- Email: [email protected]
Comparison between open and closed solar thermal systems
Applied Energy 18 (1984) 83-88
Comparison Between Open and Closed Solar Thermal Systems Said M. A. Ibrahim* Mechanical Engineering Department, Faculty of Engineering, AI-Azhar University, Nasr City, Cairo (Egypt)
SUMMARY An equation has been derived to determine the di[]erence in the output hot water temperatures of open and closed solar systems. This temperature di[]'erence is mainly made up of two factors, the collector parameter and a heat exchanger parameter. Means oJ minimising this temperature penalty are discussed and analysed. The present results are important in the design o[solar thermal systems when heat exchangers are used.
INTRODUCTION A closed-circuit solar heating system is less efficient than an open-circuit one, because its collector is required to operate at a higher temperature. This is necessary because the heat exchanger in the storage tank is not efficient enough. In an open-circuit solar thermal system, hot water is obtained directly from the collector output. In a closed-circuit system, hot fluid in the collector loop is used to heat another fluid in the tank, and the hot water output from the system is discharged from another loop in the heat exchanger. Heat exchangers are used in solar thermal systems to isolate one fluid loop from another. There are three reasons for such isolation. These are: (1) to avoid contamination of one fluid loop by another, (2) to dispense with the purchase of large amounts of an expensive anti-freeze to fill the * Present address: United Arab Emirates University, Faculty of Engineering, Post Box 15551, AI-Ain (United Arab Emirates). 83
Applied Energy 0306-2619/84/$03.00 t" Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
84
Said M. A. Ibrahim
thermal store* and (3) to avoid the use of corrosion-proof materials in the collector if water is used. Although heat exchangers represent additional expense and complexity in a solar system, they are an economical, legal and thermodynamic necessity in many cases. The use of heat exchangers, however, is always accompanied by a temperature decrement and resultant loss in available energy. This results in lower solar system energy delivery. However, the papers of Brinkworth 1 and De Winter 2 are the only two exactly pertinent studies on this subject. Basing their studies on De Winter's work, Klein et al. 3 investigated the same problem. The results of all these authors are used to present a general detailed discussion on the subject in the works of Kreith and Kreider 4 and Lunde. 5 The problem of using heat exchangers in solar thermal systems is important and deserves further investigation. It is important to study the factors that may reduce and minimise the energy loss in a closed solar thermal system. This gave rise to the present study. We have compared the output hot water temperatures from closed and open solar thermal systems. In this investigation, an equation has been derived which will enable one to determine the difference between these hot water temperatures. The results are important in the design of systems which require the use of heat exchangers.
ANALYSIS Figure 1 represents the solar thermal system under investigation. The temperature rise in the flat-plate collector is represented by: T~o - T~i = [ q i , / g o - ( T ~ -
T~)] 1 - exp
(~c,]]
(1)
where Too is the fluid temperature at the collector outlet, T~i is the fluid temperature at the collector inlet, qi, is the rate of absorption of solar radiation by the collector plate, U o is the conductance between the collector plate and its surroundings, T , is the ambient temperature, Uc is the overall conductance between the fluid and its surroundings, A¢ is the collector area, the product (rhcp) c is the flow rate multiplied by the specific * If water is used in the collector, it might freeze during cold nights and damage the collector.
Comparison between open and closed solar thermal .~ystems
TCo~
Txop I Rt4iefVa(ve
Tank
rncp)c
.~e,~
(n~cp)x Heat Exchanger loop
coltector
loop
Tci
85
Hot wofer storage Tank
Txi
toad
T
--© pump
pump Fig. 1.
Schematic of the solar thermal system.
heat of the fluid at constant pressure in the collector loop and the subscript c refers to the collector. 6 If it is assumed that a steady state exists in the system and that heat losses from the connecting pipes may be neglected, it is clear that the temperature rise (Ted- Tci) in the collector is equal to the temperature drop in the heat exchanger. In the system shown in Fig. 1, the temperature of the fluid entering the collector, T,.i, is the temperature of the fluid at the outlet of the heat exchanger in the collector-heat exchanger flow circuit (neglecting thermal losses in piping). The thermal performance of the heat exchanger with constant effectiveness, e, is given by: 7 Qx = (rhcp)m,, e(T~o - Txi)
(2)
where (rhCp),,,i. is the minimum of either (thcp)~ or (rhcp) x (where subscript x refers to the heat exchanger loop) and Txi is the water temperature at the inlet to the heat exchanger loop. From heat transfer considerations:
Qx = (rhcp),,i, e(T~o- Txi ) = ( l ? l C p ) x ( T x o - Txi)
(3)
where T~o is the water temperature at the outlet from the heat exchanger loop. From eqn. (3): Ted- Txi _ (rnCp)x (4) T~o -- T~i (rhcp),.i. Solving eqn. (4) for Txo gives:
Txo = Txi + ( T c o - Txi ) (FhCp)min[d (rhcp)x
(5)
86
Said M. A. lhrahim
For brevity, eqn. (1) will be written in the form: (6)
TOo- TO, = A B
where:
A = q,./U o - ( To, - T,)
and
B= 1 -exp{
\
U
From eqns (5) and (6):
Txo = T~i + (AB + T~i -
Txi )
(rhCp)"i"e (mcpL
(7)
Equation (7) gives the outlet temperature at the exit from the heat exchanger loop. This is the final outlet hot water temperature in a closed solar thermal system. Equation (1), and its brief form (eqn. (6)) give the outlet fluid temperature, Tco, from the collector loop. In an open system the fluid flowing through the collector is water. T~o is the final outlet hot water temperature in an open solar heating system. The difference between TOo and Txo can be determined from eqns (6) and (7) as: F TOo - Txo = (AB + To, ) - ]Txi + (AB + TOi - T~i)(rhcp)"i" e l (m%)x d
= (AB + L i -
TO,i) 1
~
(8)
,I
Substituting for A and B in eqn. (8) gives:
(mo.)<)JJ (mcp),,,, e ) (m%)x
(9)
Equation (9) is mainly made up of two parameters, the collector parameter and the heat exchanger parameter. The collector parameter is:
{qi./Uo-(Toi-Ta)}{1-exp( U
Comparison between open and closed solar thermal systems
87
The heat exchanger parameter is: 1
(Fi~Cp)rain '~: (rh% )x
The temperature difference (T,, i - T~i), in eqn. (9) depends on the design of the whole system. Equation (9) gives the temperature penalty one has to pay when a heat exchanger is used. It is a temperature loss and hence an energy loss in the delivery of the system. DISCUSSION It is evident that (Too - Txo) is always positive. Because this temperature difference is a penalty in the case of a closed system, it is important to design the system such that (T,,o - Txo) is as small as possible. Of course, when this temperature difference is zero the conditions for an open system are attained. The means of making the temperature penalty (Tco - Txo) as small as possible are not, at first sight, clear. However, it is possible to establish some guidelines for the efficient design of a closed solar heating system. Equations (8) and (9) can serve this purpose. In order for (Too - Txo ) to be small, A B + T,. i - Txi should be small and 1 - [(rhcp),,i, ~/(rhcp)~] should be small. In the first of these conditions, there are factors such as qi, and Ta which one cannot do much to bring under control. For the collector parameter to be small: (i) ( T c i - Ta) should approach qi,/Uo; however, control over this condition may prove difficult to establish initially; (ii) exp[-(U,Aj(thcp)~)] should approach unity, which implies that U~A,./(mcp) c should be small; and (iii) T~i should be close to T,,~. When these three conditions are satisfied the collector parameter would be as small as possible. For the heat exchanger parameter to be as small as possible, the term (FhCp)mi n ,~:/(FhCp) x should be as close to unity as possible. This means that the heat exchanger effectiveness, ~;, should be large and that (rhcp),,~, and (rhcr) x must be nearly identical. In this context, a counterflow heat exchanger should be used for its high degree of effectiveness. The effectiveness depends strongly on the product, mcp, in the two loops of the system. It also depends on both the area and the overall heat transfer coefficient of the heat exchanger.
88
Said M. A. Ibrahim
In addition, to make both the collector and the heat exchanger parameters small, eqn. (8) suggests that the water temperature at the heat exchanger inlet, Txi, should be close to the fluid temperature at the collector inlet, Tci. The preceding discussion shows the importance of the effect of flow rates in both the collector and the heat exchanger loops of the system. It seems that the heat exchanger parameter may be easier to control by the designer. There are several terms contained in the collector parameter and these may be more difficult to handle.
REFERENCES 1. B. J. Brinkworth, Selection of design parameters for closed-circuit forced circulation solar heating systems, Solar Energy, 17 (1975), pp. 331-3. 2. F. De Winter, Heat exchanger penalties in double-loop solar water heating systems, Solar Energy, 17 (1975), pp. 335-7. 3. S. A. Klein, W. A. Beckman and J. A. Duffle, A design procedure for solar heating systems, Solar Energy, 18 (1976), pp. 113-27. 4. F. Kreith and J. F. Kreider, Principles of solar energy, McGraw-Hill, London, 1978. 5. P. J. Lunde, Solar thermal engineering, John Wiley, New York, 1980. 6. R. W. Bliss, The derivation of several plate efficiency factors useful in the design of flat-plate solar heat collectors, Solar Energy, 3(4), (1959), pp. 55-64. 7. W. M. Kays and A. L. London, Compact heat exchangers, McGraw-Hill, New York, 1958.
Comparison Between Open and Closed Solar Thermal Systems Said M. A. Ibrahim* Mechanical Engineering Department, Faculty of Engineering, AI-Azhar University, Nasr City, Cairo (Egypt)
SUMMARY An equation has been derived to determine the di[]erence in the output hot water temperatures of open and closed solar systems. This temperature di[]'erence is mainly made up of two factors, the collector parameter and a heat exchanger parameter. Means oJ minimising this temperature penalty are discussed and analysed. The present results are important in the design o[solar thermal systems when heat exchangers are used.
INTRODUCTION A closed-circuit solar heating system is less efficient than an open-circuit one, because its collector is required to operate at a higher temperature. This is necessary because the heat exchanger in the storage tank is not efficient enough. In an open-circuit solar thermal system, hot water is obtained directly from the collector output. In a closed-circuit system, hot fluid in the collector loop is used to heat another fluid in the tank, and the hot water output from the system is discharged from another loop in the heat exchanger. Heat exchangers are used in solar thermal systems to isolate one fluid loop from another. There are three reasons for such isolation. These are: (1) to avoid contamination of one fluid loop by another, (2) to dispense with the purchase of large amounts of an expensive anti-freeze to fill the * Present address: United Arab Emirates University, Faculty of Engineering, Post Box 15551, AI-Ain (United Arab Emirates). 83
Applied Energy 0306-2619/84/$03.00 t" Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
84
Said M. A. Ibrahim
thermal store* and (3) to avoid the use of corrosion-proof materials in the collector if water is used. Although heat exchangers represent additional expense and complexity in a solar system, they are an economical, legal and thermodynamic necessity in many cases. The use of heat exchangers, however, is always accompanied by a temperature decrement and resultant loss in available energy. This results in lower solar system energy delivery. However, the papers of Brinkworth 1 and De Winter 2 are the only two exactly pertinent studies on this subject. Basing their studies on De Winter's work, Klein et al. 3 investigated the same problem. The results of all these authors are used to present a general detailed discussion on the subject in the works of Kreith and Kreider 4 and Lunde. 5 The problem of using heat exchangers in solar thermal systems is important and deserves further investigation. It is important to study the factors that may reduce and minimise the energy loss in a closed solar thermal system. This gave rise to the present study. We have compared the output hot water temperatures from closed and open solar thermal systems. In this investigation, an equation has been derived which will enable one to determine the difference between these hot water temperatures. The results are important in the design of systems which require the use of heat exchangers.
ANALYSIS Figure 1 represents the solar thermal system under investigation. The temperature rise in the flat-plate collector is represented by: T~o - T~i = [ q i , / g o - ( T ~ -
T~)] 1 - exp
(~c,]]
(1)
where Too is the fluid temperature at the collector outlet, T~i is the fluid temperature at the collector inlet, qi, is the rate of absorption of solar radiation by the collector plate, U o is the conductance between the collector plate and its surroundings, T , is the ambient temperature, Uc is the overall conductance between the fluid and its surroundings, A¢ is the collector area, the product (rhcp) c is the flow rate multiplied by the specific * If water is used in the collector, it might freeze during cold nights and damage the collector.
Comparison between open and closed solar thermal .~ystems
TCo~
Txop I Rt4iefVa(ve
Tank
rncp)c
.~e,~
(n~cp)x Heat Exchanger loop
coltector
loop
Tci
85
Hot wofer storage Tank
Txi
toad
T
--© pump
pump Fig. 1.
Schematic of the solar thermal system.
heat of the fluid at constant pressure in the collector loop and the subscript c refers to the collector. 6 If it is assumed that a steady state exists in the system and that heat losses from the connecting pipes may be neglected, it is clear that the temperature rise (Ted- Tci) in the collector is equal to the temperature drop in the heat exchanger. In the system shown in Fig. 1, the temperature of the fluid entering the collector, T,.i, is the temperature of the fluid at the outlet of the heat exchanger in the collector-heat exchanger flow circuit (neglecting thermal losses in piping). The thermal performance of the heat exchanger with constant effectiveness, e, is given by: 7 Qx = (rhcp)m,, e(T~o - Txi)
(2)
where (rhCp),,,i. is the minimum of either (thcp)~ or (rhcp) x (where subscript x refers to the heat exchanger loop) and Txi is the water temperature at the inlet to the heat exchanger loop. From heat transfer considerations:
Qx = (rhcp),,i, e(T~o- Txi ) = ( l ? l C p ) x ( T x o - Txi)
(3)
where T~o is the water temperature at the outlet from the heat exchanger loop. From eqn. (3): Ted- Txi _ (rnCp)x (4) T~o -- T~i (rhcp),.i. Solving eqn. (4) for Txo gives:
Txo = Txi + ( T c o - Txi ) (FhCp)min[d (rhcp)x
(5)
86
Said M. A. lhrahim
For brevity, eqn. (1) will be written in the form: (6)
TOo- TO, = A B
where:
A = q,./U o - ( To, - T,)
and
B= 1 -exp{
\
U
From eqns (5) and (6):
Txo = T~i + (AB + T~i -
Txi )
(rhCp)"i"e (mcpL
(7)
Equation (7) gives the outlet temperature at the exit from the heat exchanger loop. This is the final outlet hot water temperature in a closed solar thermal system. Equation (1), and its brief form (eqn. (6)) give the outlet fluid temperature, Tco, from the collector loop. In an open system the fluid flowing through the collector is water. T~o is the final outlet hot water temperature in an open solar heating system. The difference between TOo and Txo can be determined from eqns (6) and (7) as: F TOo - Txo = (AB + To, ) - ]Txi + (AB + TOi - T~i)(rhcp)"i" e l (m%)x d
= (AB + L i -
TO,i) 1
~
(8)
,I
Substituting for A and B in eqn. (8) gives:
(mo.)<)JJ (mcp),,,, e ) (m%)x
(9)
Equation (9) is mainly made up of two parameters, the collector parameter and the heat exchanger parameter. The collector parameter is:
{qi./Uo-(Toi-Ta)}{1-exp( U
Comparison between open and closed solar thermal systems
87
The heat exchanger parameter is: 1
(Fi~Cp)rain '~: (rh% )x
The temperature difference (T,, i - T~i), in eqn. (9) depends on the design of the whole system. Equation (9) gives the temperature penalty one has to pay when a heat exchanger is used. It is a temperature loss and hence an energy loss in the delivery of the system. DISCUSSION It is evident that (Too - Txo) is always positive. Because this temperature difference is a penalty in the case of a closed system, it is important to design the system such that (T,,o - Txo) is as small as possible. Of course, when this temperature difference is zero the conditions for an open system are attained. The means of making the temperature penalty (Tco - Txo) as small as possible are not, at first sight, clear. However, it is possible to establish some guidelines for the efficient design of a closed solar heating system. Equations (8) and (9) can serve this purpose. In order for (Too - Txo ) to be small, A B + T,. i - Txi should be small and 1 - [(rhcp),,i, ~/(rhcp)~] should be small. In the first of these conditions, there are factors such as qi, and Ta which one cannot do much to bring under control. For the collector parameter to be small: (i) ( T c i - Ta) should approach qi,/Uo; however, control over this condition may prove difficult to establish initially; (ii) exp[-(U,Aj(thcp)~)] should approach unity, which implies that U~A,./(mcp) c should be small; and (iii) T~i should be close to T,,~. When these three conditions are satisfied the collector parameter would be as small as possible. For the heat exchanger parameter to be as small as possible, the term (FhCp)mi n ,~:/(FhCp) x should be as close to unity as possible. This means that the heat exchanger effectiveness, ~;, should be large and that (rhcp),,~, and (rhcr) x must be nearly identical. In this context, a counterflow heat exchanger should be used for its high degree of effectiveness. The effectiveness depends strongly on the product, mcp, in the two loops of the system. It also depends on both the area and the overall heat transfer coefficient of the heat exchanger.
88
Said M. A. Ibrahim
In addition, to make both the collector and the heat exchanger parameters small, eqn. (8) suggests that the water temperature at the heat exchanger inlet, Txi, should be close to the fluid temperature at the collector inlet, Tci. The preceding discussion shows the importance of the effect of flow rates in both the collector and the heat exchanger loops of the system. It seems that the heat exchanger parameter may be easier to control by the designer. There are several terms contained in the collector parameter and these may be more difficult to handle.
REFERENCES 1. B. J. Brinkworth, Selection of design parameters for closed-circuit forced circulation solar heating systems, Solar Energy, 17 (1975), pp. 331-3. 2. F. De Winter, Heat exchanger penalties in double-loop solar water heating systems, Solar Energy, 17 (1975), pp. 335-7. 3. S. A. Klein, W. A. Beckman and J. A. Duffle, A design procedure for solar heating systems, Solar Energy, 18 (1976), pp. 113-27. 4. F. Kreith and J. F. Kreider, Principles of solar energy, McGraw-Hill, London, 1978. 5. P. J. Lunde, Solar thermal engineering, John Wiley, New York, 1980. 6. R. W. Bliss, The derivation of several plate efficiency factors useful in the design of flat-plate solar heat collectors, Solar Energy, 3(4), (1959), pp. 55-64. 7. W. M. Kays and A. L. London, Compact heat exchangers, McGraw-Hill, New York, 1958.