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Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
Pergamon
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Solar Energy Vol. 67, Nos. 1–3, pp. 53–64, 1999 2000 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 0 0 ) 0 0 0 0 3 – 7 All rights reserved. Printed in Great Britain 0038-092X / 99 / $ - see front matter
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MANTLE HEAT EXCHANGERS FOR HORIZONTAL TANK THERMOSYPHON SOLAR WATER HEATERS GRAHAM L. MORRISON†, GARY ROSENGARTEN and MASUD BEHNIA Department of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia Received 2 September 1999; revised version accepted 12 November 1999 Communicated by BRIAN NORTON
Abstract—This paper describes the characteristics of horizontal mantle heat exchangers for application in thermosyphon solar water heaters. A new correlation for heat transfer in horizontal mantle heat exchangers with bottom entry and exit ports was used to predict the overall heat transfer and stratification conditions in horizontal tanks with mantle heat exchangers. The model of a mantle heat exchanger tank was combined with the thermosyphon solar collector loop model in TRNSYS to develop a model of a thermosyphon solar water heater with collector loop heat exchanger. Predictions of stratification conditions in a horizontal mantle tank are compared with transient charging tests in a laboratory test rig. Predictions of daily energy gain in solar preheaters and in systems with in-tank auxiliary boosters are compared with extensive outdoor measurements and the model is found to give reliable results for both daily and long-term performance analysis. 2000 Elsevier Science Ltd. All rights reserved.
for systems that provide hot water only in the evening. There have been numerous studies of the performance of closed loop thermosyphon systems based on tube heat exchangers inside vertical and horizontal storage tanks (Mertol et al., 1981; Webster et al., 1987). Tube heat exchangers can provide adequate heat transfer between the collector loop and the tank, however, tube heat exchangers for thermosyphon operation are difficult to construct. The heat exchanger configuration that has been widely adopted for horizontal tank thermosyphon systems is the mantle or annular concept shown in Fig. 1. A mantle heat exchanger is easy to
1. INTRODUCTION
The thermosyphon solar water heater is the principal product concept in most major solar water heater markets. Thermosyphon systems with open loop connection between the tank and the solar collector have been widely adopted for both low pressure and pressurised water supply systems in climates that do not experience freezing conditions. Without freeze protection these systems are limited to tropical climates or locations that never experience frost. Freeze protection in open loop thermosyphon systems can be provided by water dump valves, electric heating in the collector header and by tapered riser tubes that control the growth of ice so that a rigid and expanding ice plug is not developed. Although all these techniques have been used in commercial products, they are not suitable for widely traded products that may be installed in any climate zone. The only inherently freeze tolerant designs are draindown systems or closed-loop collector circuits with a heat exchanger between the collector and the tank. The drain down concept is difficult to implement in a thermosyphon system if a pressurised water tank is used, however, drain-down thermosyphon systems are widely used in China †
Author to whom correspondence should be addressed. Tel.: 161-2-9385-4127; fax: 161-2-9663-1222; e-mail: [email protected]
Fig. 1. Full circumference mantle heat exchanger on a horizontal tank, showing alternative collector return points. 53
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construct, provides large heat transfer area and with appropriate design can promote thermal stratification in the storage tank. The primary advantage of a mantle heat exchanger is that it has low friction resistance to thermosyphon circulation and maintains the simplicity of the thermosyphon concept. Mantle heat exchangers are also used for vertical-tank pumped-circulation systems (Furbo, 1993; Baur et al., 1993; Shah and Furbo, 1998). If a mantle heat exchanger had been used in the study by Webster et al. (1987) instead of the eight immersed copper tubes, the heat transfer area would have been two and a half times larger and the heat exchanger penalty would have been significantly reduced. Furbo (1993) compared low flow solar water heating systems with a range of heat exchanger configurations and found that mantle heat exchangers outperformed immersed coil and external shell and tube heat exchangers in vertical tank systems. Although many manufacturers of thermosyphon solar water heaters use horizontal mantle heat exchangers there is very little information on the performance of this type of heat exchanger. Manufacturers of horizontal tank systems usually take a conservative approach to sizing and use the largest possible mantle (full circumference and full length of the storage tank). A wide range of mantle widths and positions of the hot inlet pipe have been used. Systems designed to operate as solar pre-heaters typically have the hot-inlet pipe mounted near the top of the annulus. Systems with in-tank electric boosting typically have the hot-inlet pipe mounted below the level of the electric heater or have both the inlet and outlet mounted in the bottom of the annulus, as shown in Fig. 1. Baur et al. (1993) studied vertical mantle heat exchangers for pumped circulation systems using an empirical heat transfer correlation for laminar flow in the mantle gap developed by Mercer et al. (1967). Baur concluded that there was little difference in the performance of vertical tank pumped circulation solar water heaters with mantle heat exchangers or external shell and tube heat exchangers. Inlet connections to the upper level in the mantle of a thermosyphon system can result in substantial heat loss due to reverse circulation at night, unless the input pipe is very well insulated. High level connections may also result in poor circulation under low radiation conditions due to opposing buoyancy in the hotter upper levels of the annulus. If in-tank boosting is used in a mantle system the input level to the mantle should be below the level of the boost element to avoid
heat dumping at night and low circulation during the day. Due to the combination of these effects a low level input point is used for most horizontal tank mantle systems. For a low level connection to the annulus, as shown in Fig. 1, the flow in the annulus is a combination of forced circulation from the collector loop and internal natural convection within the annulus. This paper presents a model of horizontal mantle heat exchangers and the integration of this model into the TRNSYS dynamic simulation package. 2. MODELLING THERMOSYPHON SYSTEM PERFORMANCE
Heat transfer correlations for mantle heat exchangers on vertical tanks have been developed by Baur et al. (1993), Furbo (1993) and Shah and Furbo (1998). The model proposed by Baur has been implemented in the TRNSYS simulation package. The modelling procedure is the same for top entry mantles on either vertical or horizontal tanks. However, for horizontal tanks with low level or bottom entry into the mantle the flow structure is influenced by mixed forced and free convection processes inside the mantle. Horizontal mantle tanks usually have a much narrower annular gap than vertical systems, typically 5 mm for horizontal systems and 20 mm or more for vertical systems. The flow entry port normal to the heat exchange surface in a horizontal mantle heat exchanger results in higher local heat flux levels near the entry, due to impingement effects. The flow structure in a horizontal mantle with bottom entry and exit points has been investigated experimentally and numerically by Nasr et al. (1997, 1998) and Morrison et al. (1997). Due to the large area of a full circumference mantle and low flow rates inherent in thermosyphon solar water heaters, the flow in horizontal mantle heat exchangers is usually in the developing laminar flow regime. For flow rates corresponding to the high end of thermosyphon circulation, mixing induced by the impinging inlet flow has been observed by Rosengarten et al. (1997). The flow structure in a horizontal mantle has been studied by Morrison et al. (1998) for both mixed and stratified inner tank conditions. The flow structure in a bottom entry mantle depends on the temperature of the inlet flow relative to the thermal stratification in the inner tank. Numerical simulation of the flow structure in a 5 mm mantle heat exchanger on a 280 mm diameter horizontal tank is shown in Figs. 2 and 3 for mixed and stratified inner tank conditions. In Figs. 2 and 3
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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Fig. 2. Simulated flow structure in a horizontal mantle heat exchanger with bottom level entry and exit for mixed inner tank temperature 308C and a mantle inlet temperature of 508C (half of the horizontal mantle circumference unwrapped), flow rate51.36 l / min, tank diameter5280 mm, mantle gap55 mm.
half of the curved mantle has been unwrapped so that the flow field can be represented on a 2-D projection. For all operating conditions there is a complex flow structure near the impinging inlet which results in 10 to 15% of the total heat transfer taking place in the jet impingement region opposite the inlet port. For a uniform inner tank and mantle inlet temperature higher than the top of the inner tank the mantle flow covers the full circumference of the heat exchange surface. For stratified inner tank conditions and a mantle inlet temperature less than the top of the tank, the mantle flow only rises to its thermal equilibrium
level, as shown in Fig. 2. For stratified conditions and a mantle inlet temperature colder than the top of the tank a recirculation zone develops above the mantle inlet as shown in Fig. 3, if the inlet is displaced slightly from the end wall. 3. HEAT TRANSFER CORRELATIONS
Heat transfer in vertical mantle heat exchangers has been modelled by Baur et al. (1993), using a correlation for developing laminar flow between parallel flat plates proposed by Mercer et al. (1967) as shown in Eq. (1).
Fig. 3. Simulated flow structure in a horizontal mantle heat exchanger with bottom level entry and exit for stratified inner tank conditions 208C–408C and a mantle inlet temperature of 308C (half of the horizontal mantle circumference unwrapped), flow rate50.68 l / min, tank diameter5280 mm, mantle gap55 mm.
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S S
D D
w 1.2 0.16 Re w Pr ] L Nu 5 4.86 1 ]]]]]]]] w 0.7 0.17 1 1 0.24 Re w Pr ] Pr L
(1)
where: Nu5Nusselt number based on log mean tempera¯ /k and the overall heat transture difference 5hw ¯ fer Q is given by hHLDT LM ; ¯h5average convective heat transfer coefficient; Re w 5Reynolds number based on mantle gap ~ /Hw)(w /m ); width5(m Pr5Prandtl number 5 m c p /k; DT LM 5log-mean temperature difference DT LM 5 ((T o 2 T wall ) 2 (T in 2 T wall )) / ln((T o 2 T wall ) / (T in 2 T wall )); T wall 5temperature of heat transfer surface; T in 5fluid inlet temperature; T o 5fluid outlet temperature from the mantle; ~ m5flow rate through the mantle; A5heat transfer surface area; w5width of mantle gap; H5width of mantle perpendicular to flow direction; k5thermal conductivity of fluid; m 5viscosity of fluid; c p 5specific heat of fluid. Baur’s simulation results were compared with experimental data reported by Furbo and Berg (1992). For vertical entry into the top of the mantle Baur found that a correction factor of 1.8 had to be applied to Mercer’s heat transfer correlation for flow between flat plates in order to obtain a match between the measured and simulated heat transfer. The heat transfer coefficient in Eq. (1) is based on the log mean temperature difference and hence requires knowledge of both the inlet and outlet temperatures of the flow through the mantle. Although this type of correlation has been successfully implemented for pumped circulation systems by Baur et al. (1993) it introduces numerical difficulties if used in a model of a thermosyphon solar water heater. Numerical solution of thermosyphon collector-loop circulation through a mantle heat exchanger requires an iteration for the collector-loop flow linked to an iteration for the tank temperature stratification. If a mantle heat transfer correlation of the type given in Eq. (1) is used in a thermosyphon model the additional iteration loop to find the log mean temperature difference for the mantle slows the convergence process. Although the log mean temperature difference form of the Nusselt number has the attraction of a constant value for fully developed flow, it is difficult to apply in a
thermosyphon loop simulation model. Mercer et al. (1967) suggested a more direct solution for heat transfer using a Nusselt number based on a heat transfer coefficient defined in terms of the temperature difference between the inlet fluid and the wall rather than the log-mean temperature difference. This modified form of Nusselt number is referred to as a non-dimensional heat flux to differentiate it from the customary log-mean temperature difference form of the Nusselt number. The modified Nusselt number Nu * based on inlet temperature difference is given by q¯ w Nu *w 5 ]]] ] T in 2 T wall k
(2)
¯ where q5average heat flux over the heat transfer surface. The form of the heat transfer correlation function that is applicable to this definition of nondimensional heat flux can be derived as follows. The variation of fluid temperature in a heat exchanger with a constant wall temperature is given by
S
D
T o 2 T wall DT o HL ]]] 5 ]] 5 exp 2 ]]h¯ ~ p T in 2 T wall DT in mc
(3)
where L5length of mantle in the flow direction. The overall heat transfer is given by Q
~ psT o 2 T ind 5 mc ~ psDT in 2 DT od 5 mc
(4)
The modified nondimensional heat transfer coefficient then becomes Nu *w
Q 1 w 5 ] ]] ] HL DT in k w 1 Lh¯ 5 Re w Pr] 1 2 exp 2 ]] ] L Re w Pr k
S
S
DD (5)
Although the wall of a mantle heat exchanger will not be isothermal, the form of the correlation given in Eq. (5) could be expected to apply to other boundary conditions if the mean wall temperature is used. Conventional heat exchanger effectiveness functions cannot be applied to mantle heat exchangers because the free convection flow rate on the tank contents side of the heat exchanger wall is not usually known. Heat transfer in horizontal mantles with the entry and exit points at the bottom of the mantle (Fig. 1) has been studied by Rosengarten et al.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
(1998, 1999a). Rosengarten measured heat transfer in a vertical-slot mantle heat exchanger with bottom entry and exit ports, for a range of flow rates, mantle widths and temperature stratification on the heat exchanger surface (set by stratification in the inner tank). Rosengarten also used a detailed CFD model of the mantle and the inner tank to determine the distribution of heat flux in a horizontal mantle. The experimental and numerical data for overall heat transfer was correlated using Eq. (5) with a value of h¯ selected to give the best fit to the wide range of measured and simulated data. For typical conditions in thermosyphon solar water heater mantle heat exchangers (1 # Re w # 100, w /L # 0.02and w /H # ¯ 0.07) Rosengarten found that a value of h5392 2 W/ m K gave the best fit to the measured data, as shown in Fig. 4. Rosengarten et al. (1999b) also developed a stratification correlation factor (St) to account for non-uniform wall temperatures due to stratification in the inner tank. The form of the correlation for bottom entry and exit mantles is
S
57
S
w 1 392L Nu *w 5 Re w Pr ] 1 2 exp 2 ]] ]] L Re w Pr k
DD
St (6)
2
where St50.9320.05u 10.12u , u 5sT in 2 T bottomd /sT in 2 T meand; T bottom 5temperature at the bottom of the mantle wall; T mean 5mean wall temperature; T in 5fluid inlet temperature to the mantle. The variation of the modified Nusselt number Nu *w with Reynolds number Re w in a typical horizontal mantle is compared in Fig. 5 with the Nusselt number for developing flow between parallel flat plates with one plate heated. This comparison indicates that the heat transfer in a horizontal mantle with mixed convection conditions is significantly higher than for laminar flow between parallel flat plates. It is interesting to note that the increase of heat transfer in a horizontal mantle is similar to the 80% increase observed by Baur et al. (1993) for vertical mantles with top entry. Although the geometry of
Fig. 4. Comparison of measured heat transfer in a horizontal mantle heat exchanger and the modified Nusselt number correlation given by Eq. (6).
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Fig. 5. Comparison of heat transfer in a horizontal mantle heat exchanger and in a parallel channel heat exchanger with heat transfer through one isothermal boundary.
these two cases is very different the flow in a vertical mantle has been shown by Shah et al. (1999) to be influenced by buoyancy effects, hence, a similar heat transfer correlation may apply for both orientations of the mantle. 4. MODELLING OF STRATIFICATION IN A SOLAR PREHEATER
The local heat transfer rate around the circumference of a horizontal mantle heat exchanger depends on the flow structure in the mantle and the variation of heat-transfer area with height. Due to the circular cross section of a horizontal tank a large proportion of the heat transfer area is in the top and bottom sections of the tank. If a horizontal tank is divided into 20 equal mass horizontal segments then 20% of the heat transfer area will be in each of the top and bottom
segments, for a 40 element tank approximately 15% of the area is in each of these elements. The development of stratification in a horizontal tank with a mantle heat exchanger was investigated using a 57 litre tank, instrumented with thermocouple grids in the inner tank as shown in Fig. 6. The collector loop hot water flow into the mantle was supplied from a temperature-regulated source. The development of stratification in the inner tank was monitored during a 3-h heat-up test while a constant temperature flow was pumped through the mantle. The test was started with a slight temperature stratification (25.38C to 27.58C) and the mantle flow was set at 0.582 l / min and a temperature of 41.78C. The development of temperature stratification in the inner tank is shown in Fig. 7. As a result of the relatively large wall area in the top of the tank a hot stratified layer develops
Fig. 6. Laboratory test rig used to measure mantle heat exchanger characteristics.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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Fig. 7. Measured and simulated heating of a horizontal tank with a mantle heat exchanger. Mantle inlet temperature 41.78C.
as soon as the mantle heating starts. The mantle effectively acts as a stratification promoter and directs a significant part of the heat input to the top of the tank. Heat transfer into the bottom of the tank, due to the large bottom contact area and the effect of jet impingement, opposite the bottom inlet, results in a relatively uniform temperature zone in the bottom of the tank.
4.1. Simulation model A thermal model of a horizontal mantle tank was developed using the correlation proposed by Rosengarten et al. (1999b) for heat transfer in the mantle passageway. Convection heat transfer inside the tank was modelled as free convection along a vertical plate. Flow along the inner surface of the tank wall was assumed to be laminar and to stratify without mixing the contents of the inner tank. The heat exchanger model was developed in the TRNSYS modelling package (Klein et al., 1996) as part of the TYPE38 stratified tank routine. The mantle gap was divided into horizontal segments in line with the segments used to model the inner tank. The TYPE38 tank model in TRNSYS uses a plug flow concept to follow the flow in and out of the tank, however, when a collector loop heat exchanger is used the only flow in the tank is the load flow. The TYPE38 model for the tank was retained for consistency with the well-established open-loop thermosyphon model in TRNSYS. Energy transfer between the mantle and the inner tank was modelled by dividing the tank into 50 equal-mass elements.
The predictions of this model for the steady heat-up tests are shown with the test data in Fig. 7. The model required solution time steps of less than 0.2 h before the predictions were independent of time step. This is less than the 0.5 h time step commonly used for TRNSYS modelling of solar water heaters. The agreement between the model predictions and the measured data was generally good, although the temperature gradients above the bottom mixed layer differed from the observed data. This error is due to the simplified stratification assumption that was used to model the natural convection process over the inner surface of the mantle wall. The model correctly predicted the initial rapid temperature rise in the top of the tank, due to the direction of the hot mantle inlet stream to the top of the mantle during the initial hour of heating. Once the temperature in the top of the tank approached the mantle inlet temperature (after 1 h of heating), the flow in the mantle gap could not reach the top of the heat exchanger surface and more heat was directed to the bottom of the tank. 5. THERMOSYHON CIRCULATION IN A SOLAR COLLECTOR LOOP WITH A MANTLE HEAT EXCHANGER
A common form of solar water heater is the horizontal-tank close-coupled thermosyphon system shown in Fig. 8. The mantle heat exchanger is formed as part of the tank and then covered with insulation. The flow connections to the mantle in Fig. 8 are at the bottom as shown in
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Fig. 8. Close-coupled thermosyphon solar water heater with a mantle heat exchanger in the collector loop.
Fig. 1. The advantage of bottom connections is that heat loss due to reverse flow at night is suppressed compared to a system with a top level input to the mantle. A model of a thermosyphon solar water heater with a collector loop heat exchanger was developed by Morrison (1994) from the detailed open-loop model in TRNSYS. Bickford and Hittle
(1995) compared the predictions of this model with measured performance data obtained in a solar simulator and showed that the model over predicted collector energy gain by up to 10%. The model also over estimated the degree of stratification in the storage tank, when it was operated as a preheater. This model has now been extended to include the heat transfer correlation developed by
Fig. 9. Effective thermal conductivity as a function of depth in a 450 mm diameter horizontal tank with 3 mm steel walls.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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Table 1. Characteristics of close-coupled thermosyphon solar water heaters used in outdoor tests Tank
Volume heat loss UA diameter
300 litres 2.8 W/ K 450 mm
Mantle
gap length
5 mm 1.8 m
Collector
Area efficiency No 1
4 m2 sT¯ 2 T ad 5 0.81 2 5.33]] sT¯ 2I T ad sT¯ 2 T ad 2 5 0.86 2 7.15]] 2 0.0103]] I I I5incident radiation T¯ 5 mean fluid temperature T a 5ambient temperature
efficiency No 2
Rosengarten et al. (1999b) and improved analysis of conduction down the shallow depth of a horizontal tank and through the curved tank walls. In the original TRNSYS horizontal tank model reported by Morrison and Braun (1985) the equivalent conductivity of the tank walls and tank contents was quantified by a single value for all elements of the tank. This is correct for a vertical tank, however, for a horizontal tank the effect of wall conduction increases significantly for the top and bottom sections. Heat conduction in the walls of a tall vertical tank with height greater than 1 m has only a minor effect on thermal stratification, however, for a horizontal tank wall heat conduction has a substantial impact on thermal stratification in the top and bottom sections of the tank, see Eames and Norton (1998). The effective thermal conductivity is based on a cross section area weighting of the tank contents and the walls as given by Eq. (7). k e 5 (k water A water 1 k wall A wall ) /A water
(7)
where k water and k wall are the thermal conductivity of water and the tank wall material. A water and A wall are the cross sectional areas of the tank contents and the tank walls. For a vertical tank k e is the same for all tank elements, however, for a horizontal tank the horizontal cross section of the tank contents varies with height. The variation of effective thermal conductivity k e with depth for a 450 m diameter steel tank with 3 mm walls is shown in Fig. 9. Due to the high wall conduction in the top and bottom of a horizontal tank, stratified conditions cannot be maintained in the top and bottom layers for extended periods. The new thermosyphon solar water heater simulation model incorporating a collector-loop heat exchanger was developed in the TRNSYS simulation package (Klein et al., 1996). The
model uses the existing TRNSYS solar collector model (TYPE1 TRNSYS subroutine), the TRNSYS stratified tank model (TYPE38) and a new heat exchanger routine integrated within the TRNSYS thermosyphon loop model (TYPE45). The heat exchanger model and the TYPE45 thermosyphon collector loop model both allow for the temperature dependent properties of propylene glycol that would usually be used in the collector loop for freeze protection. 6. COMPARISON WITH OUTDOOR MEASURED PERFORMANCE
Two mantle-tank thermosyphon solar water heaters were installed on an outdoor test rig and monitored over an extended period. The water heaters were operated as solar preheaters during one test sequence and as integrated systems with in-tank electric boosting for an extended period. During the preheater tests the systems were filled with cold water at the start of each day and allowed to operate throughout the day without any draw off. In the early evening the tanks were discharged and the net useful energy collected over the day determined by integrating the heat ~ sT out 2 T ind during a draw off discharge rate mCp that was continued until the tank outlet temperature was within 0.5 K of the inlet temperature. During the period when the systems were operated with auxiliary boosting a distributed load was applied over each day to simulate a typical domestic application. The boosted systems were operated with energy loads of 28 MJ / day in summer and 42 MJ / day in winter, to simulate typical domestic hot water demand in Australia, as specified in Australian Standard AS4234 (1994). The measured cold water temperature and solar radiation on the collector slope were used as inputs to the simulation model. The two systems had the same tank and heat exchanger configura-
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Fig. 10. Comparison of measured and simulated daily energy gain in a solar preheater, 300 l tank, 4 m 2 collector, No 1.
tion but different quality flat-plate collectors. The collector in system No 1 had a flat-plate absorber with a low emissivity chrome-black selective surface while system No 2 had a black absorber surface. The principal features of the two systems are summarised in Table 1.
6.1. Pre-heater simulation Comparison of measured and simulated performance of a thermosyphon heat-exchanger sys-
tem operated as a preheater is shown in Figs. 10 and 11 for systems 1 and 2 respectively. The data for system No 1 includes summer and winter conditions, the data for system 2 is from a single 15 day period in summer. The results in Figs 10 and 11 indicate that the simulation model is able to predict the daily energy gain of a mantle-tank solar preheater with a one standard deviation error of 1.7 MJ / day. The largest errors occur for high radiation conditions when the system reaches
Fig. 11. Comparison of measured and simulated daily energy gain in a solar preheater, 300 l tank, 4 m 2 collector, No 2.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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temperatures above 658C at the end of the day and normally minor effects such as pipe losses start to become significant.
6.2. Boosted system simulation. The two closecoupled, mantle-tank thermosyphon systems were operated as integrated systems with an in-tank auxiliary booster to provide a continuous hot water service. The systems were installed on an outdoor test rig and operated with simulated domestic load conditions over a period of 18 months. The systems were identical except for the collector quality described in Table 1. The auxiliary booster was located in the middle of the tank and controlled by a thermostat set at 658C. The auxiliary input was energised at all times under the control of the thermostat in the middle of the tank. A constant daily load distribution was used throughout the year, however, the daily load was varied each month to simulate domestic load conditions in a temperate climate as defined in Australian Standard AS4234 (1994). The simulation model used the measured load volume and cold water temperature at each load interval as inputs. The simulation results for daily auxiliary energy use of system 1 are compared with the measured daily energy use in Fig. 12 for a six month test period spanning mid-summer to midwinter in Sydney, Australia. The scatter in the daily results is partially due to slight differences in activation times of the auxiliary heater just before or after the midnight division between days. The one standard deviation error for simulation of auxiliary energy use is 2 MJ / day. The monthly average solar contribution relative to a conventional electric water heater supplying
Fig. 12. Comparison of measured and simulated auxiliary energy use for system 2 with an electric auxiliary element located at the mid height of the tank.
Fig. 13. Comparison of energy savings of system 1 relative to a conventional electric water heater.
the same loads is shown in Figs 13 and 14. The annual energy savings FR was defined as Aux NS 2 Aux S FR 5 ]]]] Aux NS
(8)
where Aux NS 5auxiliary energy used by a conventional non-solar water heater; Aux S 5auxiliary energy used by the booster in the solar water heater. Simulation of monthly energy savings showed a 2 percentage point error, however, the error in simulated energy savings over the full 18 month test period was only 0.5 percentage points.
7. CONCLUSIONS
The performance of mantle heat exchangers for close-coupled thermosyphon solar water heaters has been characterised for system configurations with bottom entry and exit ports in to the mantle. A model of a thermosyphon solar collector loop incorporating a collector-loop mantle heat exchanger has been developed in the TRNSYS solar modelling package. The model predictions of stratification development in a solar preheater tank were tested in a controlled laboratory rig and shown to give reliable results for overall heat transfer and the development of stratification in the storage tank. The model was also assessed against outdoor test results for thermosyphon solar water heaters with collector-loop heat exchangers. Predictions of daily energy gain for a solar preheater were found to have an average uncertainty of 1.7 MJ / day. Predictions of daily auxiliary energy use for in-tank boosted systems showed an average error of 2 MJ / day, the monthly energy savings predictions were found to be
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Fig. 14. Comparison of energy savings of system 2 relative to a conventional electric water heater (no test data in January).
within 2 percentage points of the measured performance. REFERENCES AS4234 (1994). Australian Standard. Solar water heatersdomestic and heat pump-calculation of energy consumption. Baur J. M., Klein S. A. and Beckman W. A. (1993) Simulation of water tanks with mantle heat exchangers. Proceedings ASES Annual Conference, Solar 93, 286–291. Bickford C. and Hittle D. C. (1995) Short term performance comparisons between a solar thermosyphon water heater and two numerical models. ASME-JSES-JSME-International-Solar-Energy-Conference, Vol 2. ASME, New York, pp. 1079–1092. Eames P. C. and Norton B. (1998) The effect of tank geometry on thermally stratified sensible heat storage subject to a low Reynolds number flow. Int. J. Heat. Mass Transfer 41, 2131–2142. Furbo S. and Berg P. (1992). Calculation of the thermal performance of small hot water solar heating systems using low flow operation, Thermal Insulation Laboratory, Technical University of Denmark. Furbo S. (1993) Optimum designed heat storage for small low flow systems. ISES Solar World Congress, Budapest, Hungary. 5, 117–122. Klein S.A. et al. (1996). TRNSYS 14.1, User Manual. University of Wisconsin Solar Energy Laboratory. Mercer W. E., Pearce W. M. and Hitchcock J. E. (1967) Laminar forced convection in the entrance region between parallel flat plates. ASME J. of Heat Transfer 89, 251–257. Mertol A., Place W. and Webster T. (1981) Detailed loop model analysis of liquid solar thermosyphons with heat exchangers. Solar Energy 27, 367–386. Morrison G.L. (1994). TRNSYS extensions for Australian solar water heating systems ( TRNAUS). Report 1994 / FMT / 1 Kensington, University of New South Wales, 1994. http: / / solar1.mech.unsw.edu.au / glm / trnaus / trnaus.htm Morrison G. L. and Braun J. E. (1985) System modelling and operation characteristics of thermosyphon solar water heaters. Solar Energy 34, 389–405.
Morrison G. L., Nasr A., Behnia M. and Rosengarten G. (1997) Performance of horizontal mantle heat exchangers in solar water heating systems. ISES Bi-annual Conference, Taejon, Korea 2, 149–158. Morrison G. L., Nasr A., Behnia M. and Rosengarten G. (1998) Analysis of horizontal mantle heat exchangers in solar water heating systems. Solar Energy 64, 19–31. Nasr A., Morrison G. L. and Behnia M. (1997) A parametric study of an annular heat exchanger with application to solar thermosyphon systems. In ICHMT, International Symposium on Advances in Computational Heat Transfer, Cesme Turkey, pp. 299–307. Nasr A., Morrison G. L. and Behnia M. (1998) A parametric study of horizontal concentric heat exchangers for solar storage tanks. J. of Computer Modeling and Simulation in Engineering. 3, 269–274. Rosengarten G., Morrison G. L. and Behnia M. (1997) Understanding mantle heat exchangers used in solar water heaters. In Solar97 Conference, Australian and New Zealand Solar Energy Society. Rosengarten G., Morrison G. L. and Behnia M. (1998) Mixed convection in a narrow rectangular cavity with application to horizontal mantle heat exchangers. In 11 th International Symposium on Transport Phenomena, The Pacific Center of Thermal-Fluids Engineering, Taiwan, pp. 126–131. Rosengarten G., Behnia M., Morrison G.L. (1999a). Some aspects concerning modelling the flow and heat transfer in horizontal mantle heat exchangers in solar water heaters. International Journal of Energy (in press). Rosengarten G., Morrison G.L., Behnia M. (1999b). Mixed convection in a narrow rectangular cavity with bottom entry and outlet. Submitted to Int. J. Heat & Mass Transfer. Shah L. J. and Furbo S. (1998) Correlation of experimental and theoretical data for mantle tanks used in low flow SDHW systems. Solar Energy 64, 245–256. Shah L. J., Morrison G. L. and Behnia M. (1999) Characteristics of vertical mantle heat exchangers for solar water heaters. In Solar99 ISES Bi-annual Conference, Jerusalem, Israel. Webster T., Coutier J., Place J. and Tavana M. (1987) Experimental evaluation of solar thermosyphons with heat exchangers. Solar Energy 38, 219–231.
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Solar Energy Vol. 67, Nos. 1–3, pp. 53–64, 1999 2000 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 0 0 ) 0 0 0 0 3 – 7 All rights reserved. Printed in Great Britain 0038-092X / 99 / $ - see front matter
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MANTLE HEAT EXCHANGERS FOR HORIZONTAL TANK THERMOSYPHON SOLAR WATER HEATERS GRAHAM L. MORRISON†, GARY ROSENGARTEN and MASUD BEHNIA Department of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia Received 2 September 1999; revised version accepted 12 November 1999 Communicated by BRIAN NORTON
Abstract—This paper describes the characteristics of horizontal mantle heat exchangers for application in thermosyphon solar water heaters. A new correlation for heat transfer in horizontal mantle heat exchangers with bottom entry and exit ports was used to predict the overall heat transfer and stratification conditions in horizontal tanks with mantle heat exchangers. The model of a mantle heat exchanger tank was combined with the thermosyphon solar collector loop model in TRNSYS to develop a model of a thermosyphon solar water heater with collector loop heat exchanger. Predictions of stratification conditions in a horizontal mantle tank are compared with transient charging tests in a laboratory test rig. Predictions of daily energy gain in solar preheaters and in systems with in-tank auxiliary boosters are compared with extensive outdoor measurements and the model is found to give reliable results for both daily and long-term performance analysis. 2000 Elsevier Science Ltd. All rights reserved.
for systems that provide hot water only in the evening. There have been numerous studies of the performance of closed loop thermosyphon systems based on tube heat exchangers inside vertical and horizontal storage tanks (Mertol et al., 1981; Webster et al., 1987). Tube heat exchangers can provide adequate heat transfer between the collector loop and the tank, however, tube heat exchangers for thermosyphon operation are difficult to construct. The heat exchanger configuration that has been widely adopted for horizontal tank thermosyphon systems is the mantle or annular concept shown in Fig. 1. A mantle heat exchanger is easy to
1. INTRODUCTION
The thermosyphon solar water heater is the principal product concept in most major solar water heater markets. Thermosyphon systems with open loop connection between the tank and the solar collector have been widely adopted for both low pressure and pressurised water supply systems in climates that do not experience freezing conditions. Without freeze protection these systems are limited to tropical climates or locations that never experience frost. Freeze protection in open loop thermosyphon systems can be provided by water dump valves, electric heating in the collector header and by tapered riser tubes that control the growth of ice so that a rigid and expanding ice plug is not developed. Although all these techniques have been used in commercial products, they are not suitable for widely traded products that may be installed in any climate zone. The only inherently freeze tolerant designs are draindown systems or closed-loop collector circuits with a heat exchanger between the collector and the tank. The drain down concept is difficult to implement in a thermosyphon system if a pressurised water tank is used, however, drain-down thermosyphon systems are widely used in China †
Author to whom correspondence should be addressed. Tel.: 161-2-9385-4127; fax: 161-2-9663-1222; e-mail: [email protected]
Fig. 1. Full circumference mantle heat exchanger on a horizontal tank, showing alternative collector return points. 53
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construct, provides large heat transfer area and with appropriate design can promote thermal stratification in the storage tank. The primary advantage of a mantle heat exchanger is that it has low friction resistance to thermosyphon circulation and maintains the simplicity of the thermosyphon concept. Mantle heat exchangers are also used for vertical-tank pumped-circulation systems (Furbo, 1993; Baur et al., 1993; Shah and Furbo, 1998). If a mantle heat exchanger had been used in the study by Webster et al. (1987) instead of the eight immersed copper tubes, the heat transfer area would have been two and a half times larger and the heat exchanger penalty would have been significantly reduced. Furbo (1993) compared low flow solar water heating systems with a range of heat exchanger configurations and found that mantle heat exchangers outperformed immersed coil and external shell and tube heat exchangers in vertical tank systems. Although many manufacturers of thermosyphon solar water heaters use horizontal mantle heat exchangers there is very little information on the performance of this type of heat exchanger. Manufacturers of horizontal tank systems usually take a conservative approach to sizing and use the largest possible mantle (full circumference and full length of the storage tank). A wide range of mantle widths and positions of the hot inlet pipe have been used. Systems designed to operate as solar pre-heaters typically have the hot-inlet pipe mounted near the top of the annulus. Systems with in-tank electric boosting typically have the hot-inlet pipe mounted below the level of the electric heater or have both the inlet and outlet mounted in the bottom of the annulus, as shown in Fig. 1. Baur et al. (1993) studied vertical mantle heat exchangers for pumped circulation systems using an empirical heat transfer correlation for laminar flow in the mantle gap developed by Mercer et al. (1967). Baur concluded that there was little difference in the performance of vertical tank pumped circulation solar water heaters with mantle heat exchangers or external shell and tube heat exchangers. Inlet connections to the upper level in the mantle of a thermosyphon system can result in substantial heat loss due to reverse circulation at night, unless the input pipe is very well insulated. High level connections may also result in poor circulation under low radiation conditions due to opposing buoyancy in the hotter upper levels of the annulus. If in-tank boosting is used in a mantle system the input level to the mantle should be below the level of the boost element to avoid
heat dumping at night and low circulation during the day. Due to the combination of these effects a low level input point is used for most horizontal tank mantle systems. For a low level connection to the annulus, as shown in Fig. 1, the flow in the annulus is a combination of forced circulation from the collector loop and internal natural convection within the annulus. This paper presents a model of horizontal mantle heat exchangers and the integration of this model into the TRNSYS dynamic simulation package. 2. MODELLING THERMOSYPHON SYSTEM PERFORMANCE
Heat transfer correlations for mantle heat exchangers on vertical tanks have been developed by Baur et al. (1993), Furbo (1993) and Shah and Furbo (1998). The model proposed by Baur has been implemented in the TRNSYS simulation package. The modelling procedure is the same for top entry mantles on either vertical or horizontal tanks. However, for horizontal tanks with low level or bottom entry into the mantle the flow structure is influenced by mixed forced and free convection processes inside the mantle. Horizontal mantle tanks usually have a much narrower annular gap than vertical systems, typically 5 mm for horizontal systems and 20 mm or more for vertical systems. The flow entry port normal to the heat exchange surface in a horizontal mantle heat exchanger results in higher local heat flux levels near the entry, due to impingement effects. The flow structure in a horizontal mantle with bottom entry and exit points has been investigated experimentally and numerically by Nasr et al. (1997, 1998) and Morrison et al. (1997). Due to the large area of a full circumference mantle and low flow rates inherent in thermosyphon solar water heaters, the flow in horizontal mantle heat exchangers is usually in the developing laminar flow regime. For flow rates corresponding to the high end of thermosyphon circulation, mixing induced by the impinging inlet flow has been observed by Rosengarten et al. (1997). The flow structure in a horizontal mantle has been studied by Morrison et al. (1998) for both mixed and stratified inner tank conditions. The flow structure in a bottom entry mantle depends on the temperature of the inlet flow relative to the thermal stratification in the inner tank. Numerical simulation of the flow structure in a 5 mm mantle heat exchanger on a 280 mm diameter horizontal tank is shown in Figs. 2 and 3 for mixed and stratified inner tank conditions. In Figs. 2 and 3
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
55
Fig. 2. Simulated flow structure in a horizontal mantle heat exchanger with bottom level entry and exit for mixed inner tank temperature 308C and a mantle inlet temperature of 508C (half of the horizontal mantle circumference unwrapped), flow rate51.36 l / min, tank diameter5280 mm, mantle gap55 mm.
half of the curved mantle has been unwrapped so that the flow field can be represented on a 2-D projection. For all operating conditions there is a complex flow structure near the impinging inlet which results in 10 to 15% of the total heat transfer taking place in the jet impingement region opposite the inlet port. For a uniform inner tank and mantle inlet temperature higher than the top of the inner tank the mantle flow covers the full circumference of the heat exchange surface. For stratified inner tank conditions and a mantle inlet temperature less than the top of the tank, the mantle flow only rises to its thermal equilibrium
level, as shown in Fig. 2. For stratified conditions and a mantle inlet temperature colder than the top of the tank a recirculation zone develops above the mantle inlet as shown in Fig. 3, if the inlet is displaced slightly from the end wall. 3. HEAT TRANSFER CORRELATIONS
Heat transfer in vertical mantle heat exchangers has been modelled by Baur et al. (1993), using a correlation for developing laminar flow between parallel flat plates proposed by Mercer et al. (1967) as shown in Eq. (1).
Fig. 3. Simulated flow structure in a horizontal mantle heat exchanger with bottom level entry and exit for stratified inner tank conditions 208C–408C and a mantle inlet temperature of 308C (half of the horizontal mantle circumference unwrapped), flow rate50.68 l / min, tank diameter5280 mm, mantle gap55 mm.
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S S
D D
w 1.2 0.16 Re w Pr ] L Nu 5 4.86 1 ]]]]]]]] w 0.7 0.17 1 1 0.24 Re w Pr ] Pr L
(1)
where: Nu5Nusselt number based on log mean tempera¯ /k and the overall heat transture difference 5hw ¯ fer Q is given by hHLDT LM ; ¯h5average convective heat transfer coefficient; Re w 5Reynolds number based on mantle gap ~ /Hw)(w /m ); width5(m Pr5Prandtl number 5 m c p /k; DT LM 5log-mean temperature difference DT LM 5 ((T o 2 T wall ) 2 (T in 2 T wall )) / ln((T o 2 T wall ) / (T in 2 T wall )); T wall 5temperature of heat transfer surface; T in 5fluid inlet temperature; T o 5fluid outlet temperature from the mantle; ~ m5flow rate through the mantle; A5heat transfer surface area; w5width of mantle gap; H5width of mantle perpendicular to flow direction; k5thermal conductivity of fluid; m 5viscosity of fluid; c p 5specific heat of fluid. Baur’s simulation results were compared with experimental data reported by Furbo and Berg (1992). For vertical entry into the top of the mantle Baur found that a correction factor of 1.8 had to be applied to Mercer’s heat transfer correlation for flow between flat plates in order to obtain a match between the measured and simulated heat transfer. The heat transfer coefficient in Eq. (1) is based on the log mean temperature difference and hence requires knowledge of both the inlet and outlet temperatures of the flow through the mantle. Although this type of correlation has been successfully implemented for pumped circulation systems by Baur et al. (1993) it introduces numerical difficulties if used in a model of a thermosyphon solar water heater. Numerical solution of thermosyphon collector-loop circulation through a mantle heat exchanger requires an iteration for the collector-loop flow linked to an iteration for the tank temperature stratification. If a mantle heat transfer correlation of the type given in Eq. (1) is used in a thermosyphon model the additional iteration loop to find the log mean temperature difference for the mantle slows the convergence process. Although the log mean temperature difference form of the Nusselt number has the attraction of a constant value for fully developed flow, it is difficult to apply in a
thermosyphon loop simulation model. Mercer et al. (1967) suggested a more direct solution for heat transfer using a Nusselt number based on a heat transfer coefficient defined in terms of the temperature difference between the inlet fluid and the wall rather than the log-mean temperature difference. This modified form of Nusselt number is referred to as a non-dimensional heat flux to differentiate it from the customary log-mean temperature difference form of the Nusselt number. The modified Nusselt number Nu * based on inlet temperature difference is given by q¯ w Nu *w 5 ]]] ] T in 2 T wall k
(2)
¯ where q5average heat flux over the heat transfer surface. The form of the heat transfer correlation function that is applicable to this definition of nondimensional heat flux can be derived as follows. The variation of fluid temperature in a heat exchanger with a constant wall temperature is given by
S
D
T o 2 T wall DT o HL ]]] 5 ]] 5 exp 2 ]]h¯ ~ p T in 2 T wall DT in mc
(3)
where L5length of mantle in the flow direction. The overall heat transfer is given by Q
~ psT o 2 T ind 5 mc ~ psDT in 2 DT od 5 mc
(4)
The modified nondimensional heat transfer coefficient then becomes Nu *w
Q 1 w 5 ] ]] ] HL DT in k w 1 Lh¯ 5 Re w Pr] 1 2 exp 2 ]] ] L Re w Pr k
S
S
DD (5)
Although the wall of a mantle heat exchanger will not be isothermal, the form of the correlation given in Eq. (5) could be expected to apply to other boundary conditions if the mean wall temperature is used. Conventional heat exchanger effectiveness functions cannot be applied to mantle heat exchangers because the free convection flow rate on the tank contents side of the heat exchanger wall is not usually known. Heat transfer in horizontal mantles with the entry and exit points at the bottom of the mantle (Fig. 1) has been studied by Rosengarten et al.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
(1998, 1999a). Rosengarten measured heat transfer in a vertical-slot mantle heat exchanger with bottom entry and exit ports, for a range of flow rates, mantle widths and temperature stratification on the heat exchanger surface (set by stratification in the inner tank). Rosengarten also used a detailed CFD model of the mantle and the inner tank to determine the distribution of heat flux in a horizontal mantle. The experimental and numerical data for overall heat transfer was correlated using Eq. (5) with a value of h¯ selected to give the best fit to the wide range of measured and simulated data. For typical conditions in thermosyphon solar water heater mantle heat exchangers (1 # Re w # 100, w /L # 0.02and w /H # ¯ 0.07) Rosengarten found that a value of h5392 2 W/ m K gave the best fit to the measured data, as shown in Fig. 4. Rosengarten et al. (1999b) also developed a stratification correlation factor (St) to account for non-uniform wall temperatures due to stratification in the inner tank. The form of the correlation for bottom entry and exit mantles is
S
57
S
w 1 392L Nu *w 5 Re w Pr ] 1 2 exp 2 ]] ]] L Re w Pr k
DD
St (6)
2
where St50.9320.05u 10.12u , u 5sT in 2 T bottomd /sT in 2 T meand; T bottom 5temperature at the bottom of the mantle wall; T mean 5mean wall temperature; T in 5fluid inlet temperature to the mantle. The variation of the modified Nusselt number Nu *w with Reynolds number Re w in a typical horizontal mantle is compared in Fig. 5 with the Nusselt number for developing flow between parallel flat plates with one plate heated. This comparison indicates that the heat transfer in a horizontal mantle with mixed convection conditions is significantly higher than for laminar flow between parallel flat plates. It is interesting to note that the increase of heat transfer in a horizontal mantle is similar to the 80% increase observed by Baur et al. (1993) for vertical mantles with top entry. Although the geometry of
Fig. 4. Comparison of measured heat transfer in a horizontal mantle heat exchanger and the modified Nusselt number correlation given by Eq. (6).
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Fig. 5. Comparison of heat transfer in a horizontal mantle heat exchanger and in a parallel channel heat exchanger with heat transfer through one isothermal boundary.
these two cases is very different the flow in a vertical mantle has been shown by Shah et al. (1999) to be influenced by buoyancy effects, hence, a similar heat transfer correlation may apply for both orientations of the mantle. 4. MODELLING OF STRATIFICATION IN A SOLAR PREHEATER
The local heat transfer rate around the circumference of a horizontal mantle heat exchanger depends on the flow structure in the mantle and the variation of heat-transfer area with height. Due to the circular cross section of a horizontal tank a large proportion of the heat transfer area is in the top and bottom sections of the tank. If a horizontal tank is divided into 20 equal mass horizontal segments then 20% of the heat transfer area will be in each of the top and bottom
segments, for a 40 element tank approximately 15% of the area is in each of these elements. The development of stratification in a horizontal tank with a mantle heat exchanger was investigated using a 57 litre tank, instrumented with thermocouple grids in the inner tank as shown in Fig. 6. The collector loop hot water flow into the mantle was supplied from a temperature-regulated source. The development of stratification in the inner tank was monitored during a 3-h heat-up test while a constant temperature flow was pumped through the mantle. The test was started with a slight temperature stratification (25.38C to 27.58C) and the mantle flow was set at 0.582 l / min and a temperature of 41.78C. The development of temperature stratification in the inner tank is shown in Fig. 7. As a result of the relatively large wall area in the top of the tank a hot stratified layer develops
Fig. 6. Laboratory test rig used to measure mantle heat exchanger characteristics.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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Fig. 7. Measured and simulated heating of a horizontal tank with a mantle heat exchanger. Mantle inlet temperature 41.78C.
as soon as the mantle heating starts. The mantle effectively acts as a stratification promoter and directs a significant part of the heat input to the top of the tank. Heat transfer into the bottom of the tank, due to the large bottom contact area and the effect of jet impingement, opposite the bottom inlet, results in a relatively uniform temperature zone in the bottom of the tank.
4.1. Simulation model A thermal model of a horizontal mantle tank was developed using the correlation proposed by Rosengarten et al. (1999b) for heat transfer in the mantle passageway. Convection heat transfer inside the tank was modelled as free convection along a vertical plate. Flow along the inner surface of the tank wall was assumed to be laminar and to stratify without mixing the contents of the inner tank. The heat exchanger model was developed in the TRNSYS modelling package (Klein et al., 1996) as part of the TYPE38 stratified tank routine. The mantle gap was divided into horizontal segments in line with the segments used to model the inner tank. The TYPE38 tank model in TRNSYS uses a plug flow concept to follow the flow in and out of the tank, however, when a collector loop heat exchanger is used the only flow in the tank is the load flow. The TYPE38 model for the tank was retained for consistency with the well-established open-loop thermosyphon model in TRNSYS. Energy transfer between the mantle and the inner tank was modelled by dividing the tank into 50 equal-mass elements.
The predictions of this model for the steady heat-up tests are shown with the test data in Fig. 7. The model required solution time steps of less than 0.2 h before the predictions were independent of time step. This is less than the 0.5 h time step commonly used for TRNSYS modelling of solar water heaters. The agreement between the model predictions and the measured data was generally good, although the temperature gradients above the bottom mixed layer differed from the observed data. This error is due to the simplified stratification assumption that was used to model the natural convection process over the inner surface of the mantle wall. The model correctly predicted the initial rapid temperature rise in the top of the tank, due to the direction of the hot mantle inlet stream to the top of the mantle during the initial hour of heating. Once the temperature in the top of the tank approached the mantle inlet temperature (after 1 h of heating), the flow in the mantle gap could not reach the top of the heat exchanger surface and more heat was directed to the bottom of the tank. 5. THERMOSYHON CIRCULATION IN A SOLAR COLLECTOR LOOP WITH A MANTLE HEAT EXCHANGER
A common form of solar water heater is the horizontal-tank close-coupled thermosyphon system shown in Fig. 8. The mantle heat exchanger is formed as part of the tank and then covered with insulation. The flow connections to the mantle in Fig. 8 are at the bottom as shown in
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Fig. 8. Close-coupled thermosyphon solar water heater with a mantle heat exchanger in the collector loop.
Fig. 1. The advantage of bottom connections is that heat loss due to reverse flow at night is suppressed compared to a system with a top level input to the mantle. A model of a thermosyphon solar water heater with a collector loop heat exchanger was developed by Morrison (1994) from the detailed open-loop model in TRNSYS. Bickford and Hittle
(1995) compared the predictions of this model with measured performance data obtained in a solar simulator and showed that the model over predicted collector energy gain by up to 10%. The model also over estimated the degree of stratification in the storage tank, when it was operated as a preheater. This model has now been extended to include the heat transfer correlation developed by
Fig. 9. Effective thermal conductivity as a function of depth in a 450 mm diameter horizontal tank with 3 mm steel walls.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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Table 1. Characteristics of close-coupled thermosyphon solar water heaters used in outdoor tests Tank
Volume heat loss UA diameter
300 litres 2.8 W/ K 450 mm
Mantle
gap length
5 mm 1.8 m
Collector
Area efficiency No 1
4 m2 sT¯ 2 T ad 5 0.81 2 5.33]] sT¯ 2I T ad sT¯ 2 T ad 2 5 0.86 2 7.15]] 2 0.0103]] I I I5incident radiation T¯ 5 mean fluid temperature T a 5ambient temperature
efficiency No 2
Rosengarten et al. (1999b) and improved analysis of conduction down the shallow depth of a horizontal tank and through the curved tank walls. In the original TRNSYS horizontal tank model reported by Morrison and Braun (1985) the equivalent conductivity of the tank walls and tank contents was quantified by a single value for all elements of the tank. This is correct for a vertical tank, however, for a horizontal tank the effect of wall conduction increases significantly for the top and bottom sections. Heat conduction in the walls of a tall vertical tank with height greater than 1 m has only a minor effect on thermal stratification, however, for a horizontal tank wall heat conduction has a substantial impact on thermal stratification in the top and bottom sections of the tank, see Eames and Norton (1998). The effective thermal conductivity is based on a cross section area weighting of the tank contents and the walls as given by Eq. (7). k e 5 (k water A water 1 k wall A wall ) /A water
(7)
where k water and k wall are the thermal conductivity of water and the tank wall material. A water and A wall are the cross sectional areas of the tank contents and the tank walls. For a vertical tank k e is the same for all tank elements, however, for a horizontal tank the horizontal cross section of the tank contents varies with height. The variation of effective thermal conductivity k e with depth for a 450 m diameter steel tank with 3 mm walls is shown in Fig. 9. Due to the high wall conduction in the top and bottom of a horizontal tank, stratified conditions cannot be maintained in the top and bottom layers for extended periods. The new thermosyphon solar water heater simulation model incorporating a collector-loop heat exchanger was developed in the TRNSYS simulation package (Klein et al., 1996). The
model uses the existing TRNSYS solar collector model (TYPE1 TRNSYS subroutine), the TRNSYS stratified tank model (TYPE38) and a new heat exchanger routine integrated within the TRNSYS thermosyphon loop model (TYPE45). The heat exchanger model and the TYPE45 thermosyphon collector loop model both allow for the temperature dependent properties of propylene glycol that would usually be used in the collector loop for freeze protection. 6. COMPARISON WITH OUTDOOR MEASURED PERFORMANCE
Two mantle-tank thermosyphon solar water heaters were installed on an outdoor test rig and monitored over an extended period. The water heaters were operated as solar preheaters during one test sequence and as integrated systems with in-tank electric boosting for an extended period. During the preheater tests the systems were filled with cold water at the start of each day and allowed to operate throughout the day without any draw off. In the early evening the tanks were discharged and the net useful energy collected over the day determined by integrating the heat ~ sT out 2 T ind during a draw off discharge rate mCp that was continued until the tank outlet temperature was within 0.5 K of the inlet temperature. During the period when the systems were operated with auxiliary boosting a distributed load was applied over each day to simulate a typical domestic application. The boosted systems were operated with energy loads of 28 MJ / day in summer and 42 MJ / day in winter, to simulate typical domestic hot water demand in Australia, as specified in Australian Standard AS4234 (1994). The measured cold water temperature and solar radiation on the collector slope were used as inputs to the simulation model. The two systems had the same tank and heat exchanger configura-
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Fig. 10. Comparison of measured and simulated daily energy gain in a solar preheater, 300 l tank, 4 m 2 collector, No 1.
tion but different quality flat-plate collectors. The collector in system No 1 had a flat-plate absorber with a low emissivity chrome-black selective surface while system No 2 had a black absorber surface. The principal features of the two systems are summarised in Table 1.
6.1. Pre-heater simulation Comparison of measured and simulated performance of a thermosyphon heat-exchanger sys-
tem operated as a preheater is shown in Figs. 10 and 11 for systems 1 and 2 respectively. The data for system No 1 includes summer and winter conditions, the data for system 2 is from a single 15 day period in summer. The results in Figs 10 and 11 indicate that the simulation model is able to predict the daily energy gain of a mantle-tank solar preheater with a one standard deviation error of 1.7 MJ / day. The largest errors occur for high radiation conditions when the system reaches
Fig. 11. Comparison of measured and simulated daily energy gain in a solar preheater, 300 l tank, 4 m 2 collector, No 2.
Mantle heat exchangers for horizontal tank thermosyphon solar water heaters
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temperatures above 658C at the end of the day and normally minor effects such as pipe losses start to become significant.
6.2. Boosted system simulation. The two closecoupled, mantle-tank thermosyphon systems were operated as integrated systems with an in-tank auxiliary booster to provide a continuous hot water service. The systems were installed on an outdoor test rig and operated with simulated domestic load conditions over a period of 18 months. The systems were identical except for the collector quality described in Table 1. The auxiliary booster was located in the middle of the tank and controlled by a thermostat set at 658C. The auxiliary input was energised at all times under the control of the thermostat in the middle of the tank. A constant daily load distribution was used throughout the year, however, the daily load was varied each month to simulate domestic load conditions in a temperate climate as defined in Australian Standard AS4234 (1994). The simulation model used the measured load volume and cold water temperature at each load interval as inputs. The simulation results for daily auxiliary energy use of system 1 are compared with the measured daily energy use in Fig. 12 for a six month test period spanning mid-summer to midwinter in Sydney, Australia. The scatter in the daily results is partially due to slight differences in activation times of the auxiliary heater just before or after the midnight division between days. The one standard deviation error for simulation of auxiliary energy use is 2 MJ / day. The monthly average solar contribution relative to a conventional electric water heater supplying
Fig. 12. Comparison of measured and simulated auxiliary energy use for system 2 with an electric auxiliary element located at the mid height of the tank.
Fig. 13. Comparison of energy savings of system 1 relative to a conventional electric water heater.
the same loads is shown in Figs 13 and 14. The annual energy savings FR was defined as Aux NS 2 Aux S FR 5 ]]]] Aux NS
(8)
where Aux NS 5auxiliary energy used by a conventional non-solar water heater; Aux S 5auxiliary energy used by the booster in the solar water heater. Simulation of monthly energy savings showed a 2 percentage point error, however, the error in simulated energy savings over the full 18 month test period was only 0.5 percentage points.
7. CONCLUSIONS
The performance of mantle heat exchangers for close-coupled thermosyphon solar water heaters has been characterised for system configurations with bottom entry and exit ports in to the mantle. A model of a thermosyphon solar collector loop incorporating a collector-loop mantle heat exchanger has been developed in the TRNSYS solar modelling package. The model predictions of stratification development in a solar preheater tank were tested in a controlled laboratory rig and shown to give reliable results for overall heat transfer and the development of stratification in the storage tank. The model was also assessed against outdoor test results for thermosyphon solar water heaters with collector-loop heat exchangers. Predictions of daily energy gain for a solar preheater were found to have an average uncertainty of 1.7 MJ / day. Predictions of daily auxiliary energy use for in-tank boosted systems showed an average error of 2 MJ / day, the monthly energy savings predictions were found to be
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Fig. 14. Comparison of energy savings of system 2 relative to a conventional electric water heater (no test data in January).
within 2 percentage points of the measured performance. REFERENCES AS4234 (1994). Australian Standard. Solar water heatersdomestic and heat pump-calculation of energy consumption. Baur J. M., Klein S. A. and Beckman W. A. (1993) Simulation of water tanks with mantle heat exchangers. Proceedings ASES Annual Conference, Solar 93, 286–291. Bickford C. and Hittle D. C. (1995) Short term performance comparisons between a solar thermosyphon water heater and two numerical models. ASME-JSES-JSME-International-Solar-Energy-Conference, Vol 2. ASME, New York, pp. 1079–1092. Eames P. C. and Norton B. (1998) The effect of tank geometry on thermally stratified sensible heat storage subject to a low Reynolds number flow. Int. J. Heat. Mass Transfer 41, 2131–2142. Furbo S. and Berg P. (1992). Calculation of the thermal performance of small hot water solar heating systems using low flow operation, Thermal Insulation Laboratory, Technical University of Denmark. Furbo S. (1993) Optimum designed heat storage for small low flow systems. ISES Solar World Congress, Budapest, Hungary. 5, 117–122. Klein S.A. et al. (1996). TRNSYS 14.1, User Manual. University of Wisconsin Solar Energy Laboratory. Mercer W. E., Pearce W. M. and Hitchcock J. E. (1967) Laminar forced convection in the entrance region between parallel flat plates. ASME J. of Heat Transfer 89, 251–257. Mertol A., Place W. and Webster T. (1981) Detailed loop model analysis of liquid solar thermosyphons with heat exchangers. Solar Energy 27, 367–386. Morrison G.L. (1994). TRNSYS extensions for Australian solar water heating systems ( TRNAUS). Report 1994 / FMT / 1 Kensington, University of New South Wales, 1994. http: / / solar1.mech.unsw.edu.au / glm / trnaus / trnaus.htm Morrison G. L. and Braun J. E. (1985) System modelling and operation characteristics of thermosyphon solar water heaters. Solar Energy 34, 389–405.
Morrison G. L., Nasr A., Behnia M. and Rosengarten G. (1997) Performance of horizontal mantle heat exchangers in solar water heating systems. ISES Bi-annual Conference, Taejon, Korea 2, 149–158. Morrison G. L., Nasr A., Behnia M. and Rosengarten G. (1998) Analysis of horizontal mantle heat exchangers in solar water heating systems. Solar Energy 64, 19–31. Nasr A., Morrison G. L. and Behnia M. (1997) A parametric study of an annular heat exchanger with application to solar thermosyphon systems. In ICHMT, International Symposium on Advances in Computational Heat Transfer, Cesme Turkey, pp. 299–307. Nasr A., Morrison G. L. and Behnia M. (1998) A parametric study of horizontal concentric heat exchangers for solar storage tanks. J. of Computer Modeling and Simulation in Engineering. 3, 269–274. Rosengarten G., Morrison G. L. and Behnia M. (1997) Understanding mantle heat exchangers used in solar water heaters. In Solar97 Conference, Australian and New Zealand Solar Energy Society. Rosengarten G., Morrison G. L. and Behnia M. (1998) Mixed convection in a narrow rectangular cavity with application to horizontal mantle heat exchangers. In 11 th International Symposium on Transport Phenomena, The Pacific Center of Thermal-Fluids Engineering, Taiwan, pp. 126–131. Rosengarten G., Behnia M., Morrison G.L. (1999a). Some aspects concerning modelling the flow and heat transfer in horizontal mantle heat exchangers in solar water heaters. International Journal of Energy (in press). Rosengarten G., Morrison G.L., Behnia M. (1999b). Mixed convection in a narrow rectangular cavity with bottom entry and outlet. Submitted to Int. J. Heat & Mass Transfer. Shah L. J. and Furbo S. (1998) Correlation of experimental and theoretical data for mantle tanks used in low flow SDHW systems. Solar Energy 64, 245–256. Shah L. J., Morrison G. L. and Behnia M. (1999) Characteristics of vertical mantle heat exchangers for solar water heaters. In Solar99 ISES Bi-annual Conference, Jerusalem, Israel. Webster T., Coutier J., Place J. and Tavana M. (1987) Experimental evaluation of solar thermosyphons with heat exchangers. Solar Energy 38, 219–231.