ejector cooler

Applied Thermal EngineeringVol. 18, Nos 3-4, pp. 93 101, 1998

Pergamon

PII: S1359-4311(97)00053-7

A NOVEL

HEAT

PIPE/EJECTOR

¢~" 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-4311/98 $19.00 + 0.00

COOLER

S. B. Riffat and A. Holt Institute of Building Technology, University of Nottingham, Nottingham NG7 2RD, UK

(Received 2 June 1997) Abstract--This paper describes the computer modelling of a novel heat pipe/ejector cooling system. The effects of the operating conditions, using different working fluids and employing multi-ejector systems, has been investigated. It has been shown that C.O.P.s of around 0.7 are achievable providing that the cold sink is at a low enough temperature and the condenser correctly designed. Enhancement of the C.O.P. could be achieved using alternative natural refrigerants and multi-ejector systems. ~ 1997 Elsevier Science Ltd. All rights reserved Keywords--Heat pipe, cooling, heat pump, solar energy, hybrid.

NOMENCLATURE C.O.P. Coefficient of performance (cooling) Q,, Evaporator cooling load Condenser load P,. Generator heading load O~ M Mach number. The velocity of the fluid relative to the velocity of sound in that medium T Temperature P Pressure Isentropic efficiency of the primary nozzle Oo Isentropic efficiency of the diffuser Od k Ratio of the specific heats Cp and C~

T,/ Tp Subscripts s p I 2 3 4

Secondary/evaporator stream Primary/generator stream Plane at the exit of the nozzle Upstream of shock wave Downstream of shock wave Exit of the diffuser

INTRODUCTION

Air-conditioning and refrigeration are usually carried out using vapour compression systems which are powered by mains electricity generated by large plants. Current technology limits these power stations to a maximum efficiency of 45%. The electricity is then transported via the national grid and eventually arrives at the point of use. There is only about 40% of the original energy left at this point. This means that vast quantities of fossil fuels are burnt with unwanted pollutants (e.g. CO2, NOx) entering the atmosphere. The coefficient of performance of vapourcompression systems is low when the inefficiencies of electrical power generation are taken into account.

In order to minimise emissions of pollutants, it is possible to use renewable energy sources such as solar energy to drive air-conditioning and refrigeration plants. This reduces the environmental impact and offers savings in running costs to users. There will be increasing pressure to use renewable energy sources and it is in the immediate interest of the UK to identify and develop technologies which can harness these sources to reduce our dependence on fossil fuel combustion. The application of solar energy to generate electricity to drive air-conditioning and refrigeration systems is not new. McNelis [1] and Naylor [2] have reported the development of 93

94

s.B. Riffat and A. Holt

air-conditioning and refrigeration units driven by photovoltaics. Most recently, Underwood [3] has considered utilisation of power by heating, ventilation and air-conditioning (HVAC) plants from photovoltaic cladding on buildings. However, the problems with photovoltaic technology are relatively low efficiency and high capital cost and, as solar energy is not always available, some means must be incorporated to store surplus electricity and release it again when it is needed. Solar radiation concentrators and flat plate collectors have also been used to drive absorption systems to provide air-conditioning and refrigeration. The main problem with absorption systems is that they are more bulky than conventional vapour-compression systems. This is because an absorption chiller has more components, and as the heat and mass transfer of absorption equipment (i.e. generator and absorber) is poor, a large surface area is required. The high capital cost of absorption systems and solar collectors makes them uneconomic in many situations. This paper describes a novel heat pipe/ejector system for building cooling and heating [4]. The system utilises solar energy or hybrid sources (e.g. solar/gas) and so reduces the demand for electricity and thus fossil fuel consumption. By consuming less fuel, the proposed system would reduce emissions of gases such as carbon dioxide, sulphur dioxide and methane to the atmosphere. The heat pipe/ejector system has no moving parts, and so is simple and reliable. It has the potential of long life and, unlike vapour-compression systems, produces no noise or vibration. The anticipated cost of production of the proposed system is low, since inexpensive construction materials (e.g. copper or aluminium) could be used. The heat pipe/ejector system uses refrigerants such as water, methanol or ethanol as the working fluid. These refrigerants have no potential to deplete the ozone layer and are not greenhouse gases.

D E S C R I P T I O N OF THE HEAT PIPE/EJECTOR COOLER

Background The proposed system is based on the combination of a heat pipe with an ejector nozzle unit. The principle and operation of the heat pipe and ejector nozzle are briefly described here. Heat pipes are devices with high thermal conductance and may consist of a sealed tube provided with an internal wick (e.g. stainless steel mesh or sintered metal powder) normally as a concentric lining to the tube (Fig. 1). The tube is charged with a refrigerant. In operation, heat applied to one end of the pipe causes the liquid refrigerant to evaporate and the resulting vapour travels to the 'cool' end where it condenses, surrendering energy. The liquid refrigerant returns through the wick by capillary action to the 'hot' end. Other methods of condensate return include gravity, centripetal and osmotic forces. The operation of a heat pipe involves phase changes (i.e. condensation and evaporation) and so large amounts of heat can be transferred between the ends of the tube. In practice, the thermal conductance of a heat pipe may be over 500 times that of the best available thermal conductors. The concept of the heat pipe, material of construction, its performance and applications have been reviewed by Dunn and Reay [5]. Ejector units are used extensively to extract air or other gases from condensers and similar pressure vessels which operate below atmospheric pressure. An ejector unit consists of a primary nozzle and mixing tube-diffuser arranged coaxially in a housing (Fig. 2). High pressure driving fluid is supplied from the primary nozzle, the low pressure region is connected to the housing, and the intermediate pressure region is connected to the diffuser. High pressure fluid expands in the nozzle to approximately the pressure in the housing, and acquires a high velocity. The jet entrains and carries with it fluid from the housing. The mixture of driving and entrained fluids passes through the mixing tube into the diffuser. The heat pipe~ejector system The basic cycle of the heat pipe/ejector system is shown in Fig. 3. The system consists of a heat pipe, ejector nozzle, evaporator and expansion valve (or capillary tube). The ejector and evaporator could be positioned in the adiabatic section of the heat pipe. When heat is supplied to the generator section of the heat pipe, the working fluid (e.g. methanol) evaporates and flows

Heat pipe/ejectorcooler

95

~ 0

Q Heat out

Heat in

~:~a:l~'~

C ~lon~rd,n~e,s

0 Wol~.~ng_fluidretin'nedto

r

Evaporator

O Heat in

\

Sealed tube

Sinteredmetalpowder A ~ orstainlesssteelmeshw

Q Heat out

IWorkingfluid

evaporatesandmigrates ~

Evaporator

(~) Workingfluidreturned ~

~

condensa

to generatorby capillaryaction Condenser

Fig. 1. (a) Heatpipe usinggravitypumping.(b) Heat pipe usingwickpumping. to the ejector where it expands through the primary nozzle, thereby entraining low-pressure refrigerant from the evaporator section producing a refrigeration effect. The ejector exhaust is discharged into the condenser section of the heat pipe where heat is removed using air or water. From the condenser, some of the liquid refrigerant is returned to the generator by the wick action, while the remainder is expanded through the expansion valve (or capillary tube) to the evaporator. If air is used as a heat source/sink, fins can be used in the generator, evaporator and condenser sections to increase the heat transfer surface area. Integration of the heat pipe with an ejector nozzle will result in a compact and high performance system. The proposed system could be driven by solar energy. In this case, the generator section of the heat pipe would consist of an evacuated tube. Alternatively, hybrid solar/gas energy sources (Fig. 4) could be used to drive the system. The gas burner would be used when solar energy is unavailable. The hybrid system has the following advantages: • • • • •

Lower running costs; Gas-fired back-up in periods of low solar radiation; Higher efficiency compared to solar heating alone due to higher generator temperature; Reduced capital cost compared to systems using solar energy alone; Combined gas and solar system would alleviate the reluctance of some potential customers to convert to renewable energy systems by providing security of energy supply;

96

S.B. Riffatand A. Holt

~mtm/

Pc

Stream

/ Diffuser

/ Mixing

Region

H V

..

tr/! I

./I I I/

1

Secondary Slrearn Fig. 2. Schematicviewof an ejector. • Minimal environmental impact--A hybrid solar/gas system would have a high environmental image, since emissions of CO2 and NOx from a natural-gas fired system are substantially lower than those produced at cool or ail-fired power stations. The use of solar energy further reduces these emissions. The minimum evaporator temperature is limited to 0°C when water is used as the refrigerant. Use of alternative working fluids such as ethanol, methanol and ammonia would allow lower operating temperatures to be achieved. The heat pipe/ejector system could be driven by heat supplied to the generator at a temperature in the range 60-80°C, depending on the working fluid. Such operating temperatures could easily be achieved using evacuated tubes to power the generator. SYSTEM MODELLING A schematic showing an ejector is presented in Fig. 2. In operation, the primary 'high' pressure stream expands through a converging-diverging nozzle to produce a low pressure supersonic jet. This primary stream entrains vapour from the evaporator producing the required cooling effect. The two streams mix before a two-stage compression, firstly across a shock wave in the constant area chamber and secondly through the subsonic diffuser. The performance of the ejector can be expressed in two ways, i.e. the entrainment ratio, which is the mass flow ratio between the secondary and primary streams: Ms Rm - Mp

(1)

or the coefficient of performance, which is the ratio of the evaporator power to the generator power: C.O.P. = Q___L Qg

(2)

Equations relating the velocity and pressure at each section within the ejector have been developed, and an iterative procedure was carried out to estimate the performance of the ejector for given generator, evaporator and condenser pressures. Details of the equations and calculation procedures areas are as follows: Thermodynamic considerations and the application of the steady state flow equations for momentum energy and continuity allow for the development of the following equations which relate the velocity at certain points within the ejector to the pressure.

Heat pipe/ejector cooler

97 Qc

QG Condensate flow

\,

Wick Refrigerant

/

Expansion valve

Fins

QE Fig. 3. Heat pipe/ejector cooler.

Stream velocities/pressure at nozzle exit. It is assumed that the velocity of the primary and secondary streams are initially zero. The introduction of the isentropic efficiency allows for friction losses within the ejector nozzle,

p =

Mls=

--

-

l

(3)

-

1

(4)

Stream velocities/pressure upstream of shock wave. It is assumed that the secondary and primary streams mix at constant pressure in a section of the ejector where the cross-sectional area is constant. In this manner, the Mach number of the combined streams may be estimated as follows: * M l p + Rm Mls~C~ M2 = (1 + Rm)(1 + Rm •)

(5)

here • M

r

[ (k + 1) M 2 / 2 = V I + (k - 1) M 2 / 2

Stream velocities/pressure downstream of shock wave. If the velocity of the combined stream is supersonic, a normal shock wave will occur in the constant area chamber. The shock wave decelerates the flow to a subsonic level, producing a sudden compression. The Mach number of the fluid after the shock wave and the compression ratio is given in Equation 6 and (7) below. M 2 + 2 / ( k - 1) M3 = [ 2 k / ( k - 1)]M~ - 1

P3

I + kM~

e2-

l+kM

(6)

(7)

98

S.B. Riffat and A. Holt QG

J

Qc Condensate flow

Vapour ,. I---~._.... -'~ ~

Generator

,- Condenser

Evaporator Wick Gas burner Refrigerant

Fins

~

Expansion valve

Fins

QE Fig. 4. Hybrid solar/gas heat pipe/ejector cooler.

Pressure recovery through the diffuser. The vapour is further compressed in the subsonic diffuser in which it is assumed the exit velocity is zero. The pressure lift in the diffuser is given by Equation 8 P4 P3

(r/d(k2

k 1 ) M 32 + 1 ) k - 1

(8)

Calculation procedure. The equations given above allow for the calculation of the pressure at any point within the ejector and more importantly provide an estimate for the flow ratio, from which the C.O.P. can be estimated. The calculation procedure is as follows: 1. 2. 3. 4. 5. 6.

Guess pressure ratio between exit of the primary nozzle and the primary stream; Calculate Mlp and Mls from Equation 3 and (4); Guess value of M2; Calculate M3 from Equation 6; Calculate pressure lift across shock wave and diffuser from Equation 7 and (8), respectively; From Equation 7 and (3) calculate pressure ratio Pp/P4 and re-estimate value of M2 until this value matches the design value; 7. Calculate Rrn from Equation 5; 8. Re-estimate value of the pressure ratio between exit of the primary nozzle and the primary stream, and reiterate until a maximum value for Rm is obtained.

RESULTS AND DISCUSSION The solution for the equations given in Section 3 is presented graphically in Figs 5-7. It is worth noting that any point on a given curve represents a single ejector operated at its design conditions. Some indication of the performance of a given ejector for varying operating conditions is provided by the single thick black line. Observations on the predicted performance of the ejector refrigeration system include: 1. The analysis carried out indicates that the ejector refrigeration system can operate at temperatures and pressures which are achievable using low grade heat, such as solar energy and ambient air as the cooling medium. 2. C.O.P.s of approximately 0.5 are achievable using operating conditions which are practically achievable. The C.O.P. of the ejector refrigeration system is similar to that of absorption refrigeration systems, whilst still maintaining the benefits of significantly cheaper capital, maintenance and operating costs. Indeed, by using solar power and a wicked structure within the generator, the operating costs will be practically negligible.

99

Heat pipe/ejector cooler 1.0 -

~"~"".

0.8-

~'~. \x,... ~

~e

-......... -----

Water Methanol Ethanol

"~.-~... % ~'<".<.~.

0.6 -

Q~N,';..

0.2 / /

E ~ a t o r t e m p = 10°C Generat°r temp = 80°C

011

I

20

I

24

"~Q'"'" ...... "~,~ I

28

I

32

I

36

Condenser temperature

Fig. 5. C.O.P.

...... 40

(°C)

versus condenser temperature for a variety o f w o r k i n g fluids.

3. The C.O.P. increases with decreasing condenser temperature. The lowest condenser temperature is governed by the source temperature of the cooling medium. As a result of this characteristic, it is imperative that the condenser design is optimised in order to obtain maximum performance from the system. In this regard, it is noteworthy that compact heat exchangers can operate effectively with approach temperature differences of only 2-3°C. This feature allows the user to obtain the maximum benefits from both the heating and cooling media that are available. 4. Systems designed to operate with higher evaporator and generator temperatures have higher C.O.Ps. In the case of the latter it can be seen from Fig. 7 that the C.O.P. of a single ejector falls dramatically with increasing generator temperature. This comes as a result of an increased condenser temperature for a given evaporator temperature. Hence, it is wise to design the ejector for the maximum generator temperature achievable with the system. 5. The effect of using ethanol and methanol as alternative refrigerants was investigated. The C.O.P. for methanol is significantly higher than that for water. This trend is more marked at lower evaporator temperatures. Indeed, for condenser and evaporator temperatures of 35 and

07[

0.6

'.. 'X~-.... ~\~',. . . . . . . . . . . . ~ ~ . . -----

0.5 ,,. 0.4

Water Methanol Ethanol

' "i"-~'...

c5

~.........

¢")0.3

, Q.......

0.2

"x,'"-...

0.1 --

Evaporator

20

24

t e m ~ ~ " - - . . 28

Condenser temperature

Fig. 6. C.O.P.

32 (°C)

36

versus condenser temperature for a variety o f w o r k i n g fluids.

S.B. Riffat and A. Holt

100

'4I 1.2 '"...

\, ..... \ 1.0 X

__

"-... "~"'....

\ \

80oc

___ 90oc ........... 100°C '.,.

.....

•

©

-~"..... 0.60.4 -

"~"

• .....

~ 0.2

Methanol. evaporator temperature = 0

""-.... "~"

I

20

I

24

I

I

28

" .....

IO°C.

32

I

36

I

40

Condenser temperature (°C)

Fig. 7. C.O.P. versus condenser temperature for a variety of generator temperatures.

5°C, respectively, the increase is of the order of 70%. Furthermore, ethanol and methanol could be used to produce evaporator temperatures below 0°C. The drawback of using ethanol and methanol are increased cost and safety related matters associated with volatile organics. 6. The effects of using a train of ejectors in a manner similar to that shown in Figs 8 and 9 were investigated• As can be seen, the C.O.P. of the system can be significantly enhanced. In most cases, the optimum number of ejectors was 2. This effect was more pronounced as the condenser temperature increased and little enhancement was achieved for temperatures below 30°C. In this regard, the use of two ejectors could enhance the performance of air cooled condensers in which the condenser temperature would be of the order of 35°C.

CONCLUSIONS

A computer modelling of a passive cooling system has been carried out using water, methanol and ethanol working fluids. The C.O.P. of methanol was found to be higher than water and To condenser

Rom generator

°•°

From evaporator

Fig. 8. Arrangement for a series of multiple ejectors.

Heat pipe/ejector cooler

101

0.25 0.20

~" 0.15 O

Methanol

~........'"""'....................

rO 0.10 0.05

MethanoF.Condenser temp = ,35°(2 "~,~.., Water:Condenser temp =36°C Generator temp = 80°C I

2

~

I

4 6 No. of ejectors

I

8

I

10

Fig. 9. C.O.P. as a function of the number of ejectors connected in series for the given operating conditions. e t h a n o l . C.O,P.s o f a r o u n d 0.7 were o b t a i n e d using a passive c o o l e r with a single ejector unit a n d the C.O.P. c o u l d be further increased using a two ejector system. E x p e r i m e n t a l w o r k is currently u n d e r w a y to investigate the p e r f o r m a n c e o f different wick structures. Acknowledgements--This project is funded by the Engineering and Physical Sciences Research Council.

REFERENCES 1. B. McNelis, Photovoltaic refrigerator. In Solar Air-Conditioning and ReJ?igeration (Edited by A. A. M. Sayigh). Pergamon Press, pp. 268-289 (1992). 2. A. 1. Naylor, Photovoltaic air-conditioning system for Barbados. Sun at Work in Britain 15, 41-47 (1982). 3. C. P. Underwood, Scenarios for the utilisation of power by HVAC plant from photovoltaic cladding on buildings. CIBSE National Conference, Eastbourne, UK, pp. 118-126, 1-3 October (1995). 4. S. B. Riffat, International Patent PCT-GB96-00855, University of Nottingham. 5. P. D. Dunn and D. A. Reay, Heat Pipes. 2nd edition, Pergamon Press, Oxford (1978).