Design, testing and mathematical modelling of a small-scale CHP and cooling system (small CHP-ejector trigeneration)

Applied Thermal Engineering 27 (2007) 68–77 www.elsevier.com/locate/apthermeng

Design, testing and mathematical modelling of a small-scale CHP and cooling system (small CHP-ejector trigeneration) J. Godefroy *, R. Boukhanouf, S. Riffat Institute for Sustainable Energy Technologies, School of the Built Environment, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 17 September 2005; accepted 25 April 2006 Available online 10 July 2006

Abstract Trigeneration is the production of heat, cooling and power from one system. It can improve the financial and environmental benefits of combined heat and power (CHP) by using the heat output from the CHP unit to drive a cooling cycle, as demonstrated in existing large-scale installations. However, small-scale systems of a few kWe output present technological challenges. This paper presents the design and analysis of possible trigeneration systems based on a gas engine mini-CHP unit (5.5 kWe) and an ejector cooling cycle. Analysis shows that an overall efficiency around 50% could be achieved with systems designed for applications with simultaneous requirements for heat and cool. While using part of the CHP electrical output into the cooling cycle boosts the cooling capacity, it does not improve the overall efficiency and increases the CO2 emissions of the system. Emissions savings compared to traditional systems could be achieved with improvements of the heat transfer from CHP to cooling cycle. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Combined heat and power (CHP); Cooling; Ejector; Thermo-compressor; Keenan model; Trigeneration

1. Introduction Deregulation of the energy industry, concerns over the security of energy supplies, and the effect of CO2 emissions on climate change have generated a growing interest in energy efficient systems, and particularly in combined heat and power (CHP). CHP is one form of distributed power generation where a generating unit is placed at or near users’ facilities to supply both thermal and electrical needs. High efficiencies, typically between 80% and 90% [1], are achieved by eliminating the transmission and distribution losses associated with the conventional set-up of centralised power stations and grid network, as well as using the heat produced in the electricity generation process [1]. In the UK, CHP is promoted by financial incentives as part of the government’s strategy to cut energy consumption and CO2 emissions [2].

*

Corresponding author. Tel.: +44 115 84 67260; fax: +44 115 95 13159. E-mail address: [email protected] (J. Godefroy).

1359-4311/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.04.029

Large-scale CHP systems have been used for decades in district heating and industries, using gas and steam turbines and internal combustion (IC) engine systems from a few hundreds of kWe to MWe of power output. Recently, the interest in CHP has widened to encompass systems in the mini (up to a few kWe) and micro (below 1.5 kWe) scale providing heat and power to individual buildings. This has been partly driven by the consideration that energy consumption in the domestic sector accounts for about a third of the final energy consumption in the UK [3]. The technology is still under development, with IC engines, fuel cells and Stirling engines emerging as the main candidates [4]. The economic viability of a CHP system depends primarily on matching the thermal and electrical loads of a particular site with the heat and power outputs of the system, so that the CHP plant runs for a maximum number of hours per year. The availability of net metering and the possibility of exporting excess electricity are also important. In many applications however, it is not possible to utilise all the available heat at certain periods of the year as the demand for space heating is greatly reduced. As this

J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77

69

Nomenclature A CHP COP GCV GWP E h IC M m o.h. P PC* R Q T v W x c g x

carbon emission factor, kg CO2/kW h combined heat and power coefficient of performance gross calorific value, MJ/m3 global warming potential emissions, kg CO2/running hour flow enthalpy, kJ/kg internal combustion Mach number mass flow rate, kg/s operating hours pressure, bar critical condenser pressure, bar CO2 emissions ratio of conventional to trigeneration systems thermal capacity, kW temperature, °C flow velocity, m/s electrical output, kW by definition = QQtri CHP specific heat capacity ratio efficiency entrainment ratio

often coincides with periods of hot weather with a demand for air conditioning, the excess heat from the CHP unit can be used to operate a heat-driven cooling cycle. Trigeneration, or the production of cool, heat and power from one system, can then enhance the efficiency of CHP, and its potential benefits in terms of fuel and CO2 emissions savings have been analysed in several studies [5,6]. Trigeneration systems ranging from tens of kWe to several MWe have been operating in several sectors, for example in the food industry [7], and their use it set to spread with the development of packaged products [8]. In this range most systems rely on IC engines and gas turbines as prime movers, with micro-turbines also gaining in importance, and on absorption chillers as cooling cycles. Micro and small-scale systems are much less common although it has been shown that even fuel cell-based domestic CHP units, with a high power-to-heat ratio, would likely produce excess heat in the summer [9]. Reported research work used fuel cells and IC engines as prime movers, with absorption and ejector cycles, as well as reversible heat pumps, as cooling systems. These studies were, however, mostly based on simulation [9–12], with few experimental results [13]. One of the main technical challenges is to design an effective small-scale cooling cycle operating from a low-temperature heat source, allowing the whole trigeneration system to be economically viable. This paper presents the design and analysis of a small trigeneration unit, based on a commercially available gas engine Dachs CHP unit and an ejector cooling cycle. The

Subscripts B boiler BK back C condenser comp mechanical compression cycle conv conventional set-up corr Keenan ‘corrected’ model E evaporator e electrical ej ejector cycle G generator g gas gr national grid id Keenan ‘ideal’ model is isentropic max maximum allowable P primary S secondary t thermal tri trigeneration

performances of the CHP unit and of the ejector system are presented, along with simulation results and analysis of the complete trigeneration system. 2. The CHP system The performance characteristics of the CHP unit, particularly its thermal output, were analysed in order to assist the design of the heat-driven cooling cycle. 2.1. Installation Two Senertec Dachs mini-CHP units were installed to provide heat and power to a Research Centre and to be used as a research and teaching tool in building services engineering in the School of the Built Environment, University of Nottingham, UK. Each unit is rated at 5.5 kWe and 12.5 kWt, and uses a natural gas-fuelled spark-ignition reciprocating prime mover. The 578 cc single stroke fourcylinder engine drives a three-phase induction generator, while heat is recovered in the form of hot water from the generator, lubrification oil, engine jacket, and exhaust gas.1 The manufacturer’s specifications of the Dachs CHP unit are presented in Table 1. The two CHP units were installed as retrofit in the building, and act as the lead heating system. They were coupled 1 On the standard Dachs unit, no use is made of the latent heat from the exhaust.

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Table 1 Dachs CHP unit specifications and monitored steady-state performance

Electrical output (kW)a Thermal output (kW) Gross fuel input (kW) Electrical efficiency (%)

Manufacturer’s specifications

Monitored performance

5.5 gross 5.34 net 12.5 (83 °C at max 70 °C return) 22.8 24 gross 23.4 net 54.8 78.2 3500 >80,000 56 dB(A) at 1 m

5.62 gross 5.28 net 13.1 (82.7 °C at 61.8 °C return) 22.8b 24.6 gross 23.2 net 57.4 80.6

acquisition system. Monitored performance data is shown alongside manufacturer’s data in Table 1. Actual performance is very close to specifications, allowing the experimental ejector cycle to be designed to operate from a heat source around 83 °C. 3. The ejector cooling system

to the existing heating circuit via a flat-plate heat exchanger, with two 65 kW modulating condensing boilers firing if required. The operation of the CHP units is driven by heat demand, i.e., they switch on or off when the return water temperature is below 70 °C or above 73 °C, respectively. Their power output is fed to the local electricity distribution network through an interface panel following the G59 regulations. A simple layout of the integration of CHP in the building is shown in Fig. 1.

There are three main types of heat-driven cooling technologies: absorption, adsorption, and ejector cycles. In this research work the ejector cycle was chosen for its mechanical simplicity, absence of moving parts, and low costs of fabrication and maintenance [15,16]. The ejector cycle also has the advantage to offer a better performance than absorption cycles when operated from low-temperature heat sources [15,17,18], such as the heat from a domestic CHP system, which typically supplies heat at 80–85 °C. Recently, a number of research projects have investigated the integration of the ejector cooling cycle with various other low temperature heat sources, such as solar thermal collectors and fuel cells [13,19]. Selection of the refrigerant was carried out according to operational and environmental criteria such as toxicity, flammability, charge pressure, ozone depletion potential, and Global Warming Potential (GWP). Based on the above criteria, HFE 7100, HFC 236fa, and steam were selected as potentially suitable for this application.

2.2. Operating characteristics

3.1. Description of the cooling cycle

Measurement of water flow temperatures, gas consumption, and power generation is carried out using a data

An ejector cycle is a thermo-compressor cycle, in which the compression effect is achieved using a heat source coupled directly to the ejector to drive the refrigerant out of the evaporator and into the condenser. A schematic diagram of an ejector cooling system is given in Fig. 2, while the crosssection of the ejector is shown in Fig. 3. In the system represented in Fig. 2, the cooling cycle is driven by heat from the CHP unit supplied through a flat-plate heat exchanger to bring the refrigerant to its vapour state. An additional heater can be placed after the heat exchanger in order to bring the refrigerant vapour to a higher temperature. The vapour then passes through a separator to ensure there are no liquid droplets in the ejector, and enters the primary

Fig. 1. Integration of the Dachs units in the research centre.

Fig. 2. Schematic of a CHP-ejector system.

Thermal efficiency (%) Overall efficiency (%)c Maintenance intervals (o.h.) Operation life (o.h.) Noise a b c

Net output = Gross output  unit’s internal consumption. Based on GCV of gas in East Midlands of 39.4 MJ m3 [14]. Based on net electrical output.

J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77

PG Primary nozzle

Suction area

Mixing area

Constant-area section

Divergent diffuser

PBK

Secondary entrance PE

Fig. 3. Schematic of an ejector.

convergent–divergent nozzle of the ejector, where it reaches supersonic state. At the exit of the nozzle, the high-velocity fluid enters the mixing chamber, creating an area of low pressure at the secondary entrance of the ejector into which the fluid from the evaporator is entrained. The two fluids then mix completely before flowing through the constant section of the diffuser throat. If the back-pressure is low enough, the mixed flow undergoes through a shock an increase in static pressure and becomes subsonic. The divergent section of the diffuser then induces an additional pressure lift, and the fluid exits the ejector to flow into a condenser where it is turned into its liquid state. At the exit of the condenser, part of the fluid is directed into the generator (primary fluid) and the other part into the evaporator (secondary fluid) [20]. 3.2. Mathematical modelling of the ejector cycle Performance of the ejector is evaluated by the entrainment ratio (x), defined as ratio of the secondary to primary flow rates: x¼

mS mP

ð1Þ

The cooling capacity obtained at the evaporator is determined as follows: QE ¼ mS ðhE  hC Þ

ð2Þ

where hE and hC are the enthalpies of the refrigerant at the exit of the evaporator and condenser, assumed to be in the saturated vapour and liquid states, respectively. Similarly, the generator capacity can be expressed as: QG ¼ mP ðhG  hC Þ

ð3Þ

where hG is the enthalpy at the exit of the generator (evaluated in the saturated vapour state). The consumption of the pumps is usually negligible compared to the generator capacity (typically less than 1% of the generator heat input), and is therefore neglected [20–22]. The coefficient of performance (COPej) of the cycle is then calculated as the ratio of cooling capacity over generator capacity: COPej ¼

QE QG

ð4Þ

71

In order to select the refrigerant and design the components of the system, the ejector cycle was analysed using the Keenan model corrected by the introduction of efficiencies representing losses due to friction and mixing processes in the different parts of the ejector. The model has been widely used, and details can for example be found in Eames et al. [20]. However, this model can result in a significant error, mostly attributed to the assumption that refrigerants behave as ideal gases with a constant heat capacity ratio. A correction can be introduced by relying, up to the shock, on the fundamental principles of conservation of mass and momentum, whereby the velocities of the primary and secondary fluids are calculated using the tabulated values of the fluids’ properties. Details are given in Appendix. Both models were applied to ejector cycles working with HFE 7100 at a range of evaporator and generator pressures corresponding to the saturated temperature ranges [70– 130 °C] at the generator and [15–15 °C] at the evaporator, in order to find the maximum condenser pressure allowable to obtain COP values of 0.2 and 0.3. The results are compared in Figs. 4 and 5. Fig. 4 shows results in terms of the maximum saturated condenser temperatures allowable. As expected, the ideal model predicts a higher permissible condenser temperature than the corrected model, from which the operating conditions are shown to be more restrictive. The relationship between ideal and corrected temperatures is linear. It is also interesting to note that this relationship does not seem to depend on the target COP. If this was verified in further calculations over a wider range of COP values, it would allow to systematically derive corrected results from ideal ones, thereby saving considerable computing time as the ideal model is much simpler to compute. Fig. 5 compares the results from each model in terms of the pressure ratios allowable for COP values of 0.2 and 0.3. Both models predict that at fixed evaporator temperature, increasing the allowable condenser pressure can be obtained by increasing the generator pressure, or by lowering the value of the target COP. At a fixed ratio PG/PE, the ideal method predicts a higher maximum allowable condenser pressure than the corrected method. The difference between ideal and corrected models increases for higher PG/PE ratios. Indeed in this case the pressure range within the ejector increases and it becomes increasingly inaccurate to attribute a constant value to the heat capacity ratio c. Finally, both models were applied to predict the COP achievable under a variety of experimental conditions (same evaporator and generator temperature ranges as before, condenser temperatures between 20 and 40 °C). In Fig. 6 the error on the COP predicted by the ideal model, id COPcorr defined as COPCOP  100, is represented along the COP corr value from the corrected model. This error is positive since the ideal model produces results on the ‘optimistic’ side, but it decreases with increasing COP, to become negligible at high COP values. In the range of performance at which the cycle is likely to run, i.e., with COP values between 0.1

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J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77 40.0

35.0

TCMAX 'corrected', °C

30.0

25.0

20.0

15.0 COP = 0.3 10.0

COP = 0.2 COP = 0.3

5.0

COP = 0.2 0.0 0.00

5.00

10.00

15.00

20.00 TCMAX

25.00

30.00

35.00

40.00

'ideal', oC

Fig. 4. Ejector ideal/corrected models: maximum saturated condenser temperatures.

5 ideal, COP = 0.2 4.5 corrected, COP = 0.2

PCMAX/PE

4 ideal, COP = 0.3 3.5

corrected, COP = 0.3

3

2.5

2 0

50

100

150

200

250

300

350

PG/PE

Fig. 5. Ejector ideal/corrected models: maximum PC/PE allowable.

and 0.3, the error is between 7% and 30%, which is significant and therefore justifies using the corrected model. 3.3. Selection of the refrigerant In order to select the refrigerant used in the experimental rig, the corrected Keenan model was applied to HFE 7100, steam, and HFC 236fa in the temperature ranges [70– 110 °C] at the generator and [15 to 15 °C] at the evaporator. The analysis showed that steam could not be used, as it would require a considerable level of superheating before entering the ejector in order to avoid any droplets during

expansion in the primary nozzle. A comparison of the expected performance of the other fluids is presented in Fig. 7, which shows the interdependence of the pressure lifts PG/PE and PC/PE, at a COP around 0.23. The corresponding conditions required at the generator with each fluid for a condenser temperature between 28 and 32 °C and an evaporator temperature between 8 and 10 °C can be obtained from the relationships established on Fig. 7, and are shown in Table 2. Even at the least restrictive conditions (TE = 10 °C and TC = 28 °C), with HFC 236fa the required generator pressure is around 20 bars. Together with the fluid’s relatively high GWP and long atmospheric

J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77

73

90 80

Error COP ideal/corr, %

70 60 50 40 30 20 10 0 -10 0

0.2

0.1

0.3

0.4 0.5 COP corrected

0.6

0.7

0.8

Fig. 6. Ejector ideal/corrected models: error on the COP from the ideal method.

100 90 80 70

PG/PE

60 50 40 30 20 HFC 236fa

10

HFE 7100 0 1.5

1

2

2.5

3

3.5

4

PC/PE

Fig. 7. Pressure ratios at COP = 0.23 with HFE 7100 and HFC 236fa.

Table 2 Operating conditions for COP = 0.23 HFC 236fa Condenser and evaporator Required generator pressure Condenser–evaporator Required generator pressure

4. Results and discussion HFE 7100

TC = 32 °C, TE = 8 °C 37 bars 3.5 bars TC = 28 °C, TE = 10 °C 20 bars 1.4 bars

lifetime [23], these operating conditions contributed to dismiss this refrigerant. With HFE 7100 on the contrary the required pressures are acceptable, and this fluid was therefore selected for the experimental work.

4.1. Experimental results on the cooling cycle Experiments were carried out on the system presented in Fig. 2 with a 6 kW boiler operating at a setting of 83 °C, in order to simulate the temperature of the hot water from a Dachs CHP unit. With this heat source temperature, the generator saturated temperature obtainable reached 74.0 °C, and averaged 72.1 °C. Results can be summarised in Fig. 8, which shows the COP obtained at two generator temperatures against the maximum (or critical) condenser pressure. These results

74

J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77 0.3 o

TE 9 C o

0.25

TE 9 C o

TE 8 C

o

TE 8 C

COP

0.2

o

0.15

TE 6 C o

TE 5 C 0.1

o

TE 5 C

0.05 TG 71 TG 73 0 0.28

0.285

0.29

0.295

0.3

0.305

0.31

0.315

0.32

PC*

Fig. 8. Ejector cycle experimental results (83 °C hot water setting).

confirm reports in the literature that for a given ejector, at a given evaporation temperature, the critical condenser pressure increases with the saturated generator temperature, but the COP decreases. At a given generator saturated temperature, increasing the evaporator temperature allows both a higher COP and a higher condenser pressure [18,20]. Experimental results can also be compared with the corrected model. The model was applied at a series of operating conditions to predict the maximum critical pressure acceptable to obtain the experimental COP. Efficiency values used in the model are given in Appendix. For saturated generator temperatures between 71 and 73 °C, and evaporator temperatures between 8 and 9 °C, the error between model and experiments on the critical pressure was below 5%. The error at lower evaporator temperatures or higher generator temperatures increased, as the ejector then departed from its design conditions. The corrected Keenan model was therefore used for the simulation of possible trigeneration systems under a range of operating conditions, with the assumption that the system would operate near design conditions. 4.2. Trigeneration systems characteristics Having determined the operating characteristics of the CHP unit as well as a model predicting the performance achievable from an ejector cycle powered by a heat source at CHP output temperature, an investigation into possible combinations of the CHP and cooling cycle was carried out using the simulation software Trnsys. The target evaporator temperature of the trigeneration system was between 8 and 10 °C. As seen from the experimental results, if the only heat source available is the water from the CHP, a COP between 0.23 and 0.25 is then available at these evaporator temperatures, but would require a

maximum saturated condenser temperature of 28 °C. To ensure that the system will work under most conditions, the design conditions were set to 32 °C at the condenser and 10 °C at the evaporator. Performance with an ejector designed for these conditions was predicted by the model. Two parameters can then influence the performance and capacities of the overall trigeneration system: – The cooling system can be sized to either utilise all the heat available from the CHP, or to use only part of it, leaving some available for direct heating purposes. Cases were therefore considered where 5 kW of the CHP thermal output were kept for heating. – While experiments were carried out with a generator temperature around 70 °C, the trigeneration system could be designed for higher generator temperatures. This would allow higher condenser temperatures and/ or a higher COP. The possibility of diverting part of the electrical output from the CHP in order to boost the generator temperature was therefore considered. Other boosting devices could be used, but this option was for the moment chosen as it allows the system to work from the existing CHP product alone. Based on these parameters and target evaporator and condenser conditions, four trigeneration systems were examined, their characteristics being detailed in Table 3. The basic system (1) uses all the heat available from one CHP unit into the cooling cycle, without diverting part of the electrical output to boost the refrigerant generator pressure. We then assumed that a generator temperature of 70 °C was achievable. Systems 2, 3, and 4 represent variations of this system, where part of the CHP output is kept for heating purposes, and/or part of the electrical output is used to boost the generator temperature.

J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77

The efficiency of the trigeneration system can then be written as

Table 3 Comparison of four variants of trigeneration systems Systems

1

2

3

4

Gas input (GCV) (kW) Heat output (kW) Additional heat input to the cooling cycle (kW) Electrical output (net) (kW)

22.8 0 0

22.8 5 0

22.8 0 1

22.8 5 1

5.34

5.34

4.34

4.34

Generator temperature (°C) Ejector cooling COP Cooling output (kW)

70 0.135 1.68

70 0.135 1.01

84.3 0.202 2.72

93.5 0.236 2.01

Electrical efficiency (%) Heating efficiency (%) Cooling efficiency (%)

23.4 0 7.4

23.4 21.9 4.4

19.0 0 11.9

19.0 21.9 8.8

Overall efficiency (%)

30.8

49.8

31.0

49.8

gtri ¼ ¼

W tri þ xQCHP þ ð1  xÞQCHP COPej Qg

Etri ¼ Ag Qg

– The overall efficiency of the basic system (1) is low (around 30%). If however the system is designed to cover heating as well as cooling requirements, the overall efficiency increases significantly (by about 19 points). Designing such trigeneration systems for applications with simultaneous heating and cooling needs would therefore be preferable. – Using part of the electrical output to boost the generator temperature increases the cooling capacity by 62% between systems 1 and 3, and by 99% between systems 2 and 4. This is related to increased generator temperatures, which translate into respective increases in COP of 50% and 75%. However, this is balanced by a loss in the net electrical output, so the effect on the overall trigeneration efficiency is insignificant. 4.4. CO2 emissions analysis The two potential designs 2 and 4, which offer simultaneous heating and cooling, and are therefore more efficient than systems 1 and 3, can be compared with each other in terms of fuel consumption. We can follow the approach of Meunier [5] and define R as the ratio of the fuel consumption from a traditional (grid-boiler-vapour compression) set-up to the consumption of the proposed trigeneration systems. Notations Wtri, Qtri and C will refer to net electrical, heating and cooling capacities of the trigeneration systems. The subscript CHP will refer to characteristics of the CHP unit alone. The variable x is defined as ratio of thermal output from the trigeneration unit to total thermal output from the CHP unit: ð5Þ

ð6Þ

ð7Þ

And for the conventional system: Econv ¼ W tri Agr þ x 

Results of the simulation are shown in Table 3. The following observations can be made:

Qtri QCHP

W tri þ Qtri þ C Qg

With Qg the gross gas input. Emissions E of the systems are, for the trigeneration system:

4.3. Simulation results

x¼

75

QCHP Ag þ ð1  xÞ gB

COPej Q Agr COPcomp CHP

ð8Þ

With Agr and Ag the emissions factors of grid electricity and natural gas, gB the boiler efficiency and COPcomp the efficiency of the mechanical compression chiller. The ratio of emissions R ¼ EEconv is then tri R ¼ ge;tri

gt;CHP Agr COPej Agr þx þ ð1  xÞ g Ag gB COPcomp t;CHP Ag

ð9Þ

When the ratio R is above 1, the trigeneration system allows emissions savings, which will increase with increasing R. Eq. (9) shows that these savings will increase with the COP of the ejector cycle, but also with the ratio Agr/Ag, i.e., with the proportion of fossil fuels in the grid COPej Agr electricity generation mix. Unless g1B 6 COPcomp , savings Ag will also increase with the ratio x of trigeneration to CHP heating output: this will be the case with the current UK grid electricity generation mix. We can apply Eq. (9) to trigeneration systems 2 and 4, with gB = 0.9, Agr = 0.568 kg CO2/kW h and Ag = 0.194 kg CO2/kW h [24],2 and all other values from Table 3. The ratio R is then equal to 0.97 and 0.87, respectively, for systems 2 and 4. Although they have the same overall fuel efficiency based on their gas consumption, the systems then offer different environmental performances: with grid electricity being responsible for high emissions, displacing part of the CHP electrical output for the cooling cycle has an adverse effect on overall emissions. However, even system 2 would result in slightly increased emissions compared with a conventional set-up. The system would become beneficial only from a COP around 0.23, which may be achieved with better heat transfer from the CHP water to the refrigerant, and better heat transfer at the condenser allowing lower condensation temperatures. Another solution would be to use the heat available from the CHP exhaust gases to boost the temperature of the refrigerant. Research in still underway in these areas.

2

Value of grid emissions related to displaced electricity.

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J. Godefroy et al. / Applied Thermal Engineering 27 (2007) 68–77

5. Conclusions A cooling cycle designed to work from the heat output from a Dachs CHP unit has been tested, and validated by a model based on the Keenan analysis applied with real instead of ideal fluid properties. The model was then used in the simulation of several designs of trigeneration systems, with the quality and quantity of the heat input to the cooling cycle as parameters. Analysis shows that it would be highly beneficial to build systems for applications with simultaneous rather than separate requirements for heat and cool, as this will improve the overall efficiency of the system. While using part of the CHP electrical production into the cooling cycle boosts the cooling capacity, it does not improve the overall efficiency and actually results in higher CO2 emissions than from conventional systems. The most attractive system does not use part of the electrical production for the cooling cycle, and offers simultaneous heat and cool. It then offers an overall efficiency around 50% and would have an almost neutral effect on overall emissions. This performance could be improved by raising the efficiency of the cooling cycle, in particular by working at higher generator temperatures. In this context, future research should be conducted in improving the heat exchange with the CHP water, and in using the heat available in the exhaust gas from the CHP unit. Acknowledgements This work was supported by Baxi Technologies UK, the EPSRC and an INREB Faraday Partnership. Acknowledgements are also due to our colleague Dr Mark Worall, now in the Engineering department at the University of Aberdeen, UK, for his advice on the Keenan method. Appendix. Mathematical modelling (corrected Keenan method) This model differs from the ideal Keenan model up to the shock. The following table highlights the differences between each method. Ideal model

Corrected model

The primary fluid exits the primary nozzle at point 1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " c1 # u u 2g qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PG c P t M P1 ¼ 1 v ¼ 2gP ðhG  hP1;is Þ P 1 c1 P1 At point 1, the primary and secondary flows are at the same pressure but are not yet mixed. The properties of the secondary fluid at point 1 are then

Ideal model vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " c1 # u u 2g PE c S t M S1 ¼ 1 c1 P1

Corrected model qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vS1 ¼ 2gS ðhE  hS1;is Þ

The two flows then mix at constant pressure Velocity and Mach Velocity and number of the mixed Mach number flow are obtained from the of the mixed flow are continuity and momentum obtained from equations the continuity and momentum equations, as well as from the fluid’s tables Comparison ideal/corrected Keenan models Calculations are then similar to the ideal Keenan method, with the exception of the value of the heat capacity ratio c, calculated within a smaller range of pressures since it is only needed after the shock. Reducing the pressure range further improves the accuracy of the calculations. Efficiencies used were the following: Primary nozzle 0.8 Suction 0.95 Mixing 0.935 Diffuser 0.8

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