CC BY
114
TRANSCRITICAL CO2 HEAT PUMP WITH EXPANDER-EJECTOR
CYCLE
SIT B., TIMCENCO D., SIT M.
Abstract. Heat pump with expander - ejector cycle, method of this cycle control of this cycle and the scheme of the heat pump with the second loop are presented in this paper.
Key words: heat pump, automatic control.
POMPA DE CALDURA PE DIOXID DE CARBON iN REGIM TRANS CRITIC DE LUCRU CU
CICLUL DETANTOR-EJECTOR
§it Boris, Timcenco Dumitru, §it Mihail Rezumat. Este demonstrat, ca la utilizarea detantorului in componenta pompei de caldura pe dioxid de carbon COP se majoreaza ca urmare a alegerii corecte a coordonatei punctului de lucru la intrare gazului in detantor. Totodata este inadmisibil de a diminua eficienta exergetica a instalatiei cu pompa de caldura conditionata de cre§terea pierderilor de presiune in schimbatorul intermediar de caldura. Alegerea caracteristicilor de debit prin supapelor de reglare a pompei de caldura se face tinand cont de functionarea racordata a acestor supape.
Cuvinte cheie: pompa de caldura, sistem de dirijare.
ТЕПЛОВОЙ НАСОС НА ДИОКСИДЕ УГЛЕРОДА В ТРАНСКРИТИЧЕСКОМ ЦИКЛЕ РАБОТЫ
ПО СХЕМЕ ДЕТАНДЕР-ЭЖЕКТОР
Шит Б.М., Тимченко Д.В., Шит М.Л.
Аннотация. Рассмотрен тепловой насос на диоксиде углерода в транскритическом цикле работы по схеме детандер-эжектор. Приведена методика выбора регулирующих клапанов для данной схемы теплового насоса.
Ключевые слова: тепловой насос, автоматическое управление.
1. Introduction
Application of heat pumps (HP) in the industry makes up a very small part from the total heat pumps amount [1]. Energy intensity decrease of the food industry production is now the purpose of innovative development in this area. So, for example, heat pumps using low grade heat from technological processes in winemaking practically are not applied, though examples of heating of a part of a factory premises from ground source heat pumps (USA). We had been offered earlier the scheme of HP use in winemaking [2] where HP is used simultaneously at cooling of fermenters and at the processing of wines by heat or at the sanitary processing, later the same heat pump is used in technological process of wine processing by a cold and simultaneously at hot water preparation (sanitary processing of the equipment, hot water for personnel needs). This heat pump is used at work of distiller after the end of the period of wine processing by cold, or in the absence of a distiller for the bleeding of heat from the boiler flue gases (serving for the preparation of steam and hot water for the technological process needs) with the purpose of fuel utilization factor increase of the boiler. Expander use is possible, in the last case, in a heat pump loop what raises its energy and economic efficiency. Heat pump station should be supplied with the replaceable gas coolers and evaporators, and also to have a second loop (intermediate heat carrier contour). It is discussed in this paper a cycle of the heat pump with the expander and ejector and HP work conditions at variable heat load assuming the use of linear control laws, and also an adjustable electric drive of the compressor. The use of ejectors for heat pumps on carbon dioxide is described in different works [3-6]. But common use of expander and ejector was not considered in heat pump till now.
2. Heat pump scheme and its control
It is shown at the Fig. 1 heat pump with the expander - ejector scheme for a case of hot gases heat utilization. The scheme works as follows.
The subcritical CO2 enters the compressor 1 in state point 1 (see Fig.2) after the internal heat exchanger 3, to which gas goes from the separator 8 at the state point 12. The compressed gas enters the gas cooler 2 at the state point 2. The supercritical CO2 is then cooled in gas cooler to the state 3, passes the internal heat exchanger and leaves it in the state point 4.
The supercritical CO2 goes through control valve 4, to the additional heat exchanger 5, where the liquid is heated from the state point 5 to state point 6 by means of hot gas. It is shown by means of the dashed-line that the gas is moved through the heat exchanger 5 by the means of the fan 11. The hot gas goes after the heat exchanger 5 to the evaporator 10. Further the refrigerant from the heat exchanger 5 enters in the expander 6 where it extends up to a biphasic state point 7. This gas-liquid mixture enters on a working ejector input 7 where after an exit from a nozzle it comes to the state point 8 (Fig.2). Saturated vapor from the evaporator 10 in the state point 15 arrives on the second ejector input 7 in which case it extends to the biphasic state 9. Further in the ejector mixing chamber at constant pressure gas mixture occurs with the biphasic state in 8 and with a state point 9 up to a state point 10. Further refrigerant from the state point 10 isentropically passes in ejector’s diffuser, to state point 11.
For the maintenance of a normal mode of expander work it is necessary to stabilize coordinate in point 6 of the thermodynamic cycle. The temperature in a state point 6 is stabilized by the automatic control system of the low grade heat carrier flow rate, and the pressure of the compressor is stabilized by the control valve 4 (see Fig. 1). Let’s consider combined work of the valves in this system.
Fig. 1. Schematic of expander-ejector heat pump cycle
We will write down the equations establishing dependencies between pressures before and after the compressor and the flow rate through the control valves.
(1)
dp4 + dp9 =p4- pu - p5_u = pd
(2)
G1 = CV1,
(3)
(4)
(5)
G2=U-Gx
Ps-n =Ps ~ Pl3
It is accepted the following nomenclature: dpj -pressure drop across the control valve
number y (Fig. 1), p] - pressure in the i point of the loop, U - entrainment ratio of ejector and
Gj - flow rates on the ejector working input and on the ejector second suction input. CVl,
C' - the flow coefficients, are dimensionless values that relate to a valves flow capacity. Superscripts correspond to the variant of compressor output setting.
It is necessary both gas cooler pressure stabilization in the system, and pressure stabilization on the exit of the evaporator. We will consider how the refrigerant flow rate through the evaporator and gas cooler will change at the refrigerant pressure disturbance in the heat pump loop.
From the equations (2 - 4) it is possible to obtain a rule for choice of the valves trims for given heat pump taking into account entrainment ratio of the ejector. As in the part of the expression (7) in brackets, obtained from expressions (1) and (6) is always more than one, it follows that it is always possible to choose such values U, CVl5 CV2 which also satisfy to
certain technical requirements to the ejector’s entrainment ratio and control valves design.
2
u2 a
(6)
Ap9=-
VI
-Ap4
V 2
(7)
Ap4
U2 Q
VI
C,
V2
= Pd
It is necessary for the equation 7 to have the solutions at certain entrainment ratio values, that expression in brackets of the equation 7 to be constant at the constant gas flow rate through the compressor or to vary to satisfy the expression 7 at change of the pressures in loop points, starting from state point 4 and finishing at state point 14. There is a considerable difference of pressures in the line after the control valve number 4 and the valve trim of this valve becomes essentially nonlinear irrespective of, whether the valve has the linear or equal percent trim rangeability. It is necessary to take this into account while designing the pressure control system of the compressor and of the evaporator.
Let’s set the value of the mass flow rate G| <g| at the constant value of pd . In this case the system equations will be the following.
Gj — Cyi M
(9)
^2 — 2 V UF9
The solution of the system will be.
(10) dp"4 = -
Pd
U\Cvl)2
1 +
(c:2)2
It is necessary for the system to have the solution taking into account (8) and (9) that ('j -| > ('j -|, u ('j -| < C(72 •
It is shown thus that the decision of the equations (8) and (9) always exists. For normal work of the valves control system it is necessary to provide a solving system (8) (9) at the current values of temperatures and pressures of the refrigerant in states points 4 ...14 of the thermodynamic loop of heat pump system and demanded heat load.
Let's consider a thermodynamic cycle when there is no regenerative heat exchanger, and the gas superheat before of the compressor is ensured by the separate heat exchanger. In this case it is necessary to make separate exergetic analysis to choose, what is more effective from the point of view of energy expenditures: to have two resistances to refrigerant flow or one, having increased the resistance for a gas through the superheater before the compressor.
This stream enters the gas-liquid separator 8, where it is divided into saturated liquid and saturated vapor streams. The liquid stream enters at the state 13 into the control valve 9, which is connected with the evaporator 10.
The pressure-enthalpy diagram is built in accordance with [8, 9]. Here heat pump station heat efficiency factor will be: COPold =8,68. If to assume that isentropic efficiency of the expander^ = 0,7, and electric generator efficiency r/d = 0.8, than new heat pump system COP (COPnew) will be equal to:
COP = ^2 ~ • COPold _
neW~ (h2-hl-(h1-h6)-Tle7ld)~
_ 63,12-33,57-8,68 _ 256,36
— ---------------------------------------- — ------- ^ 1 1. O
(63,12 - 33,57 - (112,98 - 99,03) • 0,8 • 0,7 21,74
So, COP growth will be 35,9 %. Overall consumption of energy by the installation will depend, considering the change of capacity of the ventilator for overcoming of aerodynamic resistance of the heat exchanger 5, on the compressor capacity and additional capacity of the ventilator. It is necessary to tend therefore in each specific case to choose the heat exchanger 5 with a minimal aerodynamic resistance, at the account of restrictions on its cost and dimensions. G - quality of vapor.
The increase of the compressor output occurs with a very small inertia (inertia of the frequency converter constitutes tens milliseconds). The change of level of a liquid phase in the evaporator occurs in accordance with the first order differential equation [7]. The level of the intermediate heating carrier will change in the intermediate heat exchanger according to algorithm of an intermediate contour functioning.
The temperature on an exit of the intermediate heat exchanger will change according to the lag effect of this heat exchanger depending on change of the heating agent flow rate through the heat exchanger and the heat transfer surface area.
Let's consider the heat pump dynamics on the condition of set point change on produced heat capacity if fermentation process intensity changes. The control signal appears to increase the flow rate of heat pump refrigerant at the increase of the value of fermenting liquid temperature and of the speed of change of its temperature.
PRESSURE-ENTHALPY DIAGRAM
16r
ENTHALPY, kJ/kg
Fig. 2. P-h diagram of expander-ejector heat pump cycle
Table 1
Coordinates of the basic points (NN) of heat pump thermodynamic cycle with expander,
_______________________ejector and intermediate heat exchanger______________________
NN t, °C p MPa %G h kJ/kg s, kJ/kg >7 p,kglm3
1 20 4.50 100.00 -63.12 -0.882 0 116.96
2 75.32 8.00 100.00 -33.57 -0.832 0.95 166.12
3 30.00 8.00 100.00 -222.79 -1.467 0 702.06
4 25.16 8.00 100.00 -243.27 -1.535 0 775.27
5 24.42 7.50 100.00 -243.55 -1.534 0 770.28
6 37,00 7.50 100.00 -99.03 -1.060 0 252.55
7 11.00 4.61 85.50 -112.98 -1.060 0 243.30
8 3.00 3.77 81.40 -119.07 -1.060 0 256.53
11 10.00 4.50 87.1 -140.21 -1.142 0 331.16
12 10,0 4.50 100 -81.43 -0.938 0 124,37
13 10 4.50 0.00 -281.09 -1.651 0 861.10
14 7.50 4.23 3.00 -281.09 -1.650 0 854.50
15 10 4.50 100 -83.86 -0.954 0 135.16
The level of two-phase mixture increases in the evaporator as well. The liquid temperature on an evaporator exit decreases because of heat-transfer surface area increase from the working heat pump agent to the evaporator second loop contour (contour of the intermediate heating agent). The level in the intermediate heat exchanger increases because of the increase of the set-point of its level controller simultaneously with level growth in the evaporator (as it is necessary to increase transferred heat capacity from heat pump through the evaporator in intermediate heat pump contour).
3. Conclusions
1. The use of the expander in a heat pump on carbon dioxide allows increasing its COP in case of the rational choice of a working point of the input of the refrigerant in expander. Thus should not decrease exergetic efficiency of heat pump station in whole.
2. The choice of flow coefficients of control valves in the heat pump should be defined from a condition of the maintenance of their common work.
References
1. Jovmir M.M., Utilization of low source heat from combustion products of fuels by means of heat
pumps. Industrial Heat Engineering, (in Ukrainian) 30, 2, 90-97 (2008).
2. Balanuta A.V., and others Energy efficiency decrease of wine production technological processes
due to use of heat pumps and heat pipes. Problems of the Regional Energetics, 3, (2009), http://ieasm.webart.md/data/m71 2 122.doc
3. Li D., Groll A., Transcritical CO2 refrigeration cycle with ejector-expansion device. International
Journal of Refrigeration, 28, 5, 766-773, (2005).
4. Yari M., Sirousazar M., Cycle improvements to ejector-expansion transcritical CO2 two-stage
refrigeration cycle. International Journal of Energy Research, 32, 7, 677-687 (2008).
5.Deng J-Q., Jiang P-X., Lu T., Lu W., Particular characteristics of transcritical CO2 refrigeration cycle with an ejector. Applied Thermal Engineering, 27, 12, 381-388 (2007).
6. Elbel S., Hrnjak P., Experimental validation of a prototype ejector designed to reduce throttling
losses encountered in transcritical R744 system operation. International Journal of Refrigeration, 31, 3, 411-422 (2008).
7. Tao Cheng., Xiang - Dong He., Harry Asada H., Nonlinear Observer Design and Experimental
Verification for Heat Exchangers during the Start-up Process. Proceedings of the 2005 American Control Conference, June 8-10, Portland, OR, US, 2005. pp. 4814-4819.
Sit Mihail. is the head of the Laboratory of Energy Efficiency and Control Systems of the Institute of Power Engineering of the ASM, PhD. His research interests include carbon dioxide heat pump thermodynamic cycles and coordinated control systems for heat pumps, control system for industry, agriculture, energetics, control of automatic guidance systems, e-mail: mihail [email protected].
Timcenko Dmitry - senior programmer in Energy Efficiency and Control Systems laboratory of the Institute of Power Engineering of ASM, scientific interests area: control system design, network programming; author of 4 scientific publications. E-mail: [email protected]
Sit Boris - programmer in Energy Efficiency and Control Systems laboratory of the Institute of Power Engineering of ASM, scientific interests area: control system design in economical and technical systems; network programming; author of 20 scientific publications, has 1 patent. E-mail: boris [email protected]
