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5точек зрения. Эксергетическая диаграмма потоков (диаграмма Гроссмана) показала, что все элементы системы, кроме промежуточного внутреннего теплообменника, вносят существенный вклад в необратимость работы системы.
Ключевые слова: С02 тепловой насос, эксергия, эксергетический баланс, коэффициент преобразования, эксергетические потери.
Цитирование: Карнаух, В.В. О применении С02 в качестве холодильного агента для среднетемпературных тепловых насосов / В. В. Карнаух // Журн. Сиб. федер. ун-та. Техника и технологии, 2021, 14(6). С. 703-713. DOI: 10.17516/1999-494Х-0344
1. Introduction
As the population grows, the pressure on water resources increases significantly. In many cases, the energy and water systems in a process are closely linked.
The production of food is characterized as a high water consumption industry.
There are several types of water-using operations [1]:
- heating: boiler, heat exchangers;
- process water: cooling and cooling towers;
- potable uses: in offices and canteens;
- washing: of equipment, bottles, floor and vehicles;
- rinsing: of equipment, bottles, food materials and final products;
- sanitation: general cleaning and toilet flushing;
- fire fighting; and
- transport medium.
In many food industry enterprises, waste heat flows take place that are not reused for their own needs. They are usually discharged into the sewer system or local cooling towers. This applies to factories that produce alcohol, beer, dairy products, bakery products, etc. With a steady rise in energy prices, all this ultimately leads to an increase in unit costs for the production of final products and services.
In the works devoted to increasing the level of greening of industrial enterprises among the primary directions in the field of increasing the level of greening the food and processing industry, the need is noted «... to improve the entire water management system of enterprises, to increase the volume of recycled and reused water, to reduce the consumption of fresh water, to reduce the volume of waste water, especially contaminated and dumped without cleaning, with a promising transition to closed cycles».
Replacement of cooling towers, spray basins with heat pumps allows, along with stable, year-round cooling of technological equipment, independent of weather conditions, to utilize heat discharges both for the company's own heat supply needs and for heat supply with commercial heat to third-party consumers.
In this article recycled water (/w=25.. .40°C) of food production enterprises is taken into account as a source of low potential heat for medium-temperature water-to-water vapor compression heat pump.
In this case, the choice of the «ideal» working fluid is the primary requirement for the heat pumps efficiency. Ongoing trend in cooling area is using natural refrigerants with low ODP and GWP.
Several theoretical and experimental studies have spurred further interest in carbon dioxide based systems in varied applications. Environment friendliness, low price, easy availability, with various
common materials, compactness due to high operating pressures, excellent transport properties are cited as some of the reasons behind the revival of carbon dioxide as a refrigerant.
Past studies indicate that carbon dioxide based systems have great potential in two sectors in mobile air conditioning and in heat pumps for simultaneous cooling and heating.
A large number of experimental work of CO2 heat pumps operate with low heat sources and in this case the evaporating temperature varies from -10oC to 10 °C [2-3]. It was mentioned that due to a lower critical temperature a CO2 heat pump is not suitable for high temperature heat sources and gas cooler exit temperature from 30 to 50 °C was recommended.
However, deeper analyses demonstrates several studies were the evaporating temperature varies between 15 and 20 °C, and the condensing temperature comes up to 70 °C [4].
The purpose of this work is to evaluate carbon dioxide as a working substance for medium-temperature water-to-water vapor compression heat pumps.
The object of research is the systems of recycled water supply of food production enterprises.
2. Energetic and exergetic analysis
The studies depending on the energy and exergy analysis are essential for the efficient utilization of energy recourses for a variety of systems.
Therefore, a growing trend has been observed towards these analyses in the last two decades. The traditional methods of process analysis (energy analysis) are based on the First Law of Thermodynamics. This method is the failure to consider changes in energy quality during a process, since it does not consider the properties of the environment around the system and not characterises the irreversibility of the processes within the system. Thus, it makes traditional thermodynamic analysis methods quite unsatisfactory. To overcome this inadequacy, the concept of exergy has quickly become a key instrument in recent years.
Exergy (value of energy) is a relatively alternative technique defined as the maximum useful work obtainable from the system, when its state is brought to the standard atmospheric conditions or a dead state. In the ideal energy conversion process no exergy is lost, but in any real process exergy destruction (irreversibility) takes place and it constitutes the main difference between energy and exergy. Hence, the exergy analysis is a more rational measure of environmental and economic performance of process than the energy analysis [5].
The second law of thermodynamics derives the concept of exergy, a powerful tool for analyzing both the quantity and quality of energy use. It is defined as the maximum amount of work achievable when the flow of matter is transferred from its initial state to a dead state by processes during which the flow can only interact with the environment. The exergy balance is similar to the energy balance, but it has a fundamental difference in that, although the energy balance is a statement of the law of conservation of energy, the exergy can be considered as a statement of the law of energy degradation.
Obviously, the studies depending on the energy and exergy analysis are essential for the efficient utilization of energy recourses for a variety of systems.
Provided analysis takes into account all the losses appearing in the heat pump system, for calculating exergetic efficiency. The various parameters calculated are COPhp, COPLorenz, exergetic efficiency, exergy destruction.
In this study, in order to calculate thermodynamic efficiency of the medium-temperature water-to-water vapor compression heat pump the following simplifying assumptions have been made:
- Steady state conditions are remaining in all the components;
- Pressure losses in the pipelines are neglected;
- Heat is not transferred to the system by other means, only from refrigerant in the
condenser to the outside ambient hot air or room air to refrigerant in the evaporator;
- Kinetic and potential energy and exergy losses are not considered;
- The flow is assumed to be adiabatic through the pipes, the throttle valve and compressor (for theoretical cycle);
- The isentropic efficiency of compressor is 85 %. (Y.F.GAO) for theoretical cycles; the compressor mechanical efficiency and the compressor motor electrical efficiency are 85 % and 90 %, respectively (for real cycle);
- Dead state of the refrigerants at pressure p0 = 1.013 bar and temperature T0 = 25 °C;
An average heat source temperature has been taken as 30 °C, so the evaporating temperature is 20 °C by assuming an average temperature difference of 10 °C in the evaporator. Internal heat exchanger effectiveness is taken as 60 % for the analysis. Here, comparisons of some applications are presented for outlet temperatures of 60 °C.
It is important to understand that, for CO2 to operate subcritically, the heat rejection temperature must be below the critical point, which is not high enough for water heating applications. Typically, water needs to be heated to at least 60 °C for domestic hot water applications. To achieve higher temperatures and a larger heating capacity, the system can be operated transcritically with the heat rejection pressure above the vapor dome.
Although these high pressures may pose safety risks during operation, and require robustly designed components with compatible material characteristics, the latest manufacturing technologies can easily meet the quality and safety standards required. A potential benefit of operating at high pressure is that the increased vapor density enables the use of smaller components and more compact systems [6].
In order to predict the optimum heat rejection pressure (discharge pressure) a correlation proposed by [4] was calculated:
or
The heat pump system working on CO2 consists of evaporator, a single compressor, gaz cooler, internal heat exchanger (IHE) and expansion device (Fig.1).
The main difference between theoretical cycle and real cycle in the expansion stage. Here the expansion device of the theoretical cycle configuration is substituted by an expander or turbine (Fig. 1b). Furthermore, in the compressor adiabatic compression is replaced by polytrophic compression (non-isentropic process).
The log P-h chart of one-stage carbon dioxide transcritical heat pump cycles are plotted in Fig. 2.
Fig. 1. Example for medium-temperature water-to-water vapor compression heat pump using R744
Fig. 2. Log p-h diagram of one-stage carbon dioxide transcritical heat pump cycles: 1-2'-3—4 -5'-6—1— theoretical cycle; 1-2-3-4-5-6-1 real cycle
It is known that the performance of a heat pump is defined by the coefficient of performance (COPhp) defined as the ratio of the heating capacity Qh. to the power input Wcomp and indicated in equation (1):
COPhp=-^~. (1)
hp w
comp
As mentioned in [7] for an ideal heat pump, operating between process and waste heat streams with constant heat capacities and varying temperatures (temperature glides), the maximum theoretical COP is known as the Lorenz COP and is given by equation (2):
T
COP =-LMH--(2)
v y Lorenz rp > V-)
LM.H LM .L
where - the log mean temperature, K (H for high temperature side in the cycle;
L for low temperature side in the cycle).
In practice, thermodynamic processes contain numerous losses which reduce the actual COP to a fraction of the Lorenz COP value. An efficiency term (known as a second law or exegetic efficiency), which relates the actual COP to the maximum Lorenz COP is given in Equation (3).
_ (Щч,
. (3)
' У* Lorenz
When choosing a new refrigerant for an application such parameters as affordability, safety and environment have to be considered simultaneously. Sustainability index (SI) is given by equation (4).
SI = TT—y (4)
Calculated data for both cycles are shown in Table 1.
Table 1. Calculated data for theoretical and real cycles
Cycle TLM.H TLM.L COPLorenz COPh.p ^Lorenz SI
Theoretical cycle 323 305.46 18.47 3.83 0.21 1.26
Real cycle 323 305.46 18.47 3.14 0.15 1.18
Obtained values of COPLorenz, COPhp, nLorenz have a good corresponding with other research in literature [8].
Applying an exergy balance and energy conservation to each component of the system, the following modular relations can be developed to yield the system model.
Evaporator
T
J- r\
m ex. + mam(\ - _ " ) = m ex.....- m ex
r in r 1 evap \ rp evap ' r out r i
* LPS
dest.evap '
T
1 n
m ex, , = m (ex , — ex ) — m a (\ — —)
r dest.evap r\ out in' y^ evap' rp e\'ap
LPS
or using enthalpy and entropy of specific points from diagram equation can be rewritten as
(5)
(6)
(7)
T
where = exwap- exergy had been released from low potential source (LPS) in the
^LPS
evaporator; T^p°sp - average logarithmic temperature of the LPS, K.
. ■ .■ .
LPS V^+273-+273
Compressor
External exergy losses (destruction) in the compressor and electric motor caused by mechanical friction
(8)
Internal exergy losses in the compressor caused by the irreversibility of the compression process:
Condenser
eXdest.comp ~^o(S2' /
T
mrexin = mrexout + mrqcond ( 1 - + mrexdestcond.
* HPS
(9)
(10)
TQ
eXdest.cond = (K' ~ K ~ T0(S2' ~~ S3 )) ~ ~ PFcond ^
Tc
1 TJ
T0
= (qcond ~ T0(s2' ~ S3 )) ~ Clcond(^ ~ jTcond ^
J- troc
T0
.
1 TJVÇ
where qcond (\ — —c°ond ) = excond potential source's (HPS) exergy had been taken in the condenser;
T^ - average logarithmic temperature of the HPS, K.
.
1 high 2
111
Internal heat exchanger (IHE)
mreXdes,.LVHE = mrT,( Sl~S6 = Wj/ S^S^S^+Sj. (12)
Expansion device
mr exm = mrexout + mrexdestthr v. (13)
eXdesUhr v=mr( eX,n - eXou, ) = mrT0 (S 5' ~SA )■ (14)
Total exergy destruction can be calculated as the sum of exergy destruction in different components of the system.
total __ext int
eXdest ~ eXdest.evap + eXdest.comp + ßXdest.comp + eXdest.s.c. + ßXdest.LVHE + eXdest.thrv ■
eXout + „ , ßXdest
„ ___ cotid_s.c. _ 1 _
'ex ext
eXin eXevap + eXcomp eXin
For real cycle parameters for points 2 and 5 have been used instead of 2' and 5', respectively.
This analysis takes into account all the losses appearing in the heat pump system, for calculating exergetic efficiency. The various parameters calculated are COP, exergetic efficiency, exergy destruction and efficiency defects.
All calculations and diagrams were carried out with the help of freeware CoolPack («CoolPack IPU,» n. d.) ver. 1.46, freeware REFPROF ver.9 (NIST Standart Reference Datebase 23) and Microsoft Excel 2010.
The exergy loss in the different components is shown in Fig. 3.
Process irreversibility (due to mixing, throttling, internal convection, etc.), pressure loss due to friction in inlet and outlet valves and heat loss to the environment are the basic reasons for the exergy loss in the compressor. The summarized exergy loss for real cycle is maximum in the compressor (excomp= excomp.inter + excompexter=46 %), while the summarized exergy loss for theoretical cycle is less (excomp= excomp.exter=19 %), because the internal exergy loss equals zero.
The maximum increment of irreversibility for both cycles occurred in the gas cooler (condenser) (30 % and 27 %). This may be attributed to an increase in the temperature difference in the gas cooler as well as the increase in pressure loss due to the rapid increase in flow velocity. So, an increase in compressor speed yields higher capacity due to the higher mass flow rate and higher frictional pressure loss due to the higher velocity that causes the increase in irreversibility as well.
As was mentioned in [9], irreversibilities in the evaporator and the gas cooler occur due to the temperature differences existing between the two heat exchanger fluids, pressure loss, flow imbalance
R744 Real cycle
0%
R 744 Theoretical cycle
■ External exergy losses in the
compressor excomp, ■ Internal exergy losses In the
compressor ■ exergy losses in the evaporator
■ exergy losses in the condenser
■ exergy losses in the Liquid vapour heat exchanger
■ exergy losses in the throttle valve
Fig. 3. The exergy loss in the different components of heat pump
and heat transfer with the ambient. The results show that almost 90 % of the irreversibility occurs due to the fluid temperature difference and 10 % due to the rest.
At the mean conditions, the average fluid temperature differences in the evaporator and gas cooler are about 22 and 49 °C, respectively. It is observed that the exergy losses in evaporator and in IHE for both cycles are similar, 16 % and 8 %, respectively.
Replacement of the expansion valve by a turbine is the only option available to improve the performance of the system and reduce the irreversibility of the expansion process. It was reported that an expansion work recovery turbine with isentropic efficiency of 60 % would reduce the contribution of this process to total cycle irreversibility by 31 % in the thermodynamic cycle. Hence, improvement in system performance through this technique is quite significant. However, such extensive hardware addition may not be economically feasible in many practical applications, especially for small capacities.
Schematic layout of food industry enterprises recycled water supply system with parallel functioning water-cooling tower and medium-temperature water-to-water vapor compression heat pump using R744 is shown in Fig.4.
The flow of water from the heat exchanger (1) is directed partly for cooling to the water cooling tower (7) and to the heat pump (4). The thermal potential of water (the so-called low-grade heat) is passed to the working substance of the heat pump and then is transferred to the water which comes from the consumer (high-potential source). Water flow is regulated by valves (3). Amount of water coming from the heat exchanger (1) usually is significant, and it is not advisable to chill all water in the heat pump, because the consumer does not need so such hot water.
Fig. 4. Layout of food industry enterprises recycled water supply system with parallel functioning water-cooling tower and medium-temperature water-to-water vapor compression heat pump using R744: 1 heat exchanger of technology equipment; 2 technology equipment; 3 control valve; 4 medium-temperature water-to-water vapor compression heat pump; 5 supply hot water line to the consume; 6 supply water line from the consume; 7 water-cooling tower; 8 circulation pump
Conclusion
Recycled water (tw =25.. .40 °C) of food production enterprises has a strong potential to be a source of low potential heat for CO2 medium-temperature water-to-water vapor compression heat pump for heating processes.
The exergy flow diagram shows that all the components except the internal heat exchanger contribute significantly to the irreversibilities of the system.
Experimental results for the heating performance of the CO2 trans-critical theoretical cycle show that the values of COP and second law efficiency are 3.83 and 21 %, for real cycle 3.14 and 15 %, respectively.
References
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DOI: 10.17516/1999-494X-0354 УДК 536.423: 536.24
One-Dimensional Model of Heat
and Mass Transfer in Closed-Type Cryogenic Gasifiers
Stanislav V. Borodkina, Igor L. Bataronovb, Alexey V. Ivanova and Victor I. Ryazhskikhb
aMilitary Scientific Educational Center of Military-Air Forces «N. E. Zhukovsky and Ju. A. Gagarin Military-Air Academy» Voronezh, Russian Federation bVoronezh State Technical University Voronezh, Russian Federation
Received 01.09.2021, received in revised form 14.09.2021, accepted 20.09.2021
Abstract. A one-dimensional energy transfer equation is formulated in terms of the average mass temperature of a supercritical fluid (SCF), determined by the average mass enthalpy of the flow. The kinetic equation for the heat flow of heat exchange between the SCF and the coolant is used in the form of the Newton-Richman law in the flows of liquid media and thermal resistances for a multilayer heat exchanger tube, taking into account the possibility of icing of the tube from the coolant side. The thickness of the icing layer is found in a self-consistent way when solving the model equations, similar to the Stefan problem. For the proposed model, the thermophysical conditions of heat exchange in the SCF and the coolant are analyzed and the criteria equations for calculating the heat transfer coefficients in the coolant and the environment are selected. The model was tested in various heat exchange schemes.
Keywords: one-dimensional model of heat and mass transfer, gasifier, supercritical fluid.
Citation: Borodkin, S.V., Bataronov, I.L., Ivanov, A.V. and Ryazhskikh, V. I. One-dimensional model of heat qnd mass transfer in closed-type cryogenic gasifiers, J. Sib. Fed. Univ. Eng. & Technol., 2021, 14(6), 714-730. DOI: 10.17516/1999-494X-0354
© Siberian Federal University. All rights reserved
This work is licensed under a Creative Commons Attribution-Non Commercial 4.0 International License (CC BY-NC 4.0). Corresponding author E-mail address: borodkinstanislav@yandex.ru
