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Розглянуто модель взаемозв'язку показни^в надiйностi i основних значимих параметрiв дво-каскадного термоелектричного охолоджуючого пристрою заданог конструкци, який працюе в режимi найбтьшог енергетичног ефективностi при послидовному з'еднант каскадiв. Одержат спiввiдношення, як дозволяють визначити основ-ш параметри i показники надiйностi при рiзнiм спiввiдношеннi елементiв в каскадах, робочому дiапазонi перепадiв температур для проектуван-ня охолоджувачiв тдвищеног надiйностi
Ключовi слова: термоелектричн охолоджую-чi пристрог, показники надiйностi, перепад тем-
ператури, енергетична ефективтсть
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Рассмотрена модель взаимосвязи показателей надежности и основных значимых параметров двухкаскадного термоэлектрического охлаждающего устройства заданной конструкции, работающего в режиме наибольшей энергетической эффективности при последовательном электрическом соединении каскадов. Получены соотношения, позволяющие определить основные параметры и показатели надежности при различном соотношении элементов в каскадах, рабочем диапазоне перепадов температур для проектирования охлаждающих устройств повышенной надежности
Ключевые слова: термоэлектрические охлаждающие устройства, показатели надежности, перепад температуры, энергетическая эффективность
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UDC 621.362.192
|DOI: 10.15587/1729-4061.2017.99988|
DEVELOPMENT OF A MODEL FOR PREDICTING THE RELIABILITY INDICATORS IN THE DESIGN OF CASCADE THERMOELECTRIC COOLERS
V. Zaykov
PhD, Head of Sector Research Institute "STORM" Tereshkova str., 27, Odessa, Ukraine, 65076 E-mail: [email protected] 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: [email protected] 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: [email protected]
1. Introduction
The application of cascade thermoelectric devices (CTED) is predetermined not only by the need to achieve a maximally possible level of cooling, but also to improve cost efficiency. In some cases, a designer has a number of chosen structures of CTED at his disposal, constructed based on the standardized modules. It is necessary to determine maximally possible energy effectiveness at the assigned temperature differential, to select such current mode in the operation of CTED that it would match the maximum of energy effectiveness of CTED of the assigned design (regime Еmax). The relevance of providing the maximum of energy effectiveness is caused by the need to reduce the mass-and-size indicators in the systems that provide thermal modes of the thermally loaded elements.
2. Literature review and problem statement
Expansion in the scope of application of thermoelectric coolers [1, 2] leads to more stringet requirements to energy and reliability indicators. Since the refrigeration capacity of
coolers depends first of all on the thermoelectric effectiveness of material of thermoelements, considerable efforts of designers are concentrated in this direction [3, 4]. The most impressive results are achieved in the field of nano-technolo-gies [5, 6], however, there is still a long way to go before the implementation of industrial production of such materials. Furthermore, improving the effectiveness of thermoelectric materials does not fully solve the given problem, since the reliability of functioning of coolers is not a less important indicator [7, 8]. The capability to resist mechanical impacts is one of the components of coolers reliability [9]. A transition to the planar technologies in the production of thermoelectric coolers [10, 11] and the corresponding reduction in the mass-and-size indicators does not resolve the task either. New problems occur that are related to the influence of resistances of thermoelements and the increased thermal conductivity [12]. Moreover, when we take into account the existing market for thermoelectric coolers [13], then it becomes obvious that it is necessary to search for the ways of improving the energy and reliability indicators of the existing thermoelectric modules. The models of interrelation between the indicators of thermoelectric effectiveness and reliability, presented in [14], as well as the influence of re-
©
gimes on the indicators of reliability [15], allow us to argue about the expediency of the given developments. For this purpose, it is necessary at the assigned temperature range to determine basic significant parameters, namely, relative operating currents and relative temperature differentials in the cascades, and then to estimate reliability indicators of energy-efficient CTED.
3. The aim and tasks of the study
The aim of present work is to develop a model that would make it possible to evaluate the efficiency of functioning and predicting the reliability indicators of a two-stage TED of the chosen design.
To achieve this objective, it is necessary to solve the following tasks:
- to develop a model of interrelation between reliability indicators of CTED and the design and energy indicators under the mode of the highest energy effectiveness;
- to analyze the model to identify conditions for improving the efficiency of CTED of different designs.
cal resistance of the branch of thermoelement of the second cascade, Ohm.
A general temperature differential on a two-stage CTED can be written in the form
AT=AT1+AT2=ATmaxiei+ATmax2e2,
(3)
where AT1 is the temperature differential in the first cascade, K, AT1=T1-T0; AT2 is the temperature differential in the second cascade, K, AT2=T-T^ 02 is the relative temperature differential in the second cascade, rel. un.,
e2=(T-T1)/ATm„2,
where ATmax2 is the maximum temperature differential in the second cascade, K.
A condition of the thermal joining of cascades can be written in the form
ijLA^ -B2 -02)
:1R1
2B1
1 + 01
T1
j-n
+b2 -01
(4)
4. Development and analysis of the model of a cascade thermoelectric cooler
4. 1. Development of a reliability-oriented model of CTED
In order to solve the set problem, we shall use known relationships [16]. The refrigeration capacity Q0 of a two-cascade CTED can be written in the form
Qo = n1iL1R1(2B1 -b2 -01),
(1)
where Imax1 is the maximum operating current, A; Imax1=e1T0/R1; n1 is the quantity of thermoelements in the first cascade, pieces; T0 is the temperature of the heat-absorbing joint of the first cascade, K; e1 is the coefficient of thermal EMF of the branch of thermoelements of the first cascade, V/K; R1 is the electrical resistance of the branch of thermoelement of the first cascade, Ohm; B1 is the relative operating current of the first cascade, rel. un., B1=I/Imax1; 91 is the relative temperature drop in the first cascade, rel. un.
where n is the quantity of thermoelements in the second cascade, pieces
Refrigeration coefficient of a two-stage CTED can be written in the form
E =-
Qo
(5)
' W1 + W2'
where W1 is the power of consumption of the first cascade, W,
W1 =
B1 + ATmax1 01 T
(6)
where W1 is the power of consumption of the second cascade, W,
W2 = 2n2llx2R2B2
B2 + ATmax2 02
2 T1 2
(7)
91=(T1-To)/ATm„1,
where T1 is the intermediate temperature, K; ATmax1 is the maximum temperature differential in the first cascade, K.
Sequential electrical connection of cascades defines the equality of operating currents in the cascades, which can be written in the form
By using relations (1)-(7), refrigeration coefficient can be written in the form
AT
En=2 =-
2aB,b - aBjc + 2a2B? —max1 - a
1 1 1 "y
T
AT
AT „„.
2BjX - 2B3Y + 2B1H-^T-
1 1 1 AT.
(8)
Imax1 B1 Imax2 B2,
(2) where
where B2 is the relative operating current of the second cascade, rel. un.,
, = n1Imax1R1 .
d —-2->
n2Imax2R2
B2 = I/Imax2; Imax2=e2T1/R2*'
b = _ATmax1 , Imax1 .
ATmax2 Imax2
where e2 is the coefficient of thermal EMF of the branch of thermoelements of the second cascade, V/K; R2 is the electri-
AT.
AT
-2a
1 + 2 ATmax1
n
n
I2
-2a
AT
AT
I2
max2 /
ATmax 1 1 max1 ATmax2 AT
T0 Imax2 T1 ATm
+2
Jmxi ATm L
mox2 ATmax1 „ ---d,
V Imax2 T1 ATmax2
max2
AT„
max1
T
o
In accordance with [16], for a two-stage TED, the magnitude of relative failure rate can be written in the form
n1B2(01 + C1)
B1 + ATmax1 01 1 1
\ 2
1+ATM101 1
2
-KT
Y=
I2
max2
Imax1 ATmax2 ATmax1 , a ATmax1
Imax2 T1 ATm
H=a
Imax1 ATmax2 , ATmax1
I T T
max2 1 o
Functional dependence
n2B2(02 + C2)
B2 02
2
T1
1 + ATmax2 02 T1 2
2
-Kt,
(12)
where X0 is the nominal failure rate, 1/h; C1, C2 are the relative thermal load of the first and second cascades, rel. un.,
EN=2=f(B1),
has a maximum for different designs of TED (n1/n2) and temperature differentials AT=60 K; 70 K; 80 K; 90 K at T=300 K, n1=9, l2/s2=l1/s1=10.
With an increase in temperature AT, the optimum magnitude of relative operating current B1 shifts toward larger values.
dEN 1
From condition -= 0 we shall obtain a relation for
dB1
determining the optimum magnitude of relative operating current B1, corresponding to the maximum of refrigeration coefficient EN of the TED of assigned design (n1/n2) and to the temperature differential AT:
C1 =
Q0
n1Imax1
R/
C =
Q0 + W1 ,
n2im>x2R2 '
KTi and K^ is the coefficient of significance taking into account the effect of reduced temperature [16]. The analytical model obtained provides the possibility to analyze a relation between the relative failure rate and the energy and design indicators of a thermoelectric cooler in the working range of functioning temperature.
b4
+B2
Yc-2aX
T
- 4B3
Yb + aHAT
T AT
2Xb + Hc^^-+3Y- AT
AT
-2B1X
AT
AT„,„.
AT
V ATmax2 y
2 ATmax2 )
2
= 0.
(9)
Presented relation (9) makes it possible to determine the magnitude of optimum relative operating current B1 that provides for the maximum refrigeration coefficient EN at the given values of ratio n1/n2 and temperature differential AT.
Next, we determine relative temperature differentials in cascades 81 h 62, using a successive approximation method, taking into account the temperature dependence of parameters (one-two approximations siffice):
BÎ
a=-
I2
max1
max2
- 2B1
Imax1 V Imax2
AT
AT „„.
ATmax1 + a - 2aB, AT 1 T
max2 0
0 =
AT AT
AT
AT
-01
(10)
(11)
and, according to expression (1), refrigeration capacity Q01 for the assigned design (n1/n2) of TED in regime Emax at the assigned A T.
4. 2. Analysis of results of modeling the reliability and energy indicators
The calculated data on the basic parameters are given in Tables 1-4 for l2/s2=l1/s1=10; T=300 K; AT=60 K; 70 K; 80 K; 90 K; n1=9; n1/n2^1.0; 0.67; 0.5; 0.33; 0.2; 0.1 and the averaged value of effectiveness of thermoelectric modules zM=2.540-31/K; X0=340-8 1/h; t=104 h.
At the decrease in ratio n1/n2 at the assigned value of temperature differential AT=60 K:
- the magnitude of intermediate temperature T1 decreases (Fig. 1, pos. 1);
- relative operating current of the first cascade B1 increases (Fig. 1, pos. 2);
- relative operating current of the second cascade B2 increases (Fig. 1, pos. 3);
- relative drop in temperature of the first cascade 01 decreases (Fig. 1, pos. 4);
- relative drop in temperature of the second cascade 62 increases (Fig. 1, pos. 5);
- the magnitude of operating current I increases (Fig. 1, pos. 6);
- refrigeration coefficient of TED has an absolute maximum at n1/n2=0.44 (Fig. 2, pos. 1);
- refrigeration coefficient of the first cascade s1 increases (Fig. 2, pos. 2), and of the second cascade s2 decreases (Fig. 2, pos. 3);
- the point of intersection of dependence charts of the refrigeration coefficients of cascades e1 and e2 corresponds to n1/n2=0.44 (Fig. 2);
- refrigeration capacity Q01 (Fig. 2, pos. 4) and its relative magnitude C1 (Fig. 2, pos. 5) increase;
X
X
+
- the total magnitude of failure rate A increases (Fig. 3, - total probability of failure-free operation Px decreases pos. 3); (Fig. 4, pos. 3);
- the failure rates of the first A and the second A2 cas- - the probability of failure-free operation of the first (P4) cades also increase (Fig. 3, pos. 1, 2);and the second (P2) cascade decreases (Fig. 4, pos. 1, 2).
Table 1
Results of calculation of the basic parameters and indicators of reliability of two-cascade TED of different designs under the mode Emax at AT=60 K
ni/n2 Bi B2 I, A T1, K 01 02 E1 e2 E Q01, W C1 W1, W W2, W WT, W UE, V V10-8, 1/h P
1.0 0.41 0.38 1.91 279.8 0.61 0.22 0.1 1.13 0.051 0.09 0.05 0.89 0.86 1.75 0.92 1.18 0.999882
0.67 0.43 0.405 2.0 272.8 0.51 0.31 0.35 0.83 0.133 0.32 0.17 0.92 1.49 2.4 1.21 1.79 0.99982
0.5 0.44 0.42 2.10 268.3 0.44 0.37 0.50 0.64 0.151 0.46 0.24 0.93 2.15 3.1 1.5 2.4 0.99976
0.45 0.447 0.43 2.13 267.2 0.427 0.40 0.54 0.59 0.148 0.50 0.27 0.94 2.44 3.4 1.6 2.9 0.99971
0.33 0.45 0.44 2.14 262.5 0.35 0.46 0.70 0.45 0.146 0.64 0.34 0.92 3.45 4.37 2.0 3.7 0.99963
0.2 0.45 0.45 2.13 257.0 0.27 0.55 0.92 0.27 0.114 0.79 0.42 0.86 6.05 6.9 3.2 6.5 0.999352
0.1 0.455 0.46 2.2 253.4 0.21 0.62 1.05 0.14 0.069 0.91 0.49 0.86 12.4 13.2 6.0 13.3 0.99867
Table 2
Results of calculation of the basic parameters and indicators of reliability of two-cascade TED of different designs under the mode Emax at AT=70 K
n1/n2 B1 B2 I, A T1, K 01 02 E1 e2 E Q01, W C1 W1, W W2, W WE, W UE, V ^ -10-8, 1/h P
0.67 0.53 0.49 2.43 270.3 0.69 0.34 0.12 0.68 0.044 0.15 0.086 1.28 2.114 3.4 1.4 4.3 0.99957
0.50 0.54 0.50 2.45 264.6 0.60 0.41 0.26 0.53 0.0767 0.33 0.19 1.26 3.0 4.26 1.7 5.5 0.99945
0.37 0.55 0.53 2.51 260.0 0.55 0.50 0.40 0.40 0.083 0.45 0.25 1.26 4.3 5.6 2.2 7.8 0.99922
0.33 0.547 0.53 2.52 258.7 0.50 0.52 0.40 0.36 0.0823 0.50 0.29 1.26 4.85 6.11 2.42 9.0 0.99910
0.20 0.57 0.55 2.64 253.6 0.42 0.61 0.51 0.23 0.0673 0.66 0.39 1.28 8.5 9.8 3.7 15.8 0.99842
0.10 0.573 0.56 2.66 248.2 0.33 0.71 0.66 0.12 0.0433 0.82 0.49 1.25 17.7 18.9 7.1 31.9 0.99682
Table 3
Results of calculation of the basic parameters and indicators of reliability of two-cascade TED of different designs under the mode Emax at AT=80 K
n1/n2 B1 B2 I, A T1, K 01 02 E1 e2 E Q01, W C1 W1, W W2, W WE, W UE, V V10-8, 1/h P
0.50 0.65 0.60 2.9 263.4 0.85 0.45 0.03 0.44 0.0089 0.051 0.033 1.71 4.0 5.71 1.97 12.3 0.99877
0.33 0.67 0.63 3.0 257.1 0.73 0.56 0.14 0.31 0.030 0.25 0.16 1.75 6.55 8.3 2.75 19.7 0.9980
0.20 0.68 0.65 3.1 250.2 0.60 0.67 0.26 0.19 0.034 0.45 0.29 1.72 11.5 13.2 4.3 32.5 0.99676
0.10 0.70 0.69 3.2 245.2 0.51 0.78 0.35 0.10 0.023 0.61 0.40 1.75 24.9 26.7 8.4 71.9 0.99283
Table 4
Results of calculation of the basic parameters and indicators of reliability of two-cascade TED of different designs under the mode Emax at AT=90 K
n1/n2 B1 B2 I, A T1, K 01 02 E1 e2 E Q01, W C1 W1, W W2, W WE, W UE, V ^ -10-8, 1/h P
0.20 0.83 0.77 3.6 249.4 0.89 0.71 0.05 0.16 0.0067 0.12 0.085 2.3 15.1 17.4 4.9 64.9 0.99353
0.10 0.84 0.81 3.7 243.6 0.77 0.83 0.12 0.08 0.0081 0.28 0.21 2.3 32.4 34.7 9.4 140 0.9861
lis
Tu k
280--
270--
260--
250--
240-■
B ------ 6 0 I, a
■■ 1,0 ■2,0
■■0,9 1 1,8
-0,8 1 \ ^^^ 0,8" ■ 1,6
-■0,7 yr 0,7- ■ 1,4
1 1,2
2 °'5 ■ 1,0
-■0,4 y ^ ■ 0,8
-■0,3 ^^ 0,3- ■0,6
■ 0,4
x 4 -■0,! | 1 1 1 r 1 5 0,1. 1 1 1 1 1 ■0,2
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 «/«,
Fig. 1. Dependence of the intermediate temperature T,, relative operating currents B, and B2, relative temperature differentials 0, and 02 in the cascades and the magnitude of operating current I of two-cascade thermoelectric coolers under the mode Emax on the ratio n,/n2 at T=300 K;
AT=60 K; n,=9; (l/s)=10: 1 - T1^f(n1/n2); 2 - B,=f(n,/n2); 3 - B2=f(n,/n2); 4 - 0,=f(n,/n2);
5 - 02=f(n,/n2); 6 - I=f(n,/n2)
E 0,20 0,18 0,16 0,14 0,12 0,10 0,08 0,06 0,04 0,02
E C, a, w
■l,o\v2 / 0,5- •1,0
09\Vv /5 •0,9
0,8 j / 0,4- ■0,8
0,7 4/>Sr | / " \ 1 ■0,7
0,6 / w^ ny 0,3- •0,6
05 / /^v •0,5
°'4 / / ! ^^ •0,4
■0,3 / ■0,3
/ 3
■0,2 / 0,1- •0,2
l l l ill 1 1 1 l ■0,1
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 njn2
Fig. 2. Dependence of general refrigeration coefficient E and on the cascades e, and e2, refrigeration capacity Q01 and C, of two-stage thermoelectric coolers under the mode Emax on
the ratio n,/n2 at T=300 K; AT=60 K; n,=9; (l/s)í=10: 1 - E=f(n,/n2); 2 - e,=f(n,/n2); 3 - e2=f(n,/n2);
4 - Q01=f(n,/n2); 5 - C,=f(n,/n2)
At the decrease in ratio nt/n2 at the assigned value of temperature differential AT=70 K:
- the magnitude of intermediate temperature T decreases (Fig. 5, pos. 1);
- relative operating current of the first cascade B1 and the second cascade B2 increases (Fig. 5, pos. 2 and 3);
- relative drop in temperature of the first cascade 01 decreases (Fig. 5, pos. 4);
- relative drop in temperature of the second cascade 02 increases (Fig. 5, pos. 5);
- the magnitude of operating current I increases (Fig. 5, pos. 6);
- refrigeration coefficient E has a maximum at n1/n2=0.37 (Fig. 6, pos. 1);
- refrigeration coefficient of the first cascade e1 increases (Fig. 6, pos. 2), and of the second cascade e2 - decreases (Fig. 6, pos. 3);
- refrigeration capacity Q01 (Fig. 6, pos. 4) and its relative magnitude C1 (Fig. 6, pos. 5) increase;
- the total magnitude of failure rate XL increases (Fig. 7, pos. 3);
- failure rates of the first A and the second A cascades also increase (Fig. 7, pos. 1, 2);
- total power of energy consumption W increases, (Fig. 7, pos. 4);
- the total probability of failure-free operation P decreases (Fig. 8, pos. 3);
- the probability of failure-free operation of the first P1 and the second cascade P2 decreases (Fig. 8, pos. 1, 2).
Fig. 3. Dependence of the total failure rate A and each cascade A, and A2 separately of two-stage thermoelectric coolers under the mode Emax on the ratio n,/n2 at T=300 K; AT=60 K; n1=9; (l/s)=10, A0=3-10-8 1/h: 1 - A,=f(n,/n2); 2 - A2=f(n,/n2); 3 - Ax=f(n1/n2)
Fig. 4. Dependence of the total probability of failure-free rate Px and by each cascade P1 and P2 separately of two-stage thermoelectric coolers of different designs under the mode Emax on the ratio n,/n2 at T=300 K; AT=60 K; n,=9; (l/s)=10; A0=3-10-8 1/h; t=104 h: 1 - P,=f(n,/n2); 2 - P2=f(n,/n2); 3 - Ps=f(n,/n2)
7*1, k 290
B _ 0 /, a
-1,0 •0,9 0,9- ■
■0,8 0,8- • 2,0
■0,7
■0,6 /2 °'6' ■ 1,5
■0,5 ■0,4 4 ^—0,4- ■ 1,0
-0,3 0,3-
■0,2 m 0,2- ■ 0,5
-0,1 0,1-
Fig. 5. Dependence of the intermediate temperature T1( relative operating currents B1 and B2, relative temperature differentials 01 and 02 in the cascades and the magnitude of operating current I of two-cascade thermoelectric coolers under the mode Emax on the ratio n1/n2 at T=300 K; AT=70 K; n1=9; (l/s)i=10: 1 - T1=f(n1/n2); 2 - B1=f(n1/n2);
3 - B2=f(n>2); 4 - 01=f(n1/n2);
5 - 02=f(n/n2); 6 - I=f(nt/n2)
Fig. 6. Dependence of general refrigeration coefficient E and by the cascades e1 and e2, refrigeration capacity Q01 and C1 of two-cascade thermoelectric coolers under the mode Emax on
the ratio n1/n2 at T=300 K; AT=70 K; n1=9; (l/s)i=10: 1 - E=f(n/n2); 2 - e^f^/^); 3 - £2=^1/^);
4 - Q01=f(nyn2); 5 - C1=f(n1/n2)
At the decrease in ratio nt/n2 at the assigned value of temperature differential AT=80 K:
- the magnitude of intermediate temperature T decreases (Fig. 9, pos. 1);
- relative operating current of the first cascade B1 and of the second cascade B2 increases (Fig. 9, pos. 2, 3);
- relative drop in temperature of the first cascade 01 decreases (Fig. 5, pos. 4), and of the second cascade 02 increases (Fig. 9, pos. 5);
- the magnitude of operating current I increases (Fig. 9, pos. 6);
- refrigeration coefficient E has a maximum at n1/n2=0.23 (Fig. 10, pos. 1), in this case the refrigeration coefficients of the first cascade e1 and of the second cascade e2 are equal to each other: e1=£2=0.22 (Fig. 10, pos. 2, 3);
- refrigeration capacity Q01 (Fig. 10, pos. 4) and its relative magnitude C1 (Fig. 10, pos. 5) increase;
- the total magnitude of failure rate A^ increases (Fig. 11, pos. 3), in this case the failure rates of the first A1 and of the second A2 cascades also increase (Fig. 11, pos. 1, 2), but not equally;
- total power of energy consumption WE increases (Fig. 11, pos. 4);
- the total probability of failure-free operation PE decreases (Fig. 12, pos. 3), in this case the probability of failure-free operation of the first (P1) and of the second (P2) cascades also decreases (Fig. 12, pos. 1, 2).
Fig. 7. Dependence of the total failure rate A and of each cascade A1 and A2 separately of two-cascade thermoelectric coolers under the mode Emax on the ratio n1/n2 at T=300 K; AT=70 K; n1=9; (l/s)=10; A0=3-10-8 1/h: 1 - A1=f(n1/n2); 2 - A2=f(n1/n2); 3 - AE=f(n1/n2)
Fig. 8. Dependence of the total probability of failure-free operation P2 and of each cascade separately P1 and P2 of the two-cascade thermoelectric coolers of different designs under the mode Emax on the ratio n1/n2 at T=300 K; AT=70 K; n1=9; (l/s)=10; A0=3-10-8 1/h; t=104 h: 1 - P1=f(n1/n2); 2 - P2=f(nyn2); 3 - Pv=f(n/n2)
Fig. 9. Dependence of the intermediate temperature T,, relative operating currents B, and B2, relative temperature differentials 0, and 02 in the cascades and the magnitude of operating current I of two-cascade thermoelectric coolers under the mode Emax on the ratio n,/n2 at T=300 K; AT=80 K; n,=9; (l/s) = 10: 1 - T^n,/^); 2 - B^n,/^);
3 - B2=f(n,/n2); 4 - 0,=f(n,/n2);
5 - 02=f(n,/n2); 6 - I=f(n,/n2)
0,05--
0,04--
0,03--
0,02--
0,01 -•
8 C, 0o..W
--0,5 0,5- ■ 1,0
■0,9
-•0,4 ■0,8
-- yA3 ■0,7
-•0,3 Y\\ / ^ 0,3- •0,6
/ \ 1 ■0,5
' 2/V
-•0,2 \ 0,2- ■0,4
. 5 \ . ■0,3
■ 0,1 4/ 0,\ ; 0,2
l l 1 1 1 ■0,1
0,1
0,2
0,3
0,5 njn„
Fig. 10. Dependence of general refrigeration coefficient E and by the cascades e, and e2, refrigeration capacity Q01 and C, of two-cascade thermoelectric coolers under the mode
Emax on the ratio n,/n2 at T=300 K; AT=80 K; n,=9; (l/s)i=10: 1 - E=f(n,/n2); 2 - e1=f(n,/n2); 3 - e2=f(n,/n2);
4 - Q01=f(n,/n2); 5 - C1=f(n,/n2)
At the decrease of ratio n1/n2 at the assigned value of temperature differential AT=90 K:
- the magnitude of intermediate temperature T1 decreases (Fig. 13, pos. 1);
- relative operating current of the first cascade B1 and of the second cascade B2 increases (Fig. 13, pos. 2, 3);
- relative drop in temperature of the first cascade 01 decreases (by Fig. 13, pos. 4), and that of the second cascade 02 increases (Fig. 13, pos. 5);
- the magnitude of operating current I increases (Fig. 13, pos. 6);
- refrigeration coefficient E has a maximum at n1/n2=0.127 (Fig. 14, pos. 1), in this case the refrigeration coefficients of the first cascade e1 and of the second cascade e2 are equal to each other: e1=e2=0.10 (Fig. 14, pos. 2, 3);
- refrigeration capacity Q01 (Fig. 14, pos. 4) and its relative magnitude C1 (Fig. 14, pos. 5) increase;
- the total magnitude of failure rate A^ increases (Fig. 15, pos. 3), in this case the failure rate of the first A1 and of the second A2 cascades increases (Fig. 15, pos. 1, 2);
- the total probability of failure-free operation Px decreases (Fig. 15, pos. 7), in this case the probability of failure-free operation of the first (P1) and of the second (P2) cascades decreases (Fig. 15, pos. 5, 6).
Fig. 11. Dependence of general total failure rate A^ and of each cascade A1 and A2 separately of two-cascade thermoelectric coolers under the mode Emax on the ratio n,/n2 at T=300 K; AT=80 K; n,=9; (l//s)i=10; A0=3-10-8 1/h: 1 - A,=f(n1/n2); 2 - A2=f(n,/n2); 3 - A.=f(n,/n2); 4 - W,=f(n,/n2)
Fig. 12. Dependence of the total probability of failure-free operation Px and for each cascade separately P, and P2 of the two-cascade thermoelectric coolers of different designs under the mode Emax on the ratio n,/n2 at T=300 K; AT=80 K; n,=9; (l//s)i=10, A0=3-10-8 1/h; t=104 h: 1 - P1=f(n,/n2); 2 - P2=f(n1/n2); 3 - P^n,/^)
The given qualitative description of the energy indicators of a cooler depending on the ratio of number of thermoelements in the cascades allows us to estimate the ways of designing the two-cascade thermoelectric devices with improved reliability.
7\, k 250
245
B 0 /, a
-■ 1,0 5 1,0-
-•0,9 ■ 3,8
--0,8 / 0,8 -
-•0,7 nN4 1 / I / 0?7~
-■0,6 \ / 1 / 0,6-
-0,5 y 0,5 • - 3,7
-■0,4 1 Vl 0,4-
-■0,3 l\ 1 \ 0,3-
--0,2 1 1
■■0,1 i i i 1 1 1 1 1 1 ■ 3,6
0,1
0,2 «,/«,
Fig. 13. Dependence of the intermediate temperature T1, relative operating currents B1 and B2, relative temperature differentials 01 and 02 in the cascades and the magnitude of operating current I of two-cascade thermoelectric coolers under the mode Emax on the ratio n1/n2 at T=300 K; AT=90 K;
n1=9; (l/s)=10: 1 - T1=f(n1/n2); 2 - B1=f(n1/n2); 3 - B2=f(n/n2); 4 -01=f(n1/n2); 5 - 02=f(n1/n2); 6 - I=2(n1/n2)
Fig. 14. Dependence of general refrigeration coefficient E and by the cascades e1 and e2, refrigeration capacity Q01 and C1 of two-cascade thermoelectric coolers under the mode
Emax on the ratio n1/n2 at T=300 K; AT=90 K; n1=9; (l/s)i=10: 1 - E=f(niy/n2); 2 - e1=f(n1/n2); 3 - e2=f(n1/n2); 4 - Qoi^f(ni/n2); 5 - Ci=f(ni/n2)
Fig. 15. Dependence of the total failure rate A and the probability of failure-free operation PS and of each cascade separately and A2 and P1 and P2 of two-cascade
thermoelectric coolers under the mode Emax on the ratio n1/n2 at T=300 K; AT=80 K; n1=9; (l/s)i=10, A0=3^10-8 1/h; t=104 h: 1 - A1=f(n1/n2); 2 - A2=f(n1/n2); 3 - XE=f(n1/n2); 4 - W2=f(n1/n2); 5 - P1=f(n1/n2); 6 - P2=f(n1/nJ; 7 - P£ =f(n1/n2)
5. Discussion of results of the analysis of relation between the number of elements and the energy and reliability indicators
An analysis of calculated data revealed that there is an optimum ratio %/n2, corresponding to the maximum of refrigeration coefficient E at the assigned temperature differential AT.
In the point of the maximum of refrigeration coefficient E we observe the equality of values of relative temperature differential 01 and 02 and refrigeration coefficients e1 and e2 in the cascades. Results of the calculations are given in Table 5.
Table 5
Results of the calculation of basic parameters and indicators of reliability of two-cascade TED of different designs under the
mode Emax at different values of temperature differential
AT, K n1/n2 Bi B2 I, A T1, K 01 02 e1 £2 E Q01, w C1 WE, W UE, V Às 10-8, 1/h P
60 0.44 0.45 0.43 2.1 267.2 0.43 0.43 0.58 0.58 0.151 0.50 0.27 3.4 1.6 0.11 2.9 0.99971
70 0.37 0.55 0.53 2.5 260.0 0.55 0.50 0.40 0.40 0.083 0.45 0.25 5.6 2.2 0.29 7.8 0.99922
80 0.23 0.69 0.66 3.1 253.0 0.63 0.63 0.22 0.22 0.034 0.38 0.24 11.6 3.7 1.0 27.0 0.9972
90 0.127 0.83 0.80 3.775 244.0 0.80 0.80 0.10 0.10 0.0083 0.24 0.18 31.0 8.2 4.26 115.0 0.9880
With an increase in the temperature differential AT for different designs of TED (n1/n2=1.0; 0.67; 0.5; 0.33; 0.2; 0.1):
- relative operating currents in the first (B1) and the second (B2) cascades increase;
- the magnitude of operating current I increases as well;
- the intermediate temperature T1 decreases;
- relative temperature differentials in the first (01) and the second (02) cascades increase;
- refrigeration coefficient E decreases, in this case refrigeration coefficient of the first cascade e1 and of the second e2 decrease;
- refrigeration capacity Q01 and its relative magnitude C1 decrease;
- the total power of energy consumption Wx grows;
- total voltage drop Ux grows;
- the total magnitude of failure rate A grows;
- the total probability of failure-free operation Px decreases.
6. Conclusions
1. We developed a model of the relation between indicators of reliability of a cascade thermoelectric cooler and the distribution of the number of thermoelements in the cascades of a thermoelectric cooler, temperature differential, the refrigeration capacity and thermal load. Its special feature is in providing for the possibility to design the structural and energy indicators of a cooler in accordance with a criterion of the minimum failure rate.
2. We carried out an analysis of the model under regime of the highest energy efficiency, which demonstrated a possibility to evaluate the operational efficiency of a cascade cooler, to predict the optimum values of refrigeration coefficient at the assigned temperature differential and the relation of the number of elements in cascades under varied conditions of operation.
References
1. Bell, L. E. Cooling, Heating, Generating Power, and Recovering Waste Heat with Thermoelectric Systems [Text] / L. E. Bell // Science. - 2008. - Vol. 321, Issue 5895. - P. 1457-1461. doi: 10.1126/science.1158899
2. Jurgensmeyer, A. L. High Efficiency Thermoelectric Devices Fabricated Using Quantum Well Confinement Technique [Text] / A. L. Jurgensmeyer. - Colorado, 2011. - 59 p.
3. Materials, Preparation and Characterization in Thermoelectrics [Text] / D. M. Rowe (Ed.) // Thermoelectrics and its Energy Harvesting. - Boca Raton: CRC Press, 2012. - 1120 p. doi: 10.1201/b11891
4. Simkin, A. V. Thermoelectric efficiency of low -temperature generator materials and the possibility of it's increasing [Text] / A. V. Simkin, A. V. Biryukov, N. I. Repnikov, O. N. Ivanov // Journal of nano - and electronic Physics. - 2013. - Vol. 5, Issue 4 (2). -P. 04070-04071.
5. Brown, S. R. Yb14MnSb11: New High Efficiency Thermoelectric Material for Power Generation [Text] / S. R. Brown, S. M. Kauzlarich, F. Gascoin, G. J. Snyder // Chemistry of Materials. - 2006. - Vol. 18, Issue 7. - P. 1873-1877. doi: 10.1021/ cm060261t
6. Sootsman, J. R. New and Old Concepts in Thermoelectric Materials [Text] / J. R. Sootsman, D. Y. Chung, M. G. Kanatzidis // Angewandte Chemie International Edition. - 2009. - Vol. 48, Issue 46. - P. 8616-8639. doi: 10.1002/anie.200900598
7. Zebarjadi, M. Perspectives on thermoelectrics: from fundamentals to device applications [Text] / M. Zebarjadi, K. Esfarjani, M. S. Dresselhaus, Z. F. Ren, G. Chen // Energy Environ. Sci. - 2012. - Vol. 5, Issue 1. - P. 5147-5162. doi: 10.1039/c1ee02497c
8. Choi, H.-S. Prediction of reliability on thermoelectric module through accelerated life test and Physics-of-failure [Text] / H.-S. Choi, W.-S. Seo, D.-K. Choi // Electronic Materials Letters. - 2011. - Vol. 7, Issue 3. - P. 271-275. doi: 10.1007/s13391-011-0917-x
9. Wereszczak, A. A. Thermoelectric Mechanical Reliability [Text] / A. A. Wereszczak, H. Wang // Vehicle Technologies Annual Merit Reviewand Peer Evaluation Meeting. - Arlington, 2011. - P. 18.
10. Singh, R. Experimental Characterization of Thin Film Thermoelectric Materials and Film Deposition VIA Molecular Beam Epitaxy [Text] / R. Singh. - University of California, 2008. - 54 p.
11. Nesterov, S. B. Evaluation of the possibility of increasing the thermoelectric quality of nanostructured semiconductor materials for refrigeration equipment [Text] / S. B. Nesterov, A. I. Kholopkin // Refrigerating Technique. - 2014. - Issue 5. - P. 40-43.
12. Gromov, G. Volumetric or thin -film thermoelectric modules [Text] / G. Gromov // Components and Technologies. - 2014. -Issue 9. - P. 38.
13. Market of thermoelectric modules. Analytical review [Text]. - Moscow: RosBusinessConsulting, 2009. - 92 p.
14. Zaikov, V. P. Influence of the effectiveness of raw materials on the reliability of thermoelectric cooling devices. Part I: single-stage TEDs [Text] / V. P. Zaikov, V. I. Meshcheryakov, A. A. Gnatovskaya, A. A. Gnatovskaya // Tekhnologiya i konstruirovanie v ehlektronnoj apparature. - 2015. - Issue 1. - P. 44-48. doi: 10.15222/tkea2015.1.44
15. Zaikov, V. P. Analysis of reliability improvement possibilities of thermoelectric cooling devices [Text] / V. P. Zaikov, V. I. Meshcheryakov, Yu. I. Zhuravlev // Eastern-European Journal of Enterprise Technologies. - 2015. - Vol. 4, Issue 8 (76). -P. 17-25. doi: 10.15587/1729-4061.2015.46553
16. Zaykov, V. P. Prediction of reliability on thermoelectric cooling devices. Kn. 1. Single -stage devices [Text] / V. P. Zaykov, L. A. Kirshova, V. F. Moiseev. - Odessa: Politehperiodika, 2009. - 118 p.
