Design-theoretical study of cascade CO2 sub-critical mechanical compression/butane ejector cooling cycle

Design-theoretical study of cascade CO

2

sub-critical

mechanical compression/butane ejector cooling cycle

V.O. Petrenko

_*

_{, B.J. Huang}

_{, V.O. Ierin}

a_{New Energy Center, Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan}

b_{Odessa State Academy of Refrigeration, Ejector Refrigeration Technology Center, 1/3, Dvoryanskaya St., 65082 Odessa, Ukraine}

a r t i c l e i n f o

Received 17 February 2010 Received in revised form 3 November 2010

Accepted 27 November 2010 Available online 3 December 2010 Keywords: Carbon dioxide Butane Cascade system Vapor Compression Ejector

a b s t r a c t

In this paper an innovative micro-trigeneration system composed of a cogeneration system and a cascade refrigeration cycle is proposed. The cogeneration system is a combined heat and power system for electricity generation and heat production. The cascade refrigeration cycle is the combination of a CO2mechanical compression refrigerating machine (MCRM), powered by generated electricity, and an ejector cooling machine (ECM), driven by waste heat and using refrigerant R600. Effect of the cycle operating conditions on ejector and ejector cycle performances is studied. Optimal geometry of the ejector and performance characteristics of ECM are determined at wide range of the operating conditions. The paper also describes a theoretical analysis of the CO2sub-critical cycle and shows the effect of the MCRM evaporating temperature on the cascade system performance. The obtained data provide necessary information to design a small-scale cascade system with cooling capacity of 10 kW for application in micro-trigeneration systems.

ª 2010 Elsevier Ltd and IIR. All rights reserved.

Etude sur la conception et sur un cycle the´orique de

refroidissement a` compression me´canique en cascade au CO

2

subcritique, muni d’un syste`me a` e´jecteur au butane

1.

Introduction

Trigeneration or combined heating, cooling and power (CHCP) production is becoming an increasingly important energy-saving option, particularly on a small-scale basis. Conven-tional CHCP system is the combination of a tradiConven-tional

combined heat and power (CHP) system that cogenerates electricity and heat, with an absorption cycle, which is driven by waste heat.

Different types of trigeneration systems can be designed using reliable ejector cooling machines (ECMs) operating with low-boiling point working fluids and powered by waste heat * Corresponding author. New Energy Center, Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan. Tel.:þ88 62 33662686; fax: þ88 62 23671182.

E-mail addresses:[email protected],[email protected](V.O. Petrenko).

w w w . i i fi i r . o r g

a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j r e f r i g

0140-7007/$e see front matter ª 2010 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2010.11.012

supplied from CHP systems. Recently several high-efficiency ECMs operating with refrigerants R141b and R245fa were developed and coefficients of performance (COPs) in the range of 0.5e0.7 were obtained experimentally at practical operating conditions (Huang et al., 1999; Eames et al., 2007).

Hydrofluorocarbon refrigerants, which have been devel-oped as alternatives to shlorofluorocarbon and hydro-chlorofluorocarbon refrigerants, are known to have a high Global Warming Potential (GWP). As a result of this environ-mentally benign, natural refrigerants have attracted consid-erable recent attention. The natural refrigerants include ammonia, hydrocarbons, carbon dioxide, water, air, etc. These natural refrigerants have zero Ozone Depleting Potential and the majority of them have negligible GWP.

A distinctive feature of the proposed micro-trigeneration system is that it combines a conventional CHP system and a cascade CO2sub-critical mechanical compression/heat-driven ejector cooling cycle using a natural low-boiling working fluid.

Carbon dioxide (CO2) is a good refrigerant. The key advantages of CO2include the fact that it is easily available, environmental friendly, non-toxic, and not explosive. CO2has relatively high working pressures, which give small vapor volume that leads to compact components. Thermo-physical properties of carbon dioxide are excellent. Heat transfer coefficients are high and sensitivity to pressure drop is low. Since the critical temperature of CO2is rather low (31.1C), sub-critical operation is only possible when the average heat sink temperature is rather low. In the event that sub-critical

operation is feasible it may be stated that the CO2systems compete very well in energy efficiency with systems using other refrigerants. Additionally, CO2cycle performance and reliability can be significantly increased by reducing the discharge pressure. This requires operation in the sub-critical mode (Robinson and Groll, 1998; Neksa et al., 2001; Chen and Gu, 2005; Lee et al., 2006).

This research aims to carry out a theoretical study for the design of a small-scale cascade refrigeration cycle utilizing a CO2sub-critical mechanical compression cycle and low-grade waste heat-driven ejector cooling cycle operating with low-boiling environmentally friendly working fluid. The waste-heat driven ECM is used to cool the condenser of MCRM to reduce its condensing temperature to increase the performance.

The analysis and comparison of performance characteris-tics for various low-boiling point refrigerants had shown that from the thermodynamic and operating viewpoints the most suitable for ECMs are low-pressure refrigerants which have high critical temperature Tcrit, large specific latent heat at evaporating temperature Te, small specific heat of liquid refrigerant in the range of operating temperatures (TgeTe), and normal boiling temperature Tb  Te. The calculations show that environmentally friendly working fluid R600 has higher performances than other refrigerants (Petrenko, 2001; Petrenko et al., 2005a).

Consequently refrigerant R600 (butane) is selected as the working fluid for low-grade waste heat-driven ECM in the present study.

Nomenclature

A area (mm2₎

C ejector compression ratio

cp constant pressure specific heat (kJ kg1K1)

CHP combined heat and power

CHCP combined heating, cooling and power COP coefficient of performance

E ejector expansion ratio

ECM ejector cooling machine

GWP Global Warming Potential

h specific enthalpy (kJ kg1)

ICE internal combustion engine

l specific compressor work (kJ kg1) _m mass flow rate (kg s1)

MCRM mechanical compression refrigerating machine

P pressure (bar)

Q heat flow (kW)

q specific heat of evaporation (kJ kg1)

r compressor pressure ratio

s specific entropy (kJ kg1K1)

T temperature (C or K)

v specific volume (m3kg1) _

W power (kW)

_w specific power consumption (kW kW1) Greek letters

a, b ejector area ratios

g converging angle at mixing chamber entrance

Δ difference h coefficient of efficiency u entrainment ratio Subscripts b boiling BC bottoming cycle c condenser C compressor CB condenser bottoming crit critial cs compressor isentropic e evaporator eg electric generator ET evaporator topping g generator m motor mech mechanical opt optimum p primary

pump feed pump

s secondary

sup superheating

t throat

therm thermal

2, 3 cross-sections of the ejector (Fig. 3, Equations(2) and (3))

1, 2, 3.13 cycle states in theFigs. 1 and 2, Equations (5)e(20)

2.

Design of micro-trigeneration system

A diagram of the proposed micro-trigeneration system incorporating a CHP system and a cascade refrigeration cycle is shown inFig. 1.

In CHP systems two kinds of prime movers are generally used: reciprocating internal combustion engines (ICEs) and gas micro-turbines which both can be selected to exactly match the site conditions.

FromFig. 1, the CHP system consists of ICE, electric gener-ator producing electric power _Wegand heat recovery unit. The cascade refrigeration cycle is the combination of a CO2 sub-critical mechanical compression refrigerating machine (MCRM), powered by generated electricity, and an ECM driven by waste heat. Thus, the significant part of the exhaust heat can be recovered. Such waste heat recovery would ultimately reduce overall fuel consumption and CO2emission and thus helps to alleviate global climatic change brought about by the greenhouse effect (Petrenko et al., 2005b).

The ECM acts as the topping cycle and the MCRM acts as the bottoming cycle in the cascade system. The two cycles are thermally connected through the cascade condenser, which serves as evaporator for the topping cycle and the condenser of the bottoming cycle.

The low-temperature (bottoming) cycle with CO2as working fluid can be used for refrigeration at temperature levels found suitable in supermarkets, cold stores or food processing plants. The high-temperature (topping) cycle operating with butane as refrigerant is used to condense the CO2 vapor of the low-temperature cycle in cascade condenser.

Fig. 2shows the thermodynamic processes of the CO2and R600 cycles in lgP-h diagram. The operating principle of cascade refrigeration cycle is as follows. In the MCRM the compressed carbon dioxide coming from the compressor is

condensed in the cascade condenser at a condensing temperature TCB. The liquid refrigerant then expands through an expansion valve 1 and enters the evaporator where it is evaporated at low evaporating temperature Teto produce the necessary cooling effect Qefor refrigeration purposes. After the evaporator the entrained vapor is compressed to a high pressure state by the compressor, before entering the cascade condenser. This completes the CO2 sub-critical mechanical compression refrigeration cycle.

Low-grade heat Qgis delivered from the heat recovery unit to the generator of ECM, where liquid refrigerant is vaporized at relatively high generating pressure Pgand temperature Tg. This primary vapor with a mass flow rate of _mpflows through the primary convergent-divergent nozzle of the ejector and accelerates within it. At the exit of the nozzle, the accelerated flow becomes supersonic, and induces a locally low pressure region. The relatively low pressure produced by this expan-sion causes a suctioning effect of secondary flow with a mass flow rate of _ms from the cascade condenser at low pressure PET. The primary and secondary fluids are mixed in the mixing section of the ejector and undergo a pressure recovery process in the diffuser section. The combined stream flows to the condenser where it is condensed to liquid at intermediate condensing pressure Pc and temperature Tc. The heat of condensation Qc is rejected to the environment. Then, the condensate is divided into two parts, one is pumped back to the generator, and the other is expanded through an expan-sion valve 2 to a low-pressure state and enters the cascade condenser, where it is evaporated at low pressure PET and temperature TETby the condensation heat from the MCRM. The vapor is finally entrained by the ejector, thus completing the exhaust heat-driven ejector cooling cycle. The resulting cooling effect QETis used to provide rejection of condensation heat from cascade condenser.

3.

Analysis of ejector design and ejector

cooling cycle performance

The supersonic ejector is the key component in the ejector cooling cycle. It is a simple jet device which is used in the ejector cycle for suction, compression, and discharge of the secondary vapor by force of the primary vapor.

Fig. 1e Diagram of micro-trigeneration system

incorporating a CHP system and a cascade refrigeration cycle.

Fig. 2e Cascade CO2sub-critical mechanical compression/ R600 ejector cooling cycle in lgP-h diagram.

Fig. 3illustrates the structure of supersonic ejectors with cylindrical (a) and conicalecylindrical (b) mixing chambers. The ejector assembly can be divided into four main parts: a nozzle, a suction chamber, a mixing chamber, and a diffuser. Operating conditions of the ejector are specified by oper-ating pressures PET, Pc, Pg, expansion pressure ratio E¼ Pg/PET and compression pressure ratio C¼ Pc/PET.

The performance of the ejector is measured by its entrainment ratio u which is the ratio between the secondary and the primary fluid mass flow rates _msand _mp, as shown in the following equation:

u ¼ _ms _mp

(1) The design of the ejector flow profile with a cylindrical mixing chamber is determined by the area ratio a which is defined as the cross-section area of the cylindrical mixing section A3divided by that of the primary nozzle throat area At, which can be found from Eq.(2):

a ¼A3 At

(2) The design of a conicalecylindrical mixing chamber is specified by area ratio a, converging angle g at mixing chamber entrance, and the area ratio b, which is defined as the entrance area A2of the conical part of mixing chamber divided by that of the cross-section area A3, as shown in Eq.(3): b ¼A2

A3

(3) Construction, geometry and surface condition of super-sonic ejector flow profile must provide the most effective utilization of primary flow energy for suction, compression, and discharge of the secondary vapor (Petrenko, 1978; Huang et al., 1999; Eames et al., 2004, 2007; Petrenko et al., 2005a, 2005b).

On the basis on the improved 1-D model of ejector, design area ratio a and the optimum value of b can be found with

application of variational calculation (Huang et al., 1999). The value of bopt corresponds to the maximum of entrainment ratio u. Supplementary data for the determination of the a, bopt and optimal converging angle g are given in Petrenko (1978)andPetrenko et al. (2005a).

Theoretical and experimental investigations of supersonic ejectors with conicalecylindrical and cylindrical mixing chambers operating with various refrigerants demonstrate convincingly that the application of conicalecylindrical mix-ing chambers at the same operatmix-ing conditions causes an improvement up to 25e35% in u compared with cylindrical mixing chambers. The primary cause of this improvement is decreasing of the irreversibilities of gas-dynamic processes, which occur in the mixing chamber of the supersonic ejector. The advantage of ejectors with optimal design of con-icalecylindrical mixing chambers is especially revealed at high critical condensing temperatures Tc (Petrenko, 1978; Petrenko et al., 2005a, 2005b).

The performance of the ECM is usually measured by a single COP, which is the ratio of the useful cooling effect produced in the evaporator over the gross energy input into the ejector cycle required to produce the cooling effect. But it should be taken into account that the ECM commonly utilizes a mechanical feed pump, and, consequently, an input of some amount of mechanical power _Wmechin addition to a low-grade thermal energy Qg.

However, in spite of the fact that the mechanical power _

Wmech, consumed by the feed pump is very small compared to the thermal energy Qg input to the generator to actuate ejector, it may not be omitted (Petrenko, 2001).

Therefore, from both thermodynamic and economic points of view, the efficiency of the topping ECM cycle can be correctly characterized by using separately both thermal COPthermand actual specific power consumption of mechan-ical feed pump _wmech. The value of COPthermis defined as the cooling load at the cascade condenser QET divided by the thermal energy Qg, and the value of _wmechis the ratio between the mechanical power _Wmechand the cooling effect QET. They can be expressed as Eqs.(4) and (5):

COPtherm¼ QET Qg ¼ _msqET _mpqg ¼ u qET qg (4) _wmech¼ _ Wmech QET ¼ _mpv5 Pg Pc
hpump_msqET ¼ v5 Pg Pc
hpumpu qET (5) where v5and hpumpare specific volume of intake refrigerant and feed pump coefficient of efficiency, respectively; (Pg Pc) is the generating and condensing pressure difference, kPa.

It should be observed that the electrically driven feed pump is the only component in the ejector cycle which has moving parts and therefore determines the reliability, leakproofness, and lifetime of the whole system. Instead of using the conventional electrically driven feed pumps for ECMs oper-ating with flammable refrigerants such as butane, utilization of hermetic float-type thermo-gravity feeders which are designed for application in various small capacity ejector systems is very attractive (Petrenko et al., 2005b).

From the steady energy balance for the ECM using the numbering in Figs. 1 and 2, the cooling load at the cascade condenser QET, the heat load at the generator Qg, the heat load Fig. 3e Structure of supersonic ejectors with cylindrical (a)

at the condenser Qcand the actual power consumption of mechanical feed pump _Wmechcan be expressed as Eqs.(6)e(9):

QET¼ QCB¼ ðh13 h12Þ _ms (6) Qg¼ ðh6 h11Þ _mp (7) Qs¼ QETþ Qg¼ ðh9 h10Þ _msþ _mp
(8) _ Wmech¼ _mpv5 Pg Pc
hpump (9) where h13and h12, h6and h11, h10and h9are the outlet and inlet refrigerant enthalpies at the cascade condenser, at the generator and at the condenser, respectively.

4.

Analysis of CO

sub-critical compression

refrigeration cycle

Analysis of CO2sub-critical mechanical compression refrigera-tion cycle is described as follows. From the steady energy balance for the MCRM and using the numbering inFigs. 1 and 2, a specific cooling capacity qe, a specific condensing heat qCBand a specific isentropic compressor work lcs may be computed by Eqs. (10)e(12):

qe¼ h5 h4 (10)

qCB¼ h2 h3 (11)

lcs¼ h2s h1 (12)

where h5and h4, h3and h2, h2sand h1are the outlet and inlet refrigerant enthalpies at the evaporator, at the cascade condenser and at the compressor, respectively.

Actual specific work of the compressor is defined as follows:

lC¼ h2 h1¼ ðh2s h1Þ=hcs (13)

where hcsis the isentropic efficiency of the compressor.

And the enthalpy of the outlet of the compressor can be expressed as Eq.(14):

h2¼ h1þ h2s h1

hcs

(14) For the chosen semi-hermetic CO2type compressor hcscan be written as the function of the ratio of compressor discharge and suction pressures r¼ PCB/Pe. The correlation obtained by best fitting the experimental data for CO2sub-critical refrig-eration cycle (Neksa et al., 2001; Lee et al., 2006) has the following form:

hcs¼ 0:8981  0:09238 r þ 0:00476 r2 (15)

The CO2cycle coefficient of performance is defined as the specific cooling effect at the evaporator qe, divided by the actual specific compressor work lC, as shown in Eq.(16): COPBC¼ qe lC¼ h5 h4 h2 h1 (16) R600 TET = 14 o C PET = 1.71 bar 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 28 30 32 34 36 38 40 Condensing temperature Tc, o C 1 - Tg = 80 o C 2 - Tg = 100 o C 3 - Tg = 120 o C 4 - Tg = 140 o C oit ar t ne m ni ar t n E 1 2 3 4

Fig. 4e Variation of u with Tcat different Tgfor TET[ 14C.

R600 TET = 14 o C PET = 1.71 bar 0.2 0.4 0.6 0.8 1.0 1.2 28 30 32 34 36 38 40 Condensing temperature Tc, o C 1 - Tg = 80 o C 2 - Tg = 100 o C 3 - Tg = 120 o C 4 - Tg = 140 o C P O C ec n a mr of re p f o t ne ic if fe o C m r e ht 1 2 3 4

Fig. 5e Variation of COPthermwith Tcat different Tgfor TET[ 14C. R600 TET = 14 o C PET = 1.71 bar 0 5 10 15 20 25 30 35 28 30 32 34 36 38 40 Condensing temperature Tc, o C 1 - Tg = 80 o C 2 - Tg = 100 o C 3 - Tg = 120 o C 4 - Tg = 140 o C oit ar ae r A α A = 3 A/t 1 2 3 4

Fig. 6e Variation of a [ A3/Atwith Tcat different Tgfor TET[ 14C.

The values of the refrigeration output of the compression cycle Qe, the compressor power consumption _WC, and the heat load at the cascade condenser QCBare found respectively from Eqs.(17)e(19):

Qe¼ qe_m (17)

_

WC¼ lC_m (18)

QCB¼ qCB_m (19)

where _m is the mass flow rate of carbon dioxide in the bot-toming cycle.

Internal superheating caused by the semi-hermetic compressor motor can be calculated from Eq.(20):

DTsup¼ T1 T5¼ 1 cpðh2 h1Þ  1 hm 1  (20) where cpis constant pressure specific heat of carbon dioxide, hmis the coefficient of efficiency of the motor.

All the calculations were performed using the REFPROP 8.0 (Lemmon et al., 2007).

5.

Results and discussions

In order to predict the ejector and ECM performance, a computer simulation program based on the improved 1-D model of the ejector has been used. This program calculates the performance of the ejector and ESM at critical-mode operating conditions and provides optimum design data for the ejector system (Huang et al., 1999; Petrenko et al., 2005a). The model validation against the refrigerants R141b, R236fa and R245fa experimental data has shown very good agree-ment under the wide ranges of design and off-design oper-ating conditions (Huang et al., 1999; Eames et al., 2004, 2007). The program has been used for the theoretical study of the topping ejector cycle and supersonic ejector with con-icalecylindrical mixing chambers, operating with butane. For the present study the ejector and the ESM were investigated

R744 Qe= 10 kW TCB = 20 oC 0 5 10 15 20 25 -40 -30 -20 -10 0 Evaporating temperature Te,oC 1 - QCB 2 - WC 1 2 Q d a ol t a e h g ni s n e d n o C B C W r e w o p r os s e r p m o c , C W k ,

Fig. 9e Variation of QCBand _WCwith Tefor Qe[ 10 kW at TCB[ 20C. R744 Qe=10 kW TCB = 20 oC 1 2 3 4 5 6 7 -40 -30 -20 -10 0 o Evaporating temperature Te, C P O C e c n a m r of r e p f o t n ei ci ff e o C C B

Fig. 10e Variation of COPBCwith Tefor Qe[ 10 kW at TCB[ 20C. R600 TET = 14 o C PET = 1.71 bar 0.05 0.15 0.25 0.35 0.45 0.55 28 30 32 34 36 38 40 Condensing temperature Tc, o C 1 - Tg = 80 o C 2 - Tg = 100 o C 3 - Tg = 120 o C 4 - Tg = 140 o C kr o w p m u p de ef cif ic e ps l a ut c A w h c e m W k W k , 1-1 2 3 4

Fig. 8e Variation of _wmechwith Tcat different Tgfor TET[ 14C andhpump[ 0.5. R600 TET = 14 o C PET = 1.71 bar 1.0 1.1 1.2 1.3 1.4 28 30 32 34 36 38 40 Condensing temperature Tc, o C 1 - Tg = 80 o C 2 - Tg = 100 o C 3 - Tg = 120 o C 4 - Tg = 140 o C oit ar ae r a l a mit p O t p o A = 2 A/3 1 2 3 4

Fig. 7e Variation of optimal area ratio bopt[ A2/A3with Tc at different Tgfor TET[ 14C.

over wide ranges of critical condensing temperatures Tc¼ 28e40C, and generating temperatures Tgof 80, 100, 120, 140C at the fixed evaporating temperature TET¼ 14C for application in the topping cycle of the cascade system.

The results of the theoretical study presented inFigs. 4e13 are obtained for design critical-mode operating conditions. Figs. 4e8illustrate the variations of u, COPtherm, A3/At, A2/A3 and _wmechwith Tcat different Tgfor Te¼ 14C and ejectors with optimal value of bopt¼ A2/A3. Referring toFigs. 4e6the characteristics of u, COPtherm, and A3/Athave the same trend, and they increase with decreasing Tcand increasing Tg. It can be seen fromFig. 7that boptincreases with increasing of Tcand Tg. Fig. 8 shows that actual specific power consumption of mechanical feed pump _wmech decreases with decreasing Tc and Tg.

The CO2 sub-critical cycle at the presented stage of the design-theoretical study has been investigated with fixed cooling capacity Qe¼ 10 kW and fixed condensing tempera-ture TCB ¼ 20 C with specified temperature difference

DT ¼ TCB TET¼ 6C in the CO2/R600 cascade condenser. The evaporating temperatures Teused in the parametric study are taken in the range from40_{C to 0}_{C with assumed internal} superheating in semi-hermetic compressorDTsupof 10C.

R600 Qe = 10 kW TCB = 20 oC TET = 14 oC TC = 36 oC Tg = 120 oC 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 -40 -30 -20 -10 0 Evaporating temperature Te,oC m et a r w ol f y r a d n o c e S s,m et a r w ol f y r a mi r p p s g k , 1-2 1 1 - mS 2 - mP

Fig. 12e Variation of _msand _mpwith Tefor Qe[ 10 kW at TCB[ 20C, TET[ 14C, Tc[ 36C, Tg[ 120C. R600 Qe = 10 kW TCB = 20 oC TET = 14 oC TC = 36 oC Tg = 120 oC 0 20 40 60 80 100 120 140 -40 -30 -20 -10 0 Evaporating temperature Te,oC A s a e r A t A d n a 3 ,m m 2 2 1 1 - At 2 - A3

Fig. 13e Variation of Atand A3with Tefor Qe[ 10 kW at TCB[ 20C, TET[ 14C, Tc[ 36C, Tg[ 120C.

Table 1e Design performance specification of CO2e R600

cascade cooling machine.

Parameter Value

Bottoming cycle (R744)

Cooling capacity, Qe 10 kW

Evaporating temperature, Te 20C

Evaporating pressure, Pe 19.7 bar

Compressor power input, _WC 4.07 kW

Superheating capacity in motor, Qsup 0.68 kW

Condensing heat load, QCB 14.75 kW

Condensing temperature, TCB 20C

Condensing pressure, PCB 57.3 bar

Compressor type semi-hermetic

Compressor isentropic efficiency, hcs 0.67

Design COPBC¼ Qe/ _WC 2.46

Topping cycle (R600)

Cooling capacity, QET¼ QCB 14.75 kW

Evaporating temperature, TET 14C

Evaporating pressure, PET 1.71 bar

Condensing heat load, Qs 40.65 kW

Condensing temperature, Tc 36C

Condensing pressure, Pc 3.4 bar

Generating heat load, Qg 29.5 kW

Generating temperature, Tg 120C

Generating pressure, Pg 22.1 bar

Entrainment ratio, u¼ _ms= _mp 0.81

Design COPtherm¼ QET/Qg 0.57

Pressure difference, PgPc 18.7 bar

Actual power consumption of feed pump, _Wmech

0.38 kW Actual specific power consumption

of feed pump, _wmech

0.026 kW kW1 Feed pump coefficient of efficiency, hpump 0.5

Design area ratio a¼ A3/At 10.9

Design optimal area ratio bopt¼ A2/A3 1.19 R600 Qe = 10 kW TCB = 20 oC TET = 14 oC TC= 36 oC Tg = 120 oC 10 15 20 25 30 35 40 45 50 55 60 65 -40 -30 -20 -10 0 Evaporating temperature Te,oC Q yt i c a p a c g ni l o o C T E Q = B C , g Q d a ol t a e h g ni t a r e n e g , Q d a ol t a e h g ni s n e d n o c C W k , 1 - QET 2 - Qg 3 - QC 3 2 1

Fig. 11e Variation of QET, Qcand Qgwith Tefor Qe[ 10 kW at TCB[ 20C, TET[ 14C, Tc[ 36C, Tg[ 120C.

Fig. 9shows the variations of QCBand _WCwith Teof MCRM for Qe¼ 10 kW at TCB¼ 20C. As seen inFig. 9both of QCBand

_

WCare decreasing with increasing Te.

Fig. 10 illustrates the variations of COPBC with Te for Qe¼ 10 kW at TCB¼ 20C. The results shown in this figure illustrate that increase in Teresults in a rising in the COPBCof bottoming cycle. It is obvious that the COPBCincreases from 1.3 to 6.4 when the Tevaries from40C to 0C.

Figs. 11e13 show the influence of the evaporating

temperature Teon the heat loads QET, Qg, Qc, mass flow rates _msand _mpof the ECM cycle, areas Atand A3of ejector withbopt for Qe¼ 10 kW at TCB¼ 20C, TET¼ 14C, Tc¼ 36C, Tg¼ 120C. FromFigs. 11e13 it is seen that Te not only affects the bottoming MCRM CO2cycle but also the topping ECM cycle operating with butane.

Referring toFigs. 11 and 12the heat loads QET, Qg, Qcand mass flow rates _msand _mphave the same trend, notably they are decreasing with the increasing in Te.

Fig. 13shows that Atreduces very slowly almost linearly with increasing Te, while A3falls more rapidly.

On the basis of the obtained results a pilot cascade CO2 sub-critical mechanical compression/butane ejector refriger-ating unit with design performance characteristics listed in Table 1 is developed. This small-scale refrigerating unit is designed for application in micro-trigeneration systems incorporating reciprocating internal combustion engines and gas micro-turbines.

6.

Conclusions

In this paper an innovative micro-trigeneration system, composed of a cogeneration system and a cascade refrigera-tion cycle, is proposed. The cogenerarefrigera-tion system is a combined heat and power system for electricity generation and heat production. The cascade refrigeration cycle is the combination of a mechanical compression refrigerating machine, operating with CO2, and an ejector cooling machine, driven by waste heat and using butane as the working fluid.

According to theoretical study for the design of small-scale cascade CO2e R600 refrigerating unit powered by CHP system, the most important findings are as follows.

(1) Effect of the cascade cycle operating conditions on ECM and MCRM cycles performance characteristics is studied and optimal geometry of the ejector is determined. It is defined that for Qe¼ 10 kW at TCB¼ 20C, increase in Te results in a rising in the COPBCof bottoming cycle. COPBC increases from 1.3 to 6.4 when the Tevaries from40C to 0C.

(2) The obtained data provide necessary information to design a pilot small-scale CO2e R600 cascade refrigerating unit with cooling capacity of 10 kW for application in micro-trigeneration systems.

(3) The proposed micro-trigeneration system is environmen-tally friendly, energy-saving and potentially high perfor-mance and cost-beneficial installation that consolidates the advantages of both ECM and MCRM cycles.

Acknowledgements

This publication is based on the work supported by Award No. KUK-C1-014-12, made by King Abdullah University of Science and Technology (KAUST), Saudi Arabia.

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