CC BY
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32. Correction of the operating modes of an induction motor with asymmetrical stator windings at vector control / Zagirnyak M., Ka-linov A., Melnykov V., Kochurov I. // 2015 International Conference on Electrical Drives and Power Electronics (EDPE). 2015. doi: 10.1109/edpe.2015.7325303
33. Zagirnyak M., Maliakova M., Kalinov A. Analysis of operation of power components compensation systems at harmonic distortions of mains supply voltage // 2015 Intl Aegean Conference on Electrical Machines & Power Electronics (ACEMP), 2015 Intl Conference on Optimization of Electrical & Electronic Equipment (OPTIM) & 2015 Intl Symposium on Advanced Electromechanical Motion Systems (ELECTROMOTION). 2015. doi: 10.1109/optim.2015.7426958
34. Improvement of compensation method for non-active current components at mains supply voltage unbalance / Al-Mashakbeh A. S., Zagirnyak M., Maliakova M., Kalinov A. // Eastern-European Journal of Enterprise Technologies. 2017. Vol. 1, Issue 8 (85). P. 41-49. doi: 10.15587/1729-4061.2017.87316
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36. Zagirnyak M., Kalinov A., Maliakova M. An algorithm for electric circuits calculation based on instantaneous power component balance // Przegl^d elektrotechniczny (Electrical Review). 2011. Issue 12b. P. 212-215. URL: http://pe.org.pl/articles/2011/12b/59.pdf
37. Al-Mashakbeh A. S. O. Modern control design of power system // Australian journal of basic and applied sciences. 2009. Vol. 3, Issue 4. P. 4267-4271. URL: https://www.researchgate.net/publication/294390623_Modern_control_design_of_power_system
Розглянуто модель взаемозв'язку основних показнитв динамти i надiйностi з врахуван-ням конструктивних елементiв охолоджу-ючого пристрою для рiзних режимiв роботи. Одержат стввидношення дозволяють визна-чити час виходу термоелектричного охолод-жуючого пристрою на стащонарний режим i температуру теплопоглинаючого спаю. Показано, що врахування теплофiзичних, конструктивних i енергетичних показнитв дозволяв управляти часом виходу охолоджувача в стащонарний режим
Ключовi слова: термоелектричний охолод-жувач, стащонарний режим, температура тепло поглинаючого спаю, показники надш-ностi
□-□
Рассмотрена модель взаимосвязи основных показателей динамики и надежности с учетом конструктивных элементов охлаждающего устройства для различных режимов работы. Полученные соотношения позволяют определить время выхода термоэлектрического охлаждающего устройства на стационарный режим и температуру теплопоглощающего спая. Показано, что учет теплофизических, конструктивных и энергетических показателей позволяет управлять временем выхода охладителя в стационарный режим
Ключевые слова: термоэлектрический охладитель, стационарный режим, температура теплопоглощающего спая, показатели надежности
UDC 621.362.192
|DÖI: 10.15587/1729-4061.2018.1238911
ANALYSIS OF RELATIONSHIP BETWEEN THE DYNAMICS OF A THERMOELECTRIC COOLER AND ITS DESIGN AND MODES OF
OPERATION
V. Zaykov
PhD, Head of Sector Research Institute «STORM» Tereshkova 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, Associate Professor 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
Determining the time that it takes for a thermoelectric cooling device (TED) to enter a stationary working mode
over the preset temperature range is an interesting task. This is related to the fact that dynamic indicators for the means that enable heat regimes of thermally loaded elements largely define both functional and reliable capabilities of critical
©
systems. In this case, only the mass and specific heat of an object are typically accounted for in the process of entering the mode. At the same time, experience has shown that there is a need to additionally take into consideration the heat capacity and mass of structural and technological elements, as well as current operating mode. In terms of operational control, of special interest is the current mode, and in terms of strategic control - the effect of heat capacity on the dynamic characteristics of a thermoelectric cooling device.
Thus, it is a relevant task to create a controllable dynamic system to monitor temperature at a thermally loaded element.
2. Literature review and problem statement
The issues of enabling thermal modes are integral part of the development of radio electronic equipment whose elements operate under thermally loaded modes [1]. Comparative analysis of compression and solid-state coolers [2] reveals that in terms of weight and dimensions, performance and reliability, thermoelectric coolers have a clear advantage [3]. Improved reliability indicators when designing thermoelectric coolers are achieved by taking into consideration the influence of thermal-physical, electrical properties, chemical activity of the thermoelements' materials when interacting with external environment [4]. Creation of new materials with enhanced thermoelectric efficiency [5] gives rise to new challenges associated with the growing influence of contact resistances, heat conductivity of thermal elements, linear expansion of thermoelement contact with electrode. Specification of requirements to thermoelectric coolers for cooling capacity, energy indicators, weight and dimensions, resulted in the variety of thermoelectric modules [6]. Since such an integrated indicator as reliability depends on the design and manufacturing technology, there are developed methods to investigate indicators of reliability over the entire life cycle, starting at the design stage all the way to operation of thermoelectric coolers [7]. For the on-board systems, the most important is the influence of mechanical and thermal loads. The effect of impact and harmonic mechanical load on the cooler is strengthened by the fact that lower temperatures lead to the worsening of plasticity of the thermoelement soldering with the electrode, and to the increased fragility of a thermoelectric material [8]. Heat load increases temperature gradients, which can lead to the cracking of places where dissimilar materials are connected [9].
Under the non-stationary heat flows, control over coolers for deviation is ineffective. Working out a temperature deviation at the receiving element starts only after the temperature wave reaches the sensor of a thermal control system [10]. Working out a thermal perturbation by the cooler, which is typically described bye integrating link, includes the lag time in the process of transition into a stationary mode, during which temperature of the thermally loaded element may exceed maximum permissible temperature. Proactive control implies launching a cooler prior to the moment when the heat wave reaches the cooler, therefore, it employs more complex algorithms to process data in order to make appropriate decisions [11]. The dynamics of control is directly dependent on the performance efficiency of the controlling element, which, in this case, is the cooler [12]. Studies into the inertia of single-stage thermoelectric devices have shown that it is mainly determined by the ratio of heat capacities of the load and a thermoelectric cooler [13]. At the same time, the model considered does not take into
consideration structural and technological elements of the cooler, which are a necessary component of the single-stage thermoelectric cooler. The need to improve performance efficiency of the thermoelectric cooler is in contradiction with the reliability indicators, which requires additional research.
3. The aim and objectives of the study
The aim of present study is to reduce the time it takes for a thermoelectric cooler to enter a stationary regime by taking into consideration the impact of structural and technological elements of the cooler, as well as operational modes.
To accomplish the aim, the following tasks have been set:
- to develop a dynamic model of TED that would account for the structural and technological elements of the cooler;
- to perform a reliability-oriented analysis of the model in order to estimate a possibility to control the time it takes for TED to enter a stationary regime.
4. Development of dynamic model of TED taking into consideration its structural and technological elements
The structural and technological elements on the heat absorbing junction of TED include:
- copper switching plates;
- a layer of soldering and a nickel coating;
- ceramic plate and a metallization layer in line with the switching circuit of thermoelements branches;
- a diffusion layer of a semiconductor material.
The following has to be taken into consideration:
- condition of the thermoelectric material surface, which is related to the technology of processing and storage conditions [8, 9];
- the depth of copper atoms migration in a thermoelectric material.
The thickness of a diffusion layer of the thermoelectric material, a contact area "metal-semiconductor" can be adopted equal to 100-150 ^m. We used an aluminum plate with a mass of 1 gram as the object to be cooled. Indicative data on mass and heat capacity of structural and technological elements of TED are given in Table 1. When calculating the volume, for the geometry of thermoelements l/S= =10 cm-1, we used dimensions of the branch cross-section equal to 2x2 mm at height l=4 mm.
The total magnitude of heat capacity and the mass of TED components can be represented in the form:
E miCi = mbCb + mNiCNi + mSCS +
i
+mCuCCu + mcerCcer = 175 ■ 15-4 J/K. (1)
We shall consider the process of cooling an object in time t, which is determined by the current mode selected, the magnitude of thermal load Q0, branch geometry of the cooling thermoelement (l/S), taking into consideration the temperature dependence of parameters of a thermoelectric material in the module (Fig. 1), as well as specific heat capacity Cand thermal diffusivity a (Fig. 2). The dependence of total heat capacity and the mass of structural elements on the geometry of TED branches (l/S) is shown in Fig. 3. The temperature of heat emitting junctions is accepted to be constant and equal to T=300 K due to intensive heat exchange.
Parameters and indicators of structural and technological elements of the cooler
Elements of design and technology Width 8, mm Volume V, cm3 Density of material p, g/cm3 Mass m, g Specific heat capacity, Cp, J/(g-K) mC, J/K Note
Thermoelectric material Bi2Te3 0.1 2x2x0.140-3=440-4 7.8 31.240-4 0.31 19.340-4 mbCb
Antidiffusion nickel-based coating 0.025 2x2x0.025-10- 3=140-4 8.1 8.140-4 0.427 13.840-4 mNiCNi
Solder 0.1 2x2x0.140-3=440-4 9.6 38.440-4 0.126 9.740-4 msCs
Switching plate, copper 0.2 2x2x0.240-3=840-4 9.0 7240-4 0.389 5840-4 mcuCcu
Ceramic plate 0.3 2x2x0.340-3=1240-4 1.84 2240-4 1.674 73.740-4 mcerCcer
Object to be cooled (Al) - - 2.7 1 0.894 0.894 m0C0
Fig. 1. Estimation-experimental temperature dependence of parameters of thermoelectric materials of the thermoelement branches in module: coefficient of thermoEMF e, efficiency of thermoelectric material 2, coefficient of thermal conductivity œ and electrical conductivity ô
Fig. 2. Estimation-experimental temperature dependence of specific heat capacity C and thermal diffusivity a of the thermoelement branches material in module
Fig. 3. Dependence of the total magnitude of mass and specific heat capacity of TED structural and technological elements on ratio l/S
Thermal balance conditions on the heat emitting junctions of TED can be written in the form
— m0C0 + n Y miCi j dT0 = nI^R (2B - B2 -©) d t, (2)
where m0, Co are, respectively, the mass and specific heat
eT
capacity of the cooled object; Imax =—0 is the maximum opR
erating current, A; e, R are, respectively, the averaged value of coefficient of thermoEMF, V/K, and electrical resistance of the thermoelement branch, Ohm; B=I/Imax is the relative operating current; I is the working current magnitude, A; T0 is the temperature of a heat absorbing junction, K; 0= =A7/Tmax is the relative difference in temperature; ATmax =0,5 zT02 is the maximum temperature difference, K; z is the averaged value of the efficiency of a thermoelectric material in module 1/K; AT=T-T0 is the difference in temperature at TED, K; n is the number of thermoelements, pcs.
By solving differential equation (2) under initial conditions t=0; T=T0, we shall obtain
^ + «Z rnp, bQ - B.)
' 2B,-B2-©,
nKi |1 + 2B ^
(3)
where K1 is the heat transfer coefficient, K1=x S/l, W/K;
J 2 R
j = max0 0 ■
I maxiRi
Imax0, R0 are, respectively, the maximum operating current and electrical resistance of the thermoelement branch at the beginning of the cooling process at t=0; Imax1, R1 are, respectively, the maximum operating current and electrical resistance of the thermoelement branch at the end of the process of cooling; x is the coefficient of thermal conductivity.
This formula represents an analytical dependence of the time required to enter a stationary mode on the current operating mode (the magnitude of relative current B), heat load Q0 (number of thermoelements n), taking into consideration both the mass and the heat capacity of the cooled object m0C0, and the structural and technological elements of TED at a preset temperature difference AT(0).
Given that B1=I/Imax0; B2=I/Imax1, we shall write: - for mode Q0
max
I-Imaxl, Bl= /-maYlX/maxO, Bo — 1.0;
(4)
- for mode (Qo/I )max:
I = Veimxi; B = V© ImaxJImaxO B2 = V© ;
- for mode Emax
I=®Imax1; B1=®Imax1/Imax0; B2=®;
- for mode Xmin
I=n©Imaxi; Bi=n©Imaxl/Imax0; B2="H©,
(5)
(6)
Expression (8) describes the relationship for various current operating modes and heat load for the assigned temperature difference, taking into consideration the mass and specific heat capacity of structural and technological elements of TED.
where n is the correction factor [9].
We can derive from equation (3) the temperature of heat-absorbing junction T0 depending on the cooling time t:
5. Analysis of temporal and reliability indicators of the model for different operation modes of TED
(7) The results of calculation of basic parameters and the
time required for TED to enter a stationary mode, parameters of reliability for current modes of operation Q0max, (Qo/I)max, Emax and Xmin at T=300 K; AT=40 K; l/S=10 cm-1;
mAl=1 g; Cai=0.894 J/feK) and £mtCt = 175 10-4 J/K are
i
AT„„ given in Table 2. Here t0 is the time required to enter a
stationary mode, calculated with respect to the mass and .(8) heat capacity of the object, t - with respect to the mass and heat capacity, of both the object and the elements of TED design.
Table 2
Results of calculation of basic parameters and indicators of reliability for a single-stage TED, obtained at the following original data: /max=5.02 A; 7=300 K; 7"0=260 K; A 7=40 K; //S=10 cm-1; A7"max=79.8 K; ©=0.5; R=M0-2 Ohm; material Al; CAl=0.894 J/(g-K); mAl=1 g; £mtCt = 175 10-4 J/K - per a thermoelement
T = T -
2B,(2 - B1)ATmal y
1+ 2B,
AT
1 - exp
ntK
2B,
+ 1
moCo+nZ mC,
Mode of operation Qo, A n, pcs. T0, s t', W B1/B2 I, A W, W E U, V V^-0 M08, 1/h P
Q0max 0.3 2.3 137 143.5 0.93/1.0 5.02 1.39 0.216 0.274 2.35 7.05 0.99930
0.5 3.9 90.0 96.8 2.30 0.216 0.46 4.0 12.0 0.9988
1.0 7.8 45.0 51.8 4.53 0.216 0.903 8.0 24.0 0.9976
1.5 11.7 30.0 36.8 6.83 0.216 1.37 12.0 36.0 0.9964
2.0 15.6 22.4 29.4 9.10 0.216 1.81 16.0 48.0 0.9952
3.0 23.4 15.0 21.9 13.6 0.216 2.71 23.9 71.7 0.9929
5.0 39.0 9.0 15.9 22.7 0.216 4.52 40 120 0.9881
10.0 78.0 4.5 11.3 45.4 0.216 9.0 79.7 239.1 0.9764
(Q0/I)max 0.3 2.8 144 152.3 0.66/0.707 3.55 0.88 0.34 0.25 0.73 2.19 0.99978
0.5 4.7 86.7 94.7 1.44 0.347 0.41 1.23 3.68 0.99963
1.0 9.4 43.4 51.3 2.88 0.347 0.81 2.45 7.36 0.99926
1.5 14.1 28.9 36.9 4.40 0.347 1.23 3.68 11.0 0.9989
2.0 18.8 21.7 29.6 5.88 0.347 1.66 4.9 14.7 0.9985
3.0 28.2 14.4 22.3 8.80 0.347 2.46 7.35 22.0 0.9978
5.0 47.0 8.6 16.7 14.7 0.347 4.1 12.3 36.8 0.9963
10.0 94.0 4.3 12.2 28.8 0.347 8.1 24.5 73.5 0.9926
E ^max 0.5 6.6 77.3 87.2 0.47/0.50 2.76 1.10 0.460 0.40 0.607 1.82 0.00081
1.0 13.0 38.6 48.6 2.20 0.460 0.80 1.20 3.6 0.99964
1.5 19.5 25.7 35.7 3.30 0.460 1.20 1.82 5.46 0.99946
2.0 26.0 19.3 29.3 4.40 0.460 1.60 2.42 7.26 0.99928
3.0 39.0 12.9 22.8 6.60 0.460 2.40 3.64 10.9 0.9989
5.0 65.0 7.7 17.7 11.0 0.460 4.0 6.0 18.0 0.9982
10.0 130 3.9 13.8 22.0 0.460 8.0 12.0 36.0 0.9964
^min 0.3 6.9 101 114.3 0.40/0.425 2.13 0.88 0.347 0.41 0.215 0.64 0.999936
0.5 11.6 61.3 75.0 1.40 0.347 0.68 0.361 1.08 0.999892
1.0 23.2 30.6 44.4 2.88 0.347 1.36 0.722 2.17 0.999780
1.5 34.8 20.4 34.3 4.32 0.347 2.03 1.07 3.22 0.99968
2.0 46.4 15.3 292 5.76 0.347 2.70 1.43 4.33 0.99957
3.0 69.6 10.2 24.0 8.64 0.347 4.06 2.16 6.48 0.99935
5.0 116 6.1 20.0 14.4 0.347 6.80 3.61 10.8 0.9989
10.0 232 3.0 17.0 28.8 0.347 13.5 7.22 21.7 0.99783
Data in Fig. 4-7 show that an increase in heat load Q0 (the number of thermoelements n in TED) at the assigned temperature difference AT for various current modes of operation leads to the following:
- the time required to enter a stationary mode t reduces;
- the number of thermoelements n increases;
- voltage drop U grows.
An analysis of data given reveals that the time required to enter a mode t' increases compared to t0. For example, at thermal load Q0=5.0 W:
- under mode Q0max t0=9.0 s; t'=15.9 s, that is, it is increased by 77 %;
- under mode (Q0/I)max t0=8.6 s; t'=16.7 s, that is, it is increased by 94 %;
- under mode Emax t0=7.7 s; t'=17.7 s, that is, it is increased by 130 %;
- under mode Xmin t0=6.1 s; t'=20 s, that is, it is increased by 228 %.
To, T , s N pC
80
60
40
20
1
u/ / y / y' y y
\\ v \\ \\ /y / / ' n
\\ S S xy> y'
-- — — -----
TO
u,v
0
(1 2 4 6 S Ça, w
Fig. 4. Dependence of the time required for TED to enter a stationary mode (t0, t' are, respectively, without and with
taking into consideration ^ mC ), the number of
i
thermoelements n and a voltage drop Uof a single-stage TED, on the magnitude of thermal load Q0 at 7=300 K; A 7=40 K; //¿=10 cm-1 for mode Q0max
», pC-
80
60
40
1 u / / / ny
h / / y y /
\\ \\ \\ \\ / y y y /
v y Y ^
/ / / y y II) ----
U, V
0 2 4 6 a ft, w
Fig. 5. Dependence of the time required for TED to enter a stationary mode (t0, t' are, respectively, without and with
taking into consideration ^ mfit), the number of
i
thermoelements n and a voltage drop Uof TED, on the magnitude of thermal load Q0 at 7=300 K; A7=40 K; //S=10 cm-1 for mode (Q0/I)max
pc-
80
40
20
/ /
\ V / /' / u/
n \\ \\ / /
\\ / / / x'
/y"
■CD
U, V
0 2 4 6 8 Q„, W
Fig. 6. Dependence of the time required for TED to enter a stationary mode (t0, t' are, respectively, without and with
taking into consideration ^ miCt), the number of
i
thermoelements n and a voltage drop Uof a single-stage TED, on the magnitude of thermal load Q0 at 7=300 K; A 7=40 K; l/S=10 cm-1 for mode Emax
n.
100
60 ■
40
20 ■
1 / / / U y /
i
i \ / / i
\\ \\ \\/ / / /
\ \ /y r "S T'
//
U, V
0 2 4 6 8 W
Fig. 7. Dependence of the time required for a single-stage TED to enter a stationary mode (t0, t' are, respectively,
without and with taking into consideration ^ mC,), the
i
number of thermoelements n and a voltage drop U, on the magnitude of thermal load Q0 at 7=300 K; A 7=40 K; l/S=10 cm-1 for mode 1min
Fig. 8 shows that the greatest difference between the magnitudes of t' and To is observed under a Xmin mode.
With a decrease in the time required to enter stationary mode t, the intensity of failures increases for different modes of operation ( Fig. 9, a - for modes Q0max and (Q0/I)max, Fig. 9, b - for modes Emax and 1min) - due to the increase in the number of thermoelements n in TED.
An analysis of the results of estimating the temporal process of TED entering a stationary mode of operation makes it possible to consider the relation between the mass and heat capacity of the object (m0C0) and the mass and heat capacity of structural elements at the heat absorbing junction of TED (n^ m Ci). The relation can be written in the form:
m„C„
mCT0
= f.
p, %
200
160 ■
120
80
40
Amin/
/ * max y / (Qo/i) nax /
-1-
0 2 4 6 8 g0> W
Fig. 8. Dependence of relative magnitude of the time required for a single-stage TED to enter stationary mode p=(x -t0)/t0 on thermal load at 7=300 K; A 7=40 K; l/S=10 cm-1 for different modes of operation
X/X0
\ \ \
/(TO) ----
\ I \ f(T')
\ \
\ V i \
\ \ \ \\ E,
---' ~~ -- ^min
b
Fig. 9. Dependences of the relative magnitude of failure rate in a single-stage TED on the time required to enter a stationary mode of operation, obtained without and with
taking into consideration ^miC1, at 7=300 K; A 7=40 K;
i
//S=10 cm-1 for different modes of operation: a — Q
0max,
(Q)/^max; b '
A possible range of change in the magnitude f can be represented as follows:
a) f>>1, that is, the mass and heat capacity of the object m0C0 >> n^ mC are much larger than the mass and heat
capacity of structural and technological elements of TED. In this case, the relative magnitude of the time required to enter a stationary mode x'/x0 > 1,5. The time required for TED to enter a stationary mode with respect to the mass and heat capacity of structural and technological elements exceeds the time required to enter a stationary mode with respect to the mass and heat capacity of the object by not larger than 50 %;
b) 1.5>f> 0.75, that is, there is an approximate match between the mass and heat capacity of the object, and the mass and heat capacity of structural and technological elements of TED. In this case, the magnitude x'/x0 is in the range of 2.2> x'/x0 >1.7, that is, the time required to enter a stationary mode with respect to the mass and heat capacity of structural and technological elements may exceed the time required to enter a stationary mode without taking them into consideration by the magnitude of 70 to 120 %;
c) f<<1, that is, the mass and heat capacity of the object are much smaller than the mass and heat capacity of structural and technological elements. In this case, the magnitude x'/x0 > 2,2, that is, the time required to enter a stationary mode with respect to the mass and heat capacity of structural and technological elements is much longer, by 2-10 times, than the time required to enter a stationary mode without taking them into consideration.
Dependence of relative magnitude of the time required for a single-stage TED to enter a stationary mode x'/x0 on the magnitude of fat T=300 K; AT=40 K; //5=10 cm-1 is shown in Fig. 10. It should be noted that a given dependence applies to all the considered modes of operation.
Fig. 10. Dependence of relative magnitude of the time required for a single-stage TED to enter a stationary mode of
^^ C
operation (t'/t0) on the relative magnitude f = ^ 0 0_ _ at
mCT0
-1
7=300 K; A 7=40 K; //S=10 cm
In accordance with expression (8), we shall estimate the temperature of a heat-absorbing junction T0 and other basic parameters for a single-stage TED for the operation modes Q0max, (Q 0/I )max, Emax and A,min. Initial conditions: T=300 K; AT=40 K; //S=10 cm-1 with and without taking into consideration the mass and heat capacity of TED structural and technological elements for various thermal load Q0. Calculated data are given in Tables 3-6, where T0, ATmax, ©, A,/X0 and P are those without taking into consideration the structural and technological elements; T0', AT^, 0', (l/l) and P are those taking into consideration the structural and technological elements.
a
^max, A-min
Mode Q0max 7=300 K; A7=40 K; B1=0.93; B2=1.0; /max=5.02 А; //S=10 cm-1; C=0.5 J/(g^K); m0C0=0.894; X0=3-10-8 1/s;
f=104; £ mC = 17510-4 J/K
Q0, W То, K T',K т, s n, pc. ДTmax DTmax, K e G' Ы08, 1/h P (W Г-108, 1/h P'
0,5 293,2 293.6 10 3.9 103,0 103.4 0.068 0.062 2.23 6.7 0.99933 2.21 6.62 0.99934
287.4 288.2 20 99.1 99.7 0.127 0.118 2.48 7.44 0.99925 2.44 7.33 0.999267
277.4 278.7 40 92.0 92.8 0.246 0.229 2.96 8.89 0.999111 2.90 8.70 0.99913
269.4 271.0 60 86.4 87.4 0.354 0.332 3.40 10.2 0.99898 3.32 9.95 0.9990
263 264.7 80 82.0 83.0 0.451 0.425 3.80 11.4 0.99886 3.70 11.09 0.99889
260.3 262 90 80 81.0 0.496 0.469 4.0 12.0 0.99880 3.87 11.6 0.99884
257.8 259.6 95 78.1 79.2 0.54 0.509 4.165 12.5 0.99875 4.04 12.12 0.99879
1.0 287.0 288.6 10 7.8 98.8 100.0 0.132 0.114 5.0 15.0 0.9985 4.86 14.6 0.99854
276.7 279.2 20 91.9 93.5 0.254 0.222 6.0 18.0 0.9982 5.7 17.2 0.99828
261.7 265.2 40 80.9 83.0 0.471 0.419 7.76 23.3 0.9977 7.35 22.0 0.9978
256.6 260.0 50 77.4 79.8 0.56 0.501 8.49 25.5 0.99745 8.0 24.0 0.9976
259.6 - 44 79.5 - 0.508 — 8.08 24.2 0.99758 - - -
1.5 281.6 284.6 10 11.7 94.8 96.8 0.194 0.159 8.26 24.8 0.9975 7.84 23.5 0.99765
268.5 272.8 20 85.8 88.6 0.367 0.307 10.4 31.1 0.9969 9.65 29.0 0.9971
261.4 263.9 30 80.6 82.1 0.479 0.44 11.62 34.85 0.99652 11.16 33.47 0.9967
259.8 - 31 79.6 - 0.504 - 12.05 36.2 0.9964 - - -
- 259.7 36 - 79.6 - 0.506 - - - 12.1 36.2 0.9964
Table 4 Mode (Q0/I)max 7=300 K; A7=40 K; B1=0.66; B2=0.707; I=3.55 A; //S=10 cm-1; C=0.418 J/(g^K)
Q0, W т, s То, K T',k n, pc. Д Tmax, DTm'ax, K e G' Ы08, 1/h P (W 1'-108, 1/h P'
0.5 10 292.6 293.2 102.7 103.2 0.072 0.066 0.587 1.76 0.999824 0.579 1.74 0.99983
20 286 287.1 98.2 98.9 0.143 0.130 0.69 2.07 0.99979 0.672 2.02 0.99980
40 275.1 276.7 90.4 91.5 0.275 0.255 0.882 2.65 0.99974 0.853 2.56 0.99974
60 267.9 268.4 4.7 85.4 85.7 0.376 0.369 1.04 3.12 0.99969 1.025 3.08 0.99969
80 259.7 261.8 79.6 80.9 0.506 0.472 1.22 3.67 0.99963 1.175 3.52 0.999648
85 - 260.4 - 80.0 - 0.495 - - - 1.205 3.62 0.99964
1.0 10 286 288 98.2 99.5 0.143 0.12 1.38 4.14 0.99959 1.32 3.95 0.99950
20 275.1 278.2 90.4 92.5 0.275 0.236 1.76 5.29 0.99947 1.65 4.96 0.99950
40 259.7 263.7 9.4 78.6 82.4 0.506 0.44 2.44 7.32 0.99927 2.25 6.74 0.99933
46 - 260.4 - 80.0 - 0.495 - - - 2.42 7.25 0.999275
1.5 10 280.2 283.9 93.8 96.3 0.211 0.167 2.37 7.1 0.99929 2.18 6.54 0.99935
20 267 271.8 84.8 87.9 0.389 0.321 3.18 9.53 0.99905 2.87 8.6 0.99914
30 256.9 262.7 77.5 81.8 0.556 0.456 3.94 11.83 0.99882 3.475 10.4 0.99896
33 - 259.7 - 79.6 - 0.506 - - - 3.70 11.1 0.99889
Mode Emax 7=300 K; A7=40 K; ^=0.47; B2=0.50; >=2.76 A; //S=10 cm-1; C=0.30 J/(g-K)
Q0, W t, s 70, K 70',K n, pc. ATmax, K A7m„, K © 0' V^-0 M08, 1/h P (W X'-108, 1/h P '
0.5 10 291.4 292.3 6.5 101.9 102.5 0.084 0.075 0.239 0.718 0.999918 0.232 0.70 0.999930
20 284.1 285.7 96.9 97.9 0.164 0.146 0.303 0.91 0.999910 0.29 0.87 0.999913
40 272.5 274.8 88.4 90.0 0.311 0.28 0.429 1.29 0.99987 034 1.02 0.999898
60 264.0 266.5 82.6 84.2 0.436 0.40 0.53 1.59 0.99984 0.50 1.51 0.999849
70 260.6 - 80.1 - 0.49 - 0.59 1.78 0.99982 - - -
80 - 260.3 - 80.0 - 0.50 - - - 0.60 1.79 0.99982
1.0 10 284.1 287 13.0 96.9 98.8 0.164 0.132 0.606 1.82 0.99982 0.556 1.67 0.999833
20 272.5 276.8 88.4 91.2 0.311 0.254 0.858 2.57 0.99974 0.756 2.27 0.99977
40 257.7 262.6 78.4 81.4 0.54 0.46 1.27 3.8 0.99962 1.11 3.33 0.99964
37 259.4 - 79.4 - 0.511 - 1.22 3.66 0.999634 - - -
44 - 259.5 - 79.5 - 0.497 - - - 1.19 3.58 0.99964
1.5 10 277.8 283 19.5 91.8 96.1 0.242 0.177 1.105 3.31 0.99967 0.945 2.84 0.99972
20 264.0 270.8 82.6 87.3 0.436 0.334 1.61 4.84 0.99952 1.34 4.03 0.99960
25 259.1 - 79.2 - 0.516 - 1.85 5.55 0.999445 - - -
30 - 262.2 - 81.1 - 0.466 - - - 1.70 5.1 0.99949
33 - 260.0 - 79.8 - 0.50 - - - 1.80 5.41 0.99946
Table 6 Mode Xmin 7=300 K; A7=40 K; B1=0.40; B2=0.425; 1=2.155 A; //S=10 cm-1; C=0.17 J/(g^K)
Q0, W t, s 70, K 70',K n, pc. ATmax, K A7m„, K © 0' V^-0 M08, 1/h P (V1>)' 1'-108, 1/h P '
0.5 10 288 290 99.5 100.9 0.121 0.099 0.123 0.368 0.999963 0.111 0.334 0.999967
20 278.7 281.9 92.8 95.0 0.23 0.19 0.182 0.546 0.999945 0.16 0.48 0.999952
40 266.1 270 11.5 83.9 86.4 0.404 0.347 0.293 0.878 0.999912 0.255 0.764 0.999924
60 258.5 262.2 78.9 81.1 0.526 0.466 0.375 1.125 0.999887 0.334 1.0 0.99990
66 - 260.4 - 80.0 - 0.495 - - - 0.355 1.064 0.99989
1.0 10 278.7 284.2 92.8 96.9 0.23 0.163 0.364 1.092 0.99989 0.291 0.874 0.999913
20 266.1 273.1 83.9 88.4 0.404 0.304 0.588 1.76 0.99982 0.457 1.37 0.99986
30 258.6 265.4 23 78.9 83.5 0.525 0.414 0.75 2.25 0.999775 0.436 1.31 0.99987
40 - 260 - 79.8 - 0.50 - - - 0.716 2.15 0.999785
1.5 10 271.6 280.5 88.5 94.0 0.321 0.207 0.721 2.16 0.999784 0.543 1.54 0.99985
20 258.5 268.2 34.5 78.9 85.6 0.526 0.371 1.14 3.41 0.99966 0.814 2.44 0.99976
29 - 260.5 - 80.0 - 0.494 - - - 1.062 3.19 0.99968
Fig. 11-14 show the time-temperature dependences of a heat-absorbing junction T0 and failure rate of a single-stage TED for different modes of operation and varying heat load Q0 at T=300 K; AT=40 K; l/S= =10 cm-1.
Thus, for example, at equal thermal load Q0=0.5 W the time to reach the set temperature of T0=260 K at T= =300 K and the mass and heat capacity of the object m0C0=0.894 J/K is:
- under mode Q0max (51=0.93; B2=1.0; n=1): t0=90 s; with respect to the mass and heat capacity of TED STE
t'=95 s, the time required to enter a preset mode increased by 5.5 % at the same failure rate X/^o=4;
- under mode (Q0/I)max №=0.66; B2=0.71; n=4.7): t0=80 s, t'=85 s, the time required to enter a preset mode increased by 6.3 % at X/X0=1.22;
- under mode Emax (B1=0.47; B2=0.50; n=6.5): t0=70 s, t'=80 s, the time required to enter a preset mode increased by 14 % at VX0=0.6;
- under mode Xmin (B1=0.40; B2=0.425; n=11.5): t0=57 s, t'=66 s, the time required to enter a preset mode increased by 14 % at VX0=0.36.
0 10 20 30 40 50 60 70
Fig. 11. Time-temperature dependences of a heat-absorbing
junction T0 and failure rate 1/10 for a single-stage TED, obtained without (solid lines) and with (dotted lines) taking
into consideration the magnitude of ^mC at varying heat
i
load Qo and T=300 K; AT=40 K; //S=10 cm-1 for mode Qomax
Fig. 12. Time-temperature dependences of a heat-absorbing
junction T0 and failure rate 1/10 for a single-stage TED, obtained without (solid lines) and with (dotted lines) taking
into consideration the magnitude of ^mC at varying heat
i
load Q0 and T=300 K; AT=40 K; //S=10 cm-1 for mode (Qo/l)max
Fig. 13. Time-temperature dependences of a heat-absorbing
junction T0 and failure rate 1/10 for a single-stage TED, obtained without (solid lines) and with (dotted lines) taking into consideration the magnitude of ^mC at varying heat
load Q0 and T=300 K; AT=40 K; //S=10 cm-1 for mode £max
To, K
T0 (0o=O,5 W) "
I I
To(Qo= 1,0 W)
-1---;-1-
10 20 30 40 50 60 t, S
Fig. 14. Time-temperature dependences of a heat-absorbing
junction T0 and failure rate 1/10 for a single-stage TED, obtained without (solid lines) and with (dotted lines) taking
into consideration the magnitude of ^mC at varying heat load Qo and T=300 K; AT=40 K; //S=10 cm-1 for mode Imin
An analysis of the estimation data reveals that the Xmin mode ensures minimum time required to enter a stationary mode at minimal failure rate X/X0 for a varying heat load Q 0.
At a thermal load of Q 0=1 W, the time to reach the preset temperature 70=260 K at T=300 K with a mass and heat capacity of the object of m0C0=0.894 J/K is:
- under mode Qomax (Bi=0.93; B2=1.0; n=7.8): To=44 s; t'=50 s, that is, the time required to enter a mode increased by 13.6 % at V^0=8;
- under mode (Q0/IW (Bi=0.66; B2=0.71; n=9.4): t0=40 s; t'=46 s, that is, the time required to enter a mode increased by 15 % at X/X0=2.4;
- under mode Emax (Bi=0.47; B2=0.50; n=13): t0=37 s; t'=44 s, that is, the time required to enter a mode increased by 19 % at V^0=1.2;
- under mode Xmin (B1=0.40; B2=0.425; n=23): t0=29 s; t'=40 s, that is, the time required to enter a mode increased by 38 % at X/X0=0.72.
At thermal load Q0=1.5 W, the time to reach the preset temperature of T0=260 K at 7=300 K, with a mass and heat capacity of the object of m0C0=0.894 J/K, is
- under mode Q0max (B1=0.93; B2=1.0; n=11.7): t0=31 s; t'=36 s, that is, the time required to enter a mode increased by 16.1 % at V^0=12;
- under mode (Q0/IW (B1=0.66; B2=0.71; n=14.1): t0=26 s; t'=33 s, that is, the time required to enter a mode increased by 27 % at X/X0=3.8;
- under mode Emax (B1=0.47; B2=0.50; n=19.5): t0=24 s; t'=32 s, that is, the time required to enter a mode increased by 33 % at V^=1.8;
- under mode Xmin (B1=0.40; B2=0.425; n=34.5): t0=19 s; t'=29 s, that is, the time required to enter a mode increased by 53 % at V^0=1.1.
Fig. 15 shows the dependence of relative magnitude of the time required to enter a stationary mode P=(t'-t0)/t0 and relative magnitude of the failure rate X/X0 of a single-stage TED on the magnitude of heat load Q 0 for different modes of operation at 7=300 K; AT=40 K; //5=10 cm-1.
It follows from Fig. 15 that with a growth of thermal load Q0 for different modes of operation and the preset cooling temperature level T0=260 K and the geometry of thermoelement branches l/S at T=300 K:
- the magnitude of relative time required to enter a stationary mode p increases, with the greatest magnitude p observed under the mode of Amin;
- the magnitude of relative failure rate A/A0 increases, with the largest magnitude of failure rate A/A0 observed under the mode of Q0max, and the lowest is under the mode of Amin.
With the increasing number of thermoelements n for a preset heat load Q0 and temperature difference AT (Fig. 16):
- relative operating current B and the magnitude of operating current I decrease;
- voltage drop U grows;
- functional dependence of cooling coefficient E=f(n) has a maximum;
- the time required to enter a stationary mode t0 and t' is reduced; the time required to enter a stationary mode t', taking into consideration the structural and technological elements, increases compared to t0: for example, at n=25 pcs., t'=61 s; t0=41 s, that is, t' increases by 53 % (Fig. 17);
Fig. 15. Dependence of relative magnitudes of the failure rate 1/10 and the time required to enter a stationary mode P=(t'—t0)/t0 of a single-stage TED on thermal load Q0 at 7=300 K; A 7=40 K; //5=10 cm-1; Gb=0.5 W;
10=3x10-8 1/h for different modes of operation
We shall consider a possibility of reducing the time required for a single-stage TED to enter a stationary mode by increasing the number of thermoelements n for a preset heat load Q0 and temperature difference AT: at T=300 K; AT=40 K; Q0=0.5 W; //5=10 cm-1.
Results of the calculations are given in Table 7.
Fig. 16. Dependences of parameters B, /, E, Uof a single-stage TED on the number of thermoelements n at 7=300 K; A 7=40 K; //5=10 cm-1; ©0=0.5 W
- functional dependence of the failure rate A/A0=f(n) has a minimum at nAmin; at n>nAmin, failure rate A/A0 increases (Fig. 18);
- relative magnitude of the time required to enter a stationary mode P=(t'-t0)/t0 increases (Fig. 18).
Table 7
7=300 K; To=260 K; AT=40 K; 0=0.5; /max=5.02 A; #=10.M0-2 Ohm; C0=0.5 W
Mode of operation Bl/B2 I, A U, V E W, W n, pcs. T0, s x', s ß, % M08, 1/h P
Q0max 0.93/1.0 5.02 0.46 0.217 2.30 3.9 83.0 89.5 7.6 4.0 12.0 0.99880
- 0.80/0.86 4.32 0.42 0.275 1.82 4.1 84.9 91.7 8.0 2.345 7.0 0.99930
- 0.72/0.77 3.87 0.41 0.313 1.60 4.4 85.0 92.4 8.7 1.62 4.86 0.99951
Imin 0.66/0.71 3.55 0.411 0.340 1.46 4.7 84.1 91.8 9.1 1.23 3.70 0.99968
- 0.62/0.67 3.38 0.42 0.352 1.42 5.0 83.7 91.9 9.8 1.06 3.19 0.99968
- 0.56/0.60 3.0 0.45 0.374 1.34 5.8 80.4 89.5 11.4 0.765 2.30 0.99977
E ^max 0.51/0.55 2.76 0.47 0.385 1.30 6.6 75.4 85.2 12.9 0.61 1.82 0.99982
(Q0/l2)max 0.47/0.50 2.51 0.53 0.379 1.32 7.9 72.4 83.5 15.3 0.486 1.46 0.99985
- 0.44/0.47 2.36 0.57 0.372 1.345 90. 68.7 81.0 18.0 0.428 1.28 0.99987
- 0.39/0.42 2.11 070 0.3339 1.475 12.0 60.6 74.8 23.4 0.356 1.07 0.99989
Amin 0.37/0.40 2.0 0.79 0.316 1.58 14.0 56.3 71.6 27.2 0.330 0.990 0.999901
- 0.35/0.38 1.92 0.92 0.284 1.76 17.0 51.0 67.7 33.0 0.334 1.0 0.999900
^max 0.32/0.35 1.76 1.30 0.22 2.28 25.3 41.0 61.0 49.5 0.35 1.05 0.999895
- 0.31/0.33 1.66 1.88 0.16 3.13 38.4 31.7 55.5 75.0 0.415 1.245 0.999875
- 0.30/0.32 1.61 2.61 0.12 4.18 54.0 25.0 51.5 106 0.51 1.53 0.99985
- 0.29/0.312 1.57 3.40 0.0936 5.34 72.0 21.0 50.7 141 0.62 1.85 0.99982
40
20
\ v
To t'
\ \ \ \ \
--- --- -
10 20 30 40 50 60 70 n, pc.
Fig. 17. Dependence of the time required for TED to enter a stationary mode (t0, T are, respectively, without and with
taking into consideration ^ miCl) of single-stage TED on
i
the number of thermoelements n at 7=300 K; A 7=40 K; //5=10 cm-1; C0=0.5 W
AA(T
2,0
1,5
1,0
0,5
0,0
/ p
/Xo
A
10 20 30 40 50 60
70
p, % 100 75 50 25 0
pc.
Fig. 18. Dependence of relative magnitudes of failure rate 1/10 and the time required to enter a stationary mode P=(t'-t0)/t0 of a single-stage TED on the number of thermoelements n at 7=300 K; A 7=40 K; //5=10 cm-1;
Q0=0.5 W; 10=3x10-8 1/h
It should be noted that with an increase in the relative working current B for a preset heat load Q0=0.5 W and a temperature difference AT=40 K:
- the magnitude of operating current I increases;
- the magnitudes of voltage drop U and the number of thermoelements n decrease;
- functional dependence of the cooling coefficient E=f(n) has a maximum at current under the mode of Emax (Fig. 19);
, A 6
5 ■-
n, pc.
2 --
1
-0,5 0,4 0,3 0,2 1 40 ■
N \\U 30
W \, s * / \ E 20
A / > -____ ___ ___r- 10
y n --- --- ---
U, V
1,6
1,2
0,8
0,4
0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
Fig. 19. Dependence of the magnitude of working current /, cooling coefficient E, the number of thermoelements n and voltage drop U of a single-stage TED on the relative working current B0 for different modes of operation at 7=300 K; Q0=0.5 W; A 7=40 K; //5=10 cm-1
- failure rate X/X0 grows;
- relative magnitude p decreases (Fig. 20);
- functional dependence of the time required to enter a stationary mode without taking into consideration the
structural and technological elements t0 and taking into consideration the structural and technological elements t' has a flat maximum at B=0.8 (Fig. 21).
/./.if
\
\ X/Xo / / / f
\ / / ✓ /
\ / s / s /
*
60
40
20
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0
1,0 B2
Fig. 20. Dependence of failure rate 1/10 and the magnitude of p for a single-stage TED on relative working current B2 for different modes of operation at 7=300 K; Q0=0.5 W; A7=40 K; //5=10 cm-1
Fig. 21. Dependence of the time required for a single-stage TED to enter a stationary mode T'and t0 on the relative working current B2 for different modes of operation 7=300 K; Q0=0.5 W; A7=40 K; //5=10 cm-1
Thus, it is possible, given the preset value of the time required to enter a stationary mode t, to determine graphically the magnitude of relative working current B for the assigned temperature difference AT and the magnitude of thermal load Q0 (Fig. 21).
6. Discussion of results of analysis of the time required to enter a stationary mode, energy and reliability indicators of a single-stage TED
The analytical expressions obtained allow us to determine:
- the time required to enter a stationary mode taking into consideration structural and technological elements on
the heat-absorbing junctions of a single-stage TED for different modes of operation Q0maX; (Q0/I)maxi Emax; Amin, heat load Q0 and temperature difference AT=40 K;
- the temperature of a heat-absorbing junction T0 depending on time with respect to structural and technological elements for different modes of operation of a single-stage TED and thermal load Q0.
An analysis of these expressions shows that if heat capacity and mass of an object are much smaller than the heat capacity and mass of structural and technological elements f<<1, the time required to enter a mode is much longer than the time required to enter mode t0 without taking into consideration these factors.
With an increase in heat load Q0:
- the time required to enter stationary mode t, with respect to the mass and heat capacity of structural and technological elements t', and without taking them into consideration t0, is reduced; in both cases, the mass and heat capacity of the cooled object are taken into account;
- voltage drop U and the required number of thermoelements n increase;
- relative magnitude P=(t'-t0)/t0 of the time required to enter a stationary mode grows. The largest gain in the time required to enter a stationary mode is observed under the Amin mode, the lowest - under the Q0max mode.
With a decrease in the time required to enter stationary mode t:
- failure rate A/A0 grows;
- the probability of failure-free operation P for different modes of operation decreases, both with and without taking in to consideration the mass and heat capacity of structural and technological elements.
With an increase in the number of thermoelements n at the assigned heat load Q0 and temperature difference AT:
- the time required to enter stationary mode t0 and t' is reduced;
- the relative magnitude of p grows;
- functional dependence of failure rate A/A0 has a minimum at n=10 pcs.
With a growth in the relative working current B at a preset temperature difference AT=40 K and thermal load Q0:
- the magnitude of working current I grows;
- voltage drop U and the number of thermoelements n decrease;
- functional dependence of the cooling coefficient E=f(B) has a maximum at B=0.55 (the Emax mode);
- failure rate A/A0 grows, therefore, the probability of failure-free operation P decreases;
- the relative magnitude of p decreases;
- the time required to enter stationary mode t0 and t' increases, both with and without taking into consideration the structural and technological elements.
There is a flat maximum of dependence T=f(B) for the Emax mode.
The results obtained could form the basis for the development of control algorithms over dynamic characteristics of single-stage thermoelectric coolers during work with a nonstationary thermal load for the criterion of minimum relative failure rate.
7. Conclusions
1. We have developed an analytical model for the relation between a cooling time of a single-stage thermoelectric cooler with current modes of operation, heat load in the range of working temperature difference, taking into consideration the impact of structural and technological components of the device.
2. The results of analysis of dynamic characteristics, energy and reliability indicators of a single-stage TED showed the possibility to control the time required to enter a stationary mode. Structural control, enabled by selecting the number and geometry of TED thermoelements, and the mass and heat capacity of the load makes it possible to reduce the time required for TED to enter a stationary mode by up to 2.5 times. Operational control, executed by changing working current of the cooler, makes it possible to reduce the time required to enter a stationary mode by up to 3 times.
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Розглядаються питання обгрунтування вибору конструктивна ршень гiдротехнiчних водоскидiв, робота яких заснована на ефектах контрвихорових течш. Сформульовано тдходи до гiдравлiчного розрахунку проточног частини водоскидiв та визначення гх гео-метричних розмiрiв. Наводяться основш конструкции локальних завихрювачiв, як формують початковi циркуляцшно-поздовжш течи, даються деяк схеми водоскидних систем з такими завихрювачами потоку Ключовi слова: гiдротехнiчнi скидання води, гашен-ня енерги, закручен потоки, вихровi течи, завихрю-
вач, турбуленттсть
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Рассматриваются вопросы обоснования выбора конструктивных решений гидротехнических водосбросов, работа которых основана на эффектах контрвихревых течений. Сформулированы подходы к гидравлическому расчёту проточной части водосбросов и определению их геометрических размеров. Приводятся основные конструкции локальных завихрителей, которые формируют начальные цир-куляционно-продольные течения, даются некоторые схемы водосбросных систем с такими завихрителями потока
Ключевые слова: гидротехнические водосбросы, гашение энергии, закрученные потока, вихревые течения, завихритель, турбулентность -□ □-
UDC: 532.517.2
|DOI: 10.15587/1729-4061.2018.123918|
SUBSTANTIATION OF COUNTER-VORTEX SPILLWAY STRUCTURES OF HYDROTECHNICAL FACILITIES
V. Volshanik
Doctor of Technical Sciences, Professor* E-mail: volshanik@gmail.com G. Orekhov Doctor of Technical Sciences, Associate Professor* E-mail: orehov_genrih@mail.ru *Department of Hydraulics and Hydrotechnical engineering Moscow State University of Civil Engineering Yaroslavskoye highway, 26, Moscow, Russia, 129337
1. Introduction
The construction and reconstruction of high-pressure waterworks sets a number of scientific and engineering tasks that require a new approach to their solution. One of them is to design reliable and economical culverts, able to work both in the construction and operational periods, making it possible to combine the spillway and energy flow channels. Damping of the excess energy of idle flows is one of the most important tasks when creating hydraulic spillway systems. The choice of the method for damping the kinetic energy of the flow significantly affects the overall layout of the hydraulic engineering structure.
This task becomes the most urgent in the transition to the construction of high-pressure hydraulic systems, which requires studying the phenomena associated with highspeed water flows, their interaction and the development of fundamentally new designs of spillway structures. The hydraulic sections that are used to solve the problems of transit water flows through such structures have been developed. When designing spillways in high-pressure waterworks, it is necessary to take into account the features of the interaction of high-speed flows with solid boundaries and the air environment. It is essential to take into account the probability
of various wave processes, a possible local pressure drop, phenomena of aeration and cavitation and their consequences, as well as peculiarities of energy damping. It is important to ensure ventilation in the case of gravity and partial pressure in closed conduits, as well as take into account other phenomena of hydraulic nature. The resulting hydrodynamic loads under these phenomena are transferred to the building structures, and they must be taken into account in the design, construction and operation of spillway systems.
One of the promising areas for solving these and a number of other problems is the use of swirling water flows in hydrotechnical facilities. The so-called counter-vortex flows of liquid and gas and consideration of the prospects for their practical application have been studied at Moscow State University of Civil Engineering (MGSU, Russia) for several years.
2. Literature review and problem statement
The creation of effective designs of spillway structures for hydrotechnical and hydropower facilities ensures sustainable performance of the entire complex. The design and construction of such systems first and foremost solves the
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