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Розглянуто вплив геометри гшок тер-моелементiв i розподшу термоелементiв в каскадах двокаскадних термоелектрич-них охолоджуючих пристрогв на показники надiйностi. Аналiз наведено дляробочого дiа-пазону перепаду температур, номтального теплового навантаження в режимi максимальноI холодопродуктивностi при задано-му струми Показано, що варшщею геометрп термоелементiв i розподшом термоелемен-тiв в каскадах можна досягти двократного зниження iнтенсивностi вiдмов
Ключовi слова: двокаскадний термоелек-тричний охолоджуючий пристрш, геометрiя
гшок термоелементiв, показники надiйностi □-□
Рассмотрено влияние геометрии ветвей термоэлементов и распределения термоэлементов в каскадах двухкаскадных термоэлектрических охлаждающих устройств на показатели надежности. Анализ проведен для рабочего диапазона перепада температур, номинальной тепловой нагрузки в режиме максимальной холодопроизводи-тельности при заданном токе. Показано, что вариацией геометрии термоэлементов и распределением термоэлементов в каскадах можно добиться двукратного снижения интенсивности отказов
Ключевые слова: двухкаскадное термоэлектрическое охлаждающее устройство, геометрия ветвей термоэлементов, показатели надежности
UDC 621.362.192
DOI: 10.15587/1729-4061.2017.108586
ANALYSIS OF THE MODEL OF INTERRELATION BETWEEN THE GEOMETRY OF THERMOELEMENT BRANCHES AND RELIABILITY INDICATORS OF THE CASCADE COOLER
V. Zaykov
PhD, Head of Sector Research Institute «STORM» Tereshkovoi str., 27, Odessa, Ukraine, 65076
E-mail: gradan@i.ua V. Mescheryakov Doctor of Technical Sciences, Professor, Head of Department Department of Informatics Odessa State Environmental University Lvivska str., 15, Odessa, Ukraine, 65016 E-mail: gradan@ua.fm Yu. Zhuravlov PhD, Senior Lecturer Department of Technology of Materials and Ship Repair National University «Odessa Maritime Academy» Didrikhsona str., 8, Odessa, Ukraine, 65029 E-mail: zhuravlov.y@ya.ru
1. Introduction
Thermoelectric coolers under conditions of elevated thermal loads or under switching modes significantly decrease their reliability inficators. This is due, among others, to thermal stresses in the places where thermoelements and electrodes are coupled. It is obvious that the higher the range of the generated temperature drops, the lower the reliability indicators of thermoelectric systems for maintaining thermal regimes of thermally-loaded radio electronics. Cascade coolers provide for a larger temperature difference compared with single-cascade devices, which is why the requirements to reliability indicators turn out to be more stringent. Stricter requirements to the operation of thermally-loaded equipment and, consequently, to the thermoelectric systems that maintain thermal regimes makes it a relevant task to search for approaches to improve reliability indicators of cascade coolers. In the present studies, we consider structural approaches for enhancing the reliability indicators of two-cascade thermoelectric coolers.
2. Literature review and problem statement
The issue of operational reliability (failure rate and the probability of non-failure operation) of thermoelectric
coolers was addressed in numerous studies, for example [1-3]. Research is carried out from different perspectives: the impact of technology of the fabrication of devices on reliability indicators [4], protection from the effect of moisture [5], mechanical [6] and climatic impacts [7], thermal load [8], temperature differences [9], operating modes [10]. Operational reliability of the thermoelectric devices of the specified design is ensured by the choice of working currents, alignment of energy indicators with temperature drops and thermal load. At the design phase, the potential of reliability is laid out, which may only get worse during operation through the inefficient use of the device. In paper [11], authors rather insufficiently, mainly at the qualitative level, outlined results of the impact of the design of single-stage thermoelectric coolers on reliability indicators. The reliability-oriented quantitative research into a single-cascade thermoelectric cooler, presented by the authors of article [12], cannot be automatically applied to the two-cascade device, because it is necessary to take into account the patterns of temperature distribution in the cascades [13]. Given the fact that the single-stage thermoelectric coolers have a limited range of the generated temperature differential, employing the cascading is a required condition in order to increase temperature differential. And this special feature implies undertaking research into defining a connection between re-
3. The aim and objectives of the study
The goal of present work is to improve reliability indicators of the two-cascade thermoelectric cooler by optimizing the design of thermoelements and their distribution in the cascades.
To accomplish the set goal, the following tasks have been set:
- to devise a model that connects reliability indicators of the two-cascade cooler with the geometry of thermoelement branches and their distribution in the cascades for different temperature differential and fixed thermal load;
- to analyze the connection between indicators of reliability and the geometry of thermoelements, distribution of thermoelements in the cascades, energy parameters in the operating temperature range of the cooler's functioning.
4. Development and analysis of the connection model between reliability indicators and the design and energy parameters of a two-cascade cooler
4. 1. Model of interrelation between reliability indicators and the geometry of thermoelement branches
Interest in the application of the cascade thermoelectric coolers (CTEC) is caused not only by the necessity to achieve the highest possible level of cooling, but also by improving cooling efficiency at a given temperature differential. In some cases, when designing CTEC, a developer may refer to a number of different designs of CTEC, which differ in the quantity of thermoelements n1, n2 in the cascades (n/n2 ratio) and the geometry of their branches. The geometry of branches is understood as the ratio of height l of the cascade branch cascade to the area of its cross-section S. A designer's task is to choose rationally the geometry of thermoelement branches, taking into account various constraints on dimensions, weight, power consumption, reliability indicators at sequential electrical connection of the cascades.
We shall estimate basic parameters and reliability indicators of the two-cascade TEC of different designs (n4/n2=var) when used in the cascades of branches of thermoelements with different geometry under condition (l/S)1= (l/S )2 for different temperature differential AT under mode (Q0/I)max.
In order to solve the set problem, we shall apply ratios [13].
A condition of thermal coupling of the cascades can be written in the form
Q0 + ^1=Q02,
(1)
where Q0 is the thermal load, W; W1 is the power consumption of the first cascade, W:
W = 2v Lr^
(2)
Q02 is the refrigeration capacity of the second cascade, W:
Oo2 = n2ILA (2B2 -B22 -02);
R1, R2 is the electric resistance of the thermoelement branch in the cascades, Ohm, R = (l/S); /o;, R2 = (l/S)2 /o2;
e1, o;, e2, o2 are, respectively, averaged values of the coefficient of thermoEMF, V/C, and electrical conductivity, Cm/cm, of the thermoelement branch in the cascades;
B1, B2 is the relative operating current in the cascades,
B1=I/Imax1, B2=I/Imax2;
I is the magnitude of operating current, A; T0 is the temperature of heat-absorbing junction, K; T1 is the intermediate temperature, K; Tis the temperature of the heat-absorbing junction, K; ATmax1, ATmax2 is the maximum temperature differential in the cascades, K, ATmax; = 0,5z; T02, ATmax2 = 0,5z2 T;2;
z;, z2 are the averaged efficiency values of the material of thermoelement branches in the cascades, 1/K;
©1, ©2 is the relative difference of temperature in the cascades ©l=ATl/ATm„l=(Tl-To)/ATm„l, ©2=AT2/ATmax2= = ( T T[ )/A Tmax2.
Refrigeration capacity of the two-cascade TEC is determined by the first cascade:
Qo = VL1A1 (2B; -B;2 -0; ) = «J; (2 B; - fif -Q ), (4)
while the sequential electric connection of cascades defines equality of operating currents in the cascades:
Imax1B1 Imax2B2 1
(5)
The total temperature differential on the two-cascade TEC AT consists of temperature differentials in cascades AT1
and AT2:
AT=AT1+AT2=ATn
max1®1+ATmax2®2.
(6)
We shall transform expression (1) considering (2)-(6) and obtain a formula to calculate relative refrigeration capacity of the two-cascade TEC
r = Qo
r; = „ t-2
where
nJixR
«2Imax2R2 _
: v LA ;
AT.
2B;3 ATmaxi - B;2 A + 2B; aF - a-^— ; T AT
_f_0_ max2 (7)
AT AT ' (/)
;+a*^max; -2B; max;
AT
T 1 n
A = 2 + 4
T
1 ft
AT.
AT
max2
F = Imax; | ATmax;
(3)
1 max 2 ATmax2
From condition dC1/(dB1)=0, we shall obtain a ratio to determine the optimal relative operating current of the first cascade B1opt, corresponding to a maximum of ratio (Q0/I)max of the two-cascade TEC with different designs (n1/n2=var):
4B4
+B2
AT
- 4B3
1 + fl ■A7max2
■3 A7max1
7 1 n
1+a -A7max1
A7
A7
+4B2 a A7max1
max2
AT
- 4aF A7max1 7
AT
T0 A7max2 A7max2
1+a ATmax1
AT
= 0.
(8)
max2 /
The value of intermediate temperature 71 can be obtained taking into account the temperature dependence of parameters of the thermoelement material employing the method of successive approximations [13]. Next, it is possible calculate basic significant parameters of the two-cascade cooler, such as B1, B2, ©1 and ©2.
Relative magnitude of the failure rate is calculated in the following way
^ = _X1 + X_: Xa XA XA
«BÎ (©1 + C^
B1 +A7mMi 01
2
1 + ^1^x1 © T1
2
-KT
n2B22 (©2 + C2
B2 + ATmax2 ©, T1
\2
1+A7-2 © 7
2
K
(9)
where l0 is the nominal failure rate, l0=340-8, 1/h; C2 is the relative magnitude of thermal load of the second cascade, C2=(Q0+W1)/(n2I2max2R2); KT1, KT2 are the coefficients of significance, taking into account the impact of reduced temperature [13].
A probability of the failure-free operation P of the two-cascade TEC can be determined from expression
P=exp(-lit), where t is the preset resource, t=104 h.
(10)
4. 2. Analysis of results of modeling the energy, design, and reliability indicators of the cooler
Calculations of basic relevant parameters and indicators of reliability of the two-cascade TEC were conducted under the mode of maximum refrigeration capacity at assigned current (Q0/I)max for different configurations of the thermoelement branches. Conditions: (l/S )1=(l/S )2=l/S=var at the averaged efficiency value of thermoelectric module zm=(2,4-2,5>10-3 1/K, for different values of ratio of the number of thermoelements in the cascades n/n2, temperature differential AT at 7=300 K and thermal load Q0=1.0 W. Results of the calculations are summarized in Table 1-4.
As can be seen from the data obtained, with a decrease in ratio n/n2 at fixed values of l/S, temperature differential A7 and thermal load Q0, basic parameters of TEC change in the following way:
- intermediate temperature 7 decreases (Fig. 1);
- relative temperature differential in the first cascade ©1 decreases, while in the second ©2 increases; in this case, there are values of n1/n2, for which ©1=©2, in particular, ©1=©2=0.4 at AT=60 K and n1/n2=0.4; ©1=©2=0.51 at AT=70 K and
n1/n2= 0.33; ©1=©2=0.66 at AT=80 K and n1/n2=0,22; ©1=02=0.81 at A7=90 K and n1/n2=0.11 (Fig. 2);
- relative operating current in cascades B1 and B2 increases (Fig. 3);
- relative thermal load of the first cascade C1 increases, while in the second C2 second decreases; in this case, there are values of n1/n2, for which C1=C2, in particular: C1=C2=0.38 at A7=60 K and n1/n2=0.45; C1=C2=0.34 at A7=70 K and n1/n2=0.33; C1=C2=0.27 at A7=80 K and n1/n2=0.24; C= =C2=0.17 at A7=90 K and n1/n2=0.125 (Fig. 4, a);
- dependence of refrigeration coefficient E on the ratio n1/n2 passes a maximum at A7=60 K and n1/n2=0.5; A7=70 K and n1/n2=0.33; A7=80 K and n1/n2=0.20; A7=90 K and n1/n2=0.5 (Fig. 4, b);
- operating current I increases for different values of ratio l/S (Fig. 5);
- functional dependence of the total number of thermoelements n1+n2 on the ratio n1/n2 passes a minimum at A7=60 K and n1/n2= 0.33, at A7=70 K and n1/n2=0.5, at A7=80 K and n1/n2=0.2, at A7=90 K and n1/n2=0.15 for different values of l/S (Fig. 6).
- functional dependence of failure rate X/^o on the ratio n1/n2 passes a minimum at A7=60 K and n1/n2=0.67, at 7=70 K and n1/n2=0.33, at A7=80 K and n1/n2=0.2, at A7=90 K and n1/n2=0.15 for different values of l/S (Fig. 7);
- functional dependence of the probability of failure-free operation P on the ratio n1/n2 passes a maximum at A7=60 K and n1/n2=0.67;A7=70 K and n1/n2=0.5; A7=80 K and n1/n2=0.33; A7=90 K and n1/n2=0.2 (Fig. 8).
In this case, it should be noted that the relative operating currents B1 and B2, relative temperature differentials ©1 and ©2, refrigeration coefficient E, relative thermal load C1 and C2 are not dependent on the geometry of thermoelement branches in the cascades.
T], K
280
270
260
250
240
A T = 60 K
90 K
0,0
0,2
0,4
0,6
0,i
"1 /«2
Fig. 1. Dependence of intermediate temperature T1 of the two-cascade cooler on the ratio n1/n2 for different values of A7"at 7=300 K; Q0=1.0 W under mode (Q0/y)max
It follows from the constructed charts that failure rates and the probability of failure-free operation display clearly pronounced extrema, which can be applied when designing the two-cascade thermoelectric cooling devices with enhanced reliability.
+
l/S Rr103, Ohm R2403, Ohm T A max1' T A max2' I, A n1, pcs. n2, pcs. n1+n2, pcs. U1, V U2, V UE, V V K M08, 1/h P
n1/n2=l,0 -Tj=280 K; Br0.435; B2=0.40; ©r0.62; ©2=0.21; KT1=1.035; KJ2=1.018; Wr8.45 W; W2=8.24 W; WE=16.7 W; E=0.060; Cr0.062
40 36.4 41.67 1.215 1.33 0.53 300 300 600 16.0 15.5 31.5 16.6 49.8 0.9950
20 18.2 20.83 2.43 2.66 1.06 150 150 300 8.0 7.8 15.8 8.3 24.9 0.9975
10 9.1 10.4 4.86 5.32 2.10 75.1 75.1 150 4.0 3.9 7.9 4.15 12.4 0.99876
4.5 4.1 4.7 10.8 11.8 4.7 33.8 33.8 67.6 1.8 1.75 3.55 1.87 5.6 0.99944
2.0 1.82 2.08 24.3 26.7 10.6 15.0 15.0 30.0 0.80 0.78 1.58 0.83 2.48 0.99975
n1/n2=0.67 T1=274 K; ß1=0.49; B2=0.464; ©r0.53; ©2=0.29; KT1=1.035; KT2=1.018; W1=3.0 W; W2=4.9 W; WE=7.9 W; E=0.127; Q=0.21
40 35.1 41.2 1.24 1.31 0.61 89.5 133.6 223.1 4.9 8.1 13.0 10.5 31.4 0.99686
20 17.5 20.6 2.48 2.62 1.21 44.7 66.7 111.4 2.46 4.04 6.50 5.2 15.7 0.99843
10 8.77 10.3 4.95 5.24 2.43 22.3 33.4 55.7 1.23 2.0 3.20 2.6 7.84 0.99922
4.5 3.95 4.64 11.0 11.6 5.40 10.0 15.0 25.0 0.56 0.91 1.47 1.17 3.52 0.99965
2.0 1.75 2.06 24.8 26.2 12.2 4.5 6.7 11.2 0.25 0.40 0.65 0.53 1.6 0.99984
n1/n2=0.50 T1=269 K; B1=0.525; B2=0.506; ©1=0.46; ©2=0.36; KT1=1.035; ^=1.017; W1=2.14 W; W2=5.0 W; WE=7.14 W; E=0.140; C1=0.32
40 34.8 40.8 1.24 1.29 0.65 58.7 117.5 176.2 3.3 7.67 11.0 11.5 34.5 0.99655
20 17.4 20.4 2.48 2.58 1.30 29.3 58.6 87.9 1.65 3.85 5.5 5.7 17.2 0.9983
10 8.7 10.2 4.97 5.17 2.61 14.7 29.4 44.1 0.82 1.92 2.74 2.88 8.64 0.99914
4.5 3.91 4.6 11.0 11.5 5.78 6.6 13.3 20.0 0.37 0.865 1.24 1.30 3.9 0.99961
2.0 1.74 2.04 24.8 25.9 13.0 2.9 5.9 8.8 0.165 0.385 0.55 0.57 1.71 0.99983
n1/n2=0.33 T1=262 K; B1=0.57; B2=0.56; ©r0.35; ©2=0.47; KT1=1.035; KI2=1.021; W1=1.63 W; W2=6.2 W; WE=7.8 W; E=0.128; C1=0.464
40 34.2 40.0 1.24 1.27 0.71 40.9 122.6 163.5 2.3 8.73 11.0 16.0 48.1 0.9952
20 17.1 20.0 2.48 2.54 1.42 20.4 61.3 81.7 1.15 4.35 5.50 8.0 24.0 0.9976
10 8.55 10.0 5.0 5.08 2.83 10.2 30.6 40.8 0.58 2.16 2.74 4.0 12.0 0.99880
4.5 3.85 4.5 11.0 11.3 6.27 4.6 13.9 18.5 0.26 0.98 1.24 1.82 5.45 0.999455
2.0 1.71 2.0 24.8 25.4 14.2 2.0 6.0 8.0 0.07 0.24 0.31 0.79 2.4 0.99976
n1/n2=0.20 T1=254 K; B1=0.605; B2=0.609; ©1=0.22; ©2=0.60; KT1=1.035; K,= 1.025; W1=1.29 W; W2=9.0 W; WE=10.3 W; E=0.097; C1=0.621
40 33.9 40.0 1.246 1.237 0.75 30.6 153.0 183.6 1.71 12.0 13.7 25.9 77.7 0.99226
20 17.0 20.0 2.49 2.46 1.51 15.3 76.5 91.8 0.85 6.0 6.85 12.9 38.8 0.9961
10 8.47 10.0 5.0 4.93 3.0 7.6 38.2 45.8 0.43 3.0 3.43 6.46 19.4 0.9981
4.5 3.81 4.5 11.1 10.95 6.71 3.4 17.2 20.6 0.19 1.34 1.53 2.9 8.7 0.99913
2.0 1.69 2.0 25.0 24.6 15.1 1.5 7.6 9.1 0.085 0.60 0.69 1.28 3.85 0.99962
n1/n2=0.1 T1=247 K; B1=0.632; B2=0.655; ©1=0.11; ©2=0.74; KT1=1.035; KKI2^1.030; W1=1.11 W; W2=16.6 W; WE=17.7 W; E=0.0565; C1=0.751
40 33.3 39.2 1.26 1.215 0.80 25.2 252 277.2 1.39 20.75 22.1 54.0 162.2 0.9839
20 16.7 19.6 2.51 2.42 1.58 12.7 127 139.7 0.70 10.5 11.2 27.2 81.7 0.99186
10 8.33 9.8 5.01 4.84 3.17 6.4 63.7 70.1 0.35 5.24 5.6 13.7 41.0 0.9959
4.5 3.75 4.41 11.1 10.75 7.04 2.9 28.6 31.5 0.16 2.36 2.52 6.14 18.1 0.9982
2.0 1.67 1.96 25.0 24.2 15.8 1.3 13.0 14.7 0.07 1.05 1.12 2.8 8.4 0.99916
l/S flj-103, Ohm R2403, Ohm T A max1' T A max2' I, A n1, pcs. n2, pcs. n1+n2, pcs. Ult V U2, V UE, V M08, 1/h P
n1/n2=0.67 Tj=271 K; B1=0.55; B2=0.506; ©1=0.71; ©2=0.33; KT1=1.043; ^=1.016; Wr8.6 W; W2=14.0 W; WE=22.6 W; £=0.0442; Q=0.094
40 34.2 40.82 1.197 1.31 0.66 218 325 543 13.0 21.2 22.6 22.6 40.9 0.9878
20 17.1 20.4 2.39 2.61 1.32 109 162 271 6.5 10.6 17.1 17.1 20.4 0.9939
10 8.55 10.2 4.79 5.23 2.64 54.5 81.3 136 3.3 5.3 8.6 8.6 10.2 0.9969
4.5 3.85 4.6 10.6 11.6 5.87 24.5 36.6 61.1 1.47 2.39 3.86 3.86 4.6 0.9986
2.0 1.71 2.04 23.9 26.1 13.2 10.9 16.3 27.2 0.65 1.06 1.71 1.71 2.05 0.99939
n1/n2=0.50 T1=266 K; B1=0.59; B2=0.556; ©r0.64; ©2=0.40; KT1=1.043; KT2=1.018; Wr4.54 W; W2=10.5 W; WE=15.0 W; E=0.067; Q=0.185
40 33.9 40.8 1.20 1.27 0.71 105 2102 315 6.4 14.8 21.2 32.7 65.4 0.9935
20 17.0 20.4 2.40 2.56 1.42 52.4 105 157 3.2 7.4 10.6 16.3 49.0 0.9951
10 8.5 10.2 4.8 5.1 2.84 26.2 52.3 78.5 1.60 3.7 5.3 8.1 24.4 0.9975
4.5 3.8 4.6 10.7 11.4 6.3 11.8 23.6 35.4 0.72 1.66 2.4 3.67 11.0 0.9989
2.0 1.70 2.04 24.0 25.6 14.2 5.3 10.5 15.8 0.32 0.74 1.06 1.64 4.9 0.99951
n1/n2=0.33 T1=259 K; B1=0.64; B2=0.61; ©r0.52; ©2=0.51; KT1=1.043; K^=1.022; W1=2.8 W; W2=10.5 W; WE=13.3 W; £=0.0752; C1=0.351
40 33.6 40.0 1.198 1.26 0.767 59.1 177.2 236.3 3.65 13.7 17.4 35.0 105 0.9896
20 16.8 20.0 2.40 2.512 1.53 29.5 88.6 118.1 1.83 6.85 8.7 17.5 52.4 0.9948
10 8.4 10.0 4.79 5.03 3.07 14.8 44.3 59.1 0.91 4.33 5.2 8.75 26.2 0.9974
4.5 3.78 4.5 10.65 11.2 6.82 6.7 20.0 26.7 0.41 1.54 1.95 3.9 11.8 0.9988
2.0 1.68 2.0 24.0 25.1 15.3 3.0 9.0 12.0 0.18 0.69 0.87 1.8 5.3 0.99947
n1/n2=0.20 11=252 K; B1=0.68; B2=0.67; ©1=0.40; ©2=0.64; KT1=1.043; ^=1.027; W1=2.14 W; W2=14.4 W; WE=16.5 W; £=0.0606; C1=0.50
40 32.3 39.2 1.218 1.234 0.83 41.7 208.7 250.4 2.54 17.3 19.8 54.2 162.7 0.9839
20 16.1 19.6 2.44 2.47 1.66 20.8 104.1 124.9 1.29 8.67 9.96 27.0 81.2 0.9919
10 8.06 9.8 4.88 4.94 3.32 10.4 52.1 62.5 0.65 4.33 5.0 13.5 40.6 0.9960
4.5 3.63 4.41 10.8 11.0 7.36 4.7 23.5 28.2 0.29 1.96 2.25 6.1 18.3 0.9982
2.0 1.61 1.96 24.4 24.7 16.6 2.1 10.4 12.5 0.13 0.87 1.0 2.7 8.1 0.99919
n1/n2=0.1 11=246 K; B1=0.715; B2=0.722; ©1=0.29; ©2=0.77; KT1=1.043; ^=1.031; W1=1.77 W; W2=25.4 W; WE=27.1 W; £=0.0369; C1=0.632
40 32.0 38.5 1.22 1.21 0.87 33.1 331 364.1 2.03 29.0 31.0 106.5 319.4 0.9686
20 16.0 19.2 2.44 2.42 1.75 16.6 166 182.6 1.01 14.5 15.5 53.4 160 0.9841
10 8.0 9.6 4.89 4.84 3.5 8.3 83 91.3 0.51 7.26 7.8 26.7 80.0 0.9920
4.5 3.6 4.33 10.9 10.75 7.8 3.7 37 40.7 0.23 3.27 3.5 11.9 35.7 0.9964
2.0 1.6 1.92 24.4 24.2 17.5 1.7 17 18.7 0.10 1.45 1.55 5.47 16.4 0.9984
l/S Rr103, Ohm R2-103, Ohm I A max1' T A max2' I, A n1, pcs. n2, pcs. n1+n2, pcs. U„ V U„ V U„ V V K M08, 1/h P
nj/n2=0.5 Tr263 K; Bj=0.665; B2=0.602; ©r0.846; ©2=0.445; KT1=1.052; KT2=1.02; Wr27.5 W; W2=64.0 W; WE=91.5 W; £=0.0109; Q=0.0416
40 33.0 40.4 1.153 1.274 0.767 548 1096 1644 35.8 83.4 119.2 261.2 783.5 0.9246
20 16.5 20.2 2.307 2.549 1.53 273.7 547.5 821.2 18.0 41.8 59.8 130.4 391.3 0.9616
10 8.26 10.1 4.61 5.10 3.07 137 273.9 411.0 8.96 20.8 29.8 65.2 195.7 0.9801
4.5 3.72 4.55 10.23 11.31 6.80 61.8 123.5 185.3 4.0 9.41 13.4 29.4 58.8 0.9941
2.0 1.65 2.02 23.1 25.5 15.4 27.3 54.6 81.9 1.8 4.2 6.0 13.0 39.0 0.9961
n1/n2=0.33 T1=258 K; B1=0.715; B2=0.667; ©r0.746; ©2=0.552; KT1=1.052; ^=1.025; W1=7.35 W; W2=27.5 W; WE=34.8 W; £=0.0287; Cr0.1726
40 32.26 40.0 1.159 1.242 0.83 133.7 401.1 534.8 8.86 33.2 42.0 120.7 362.0 0.9644
20 16.1 20.0 2.32 2.503 1.66 66.7 200.0 266.7 4.42 16.6 21.0 60.2 180.6 0.9821
10 8.06 10.0 4.64 5.0 3.32 33.4 100.2 133.6 2.21 8.28 10.5 30.2 90.5 0.9910
4.5 3.63 4.5 10.3 11.12 7.36 15.0 45.1 60.1 1.0 3.74 4.74 13.6 40.7 0.9959
2.0 1.61 2.0 23.2 25.0 16.6 6.67 20.0 26.7 0.44 1.66 2.10 6.0 18.0 0.9982
I n1/n2=0.2 =251 K; B1=0.765; B2=0.728; ©1=0.63; ©2=0.68; KT1=1.052; ^=1.027; W1=4.34 W; W2=14.42 W; WE=18.8 W; £=0.0532; C1=0.318
40 31.75 39.2 1.164 1.223 0.89 73.2 365.5 438.6 4.88 16.2 21.2 136.7 273.3 0.9730
20 15.87 19.6 2.329 2.459 1.78 36.5 182.5 219.0 2.44 8.10 10.5 68.2 204.7 0.97974
10 7.94 9.8 4.655 4.92 3.56 18.3 91.4 109.7 1.22 4.05 5.3 34.2 102.5 0.9898
4.5 3.57 4.41 10.35 10.93 7.92 8.2 41.1 49.3 0.55 1.89 2.37 15.3 45.9 0.9954
2.0 1.59 1.96 23.3 24.6 17.8 3.6 18.3 21.9 0.24 0.81 1.05 6.82 20.46 0.9980
n1/n2=0.1 T1=245 K; B1=0.815; B2=0.80; ©r0.52; ©2=0.81; KT1=1.052; K^=1.031; W1=3.39 W; W2=47.6 W; WE=51.0 W; £=0.0196; Cr0.4474
40 30.77 38.46 1.173 1.196 0.956 52.8 528 580.8 3.55 49.8 53.4 259.4 778.2 0.9251
20 15.4 19.23 2.343 2.42 1.91 26.4 264.0 290.4 1.77 24.9 26.7 129.7 389.1 0.9618
10 7.69 9.62 4.69 4.84 3.82 13.2 132 145.2 0.89 12.46 13.4 64.85 194.6 0.9807
4.5 3.46 4.33 10.43 10.75 8.50 5.9 59.0 64.9 0.40 5.6 6.0 29.0 87.0 0.99134
2.0 1.54 1.92 23.4 24.2 19.1 2.64 26.4 29.0 0.18 2.49 2.67 13.0 38.9 0.9961
Table 4
Basic parameters and indicators of reliability of the two-cascade cooler at A 7=90 K, 7=300 K, Q0=1.0 W, N=2, (//S), =(//S)2=//S=var for different values of ratio n1/n2 under mode (Q0//)max
l/S Rr103, Ohm R2-103, Ohm Tmax1, A Imax2, A I, A n1, pcs. n2, pcs. n1+n2, pcs. U„ V U„ V U„ V M08, 1/h P
n1/n2=0.2 T1=250 K; B1=0.845; B2=0.772; ©1=0.866; ©2=0.71; KT1=1.062; KK^=1.029; W1=15.8 W; W2=105.0 W; WE=120.8 W; £=0.0083; C1=0.11; C2=0.24
40 30.77 39.2 1.12 1.224 0.945 236 1180 1416 16.7 111.0 127.7 584.8 1754 0.83912
20 15.4 19.6 2.239 2.43 1.89 117.9 589.5 707.4 8.35 55.5 63.9 292.2 876.5 0.9161
10 7.69 9.8 4.48 4.86 3.79 58.9 295 353.5 4.17 27.8 32.0 146.0 438.0 0.9571
4.5 3.46 4.41 9.95 10.8 8.41 26.5 132.6 159.1 1.88 12.5 14.4 65.7 197.2 0.9805
2.0 1.54 1.96 22.4 24.3 18.9 11.8 59.0 70.8 0.84 5.55 6.40 29.3 87.8 0.99126
n1/n2=0.1 T1=244 K; B1=0.89; B2=0.85; ©1=0.80; ©2=0.83; KT1=1.062; KI2=1.032; W1=9.84 W; W2=135.8 W; WE=145.6 W; £=0.0069; Q=0.19; C2=0.146
40 29.85 38.46 1.133 1.186 1.0 137.4 1374 1511 9.84 135.8 145.6 866.8 2600 0.77105
20 14.92 19.23 2.266 2.41 2.0 68.7 687 755.7 4.92 67.9 72.8 433.4 1300 0.871
10 7.463 9.62 4.53 4.82 4.03 34.4 344 378.4 2.44 33.7 36.1 217.0 651 0.9370
4.5 3.36 4.33 10.0 10.71 8.9 15.7 157 172.7 1.11 15.3 16.4 99.0 297.0 0.9707
2.0 1.49 1.92 22.7 24.15 20.2 6.9 69 75.9 0.49 6.72 7.20 43.5 130.6 0.9870
T1=240 K; B1=0.912; B2=0.88; © =0.71; ©2=0.91; KT n1/n2=0.05 = 1.062; KI2=1.036; W1=6.81 W; W2=194.7 W; WE=201.5 W; £=0.0050; C1=0.282; C2=0.079
40 29.80 38.4 1.133 1.176 1.03 92.5 1851 1944 6.62 189.0 195.6 1253 3757 0.6868
20 14.93 19.23 2.264 2.371 2.06 46.3 926.8 973.1 3.31 94.5 97.8 633.5 1900 0.8270
10 7.46 9.62 4.53 4.74 4.13 23.2 463.1 486.3 1.65 47.1 48.8 316.6 949.8 0.9094
4.5 3.36 4.33 10.0 10.53 9.12 10.6 211.0 221.6 0.75 21.3 22.0 144.2 432.7 0.9577
2.0 1.49 1.92 22.7 23.75 20.7 4.6 92.4 97.0 0.33 9.40 9.73 63.1 189.4 0.9812
Fig. 2. Dependence of relative temperature differential of the first (0,) and the second (02) cascades of the two-cascade cooler on the ratio n,/n2 for different values of DTat T=300 K; Q0=1.0 W under mode (Q0/^max
0,4 0,6 0,8 nxln2 a
0,2 0,3 b
Fig. 3. Dependence of relative operating current of the first (B) and the second (B2) cascades of the two-cascade cooler on the ratio n1/n2 at 7=300 K; Q0=1.0 W; under mode (Q0//)max: a - D7=60, 70 K; b - D7=80, 90 K
Ar=60K\
\70K
80K
--1- 90 K -1- -1- -1- -1-1
0,2 0,3 a
,0 0,2
0,4 0,6 0, b
n | /«2
Fig. 4. Dependence of relative thermal load C1 and refrigeration coefficient E of the two-cascade cooler on the ratio n,/n2 for different values of DTat T=300 K; Q0=1.0 W under mode (Q0/^max: a — thermal load C,; b — refrigeration coefficient E
A7"= 80 K ■
* ■— A7"= yOK --
i/s= 2,0 cm"1
—- — ■— __ 4,5
10
20
—*— -1- -1- -1- 4"~i
0,4 0,6 a
1,0 0,1
0,2 0,3 b
0,4
> I //»->
Fig. 5. Dependence of operating current / of the two-cascade cooler on the ratio n,/n2 for different values of //Sat T=300 K;
Q0=1.0 W under mode (Q0//)max: a - A T=60, 70 K; b - A T=80, 90 K
Fig. 6. Dependence of the total number of thermos elements of the two-cascade cooler on the ratio n,/n2 for different values of //Sat T=300 K; Q0=1.0 W under mode (Q0//)max: a - AT=60 K; b - AT=70 K; c - AT=80 K; d - AT=90 K
c
k/h, T
120 --
100 ■•
80 -■
60 ■•
40 --
20
0,4 0,6 a
0,0 0,! 0,2 0,3 0,4 0,5 0,6 n,/n2 b
20 US = 40 cm"1
-
A T = 80K
■
10
■
4,5
? n
--1- -1- -1- -1- -1-1
Ji/X«.
350 -
300 ■
250 -
200 -
150 -
100 ■
50 -
0
l/S = 20 cm1 \
10
AT= 90K
4,5
2,0
--■-
-'- -'- -1-1
0,0 0,1
0,2 0,3 c
0,4 nt/nj 0,00 0,05
0,10 d
0,15 /»2
Fig. 7. Dependence of relative failure rate X/X0 of the two-cascade cooler on the ratio n,/n2 for different values of //Sat T=300 K; Q0=1.0 W; X„=3-10-81/h; under mode (Q0//)max: a - AT=60 K; b - AT=70 K;
c - AT=80 K; d- AT=90 K
0,999
0,998 -
0,997 -
0,996
0,995 -
0,994
0,993
0,992 -
0,991
2,0/
4,5/
10/
AT = 60K
20 / /
US = 40 -1-
--1- -1- -1- -1-1
0,0
0,2
0,4
0,6
0,8
P 1
0,99 -
0,98
0,97 -
0,96 -
0,95
0,94 -
0,93 -
0,92
2,0 4,5 ---
10
20
AT = 80 K
1/S = --1- 40 cm"1 -■- -1- -1- -1-1
0,998
0,996
0,994
0,992
0,990
0,988
0,986
0,984
0,982
. 2,0.
4,5
10
AT= 70 K
20
- l/S = 40 cm"1 -1- -1
0,0 0,1 0,2 0,3 0,4 0,5 0,6 njn2
b
P T
0,95 -
0,90
0,85
0,80
■ 2,0 --
20
AT= 90 K
l/S = 40 cm"1
0,0
0,1
0,2
0,3
0,4
rt\im
0,05
0,10
0,15
H\ffl2
Fig. 8. Dependence of the probability of failure-free operation P of the two-cascade cooler on the ratio for different values of //Sat 7=300 K; G0=1.0 W; t=104 h; under mode (Qo/4max: a - AT=60 K; b - A 7=70 K; c - A 7=80 K; d- AT=90 K
of separate elements, a reduction of the quantity of thermoelements leads to a growth of the probability of failure-free operation and reduction in the failure rate.
These changes could be quite considerable. For example, when reducing l/S from 10 to 4.5, the value of I increases by
more than two times at AT=60 K and ^/^=0.5 (from 2.6 to 2.8 А), at AT=70 K and ^/^=0.5 (from 2.8 to 6.3 А), at AT=80 K and ^/^=0.5 (from 3.1 to 6.8 А), at AT=90 K and ^2=0.2 (from 3.8 to 8.4 А). When reducing l/S from 10 to 4.5, the total quantity of thermoelements n^n decreases by more than twice at AT=60 K and ^/^=0.5 (from 44 to 20 pcs.), at AT=70 K and ^/^=0.5 (from 80 to 35 pcs.), at AT=80 K and ^/^=0.33 (from 130 to 60 pcs.), at AT=90 K and ^/^=0.2 (from 355 to 160 pcs.).
As far as the failure rate is concerned, at lowering l/S from 20 to 10, the value of ^/^0 decreases by more than
2 times at AT=60 K and ^/^=0.5 (from 6.0 to 2.5), at
AT=70 K and ^/^=0.5 (from 16.3 to 8.0), at AT=80 K and n1/n2= 0.33 (from 60 to 30), at AT=90 K and ^/^=0.2 (from 290 to 145).
It is shown that the dependences of refrigeration coefficient of the two-cascade cooler and relative failure
6. Discussion of results of the analysis of influence of the geometry of branches and the distribution of thermoelements in cascades on the reliability indicators of the two-cascade TEC
Research into influence of the geometry of thermoelement branches in the cascades of thermoelectric cooler on the basic parameters and reliability indicators was performed for the regime of maximum refrigeration capacity at the assigned current, different temperature differential AT=60 K; 70 K; 80 K; 90 K and thermal load &,=1.0 W. In contrast to [13], where the geometry of branches of the cascades is fixed (l/S)=(l/S)2=10, and, therefore, operating currents of the cascades are also fixed, we examined the variant (l/S)=(l/S )2=var=40; 20; 10; 4.5; 2.0.
It follows form the conducted research that at the preset values of AT and nx/n2, a decrease in the ratio l/S leads to increased operating current and reduced number of thermoelements. Given the sequential order of turning on the thermoelements in a cooler, the probability of failure-free operation for which equals to the product of probabilities
c
intensity on the distribution of thermoelements in the cascades demonstrate clearly expressed extrema in the operating temperature range, which makes it possible to receive additional gain on the mass and weight parameters of designed products by reducing the required number of thermoelements and by the optimization of energy distribution in the cascades.
7. Conclusions
1. We designed a reliability-oriented model of the two-cascade thermoelectric cooling device that links reli-
ability indicators of the cooler and the geometry of thermoelements, distribution of thermoelements in the cascades, differences of temperatures in the cascades, operating currents, and thermal load.
2. It is shown that with a decrease in the geometry of thermoelements in the cascades from 10 to 2, the total number of thermoelements decreases and the failure rate reduces by more than twice. Joint application of the variation of geometry and the optimized distribution of thermoelements in the cascades within the operating range of temperature differential makes it possible to lower the failure rate up to 10 times and to reduce mass and weight parameters of the two-cascade coolers.
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