ¼ 51 mm and b ¼ 3 mm. The physical parameters of air used in computations are: lair ¼ 0.0257 W/m C, gair ¼ 1.205 kg/m3, mair ¼ 18.63 106 kg/ms, Pr ¼ 0.713, [20]. The Nusselt number is given by the equation,
1
Nu ¼ 2 6 6 6 6 4
1 Re
Pr 2
3 þ
30:33
(14)
7 7 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!3 7 7 pffiffiffiffiffiffi 3:65 5 0:664 RePr0:33 1 þ pffiffiffiffiffiffi Re 1
Finally, the heat transfer coefficient has the relation,
kair ¼
Nulair b
(15)
The variation of the heat transfer coefficient for different air speed values is shown in the graphic from Fig. 5. Also, on the same graphic, the experimental values are presented. It observes a good correlation between computed (kair_calc) and experimental (kair_exp) values till approximate an air speed of 3 m/s. The differences can be explained because of the complex heat sink geometry (Fig. 4.4), the approximations for the parameters L and b used in equations (13) and (15) and because actually, there is a nonuniform spatial distribution of the thermal transfer coefficient on the surfaces of the heat sink. Further on, some steady state thermal simulations have been done. The temperature distribution inside the fuse and through a fuse link element is shown from Fig. 6.1e6.5. Also, the fuse link lengthwise temperature distribution is presented in Figs. 7 and 8, according to above analysed cases. 4. Discussion of the results As it can be seen in the pictures, Fig. 6.1e6.5, the maximum temperature is obtained in the middle of the fuse link elements. This is explained because of notches made on the fuse links in order to clear the fault current as soon as possible and to interrupt the electric circuit without high over voltages. It was assumed that every
Fig. 4. 1. Thermal model of the high breaking capacity fuse with one heat sink mounted on the upper side of the ceramic body (M e measurement point). 2. Thermal model of the high breaking capacity fuse with two heat sinks mounted on the lateral
sides of the ceramic body (M e measurement point). 3. Thermal model of the high breaking capacity fuse with three heat sinks mounted on the upper and lateral sides of the ceramic body. 4. Thermal model of the high breaking capacity fuse with heat sink and fan mounted on the top of the heat sink.
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70 60
kair[W/m 2°C]
50 40 30 20 10 0 0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
v[m/s] kair_exp
kair_calc
Fig. 5. Thermal transfer coefficient variation against air speed. Comparison between experimental (kair_exp) and computing (kair_calc) values.
fuse link element has to dissipate the same quantity of heat; hence the maximum temperature is the same for any of these. The maximum temperature value is 80.12 C for the fuse without heat sinks (Fig. 6.1), 74.18 C in the case when the fuse has mounted a heat sink on the upper side of the ceramic body (Fig. 6.2), 71.3 C when the fuse has on both lateral sides mounted two heat sinks (Fig. 6.3) and 68.12 C in the last case when the fuse has mounted three heat sinks on upper and lateral sides of the ceramic body (Fig. 6.4). In the case of fuse with forced cooling, the maximum temperatures are: 76.16 C for no air speed, 71.38 C when air speed is 2 m/s, 70.37 C for an air speed about 3.6 m/s and 69.56 C when air speed has 5 m/s (Fig. 6.5). It observes approximately the same temperature decrease when the fuse is equipped with three similar heat sinks and only one heat sink but with forced cooling. Hence, there is a maximum temperature decrease of 12 C, when the fuse is equipped with three same aluminium heat sinks with respect to the case when the fuse has not any type of heat sink mounted on the ceramic body. Therefore, there is the possibility to overload the fuses which are equipped with heat sinks. The maximum temperature in the middle of the fuse links will be the same but the power loss can be increased. Consequently, the operating current for the fuse with heat sinks will be higher with respect to the fuse without heat sinks. It may define an over current coefficient ks with the formula:
Is 1 ks ¼ ¼ In In
sffiffiffiffiffiffi Ps Rn
(16)
In the case of the analysed fuse with rated current of 160 A and rated power loss of 12.8 W, results a rated resistance of the fuse about 0.5 mU. For every analysed case of fuse with different types of heat sinks and forced cooling, the supplementary power loss Ps has been established from steady-state thermal simulations in order to obtain the same maximum temperature in the middle of the fuse link elements as in the case of fuse without mounted heat sinks. The values for supplementary power loss and over current coefficient are concluded in Table 2. As expected, the highest value of the over current coefficient is outlined in the case of fuse with three same heat sinks mounted on the ceramic body. Hence, the fuse can operate at an over current of 160 A 1.125 ¼ 180 A, with 20 A more than the rated current of the fuse without heat sink. Of course, the over current value will be
higher at fuses with higher rated current. In the case of fuse with forced cooling, the best over current coefficient (1.109) has been obtained for an air speed of 5 m/s. A better coefficient means higher air speed values or an optimal geometry for the heat sink used at forced cooling. Also, the steady-state thermal simulations provide the fuse link lengthwise temperature distribution, Figs. 7 and 8. As expected, the maximum temperatures are in the middle of the fuse links. There is a decrease with 12 C for the situation when the fuse has mounted three same heat sinks (3heatsink) compared to the case of fuse without heat sink (0heatsink). In the situation of forced cooling, Fig. 8, there is a decrease of 6.6 C from the case when the fuse is equipped with only one heat sink and no air speed (v ¼ 0) to the case when the fuse has the same heat sink but the air speed is about 5 m/s (v ¼ 5). The end terminals of the fuse link have lower temperature values because of the influence of the knife contacts which act as real heat sinks for the fuse link elements. As can be noticed from the diagrams, actually there is a translation of the curve for fuse link lengthwise temperature distribution in the case of fuse without heat sink to lower temperatures in correspondence with the cases with one, two and three heat sinks mounted on the fuse. The same translation can be noticed in the case of forced cooling, from fuse with heat sink but no air speed (v ¼ 0) to lower temperatures in correspondence with air speed up to 5 m/s, Fig. 8. Therefore, the effects of the heat sinks and forced cooling on the fuse, is like ambient temperature has been decreased with the same values. From steady-state thermal simulations, results that show the most important decrease of the maximum temperature of the fuse link element occurs in the case of fuse with three same aluminium heat sinks mounted on upper and both lateral sides of the ceramic body. Of course, if the heat sinks will be equipped with fans mounted on the top side, the decrease of the maximum temperature of the fuse links will be higher. Further on, this type of heat sink has been analysed from geometrical point of view in order to obtain the minimum temperature in the middle of the fuse link elements at the rated current. First, the length of the fins has been varied. The power loss was constant, 12.8 W and a value of 23 C for the ambient temperature has been considered during all steadystate thermal simulations. To analyse the influence of different geometric parameters of the heat sink, the thermal resistance fuse link to environment has been computed. Hence, Fig. 9 presents the
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149
Fig. 6. 1. Temperature distribution of fuse without heat sinks. 2. Temperature distribution of fuse with one heat sink. 3. Temperature distribution of fuse with two heat sinks. 4. Temperature distribution of fuse with three heat sinks. 5. Temperature distribution of fuse with forced cooling (air speed about 5 m/s).
variation of the thermal resistance at different length of the fins, thickness of the base plate and number of the fins. It is to be observed the decrease of the thermal resistance when the length of the fins increases. This length cannot be increased too much because of technological and economical reasons. The thickness of the base plate was another geometrical parameter which has been varied. In this case, the thermal resistance decrease is not so important when the base plate thickness is increased. At a thickness variation from 1 to 10 mm, results a thermal resistance decreasing only by 0.04375 C/W. Unlike previous parameter, the number of the fins leads to an important variation of the thermal resistance fuse link to environment. Obviously, the more fins, the lower thermal resistance. On the other hand, the number of fins cannot be increased too much because of technological problems which occur when this type of heat sink has to be manufactured. The shape of the crosssection fin was the last parameter which has been analysed. It was considered a rectangular 1.5 mm 3.2 mm cross-section, a circular one with the diameter of 3 mm and an ellipse cross-section with the greater focus of 3.2 mm and the small axis of 1.5 mm. The lower value for the thermal resistance is in the case of circular
cross-section of the fin, 3.478 C/W, then the value in the case of rectangular cross-section, 3.518 C/W, and finally the case of ellipse cross-section with a value for thermal resistance of 3.564 C/W. It can be noticed slightly differences among these thermal resistances; the highest difference is only 0.086 C/W. Apart from the fact that the circular cross-section of fins has the lowest thermal resistance (3.478 C/W), this configuration is easily constructed from technologically point of view and more suitable to be mounted on the fuse in order to get a minimum value for the fuse link temperature. In the case where the fuse together with the heat sinks, is placed within fuseboards or close the different electrical devices or busbars, there is the risk that the overvoltage operation surge finds path for the electric arc through the fins of the mounted heat sinks. To reduce the risk of electric arc discharges, the fins of the heat sinks or the whole heat sinks can be covered with a thin layer of insulating varnish in order to increase the electrical insulation of the heat sink and to avoid electric arc occurrence between fins of the heat sinks. To validate the 3D thermal models, some experimental tests have been made in the same conditions as in the case of thermal
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Fig. 6. (continued).
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151
90 80
θ[°C]
70 60 50 40 30 0
10
20
30
40
50
x[mm] 2h_sim
1h_sim
0h_sim
3h_sim
2h_exp
1h_exp
0h_exp
3h_exp
Fig. 7. Fuse link lengthwise temperature distribution. Comparison between experimental results (0 h_exp e fuse without heat sinks; 1 h_exp e fuse with one heat sink; 2 h_exp e fuse with two heat sinks; 3 h_exp e fuse with three heat sinks) and simulations (0 h_sim e fuse without heat sinks; 1 h_sim e fuse with one heat sink; 2 h_sim e fuse with two heat sinks; 3 h_sim e fuse with three heat sinks).
80 75 70
θ[°C]
65 60 55 50 45 40 0
10
20
30
40
50
x[mm] v0_sim
v2_sim
v3.6_sim
v5_sim
v0_exp
v2_exp
v3.6_exp
v5_exp
Fig. 8. Fuse link lengthwise temperature distribution in the case of forced cooling. Comparison between experimental results (v0_exp e no air speed; v2_exp e air speed of 2 m/s; v3.6_exp e air speed of 3.6 m/s; v5_exp e air speed of 5 m/s) and simulations (v0_sim e no air speed; v2_sim e air speed of 2 m/s; v3.6_sim e air speed of 3.6 m/s; v5_sim e air speed of 5 m/s).
simulations. An electric circuit diagram used for experimental tests is shown in Fig. 10. The main switch K, allows supplying with low-voltage the autotransformer ATR, which adjusts the input voltage for the current supply CS. This is an electromagnetic power device built on the transformer principle. It has an adjustable primary voltage and on the secondary side, high value current can be obtained. The high current from CS, flows through the high breaking capacity fuse F, and will warm it. The current value is measured by an ammeter A, through a current transformer CT. Using proper thermocouples Th, type K, the temperatures in the middle of the fuse link, in the middle of the upper and/or lateral surface of the external surface of the ceramic body and the extreme point of the external end surface of the heat sink, have been acquired. The thermocouples have been
bonded on the fuse links and ceramic body using a special adhesive paste which withstand at high temperatures. This paste sticked the thermocouple on a very small surface very close to the hot junction in order to provide the necessary contact force for the hot junction on the fuse elements or ceramic body. The hot junction of the thermocouples has not been covered with adhesive paste, so there is a good contact of the hot junction with the surfaces to be measured. After the fitting was done, some experimental tests have been made in order to measure the temperatures both with thermocouples and an infrared camera type FLIR E40. The difference between temperatures measured with thermocouples and with infrared camera was less than 2.3 C, within a range of 100 C. Thus, the error because of temperature measurement using thermocouples is about 2.3%. The measurement points are the same
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100
12
90 10
80
8
60 50
6
40
g[mm]
l[mm], N
70
4
30 20
2
10 0
0 3,2
3,3
3,4
3,5
3,6
3,7
3,8
3,9
Rthfa[°C/W] l[mm]
N
g[mm]
Fig. 9. Comparison among thermal resistance fuse link to environment variation against length of the fins l[mm], thickness of the heat sink base plate g[mm] and number of the fins (N) in the case of fuse with three identical heat sinks.
A K
PC/DAQ ATR CS Th
CT
~
F
Fig. 10. Experimental main circuit.
as in the thermal simulations. The small voltage signals provided by thermocouples have been amplified using a signal conditioning board type AT2F-16 with the error of 0.5%. The amplified signal was the input for a data acquisition board type PC-LPM-16 which can be programmed with LabVIEW software. The sampling rate was 50 kS/s and the analogue inputs have a resolution on 12 bits. The comparisons between simulation and experimental results are presented in Figs. 7 and 8. The experimental temperature values are smaller than the simulation ones. This is because during the experimental tests the high breaking capacity fuse was mounted on its fuse-carrier and there are busbars to connect the fuse with protected device. Because of their volume and thermal capacity, these entire external components act like real heat sinks for the fuse link, resulting in an important heat dissipation rate. Thus, the experimental values are placed under the thermal simulation ones. On the other hand, the differences between the temperature values resulting from experimental tests and those obtained during simulations are due to various factors: measurement errors, Table 2 Supplementary power loss and overload coefficient. Analysed case
Ps [W]
ks
Fuse Fuse Fuse Fuse Fuse Fuse
14.3 15.2 16.2 15.1 15.48 15.76
1.056 1.089 1.125 1.086 1.099 1.109
with with with with with with
one heat sink two heat sinks three heat sinks forced cooling, air speed of 2 m/s forced cooling, air speed of 3.6 m/s forced cooling, air speed of 5 m/s
thermal model simplifications, unbalanced current distribution through fuse links and mounting test conditions. The thermal model has not included different types of current busbars from the fuse to other devices to be protected like motors or other type of loads. Nevertheless, the maximum difference between the experimental and simulation results is less than 3.5 C.
5. Conclusion Understanding and optimizing the operating mechanisms of high breaking capacity fuses, the thermal behaviour of the fuse itself and its application are of major interest. Further on, the main conclusions of the simulation study and experimental results are presented: the 3D thermal model has been included all the necessary components for a high breaking capacity fuse such as outer caps, end tags, rivets, inner caps, ceramic body, fuse link elements, special alloy for M-effect and granular quartz; the simulations have been considered the whole thermal model, not parts of it or cross-sections; in steady-state conditions there is a maximum temperature in the middle of fuse links and the minimum values at the endterminals; in order to improve the fuse link cooling, which leads to whole fuse cooling, on the lateral surfaces of the ceramic body of the fuse, one or more heat sinks have been mounted. The case of
A. Ples¸ca / International Journal of Thermal Sciences 70 (2013) 144e153
fuse with three aluminium simple heat sinks mounted on the upper and lateral sides of the ceramic body, leads to the best cooling of the fuse. Another solution, is to mount a fan on the upper side of the heat sink. This solution can be applied to one, two or three heat sinks mounted on the lateral sides of the fuse ceramic body. An optimal designing for the heat sink together with a fan may offer the best solution for fuse cooling; there is the possibility to overload the new type of fuses equipped with heat sinks and fan; depending on the heat sink type and/or forced cooling, the timeecurrent characteristics for the new situation will be translated to the right side of the timeecurrent plane and will influence the discrimination possibilities within overload range, between fuses and/or between fuses and circuit breakers; besides power supply issues, the fan placed on the heat sink only slightly improves the fuse cooling, thus it is not recommended to use a fan for the exploitation; there is a good correlation between experimental and simulation temperature values; using the 3D simulation software package it can improve the high breaking capacity fuse designing from thermal point of view, also having the possibility to get new solutions for a better protection of power electrical devices.
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