CC BY
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ходные процессы с учетом неодновременности размыкания-замыкания контактов выключателей, при отключениях фаз и работе ОАПВ и разрядников, восстанавливающиеся напряжения на контактах выключателей и др.
Литература
1. Бернас, Цек З. Математические модели элементов электроэнергетических систем: Пер. с англ.. - М.: Энергоиз-дат, 1982. - 312 с.
2. Джуварлы Ч.М., Рустамов С.А., Гаимов А.М. и др. Расчеты электромагнитных процессов при неполнофазном включении электропередачи 110 кВ с ненагруженными трансформаторами. Электричество, 2004, № 8. С 16.
3. Ефимов Б.В., Фастий Г.П., Якубович М.В. Наведенные напряжения на воздушных линиях при неоднородных трассах сближения. - Эл станции, 2002, № 8.
4. Веприк Ю.Н., Минченко А.А. Коммутационные перенапряжения в электропередаче 750 кВ. Электротехника и электромеханика. Ежекварт. научно-практический журнал. Харьков: НТУ ‘ХПИ’ - 2009. № 4. с.
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Досліджено фазову поведінку та теплофізичні властивості сумішей типу R1234yf
- HFE, як заміни R134a. Погрішність прогнозу за допомогою нейронних мереж холодильного коефіцієнту та відношення тиску не перевищує 3%.
Ключові слова: рівняння стану; азеотропний стан; нейронні мережі; критерій сталого розвитку; розпливчата логіка
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Исследовано фазовое поведение и теплофизические свойства смесей типа R1234yf
- HFE, как замены R134a. Погрешность прогноза с помощью нейронных сетей холодильного коэффициента и отношение давлений не превышает 3%
Ключевые слова: уравнение состояния; азеотропное состояния; нейронные сети; критерий устойчивого развития; нечеткая логика
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The phase behavior and thermophysical properties ofR1234yf- HFE systems as alternative to R134a are investigated. Accuracy of COP and pressure ratio predicted by neural networks does not exceed 3%
Keywords: equation of state; azeotrope; neural networks; sustainable development criteria; fuzzy logic -------------------□ □----------------------
УДК 538.953:54.139
SUSTAINABLE REFRIGERANT SELECTION IN BINARY BLENDS OF THE R1234YF -HYDROFLUOROETHERS
С.В. Артеменко
Кандидат технических наук, старший научный сотрудник, докторант Кафедра инженерной теплофизики* Контактный тел.: 067-486-05-01 Е-mail: sergey.artemenko@gmail.com
Д.Н. Никитин
Кандидат технических наук, доцент Кафедра программирования* *Одесская государственная академия холода ул. Дворянская, 1/3, г. Одесса, Украина, 65082 Контактный тел.: (048) 238-95-00 Е-mail: dnn@te.net.ua
1. Introduction
The sustainable refrigerant selection is one of the most important stages in the design of refrigeration systems.
The compromise among such properties as contribution to greenhouse effect, flammability, toxicity, thermodynamic behaviour, performance specifications, and the others define a sustainable decision. It is obvious; a pure substance that
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combines all desirable properties and has no undesirable properties does not exist. The most promising roadmap to seek a harmonious decision is based on the improvement of “backbone” substance performances via the “breeding” components that amend its objectionable properties. The entire set of design indices includes: economic (LCC life cycle cost), thermodynamic (specific refrigerating effect, volumetric capacity, specific adiabatic work, condenser/evaporator pressure ratio, coefficient of performance, adiabatic power), and environmental (flammability, toxicity, and GWP) criteria. The attainment of the sustainable decision corresponds to a compromise among different criteria. The accuracy of prognosis for experimentally observable thermodynamic and design characteristics narrows the area of search in the space of competitive economic, environmental and technological criteria. The general approach to sustainable design of the refrigerants based on fuzzy thermoeconomic optimization was developed as a trade off solution of multicriteria problem [5]. The aim of present work is to apply a fuzzy set methodology providing sustainability among thermodynamic, economic, and environmental goals for the IV generation of refrigerants. The class of refrigerants under consideration scrutinizes most prospective working “backbone” fluid R1234yf [9] as R134a replacement for MAC applications in combination with hydrofluoroethers (HFE) as possible “breeding” components. The HFE additives enable to decrease high compressor discharge temperatures and to increase vaporization heat.
This paper is organized as follows. In Section 2 the Peng
- Robinson one-fluid model of equation of state is applied to predict an azeotrope appearance in terms of critical parameters of mixture components and interaction parameters k12 and l12. It is shown that R1234yf - HFE blends form azeotrope practically for all systems under consideration. In Section 5 the cycle performances (COP, pressure ratio) for restricted number of refrigerants are considered as training set for ANN to reproduce missing data for all HFE refrigerants. Section 6 considers new approach to sustainable refrigerant selection based on a fuzzy set methodology providing a trade off solution among thermodynamic, economic, and environmental goals. The Bellman - Zadeh model as the intersection of membership functions (fuzzy criteria mappings) is applied to sustainable selection of refrigerants.
Nomenclature
a equation of state parameter v volume
(long range attraction) X control variabl
aii long range attraction vector
between xi mole fraction o
b i - i components component i
equation of state parameter Z- dimensionless
(excluded volume) parameters of
bii excluded volume for model.
component Greek
COP i symbols
k12 coefficient of performance m acentric factor
Ki binary interaction relationship
parameter function
112 binary P density
M local criterion ¥ flammability
nj interaction parameter for index
p excluded Subscripts
PR molar mass c critical
T number of atomic species (i) k condenser
pressure ev evaporator
pressure ratio i component i
temperature, K mod model
2. Azeotropic states in the R1234yf - hydrofluoroether blends
The one-fluid modified Peng - Robinson model of equation of state (PR78) was used to simulate thermodynamic and phase behaviour of the R1234yf - HFE blends [8].
p =
a(T)
RT
v -bj v(v + b) + bj(v-b) ’
RT
a-- = 0.45723553
pCii
(RTCjii)2
(1)
(2)
T
[1 + mi(1 -j^)]2, (3)
pc,ii VT„,
mi = 0.37464 + 1.5422mi -0.26992m2, if mi < 0.491 ;
mi = 0.37964 + 1.48503mi --0.164423m2 + 0.016666m3, if m- > 0.491
N N
(4)
NN
a=XX x-xjaij, b=XX x-xA, a-j=(1 - ,
i=1 j=1 i=1 j=1
, b-- + b.. v (1 - ls)"Yi
(5)
where R is the universal gas constant, and the EoS parameters a and b of a mixture depend on the mole fractions xi and xj of the components i and j and the corresponding parameters aij and bij for different pairs of interacting molecules.
Critical properties of R1234yf, i.e., critical temperature Tc, critical density pc, and critical pressure pc, were taken from [10] measurements: molar mass M = 144.042 g/mol, Tc = 367.85 ± 0.01 K, pc = 3382 ± 3 kPa, pc = 478 ± 3 kg/m3, and acentric factor m = 0.280, respectively. Critical properties of HFEs were taken from [1]. Allocation of HFE critical points in vicinity of R134a and R1234yf vapour pressure curves is shown in Fig. 1.
Ps(T) R1234yf Ps(T) R134a
« ♦ ♦
/♦ ♦ 1 ♦ ♦ « «. r
/♦♦♦< / ♦ I
/ ♦ ♦ O ♦ ♦ * ♦
♦
300
400
Temperature, K
500
600
Fig. 1. Critical points of HFEs and vapour pressure curves of R1234yf and R134a
6
5
4
3
2
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Critical properties of HFE components with critical temperatures below 500 K and their flammability indices correlated to atomic species by simple ratio of fluoride (nF) and and hydrogen (nH) atoms ¥ = nF/(nF+nH) are given in Table
1. The normal boiling points (acentric factor) for HFEs were restored from Murata et al. data [7].
Table 1
Critical parameters and flammability indices for hydrofluoroethers
HFEs M, g mol-1 Tc, K Pc , MPa Pc , g cm-3 Zc ¥ = nF/(nF+nH)
C2HF5O 136.021 354.49 3.35 0.579 0.267 0.83
C2H2F4O 118.030 420.25 4.23 0.529 0.270 0.67
C2H3F3O 100.040 498.50 4.82 0.485 0.240 0.50
C3F6O 166.022 361.90 3.06 0.610 0.277 1.00
C3F6O 166.022 357.20 2.84 0.540 0.307 1.00
C3F6O 166.022 359.60 2.93 0.570 0.285 1.00
C3F8O2 220.018 372.40 2.33 0.610 0.271 1.00
c3hf7o 186.028 377.26 2.62 0.580 0.268 0.88
c3hf7o 186.028 387.80 2.62 0.550 0.275 0.88
C3H2F6O 168.038 428.90 3.04 0.553 0.269 0.75
C3H3F5O 150.047 462.03 3.54 0.553 0.259 0.63
C3H3F5O 150.047 406.82 2.89 0.500 0.256 0.63
C3H5F3O 114.066 449.05 3.51 0.412 0.260 0.38
C4F8O 216.029 400.00 2.69 0.680 0.257 1.00
C4F10O 254.026 391.70 1.87 0.630 0.232 1.00
C4HF7O2 214.038 452.88 2.87 0.597 0.273 0.88
C4HF7O2 214.038 435.06 2.65 0.569 0.275 0.88
C4HF9O 236.036 412.63 2.26 0.499 0.311 0.90
C4H2F8O 218.045 421.60 2.33 0.533 0.272 0.80
C4H2F8O 218.045 444.63 2.57 0.581 0.261 0.80
C4H2F8O2 234.045 449.81 2.41 0.571 0.265 0.80
C4H3F5O 162.058 455.03 2.91 0.486 0.258 0.63
C4H3F7O 200.055 455.10 2.77 0.576 0.255 0.70
C4H3F7O 200.055 437.60 2.48 0.530 0.257 0.70
C4H3F7O 200.055 433.21 2.55 0.542 0.261 0.70
C4H3F7O 200.055 463.89 2.71 0.541 0.260 0.70
C4H4F6O 182.064 459.60 2.70 0.481 0.267 0.60
C4H4F6O 182.064 476.31 2.78 0.500 0.256 0.60
C4H5F5O 164.074 431.13 2.53 0.448 0.258 0.50
C5F10O 266.037 427.00 1.90 0.600 0.237 1.00
C5H2F6O2 208.059 485.10 2.77 0.720 0.198 0.75
C5H2F10O 268.053 447.40 2.14 0.582 0.265 0.83
C5H3F7O 212.066 476.55 2.58 0.538 0.256 0.70
C5H3F7O 212.066 467.64 2.52 0.518 0.266 0.70
C5H3F9O 250.062 475.74 2.23 0.563 0.251 0.75
C5H3F9O 250.062 462.72 2.37 0.558 0.276 0.75
C5H3F9O 250.062 473.01 2.24 0.550 0.259 0.75
C5H5F5O 176.085 475.54 2.64 0.494 0.238 0.50
C5H5F7O 214.081 481.54 2.38 0.497 0.256 0.58
C6H3F9O 262.073 498.97 2.20 0.520 0.267 0.75
C6H3F11O 300.070 486.48 1.95 0.567 0.255 0.79
C6H5F9O 264.089 482.02 1.98 0.518 0.251 0.64
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3. Azeotropy boundaries for R1234yf - HFE
Some criteria for azeotropy in binary fluids can be obtained analytically in the frameworks of global phase diagrams. The corresponding boundary state is called a degenerated critical azeotropic point and represents the limit of the critical azeotropy at xi^ 0 or at xi^ 1. As a result of solving the system of thermodynamic equations for a degenerated critical azeotrope:
Sv
dp
9v2
= IE =0
-1
(6)
one can obtain the following relationship for dimension less interaction parameters [2]:
(1 - Z
Z2 = +Z1 - 0.7(1± Z1)
1± Za
(7)
where the upper signs + or - correspond to x2= 0 and the lower signs - to x2 = 1, respectively.
The set of dimensionless parameters for the Peng - Robinson model is defined as follows:
Z1 = (a22 - a11) / (a22 + a11) ,
Z2 = (a22 - 2a12 + a11) / (a22 + a11) ,
Z3 = (b22 - b11)/ (b22 + b11) ,
Z4 = (b22 - 2b12 + b11)/ (b22 + b11) .
(8)
According to Eq. (7) the boundary between azeotropic and non-azeotropic states in Zj - Z2 plane at fixed values of Z3 and Z4 is a straight line. A membership of binary mixture to azeotropic state is defined for given interaction parameter k12 as follows. Critical parameters (pc, Tc) and the acentric factor (m) or the normal boiling temperature (TB) of the individual components are selected and the Z1, Z3 values are calculated via relationships (8). Value k12 generated from ANN model [2] for natural and synthetic refrigerants and critical parameters of pure components at l12 = 0 define the dimensionless co-ordinates Z2 and Z4 from (8). Azeotropy boundaries (7) are calculated and position of the characteristic point within the one of quadrants generated by the straight lines Z2 ( Z1) intersection is established (Fig. 2).
Fig. 2. Distribution of azeotrope pairs in the R1234yf — HFEs mixtures
T,v
Z
1
To visualize the appearance of azeotrope for system R1234yf - C4HF7O2 (Tc = 452.88 K, pc = 2.866 MPa, m = 0.390) boundaries were shown by solid lines in Figure 2. The characteristic point allocations both for the R1234yf
- C4HF7O2 and R1234yf - HFE blends are presented in Figure 2. If a characteristic point is located in the northern or southern quadrants (Fig. 2) then azeotropy phenomena should appear in the binary refrigerant mixture. It is apparent the overwhelming majority of the R1234yf - HFE gives evidence of azeotropy.
4. Phase equilibria in the R1234yf - HFE blends
Set of parameters for given equation of state model un-ivocally defines a global phase diagram and, accordingly, evolution of phase behaviour for binary mixture in wide range of temperatures and pressures which include all possible phenomena ( zeotropic and azeotropic states, liquid - vapour and liquid - liquid - vapour equilibria, and etc.). Some refrigerant mixtures can exhibit all varieties of the phase equilibria phenomena, including transitions from zeotropic to aze-otropic state and vice versa with change of state parameters. This opportunity follows from the type of phase behaviour which is defined by the equation of state parameters.
Experimental phase equilibria data for R1234yf - HFE blends are not available in current literature and only theoretical estimations give an opportunity to make decision regarding new refrigerant blends. Phase equilibria calculations were realized in MATLAB software on the base of Michel-sen, Mollerup algorithms [6]. The results for some R1234yf
- HFE blends are presented in Figs. 3 - 6.
P = 1
0,0 0,2 0,4 0,6 0,8 1,0
x (C4H2FP2)
Fig. 5. T — x diagram for the R1234yf — C4H2F8O2
t- 3 = 0.1 MPa
P = 1 Ml
Fig. 6.
0,0 0,2 0,4 0,6 0,8 1,0
x (C5H3FsO)
T — x diagram R1234yf — C5H3F9O blend at different pressures blend at different pressures
The R1234yf - C2HF5O blend clearly exhibits a positive azeotrope (Fig. 3). Azeotropic and near azeotropic behaviour practically within all concentration range is observed for the R1234yf — C3F6O mixture (Fig. 4). An increase of carbon atoms (C3 - C5) leads to heteroazeotrope appearance at low R1234yf concentrations (Figs. 5 and 6). Main advantage of the R1234yf - HFE blends is a boiling temperature decreasing in comparison with pure components. For example, the R1234yf - C2HFsO mixture has a normal boiling temperature 6K below the low-boiling component. It compensates the lower energy efficiency R1234yf in comparison with R134a.
x (C2HF 5O)
Fig. 3. T — x diagram for the R1234yf — C2HF5O
P = 1.0 MPa
P = 0.5 MPa
P = 0.1 MPa
0,0 0,2 0,4 0,6 0,8 1,0
x (C3F6O)
Fig. 4. T — x diagram R1234yf — C3F6O blend at 0.1 MPa blend at different pressures
5. Performances of vapour compression cycle
To develop a blend with better properties than those of R1234yf we need preliminary to estimate properties of breeding components. Sustainable selection suggests a compromise among set of alternatives. It requires the assessment of different efficiency criteria. To evaluate the cycle performance data the ANN approach capable of learning to recognize complex input - output relationships is applied.
At first step the training set was used to calculate the main cycle characteristics. The cycle was chosen to simulate typical MAC operating conditions, and is specified by system cooling capacity of 5.8 kW, a constant evaporation temperature of 273 K, a constant condensation temperature of 323K, an evaporator superheat of 5 K, a condenser subcooling of 5 K, and a compressor isentropic efficiency of 70 %. Vapour compression cycle includes isentropic compression,
E
isobaric cooling + condensation + subcooling, throttling, and isobaric cooling + evaporation + superheating.
A multitude of R1243yf - HFE combinations puts obstacles in thermodynamic property calculations for little-studied refrigerants. To avoid this problem the cycle performance is restored from relationships “EoS parameters - cycle performance” based on artificial neural networks (ANN). The ANN correlations for COP and pressure ratio (output) as function of critical temperature, critical pressure and acentric factor - m (input) are built on the known refrigerant database. The training set included 15 components (R134a, R123, R1270, R717, R600a, R290, R245fa, R245ca, R236fa, R227ea, R142b, R125, R113, R22, R32) where REFPROP 8.0 [4] was used to determine the thermodynamic properties of refrigerants. The ANN architecture for prediction of pressure ratio included the 2 layers with 6 and 1 neurons, correspondingly. The ANN for COP prognosis considered 3 layers with 2, 6, and 1neurons, correspondingly. The back propagation algorithm was applied for training procedure. The MATLAB Neural Network Toolbox is used in this application. The accuracy of ANN prediction for the cycle performances does not exceed 4% relative to the training set values. Figures 7 and 8 present the simulation results of COP and pressure ratio (PR) versus the critical temperatures of the individual HFEs. The ANN COP of the R1234yf cycle is 3.75 and that of the R134a cycle is 3.95, that is, the R134a COP is 5 % higher than the R1234yf cycle. The ANN model agrees with Zilio et al. [11] results within uncertainty of calculations.
6. Sustainable refrigerant selection
O 4,0
o
J1 © ^ 1
A 1 6 , ■ *
** A A • #'
A "s • •a "■ , ■
• O .■ ■
A Training set • ANN model ♦ R1234yf forecast via ANN ■ HFE forecast via ANN —1 1 1 1 -
« m F
320 340 360 380 400 420 440 460 480 500
Critical Temperature, K
Fig. 7. COP — critical temperature relationships
•
« • A O A a i fia &■
A ■
■ r
■
A Training set
• ANN model
■ HFE forecast via ANN
♦ R1234yf forecast via ANN
320 340 360 380 400 420 440 460 480 500 520
Critical Temperature, K Fig. 8. PR — critical temperature relationships
Design objectives usually contradict with each other, so that is difficult to provide sustainable solution, which simultaneously satisfies both of them. Meaningful analysis of this ill-structured situation should include uncertainty conception. For the multicriteria problems the local criteria usually have a different physical meaning, and consequently, incomparable dimensions. It complicates the solution of a multicriteria problem and makes it necessary to introduce the procedure of normalizing criteria or making these criteria dimensionless. There is no unique method for the criteria normalizing and a choice of method depends on statement of problem having subjective nature. In the present study, a next sequence of decision-making steps is applied [5]:
- Determination of the Pareto optimum ( or compromise, or trade off ) set XP as the formal solution of multicriteria problem to minimize uncertainty sources;
- Fuzzification of goals as well as constraints to represent an ill-structured situation;
- Informal selection of convolution scheme to transform a vector criterion into scalar combination of vector components.
To illustrate our approach we consider only two local criteria: COP and pressure ratio that can be represented by membership functions. Mole fraction of HFE additive is chosen as X variable. The results of refrigerant blend composition selection for system R1234yf - C4HF7O are shown in Fig. 9 where concurrent criteria reflect the opposite tendencies for COP and PR. The membership functions |icOp(X) and |iPR(X) are varied from maximum (minimum) value (COPHFE = 3.75; PRHFE = 2.5) at mole fraction xHFE = 1 to mini-mum (maximum) value for pure R1234yf (COPR1234yf = 4.35; PRRi234yf = 4.2). Sustainable decision corresponds xhfe = 0.61 (Fig. 9).
Mole fraction, X h
Figure 9. Sustainable decision as intersection membership function
7. Conclusions
A majority of R1234yf - HFE exhibits azeotropes and have no temperature glide in the heat exchangers similar pure refrigerants. A multitude of R1243yf - HFE combinations puts obstacles in thermodynamic property calculations for little-studied refrigerants. To avoid this problem the cycle performance is obtained from quantitative relationships “critical parameters - cycle performance” based on artificial neural networks (ANN). The ANN training set is chosen
4,6
4,4
4,2
3,8
3,6
3,4
5,0
4,5 -
4,0
3,5
3,0
2,5 -
2,0
3
to calculate the main cycle characteristics for well-studied refrigerants via REFPROP program. The sustainable performances of the R1234yf - HFE blends appear quite perspective. The disadvantage of R1234yf (low COP) is overcome through addition of HFE with high COP.
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