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Performance of an improved design for storage-type domestic electrical water-heaters
Applied Energy 71 (2002) 287–306 www.elsevier.com/locate/apenergy
Performance of an improved design for storage-type domestic electrical water-heaters Adel A. Hegazy*, M.R. Diab Mechanical Power Engineering and Energy Department, Faculty of Engineering, Minia University, Minia-61517, Egypt Received 24 September 2001; received in revised form 7 December 2001; accepted 8 December 2001
Abstract Performance of an improved design for storage-type domestic electrical water-heaters (EWHs) was experimentally investigated for energy conservation. The results were compared with those of conventional design EWHs having the same tank size and power rating. Data were obtained for two tanks with aspect ratios of 1 and 2, two draw-off rates of 5 and 10 l/ min, and using three heating elements of different heights. It is found that improved design EWHs provide more hot water at almost constant temperature in the first mean residence time, which is of prime concern for the user. Thus, they exhibit higher discharging efficiencies due to better thermal stratification inside the heater storage tank. Also, thermal performance is enhanced with increasing tank aspect ratio and decreasing draw rate. These characteristics have a direct impact on energy consumption and result in lower electricity bills. The design improvements are simple to adapt as they only require minor modifications to be made to existing EWH models. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Electric water heaters; Energy conservation; Thermal storage; Thermal stratification
1. Introduction Storage-type electrical water-heaters (EWHs) are widely used in many countries all over the world for generating hot water in numerous domestic, commercial and industrial installations. In particular, they are very popular in the urban and suburban areas of developing countries, where the majority of the residential building
* Corresponding author. Tel.: +20-86-362083x237; fax: +20-86-346674. E-mail address: [email protected] (A. A. Hegazy). 0306-2619/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-2619(02)00006-5
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Nomenclature A B cp Con D E(t) Est(t) h H Im j t tres T T* v V Vj Vst z 1, 2, 3
electrical water heater A of aspect ratio H/D=1 electrical water heater B of aspect ratio H/D=2 specific heat of water conventional design internal diameter of the heater tank net energy delivered by water volume V during time t energy stored in the heater tank relative to Ti at time t height of the heating element height of the heater storage tank improved design water layer counter time mean residence time=Vst/ water temperature dimensionless temperature inside the heater tank, Eq.(7) outflow (=inflow) volumetric flow rate outflow (=inflow) volume of water during time t water volume of the j-th layer volume of the heater storage tank vertical distance from the bottom of the heater storage tank heating elements 1, 2 and 3 of heights 13, 28 and 33.4 cm, respectively
Greek letters dis discharging efficiency, Eq. (6) ðVÞ dimensionless water draw-off temperature profile, Eq. (2) water density dimensionless time=t=tres ¼ V=Vst Subscripts i inflow o outflow
stock consists of multi-family (multi-storey) buildings with individual domestic water heater for each apartment/unit. Compared to large central hot-water systems, the simplicity, reliability and low cost of storage-type EWHs are their main advantages in addition to the decrease in water consumption as the time spent waiting for the water to achieve acceptable temperatures at the fixture is less. Also, they do not require re-pressurization of the hot water, which is maintained inside the storage tank at the mains pressure along with the heating element (electric-resistant type). Accordingly, this allows substantial savings in piping, pumping, plumbing and heat-exchanger costs. Further,
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the temperature of the hot water inside the storage tank can be easily controlled by the user adjusting the thermostat setpoint within the range of 40–90 C. Furthermore, it has been shown by Reddy [1] that it is economically advantageous for a family of five persons or less to use an EWH than installing a solar WH in the absence of any governmental subsidy. The only disadvantage of storage-type domestic EWHs is their excessive consumption of electrical energy. As pointed out by Hiller et al. [2], such water-heating systems have historically been generously overdesigned to ensure adequate hotwater availability. The installation setpoint for the thermostat of most EWHs available in the market is between 60 and 65 C. Also, it is generally advised that when a large demand of hot water is required, the thermostat setpoint should be adjusted higher by the user, thereby increasing the thermal capacity of the storage water. A higher setpoint also offsets the effect of mixing between the incoming cold water and the storage hot-water during a water draw as mixing results in a lower water temperature at the fixtures. Therefore, it is a common practice in the design of such EWHs to assume that only 70% of the hot water in the storage tank is usable at an acceptable temperature level [3], i.e. at 43 C or higher. To overcome the problem of mixing between the incoming cold water and the storage hot-water, Minguez [4] suggested the use of two EWHs connected in series each with half the capacity and power rating of the single tank heater. Of course, a water heating system consisting of two identical EWHs connected in series is less aesthetically attractive and less compact than a single-tank heater. Therefore, such a system is more suitable for householders as recommended by Lacroix [5]. Kar and Kar [6] compared the performance of dual-tank EWHs in series with a single-tank EWH in terms of daily hot water output and energy saving per litre of maximum hot water producible. They concluded that a dual-tank EWH of the same volume and power rating as a single-tank EWH, where the second tank has 25% of the total volume and 75% of the total power rating, provides more hot water and reduces electricity consumption. However, this idea requires modifications in the classical design of EWHs, which increase the cost and complexity of such cheap and simple units. The other attractive alternative for the above suggested two-tank EWHs is the use of the conventional single-tank heater but incorporating the phenomenon of natural stratification to separate, without employing any physical barrier, between the hot and cold water masses. In stratified storage tanks, buoyancy is the only mechanism that is exploited to keep the hot water, of low density, floating above the cold water of higher density, resulting in a region of steep temperature gradient called a ‘thermocline’. Regarding storage-type EWHs, the thermocline region will always migrate from the bottom to the top of the tank as the cold water is charged near the bottom and the hot water is simultaneously discharged at an equal rate near the top. A survey of the literature revealed that the intensity of mixing (destratification) between the inlet cold (hot) water and the hot (cold) water in storage tanks during charging/discharging process depends on several dynamic and geometric parameters such as flow rates and temperatures of hot and cold water streams, storage-tank
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volume and aspect ratio, locations of inlet and outlet ports, and the geometry of the inlet diffuser [7–17]. The last parameter is found to be the most determinant one. This has led several investigators to search for other diffuser designs, which are rather different from the simple pipe inlet but are capable of reducing mixing that is induced by the incoming water flow. The range of the suggested diffuser designs include the use of slotted tubes, pipes with inverted cups, solid baffle plates, perforated circular plates, radial-flow disks, distributed nozzles, and perforated tubes. These diffuser designs have proven to be very effective in restraining mixing and, thus, they allow water stratification to be maintained for longer periods of time, which noticeably improves the tanks storage-efficiency. The objective of this investigation is to examine experimentally the performance of domestic EWHs when a horizontal wedged-pipe is employed as an inlet diffuser instead of the conventional vertical pipe inlet. Compared to the above mentioned diffuser types, the horizontal wedged-pipe inlet is still a simple device to adapt, much less expensive to manufacture, and only requires minor modifications to be made to existing models of EWHs. The effects of storage-tank aspect-ratio, height of heating element and the rate of water draw on the heater performance have been investigated. The heater performance is characterized by the percentage of energy delivered after drawing one tank volume and by the water draw-off temperature profile. Both parameters are obtained through a ‘‘mixing’’ experiment in which the water inside the heater storage tank is initially heated before pumping in three tank-volumes of cold water [18,19]. Also, a flow-visualization study is conducted to clarify the differences in the mixing mechanisms and the flow patterns inside the storage tank for both inlet diffusers.
2. Conventional and improved designs for domestic electric water heaters Residential storage-type EWHs are available in the markets as various brands, but all have cylindrical shape of different aspect-ratios and various capacities ranging from 20 to 500 l [3]. However, the 50 l tank-capacity model, hereafter referred as the conventional EWH, is the most popular since it occupies a relatively limited space and can be easily hanged on any wall in the kitchen or the bathroom of any apartment/unit. A typical domestic EWH of conventional design is shown schematically in Fig. 1(a). It is widely manufactured in Europe, region of the Middle East and in many other developing countries worldwide. Basically, each EWH consists of a cylindrical storage tanks which is generally made of steel and insulated with a layer of fiberglass or urethane foam that is placed between the tank and the external envelope to reduce heat loss to the ambient environment. Water is usually heated with a single immersed heating element (electrical-resistance type), which comes in different styles, lengths, heights and powerratings ranging from 8 to 26 W/l [6]. A sacrificial rod of magnesium alloy is often employed to minimize corrosion inside the tank. The heating element and the thermostat which regulates its functioning, and consequently the water temperature, are usually manufactured as one unit with a flange, so that it can be easily inserted
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Fig. 1. Domestic electrical water heater of: (a) conventional design and (b) modified design, which incorporates an improved design inlet diffuser as shown in (c).
vertically at the centre of the tank bottom. As shown in Fig. 1(a), the cold water enters the tank directly from the bottom through a short pipe, while the hot water leaves the tank near the top but is also brought to the bottom via an internal pipe through the water body. Each EWH is equipped with the necessary safety devices and associated fittings. Regarding the improved design of EWH, the literature survey has indicated that to achieve natural stratification in a storage tank, the inlet diffuser should be placed as close to the bottom of the tank as possible to minimize mixing between the incoming cold water and the storage hot-water. Also, the inlet diffuser should be carefully designed to distribute the incoming flow near the tank bottom with low velocities to retain natural stratification. To satisfy these conditions, while keeping the diffuser design quite simple to interest the manufactures of these EWHs, the proposed diffuser is made from a standard 12.7 mm (0.5 in) steel pipe positioned horizontally close to the tank bottom and normal to its perimeter, but only spanning 10 cm (25–31%) of the storage-tanks inside diameter. The lower half of this 10 cm inlet pipe was wedged [Fig. 1(c)] to direct the inflow towards the tank floor and, in turn, avoiding direct vigorous mixing with the hot water mass. In this way, the incoming cold water of higher density will gently push the hot water in the tank up out of the way with minimum mixing occurring at the interface. Compared to the conventional design, Fig. 1(a), this necessitates the fixing the inlet port to the tanks lateral surface as illustrated in Fig. 1(b). Further, to eliminate heat-exchange between the hot water draw and the rest of the water body in the tank, as in the conventional design, the outlet port is also relocated at the lateral surface of the storage-tank directly above the inlet port but as higher as possible. The outlet
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diffuser is simply a 12.7 mm (0.5 in) standard steel-coupling, flush welded to the tank surface.
3. Experiments Performance tests were made for two specially-designed domestic EWHs, having an equal storage capacity of 50 l, but of different dimensions. Heater A has a cylindrical storage tank of height H=0.4 m with an internal diameter D=0.4 m (i.e. an aspect ratio of 1), while the tank of heater B is 0.634 m height and 0.317 m inside diameter, yielding an aspect ratio of 2. Both storage tanks were made from the same 2 mm thick galvanized steel sheet and were insulated on the lateral surface and top and bottom with the same thickness of fiberglass mats. A typical test heater is shown schematically in Fig. 2. Each heater has two inlets for incoming cold water located at the same level 4 cm from the bottom of the tank (zi) and two outlets for hot water draw located also at the same level but 4 cm from the top of the tank (H-zo). Inlet (1) and outlet (2) are of conventional design and are normal to the tank bottom while inlet (3) and outlet (4) have the modified design and configuration as explained above. Both test heaters A and B are equipped with the necessary valve-arrangement and associated plumbing to switch from the conventional inlet–outlet combination to the
Fig. 2. Schematic of test heater.
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improved one. The flow rate of the incoming cold water, and consequently the flow rate of hot water draw, was adjusted by using control valves attached at the outlet ports, while keeping the inlet valves fully opened during testing. The draw-off rate was measured using a calibrated catch tank and a stopwatch. Much care was taken in adjusting the opening of the outlet control valve so that the accuracy of the measured flow rate was always within 0.1 l/min or better. Nevertheless, cold water inflow was supplied from a large constant-head elevated tank to ensure steady flow conditions. Experiments were carried out for two draw-off rates of 5 and 10 l/min. The water flowrate is the same at the inlet and outlet ports as long the storage tank behaves as an open system during the experiment. Three heating elements, having a nominal power rating of 1200 W, but of different heights equal to 13, 28 and 33.4 cm, were used to initially heat the water inside the storage tanks of test heaters A and B. The shortest heating element (No. 1) is typical to the second one (No. 2) of height 28 cm, but it was formed to have an inverted Ushape [see Fig. 1(a)] of 13 cm height, which is approximately half the original height. These heating elements were welded to three identical brass flanges, so that they can be easily interchanged and installed at the central opening in the tank bottom of either heaters A or B. Transient temperature distributions for the water inside the storage tank of each EWH were measured using nine copper-constantan thermocouples made of wires 0.315 mm in diameter. The thermocouple probes was inserted vertically from a sealed opening in the tank top and close to its axis as shown in Fig. 2. The junctions of the thermocouples were located at the centres of nine equal volumes of the storage water. For conventional and improved designs, these temperature measurements were employed in determining the characteristics of thermal stratification inside the storage tanks of both heaters A and B during the hot/cold water discharging/charging processes. Two more pairs of thermocouples were placed in the inlet and outlet ports for continuously monitoring the inflow and outflow water temperatures. These two temperatures, in conjunction with water draw-off rate, were used to evaluate the amount of energy delivered out of the heater storage tank. Temperature signals were collected from the test heater by a data logger interfaced to a personal computer. Regardless of the water flowrate, water-temperature data inside the tank were sampled at 30-s intervals. Calibration of the thermocouples showed that the overall accuracy of the measurements was within 0.2 C. Flow visualization experiments were also made to study the characteristics of the incoming cold-water stream when it was introduced either from the conventional inlet or the improved one. Experiments were conducted in a steel tank sized 707070 cm3 and having a 6060 cm2 glass window on the front side. Initially, the tank was filled with clear hot-water having a uniform temperature of 70 C. In contrast, the inflow cold water was separately maintained at the uniform temperature of 25 C in the constant-head elevated tank and was colored with black dye to facilitate the observation of the flow pattern and its characteristics. Visualization of flow was performed by introducing the colored cold-water into the rectangular tank through either the conventional inlet or the modified one. Photographic flow visualization records were also made using a 35 mm single-lens reflex camera for later inspection.
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4. Test procedure and discharging efficiency The basic sequence of the present test procedure is similar to the procedure of Collector and System Testing Group of the European Community [18,19] except for some minor differences in details to simulate the actual operation of a domestic EWH. Before the start of the experiment, water was allowed to discharge from the storage tank of a particular EWH while carefully controlling the draw-off rate (v) to the desired value of 5 or 10 l/min either through the conventional or the improved inlet-outlet ports. Then, the valve of the outlet port was closed, so that the storage tank becomes full with cold water at a uniform temperature (Ti) before activating the heating element. After 150 min, the electrical heater was turned off and the initial temperature distribution inside the storage tank was recorded. Immediately, the valve of the outlet port was opened to discharge an amount of water (Vo) equivalent to three tank volumes (3Vst) while simultaneously charging the storage tank, at the same rate, with cold water (Vi) at temperature (Ti). During this discharging/charging process with Vo ¼ Vi ¼ V, the outflow and inflow temperatures (To, Ti) as well as the temperature of the nine thermocouples inside the storage tank (T1, . . . Tj, . . . T9) were monitored and recorded for subsequent data processing. Of course, the duration of each test depends on water volumetric flowrate but, in general, it could be said that each test lasts three times the mean residence time (3tres) necessary to fully charge the storage tank with an equal water volume at a given volumetric flowrate: tres ¼ Vst =v
ð1Þ
Although the temperature data were recorded as a function of time (t), these data can be expressed in terms of the withdrawn volume (V) since for a constant volumetric flowrate V ¼ tv. Accordingly, the temperature history To(V) of the water leaving the EWH can be easily related to the withdrawn volume (V) and it is called ‘‘The draw-off temperature profile’’, To(t) [19]. Also, it may be expressed in dimensionless form as: ðVÞ ¼ ðTo ðVÞ Ti Þ=ðTo ðV ¼ 0Þ Ti Þ;
ð2Þ
where ðVÞ is the draw-off profile. Note that To ðV ¼ 0Þ is actually the highest temperature of water initially present in the heater tank and at the entrance of the outlet port of either design at t=0. The initial temperature distribution inside the storage tank, which was recorded immediately before drawing off the hot water, is employed in computing the initial energy stored in the tank relative to the temperature of the cold water Ti: Est ðt ¼ V ¼ oÞ ¼
9 X Vcp j Tj Vj Ti j¼1
ð3Þ
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where and cp are the density and specific heat of the water sub-volume Vj of the tank j-th layer. The total number of layers are nine corresponding to the number of thermocouples in the tank. In writing Eq. (3), it is assumed that the temperature measured by each thermocouple Tj prevails over the entire sub-volume Vj. Eq. (3) was also used to compute the water stored energy relative to Ti at any time t. On the other hand, the amount of useful energy delivered by the water leaving the storage tank up to a certain time t can be calculated by: ðt EðtÞ ¼ vcp ðTo ðtÞ Ti Þdt ð4Þ 0
on the basis of the same volumetric flowrate at the inlet and outlet ports and incorporating the measured temperatures of the water inflow and outflow. Employing Eq. (1), however, the delivered energy could be expressed in terms of the dimensionless time ¼ t=tres , which is also equal to ðV=Vst Þ, as follows: ð Eð Þ ¼ Vst cp ðTo ð Þ Ti Þd ð5Þ 0
where the upper limit of is 3. It is important to evaluate the effect of the proposed design improvements on the thermal stratification inside the heater tank during the discharging process and, in turn, on the performance of EWHs A and B. This is assessed by computing the discharging efficiency, which is defined as the ratio of the net thermal energy delivered in the first mean residence time 0 4 4 1 (i.e. after pumping through one tank volume of cold water V=Vst) to the initial thermal energy stored in the heater tank. Hence, the discharging efficiency dis could be expressed as : dis ¼ Eð ¼ 1Þ=Est ð ¼ 0Þ
ð6Þ
after using Eqs. (3) and (5). It should be mentioned that the discharging efficiency dis is the same as the storage efficiency defined by Mavros et al. [18], but it is the opposite to the figure of merit (FOM) proposed by Wildin and Truman [20], the storage efficiency utilized by Yoo and Pak [21], and the charging efficiency employed by Hahne and Chen [22] as a measure of the performance of the hot-water charging process. In fact, fluid mixing is unavoidable during hot-water discharging. So that, the discharging efficiency varies between two limiting values. The upper limit is dis=100%, corresponding to a perfectly-stratified tank in which the cold water inflow is continuously pushing the hot water up in an ideal plug flow manner without any mixing or disturbance. The other limiting case is the perfect mixing of the cold and hot fluids in the tank throughout the discharging process. For this unstratified case, with water initially isothermal in the tank, it can be easily proved that dis is equal to 63.2% after withdrawing one tank volume of water, V=Vst, [19,21]. By increasing the volume of the water draw, the discharging efficiency increases
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correspondingly but with a slower rate, approaching the value of 95% for V=3Vst. Achieving nearly the upper limit of discharging efficiency after pumping through one tank volume is the aim of the present design improvements, which means effective use of the thermal energy stored in the heater tank and, in turn, significant savings in the electricity consumption.
5. Results and discussion Twenty four experiments were conducted during the course of this study to investigate the effects of storage tank aspect ratio H/D, heating element relative height h/H, discharging flow rate v, the design and configuration of inlet and outlet ports on the performance characteristics of such 50 l, popular size EWHs. Also, the transient temperature distributions of water inside the heater tank were examined to reveal the affects of these parameters on the thermal stratification of the storage water and how it affects the heater performance. These distributions are presented in terms of the dimensionless height (z/H) and temperature T* defined by: T ðz; tÞ ¼ ðTðz; tÞ Ti Þ=ðTo ðt ¼ 0Þ Ti Þ
ð7Þ
where T(z, t) is the temperature of the storage water at height z and given time t. The initial (t ¼ 0) temperature distributions of storage water inside EWHs A and B after a heating period of 150 min are shown in Fig. 3, on an average basis, and are parameterized by the heating element relative height, h/H. Clearly, the temperature of water in the upper half of any tank is almost uniform in contrast to those in the lower halves of tanks A and B which are seen to depend remarkably on the tanks aspect ratio (H/D) and on the element relative height (h/H). Thus, more uniform
Fig. 3. Initial temperature distributions of water inside test heaters A and B using heating elements 1, 2 and 3.
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temperature inside the storage tank, which is highly desirable, could initially be obtained by using storage tanks of high aspect-ratios and equipped with short heating elements. For the extreme case of heater B (H/D=2) with heating element No. 1 (h/H=0.205), however, part of the slight variation in the temperature distribution in the region adjacent to the tank bottom is attributed to the conduction heat loss through the metal pipework and the supporting rods of the EWH since both act as cooling fins. Experiments were conducted for different days of different ambient temperatures. Therefore, heat losses due to the fin effect are expected to vary, resulting in variations in the initial (t=0) readings of the thermocouples. In general, the initial temperature distributions at t=0 of a particular EWH A or B, energized with a certain heating element 1, 2 or 3, are almost the same except for the first thermocouple since it is close to the tank bottom. The transient temperature distributions (t > 0) of storage water in EWHs A and B during hot/cold water discharging/charging process as at a rate of 5 l/min are shown in Figs. 4 and 5, respectively, for both conventional (a, c) and improved (b, d)
Fig. 4. Transient temperature distributions for the water during discharging at 5 l/min from heater A (H/D=1) with (a, c) conventional or (b, d) improved design and heating elements Nos. 1 and 2.
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Fig. 5. Transient temperature distributions for the water during discharging at 5 l/min from heater B (H/D=2) with (a, c) conventional or (b, d) improved design and heating elements Nos. 1 and 2.
designs with heating elements Nos. 1 and 2. For the sake of brevity, the results of heating element No. 3 are not presented since they are similar in behaviour and close to those of heating element No. 2. In general, the transient temperature-distributions are seen to be significantly dependent on the inlet/outlet configuration and design as well as on the storage tanks aspect ratio H/D. Although the temperature distributions for the improved design EWHs A and B are similar in character see Figs. 4(b and d) and 5(b and d), there are quantitative differences among them, and also they differ from the corresponding distributions for the conventional design. However, the temperature distributions for the conventional design EWHs A and B exhibit different characteristics as illustrated in Figs. 4(a and c) and 5(a and c). Attention may first be turned to the transient temperature distributions shown in Figs. 4(a and c) and 5(a and c) for the conventional design with short and long pipes inserted vertically from the bottom of the storage tank as inlet and an outlet diffusers, respectively. Obviously, the temperature distributions for heater A are quite
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different from those of heater B. Also, it is noticeable in Fig. 4(a and c) that heater A has a well-mixed tank, i.e. uniform temperature, at any time > 0.1. In contrast, the temperature distributions of heater B show a relatively strong thermal stratification along with a thick thermocline region due to the presence of a large circulation in the lower half of the tank as can be identified in Fig. 5(a and c). However, the size of this circulation gets larger and stronger when element No. 1 is used in heating the storage water. This is attributed to the inverted U-shaped element, which evidently influences the flow and mixing, resulting in smaller temperature gradients. Such a flow behaviour could be explained with the aid of flow-visualization tests which showed that the simple vertical-pipe inlet diffuser produces severe mixing and entrainment between the inflow cold water and the hot water in the tank due to the jet-like flow of the incoming water. For a flow rate of 5 l/min and water height of the order of 40 cm ( HA), the mixing region occupies most of the test tank and thus water mixing is greatly enhanced, resulting in a well-mixed tank. On the other hand, when the height of the hot water is of the order of 60 cm ( HB), the flow pattern in the test tank resembles a mushroom-shape submerged jet, while the circulation region shrinks in size to occupy only most of the tanks lower half. Attention may now be turned to the transient temperature-distributions of the improved design EWHs shown in Figs. 4(b and d) and 5(b and d). For this design, the inflow diffuser is simply a short horizontal-pipe with a wedged-cut in its lower half and is fixed near the tanks bottom, while the outflow port is directly above and parallel to the inflow port but far as possible on the tanks lateral surface. Therefore, the cold inflow water is directed towards the bottom of the tank and tends to stay there since it has a negatively buoyant force relative to the storage hot water. This reduces mixing with the upper layers and results in a stable stratification with a relatively thin thermocline region separating the hot top layers and cold bottom ones. As seen in Figs. 4(b and d) and 5(b and d), the decrease in the temperature of the bottom layers is initially faster due to the smaller thickness of the mixing zone. These thermofluid characteristics are more apparent in Fig. 5(b and d) for heater B of aspect ratio 2 as the outlet port is relatively away from the mixing zone at the inlet. The flow visualization study has indicated that the flow behaviour of the cold water downstream of the wedged inlet diffuser is close to that of an offset wall-jet so, creating a small circulation zone at the tanks lowermost region, which causes limited mixing between the incoming cold-water and the storage hot-water. Consequently, moderate thermal stratification is initially developed which gets stronger with time as more cold water is charged up to =0.3–0.4 for heater A and =0.5–0.6 for heater B; see Figs. 4(b and d) and 5(b and d). This is accompanied by a substantial difference in the temperature of water in the uppermost and lowermost layers in the tank along with a continuous upward movement for the thermocline region. With further increase in the dimensionless time , thermal stratification decays and the thermocline region fades away until the temperature of the water in the tank becomes uniform but decreasing steadily to approach the inlet one. These characteristics are more pronounced in Fig. 5(b and d) for heater B of the higher aspect ratio. Further inspection of Figs. 4(b and d) and 5(b and d) reveals that the relative height (z/H) of the circulation region at the bottom of heater A tank is greater than the
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corresponding one with heater B. In fact, the actual height (z) of the circulation zone in both tanks is almost the same, since it depends only on the design of the inlet diffuser, while the height of heater A (40 cm) is almost two-thirds that of heater B (63.4 cm). However, it is obvious from these figures that the height of this circulation region was also affected by employing heating element No. 1 due to its inverted U-shape, which enhances the water mixing and increases the thickness of the thermocline. The draw-off temperature-profiles for the previously considered cases are plotted in Figs. 6 and 7 for EWHs A and B, respectively. Also superimposed on these figures are the initial temperature-distributions, which represent the draw-off profiles under
Fig. 6. Draw-off temperature profiles of water discharging at 5 l/min from heater A (H/D=1) with conventional or improved design and heating elements Nos. 1 and 2.
Fig. 7. Draw-off temperature profiles of water discharging at 5 l/min from heater B (H/D=2) with conventional or improved design and heating elements Nos. 1 and 2.
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the conditions of an ideal plug flow, to fairly assess the effects of design improvements on the performances of such EWHs. For the conventional design, examination of Figs. 6 and 7 reveals that heaters A and B perform in a markedly different fashion. As is expected, the draw-off profiles for heater A display the classical shape that is characteristic of a perfectly-mixed tank over the experiment duration =0–3. On the other hand, the draw-off profiles for heater B show a different behaviour by comparison. In the interval of < 0:5 for element No. 1 and < 0:7 for element No. 2, the draw-off profiles resemble those of flow through a double-pipe heat-exchanger before they drop sharply and then continue to decrease, but with a slow rate for > 1:2. In general, the profiles for both heaters A and B have long ‘‘tails’’, which means that appreciable amounts of hot water are trapped in the side corners and, hence, such a conventional design is less efficient in terms of energy delivery during the first mean residence-time, i.e. 0 4 4 1. The draw-off profiles of improved design EWHs are quite different from those of the conventional design. As shown in Figs. 6 and 7, the temperature profiles of water out from EWHs A and B display a profile that is close to the ideal plug flow case. This is clearly evident for heater B (H/D=2) compared to heater A (H/D=1). In other words, heater B is capable of delivering a greater volume of hot water at nearly constant temperature than heater A. This is the desired characteristic which motivated the present study. The second set of experiments is similar to the first one, except that the draw-off rate is doubled to 10 l/min. For brevity, representative transient temperature distributions from this set of experiments are plotted in Figs. 8 and 9 for EWHs A and B and employing heating-element No. 2. The corresponding draw-off profiles are presented in Fig. 10. To place the effect of doubling water draw in perspective, these temperature distributions should be compared with those of draw rate 5 l/min shown in Figs. 4 and 5. For heater A (H/D=1) with the conventional design, it is seen in Fig. 8(a) that the transient temperature-distributions are almost uniform for
Fig. 8. Transient temperature distributions for the water during discharging at 10 l/min from heater A (H/D=1) with (a) conventional or (b) improved design and heating element No. 2.
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Fig. 9. Transient temperature distributions of water during discharging at 10 l/min from heater B (H/ D=2) with (a) conventional or (b) improved design and heating element No. 2.
5 0:2, indicating a fully mixed tank. By examining and comparing Figs. 8(a) and 4(c), however, it is seen that the transient temperature-distributions for v=10 l/min are at higher values than the corresponding distributions for v=5 l/min at any time > 0:1. This warming up is a consequence of better mixing inside the tank of the EWH since the momentum of the inlet flow jet for v=10 l/min is much greater than the one for v=5 l/min. Turning to heater B (H/D= 2) with the conventional design, inspection of Figs. 9(a) and 5(c) reveals that doubling the charge rate gives rise to a greater mixing intensity of the cold water emerging from the inlet diffuser so that a fully mixed tank is left after each withdrawal. Also the comparison between the draw-off profiles illustrated in Figs. 10(b) and 7(b) confirms that for v =10 l/min water mixing is much vigorous due to the inertia of the incoming cold water and, in turn, mixing extends far from the inlet to include the whole tank for this case. Therefore, the draw-off profile in Fig. 10(b) seems to be close to the profile of Fig. 10(a) instead of the profile shown in Fig. 7(b). A further exploration of the effect of doubling water draw-off rate to 10 l/min can be made by comparing Figs. 8(b) and 9(b) with Figs. 4(d) and 5(d) for v=5 l/min, where the transient temperature-distributions are shown for improved design heaters A and B, respectively. The comparison reveals that with doubling the flow rate, the thermocline gets thicker, while the mixing region in the neighborhood of the tank bottom is increased in size by almost 50%. This is due to the increase in water mixing downstream of the inlet diffuser. In contrast to the conventional design, mixing is not so vigorous and, in turn, the temperatures in the mixing region exhibit an appreciable departure from uniformity for < 0:9. Such a behaviour is attributed to the damping effect of the improved design inlet-diffuser. For heater A of aspect ratio 1, it can be noticed that the thermocline is much thicker and degrades faster when v=10 l/min since the mixing region occupies two-thirds of the tank volume. This means that such EWHs should be designed with higher aspect-ratios for better
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thermal performances. The draw-off profiles shown in Fig. 10 confirm this conclusion. As is obvious, heater B (H/D=2) delivers more hot water than heater A (H/ D=1) in the first mean residence time 0 4 st ð¼ V=Vst Þ 4 1. Nevertheless, almost 70% of this amount of hot water ð0 < < 0:7Þ exhibits a nearly constant temperature, which is of prime concern for the users of such heaters. To quantify the effects of design improvements on the performance of conventional design EWHs, Fig. 11 has been prepared. The figure consists of two graphs; the first one (a) is for test heater A of aspect ratio 1 while the second (b) is for heater B of aspect ratio 2. In each graph, the discharging efficiency dis is plotted versus the heating-elements relative height (h/H) for the considered draw-off rates v=5 and 10 l/ min. To distinguish between the different sets of results, the data for improved
Fig. 10. Draw-off temperature profiles for water discharging at 10 l/min from heaters A and B with the conventional or improved design and heating element No. 2.
Fig. 11. Comparisons among the discharge-efficiency results for improved and conventional design heaters A and B under different test conditions.
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design (dark symbols) are represented by lines, while data for conventional design (open symbols) are fitted with dashed lines. However, the effect of aspect ratio on the performance of such heaters can be deduced by comparing the efficiency values reported in Fig. 11(a) and (b) under similar test conditions. An overview of the results in Fig. 11 shows that the proposed design improvements are successful in enhancing the thermal performance, as indicated by the higher values for discharging efficiency (dark symbols). Regardless of the heater design, it is generally seen that the discharging efficiency increases with increasing tanks aspect-ratio, but it decreases with increasing draw rate. These trends are, in line with the experimental information for thermal-energy-storage tanks, as deduced from trendwise comparisons with the available literature (e.g. [7,10–12,14–16,20]. From a careful examination of Fig. 11, several significant flow-related effects can be identified. First, the discharging efficiency of the conventional design is more or less constant and independent of the heating-elements relative height, h/H. This is due to the vigorous mixing between the inflow cold water and the storage hot water. For the draw rate of 5 l/min, therefore, the discharging efficiency is of the order of 68% (well-mixed tank) for heater A (H/D=1) but increases slightly to around 73% for heater B of higher aspect ratio (H/D=2) since flow mixing does not extend far in the vertical direction from the inlet port and, thus, relatively strong stratification is developed, as discussed before. With doubling the draw rate to 10 l/min, the discharging efficiency for both heaters A and B drops to around 60%, which is close to the perfectly-mixed limit of 63.2%. This is due to better mixing by the charging-jets induced entrainment, which becomes more vigorous with increasing flow rate. Hence, it can be concluded that conventional design EWHs are less efficient in terms of energy delivery during the first mean residence-time, 4 1. Secondly, the increase in the discharging efficiency for improved design EWHs is, however, comparatively small ( < 11%) as the aspect ratio is doubled from 1 to 2. These small differences in the efficiency values are reflective of the slight differences in the flow fields with heaters A and B. This means that the proposed simple design and configuration for the inlet and outlet ports are successful in restraining the extent of the mixing region and in confining it to the lowermost layers of the heater tank. Nevertheless, the noticeable decrease in the discharging efficiency of heater A (H/D=1) activated by element No. 1 (h/H=0.325) is attributed to the element shape (inverted U) which gives rise to better mixing and, in turn, increases the relative height of the mixing region. In contrast to heater A, the use of element No. 1 (h/ H=0.205) resulted in a slight decrease in the discharging efficiency of heater B since HB (63.4 cm)=1.58 HA (40 cm), Fig. 11(b), which overshadows the increase in the height of the mixing region. Finally, it is important to point out that the efficiency data shown in Fig. 11 highlight the major role of thermal stratification in determining the performance of such heaters. This is particularly true if the flow characteristics inside the heater tank facilitate the development of a thermocline region and consequently the existence of thermal stratification. With the conventional design and discharge rate v=5 l/min, for example, a better thermal stratification was observed in the tank of heater B (H/ D=2) that resulted in efficiency values ( 73%) higher than those ( 68%) of heater
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A (H/D=1) which always had a well-mixed tank. In contrast, improved design heaters lead to a stronger thermal stratification and, hence, higher discharging efficiency values (see Fig. 11) for both draw-off rates of 5 and 10 l/min. Accordingly, the discharging efficiency could be used with great confidence to assess thermal stratification inside the storage tanks of such type of EWHs.
6. Conclusions An experimental investigation of the thermal performance of an improved design for storage-type domestic EWHs was carried out. The performance, in terms of water draw-off temperature profile and discharging efficiency, was compared with that of conventional comparable design units of, 50 l tank capacity and 1200 W power rating. The results showed that the design improvements are very effective in enhancing the performances of such small capacity heaters as they could provide more hot water at almost constant temperature compared to conventional design EWHs. Moreover, the transient temperature-distributions in the storage water during hot/cold water discharging/charging process indicated the effectiveness of the horizontal wedged-pipe inlet in promoting thermal stratification inside such small size tanks, this had a direct impact on the heater performance as indicated by the higher discharging efficiency values. Further, better thermal stratification was obtained with increasing tank aspect-ratio and decreasing draw-off rate, which is consistent with the experimental information available in the literature concerning thermal energy storage tanks. Finally, this improved design for storage-type EWHs is still simple to adopt as it only requires minor modifications to be made to existing models for EWHs.
References [1] Reddy BS. Electrical vs. solar water-heater: a case study. Energy Conversion and Management 1995; 36(11):1097–106. [2] Hiller CC, Lowenstein AI, Merriam RL. Detailed water heating simulation model. ASHRAE Transactions 1994;100(1):948–54. [3] Hejazi SA. Sizing a storage type water heating system. ASHRAE Journal 1989;31(2):35–40. [4] Minguez JM. International Journal of Energy Research 1987;11:145 (as cited in [6]). [5] Lacroix M. Electric water heater designs for load shifting and control of bacterial contamination. Energy Conversion and Management 1999;40(12):1313–40. [6] Kar AK, Kar U. Optimum design and selection of residential storage-type electric water heaters for energy conservation. Energy Conversion and Management 1996;37(9):1445–52. [7] Wildin MW, Truman CR. A summary of experience with stratified chilled water tanks. ASHRAE Transactions 1985;91(1B):956–76. [8] Hollands KGT, Lightstone MF. A review of low-flow, stratified-tank solar water heating systems. Solar Energy 1989;43(2):97–106. [9] Zurigat YH, Ghajar AJ, Moretti PM. Stratified thermal storage tank inlet mixing characterization. Applied Energy 1988;30:99–111.
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[10] Wildin MW. Performance of stratified vertical cylindrical thermal storage tanks, part II: prototype tank. ASHRAE Transactions 1989;95(1):1096–105. [11] Wildin MW. Diffuser design for naturally-stratified thermal storage. ASHRAE Transactions 1990; 96(1):1094–102. [12] Zurigat YH, Liche PR, Ghajar AJ. Influence of inlet geometry on mixing in thermocline thermal energy storage. International Journal of Heat and Mass Transfer 1991;34(1):115–25. [13] Ghajar AJ, Zurigat YH. Numerical study of the effect of inlet geometry on stratification in thermal energy storage. Numerical Heat Transfer, Part A 1991;19:65–83. [14] Abu-hamdan MG, Zurigat YH, Ghajar AJ. An experimental study of a stratified thermal storage under variable inlet temperature for different inlet designs. International Journal of Heat and Mass Transfer 1992;35(8):1927–34. [15] Musser A, Bahnfleth WP. Evolution of temperature distributions in a full-scale stratified chilledwater storage tank with radial diffusers. ASHRAE Transactions 1998;104(1A):55–67. [16] Eames PC, Norton B. The effect of tank geometry on thermally-stratified sensible heat storage subject to low Reynolds number flows. International Journal of Heat and Mass Transfer 1998;41(14): 2131–42. [17] Berkel JV. Mixing in thermally stratified energy stores. Solar Energy 1996;58(4–6):203–11. [18] Mavros P, Belessiotis V, Haralambopoulos D. Stratified energy storage vessels: characterization of performance and modeling of mixing behavior. Solar Energy 1994;52(4):327–36. [19] Bourges B, Rable A, Leide B, Carvalho MJ, Collares-Pereira M. Accuracy of the European solar water heater test procedure, part 1: measurement errors and parameter estimates. Solar Energy 1991; 47(1):1–16. [20] Wildin MW, Truman CR. Performance of stratified vertical cylindrical thermal storage tanks, part 1: scale model tank. ASHRAE Transactions 1989;95(1):1086–95. [21] Yoo H, Pak E. Theoretical model of the charging process for stratified thermal storage tank. Solar Energy 1993;51(6):513–9. [22] Hahne E, Chen Y. Numerical study of flow and heat transfer characteristics in hot-water stores. Solar Energy 1998;64(1–3):9–18.
Performance of an improved design for storage-type domestic electrical water-heaters Adel A. Hegazy*, M.R. Diab Mechanical Power Engineering and Energy Department, Faculty of Engineering, Minia University, Minia-61517, Egypt Received 24 September 2001; received in revised form 7 December 2001; accepted 8 December 2001
Abstract Performance of an improved design for storage-type domestic electrical water-heaters (EWHs) was experimentally investigated for energy conservation. The results were compared with those of conventional design EWHs having the same tank size and power rating. Data were obtained for two tanks with aspect ratios of 1 and 2, two draw-off rates of 5 and 10 l/ min, and using three heating elements of different heights. It is found that improved design EWHs provide more hot water at almost constant temperature in the first mean residence time, which is of prime concern for the user. Thus, they exhibit higher discharging efficiencies due to better thermal stratification inside the heater storage tank. Also, thermal performance is enhanced with increasing tank aspect ratio and decreasing draw rate. These characteristics have a direct impact on energy consumption and result in lower electricity bills. The design improvements are simple to adapt as they only require minor modifications to be made to existing EWH models. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Electric water heaters; Energy conservation; Thermal storage; Thermal stratification
1. Introduction Storage-type electrical water-heaters (EWHs) are widely used in many countries all over the world for generating hot water in numerous domestic, commercial and industrial installations. In particular, they are very popular in the urban and suburban areas of developing countries, where the majority of the residential building
* Corresponding author. Tel.: +20-86-362083x237; fax: +20-86-346674. E-mail address: [email protected] (A. A. Hegazy). 0306-2619/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-2619(02)00006-5
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Nomenclature A B cp Con D E(t) Est(t) h H Im j t tres T T* v V Vj Vst z 1, 2, 3
electrical water heater A of aspect ratio H/D=1 electrical water heater B of aspect ratio H/D=2 specific heat of water conventional design internal diameter of the heater tank net energy delivered by water volume V during time t energy stored in the heater tank relative to Ti at time t height of the heating element height of the heater storage tank improved design water layer counter time mean residence time=Vst/ water temperature dimensionless temperature inside the heater tank, Eq.(7) outflow (=inflow) volumetric flow rate outflow (=inflow) volume of water during time t water volume of the j-th layer volume of the heater storage tank vertical distance from the bottom of the heater storage tank heating elements 1, 2 and 3 of heights 13, 28 and 33.4 cm, respectively
Greek letters dis discharging efficiency, Eq. (6) ðVÞ dimensionless water draw-off temperature profile, Eq. (2) water density dimensionless time=t=tres ¼ V=Vst Subscripts i inflow o outflow
stock consists of multi-family (multi-storey) buildings with individual domestic water heater for each apartment/unit. Compared to large central hot-water systems, the simplicity, reliability and low cost of storage-type EWHs are their main advantages in addition to the decrease in water consumption as the time spent waiting for the water to achieve acceptable temperatures at the fixture is less. Also, they do not require re-pressurization of the hot water, which is maintained inside the storage tank at the mains pressure along with the heating element (electric-resistant type). Accordingly, this allows substantial savings in piping, pumping, plumbing and heat-exchanger costs. Further,
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the temperature of the hot water inside the storage tank can be easily controlled by the user adjusting the thermostat setpoint within the range of 40–90 C. Furthermore, it has been shown by Reddy [1] that it is economically advantageous for a family of five persons or less to use an EWH than installing a solar WH in the absence of any governmental subsidy. The only disadvantage of storage-type domestic EWHs is their excessive consumption of electrical energy. As pointed out by Hiller et al. [2], such water-heating systems have historically been generously overdesigned to ensure adequate hotwater availability. The installation setpoint for the thermostat of most EWHs available in the market is between 60 and 65 C. Also, it is generally advised that when a large demand of hot water is required, the thermostat setpoint should be adjusted higher by the user, thereby increasing the thermal capacity of the storage water. A higher setpoint also offsets the effect of mixing between the incoming cold water and the storage hot-water during a water draw as mixing results in a lower water temperature at the fixtures. Therefore, it is a common practice in the design of such EWHs to assume that only 70% of the hot water in the storage tank is usable at an acceptable temperature level [3], i.e. at 43 C or higher. To overcome the problem of mixing between the incoming cold water and the storage hot-water, Minguez [4] suggested the use of two EWHs connected in series each with half the capacity and power rating of the single tank heater. Of course, a water heating system consisting of two identical EWHs connected in series is less aesthetically attractive and less compact than a single-tank heater. Therefore, such a system is more suitable for householders as recommended by Lacroix [5]. Kar and Kar [6] compared the performance of dual-tank EWHs in series with a single-tank EWH in terms of daily hot water output and energy saving per litre of maximum hot water producible. They concluded that a dual-tank EWH of the same volume and power rating as a single-tank EWH, where the second tank has 25% of the total volume and 75% of the total power rating, provides more hot water and reduces electricity consumption. However, this idea requires modifications in the classical design of EWHs, which increase the cost and complexity of such cheap and simple units. The other attractive alternative for the above suggested two-tank EWHs is the use of the conventional single-tank heater but incorporating the phenomenon of natural stratification to separate, without employing any physical barrier, between the hot and cold water masses. In stratified storage tanks, buoyancy is the only mechanism that is exploited to keep the hot water, of low density, floating above the cold water of higher density, resulting in a region of steep temperature gradient called a ‘thermocline’. Regarding storage-type EWHs, the thermocline region will always migrate from the bottom to the top of the tank as the cold water is charged near the bottom and the hot water is simultaneously discharged at an equal rate near the top. A survey of the literature revealed that the intensity of mixing (destratification) between the inlet cold (hot) water and the hot (cold) water in storage tanks during charging/discharging process depends on several dynamic and geometric parameters such as flow rates and temperatures of hot and cold water streams, storage-tank
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volume and aspect ratio, locations of inlet and outlet ports, and the geometry of the inlet diffuser [7–17]. The last parameter is found to be the most determinant one. This has led several investigators to search for other diffuser designs, which are rather different from the simple pipe inlet but are capable of reducing mixing that is induced by the incoming water flow. The range of the suggested diffuser designs include the use of slotted tubes, pipes with inverted cups, solid baffle plates, perforated circular plates, radial-flow disks, distributed nozzles, and perforated tubes. These diffuser designs have proven to be very effective in restraining mixing and, thus, they allow water stratification to be maintained for longer periods of time, which noticeably improves the tanks storage-efficiency. The objective of this investigation is to examine experimentally the performance of domestic EWHs when a horizontal wedged-pipe is employed as an inlet diffuser instead of the conventional vertical pipe inlet. Compared to the above mentioned diffuser types, the horizontal wedged-pipe inlet is still a simple device to adapt, much less expensive to manufacture, and only requires minor modifications to be made to existing models of EWHs. The effects of storage-tank aspect-ratio, height of heating element and the rate of water draw on the heater performance have been investigated. The heater performance is characterized by the percentage of energy delivered after drawing one tank volume and by the water draw-off temperature profile. Both parameters are obtained through a ‘‘mixing’’ experiment in which the water inside the heater storage tank is initially heated before pumping in three tank-volumes of cold water [18,19]. Also, a flow-visualization study is conducted to clarify the differences in the mixing mechanisms and the flow patterns inside the storage tank for both inlet diffusers.
2. Conventional and improved designs for domestic electric water heaters Residential storage-type EWHs are available in the markets as various brands, but all have cylindrical shape of different aspect-ratios and various capacities ranging from 20 to 500 l [3]. However, the 50 l tank-capacity model, hereafter referred as the conventional EWH, is the most popular since it occupies a relatively limited space and can be easily hanged on any wall in the kitchen or the bathroom of any apartment/unit. A typical domestic EWH of conventional design is shown schematically in Fig. 1(a). It is widely manufactured in Europe, region of the Middle East and in many other developing countries worldwide. Basically, each EWH consists of a cylindrical storage tanks which is generally made of steel and insulated with a layer of fiberglass or urethane foam that is placed between the tank and the external envelope to reduce heat loss to the ambient environment. Water is usually heated with a single immersed heating element (electrical-resistance type), which comes in different styles, lengths, heights and powerratings ranging from 8 to 26 W/l [6]. A sacrificial rod of magnesium alloy is often employed to minimize corrosion inside the tank. The heating element and the thermostat which regulates its functioning, and consequently the water temperature, are usually manufactured as one unit with a flange, so that it can be easily inserted
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Fig. 1. Domestic electrical water heater of: (a) conventional design and (b) modified design, which incorporates an improved design inlet diffuser as shown in (c).
vertically at the centre of the tank bottom. As shown in Fig. 1(a), the cold water enters the tank directly from the bottom through a short pipe, while the hot water leaves the tank near the top but is also brought to the bottom via an internal pipe through the water body. Each EWH is equipped with the necessary safety devices and associated fittings. Regarding the improved design of EWH, the literature survey has indicated that to achieve natural stratification in a storage tank, the inlet diffuser should be placed as close to the bottom of the tank as possible to minimize mixing between the incoming cold water and the storage hot-water. Also, the inlet diffuser should be carefully designed to distribute the incoming flow near the tank bottom with low velocities to retain natural stratification. To satisfy these conditions, while keeping the diffuser design quite simple to interest the manufactures of these EWHs, the proposed diffuser is made from a standard 12.7 mm (0.5 in) steel pipe positioned horizontally close to the tank bottom and normal to its perimeter, but only spanning 10 cm (25–31%) of the storage-tanks inside diameter. The lower half of this 10 cm inlet pipe was wedged [Fig. 1(c)] to direct the inflow towards the tank floor and, in turn, avoiding direct vigorous mixing with the hot water mass. In this way, the incoming cold water of higher density will gently push the hot water in the tank up out of the way with minimum mixing occurring at the interface. Compared to the conventional design, Fig. 1(a), this necessitates the fixing the inlet port to the tanks lateral surface as illustrated in Fig. 1(b). Further, to eliminate heat-exchange between the hot water draw and the rest of the water body in the tank, as in the conventional design, the outlet port is also relocated at the lateral surface of the storage-tank directly above the inlet port but as higher as possible. The outlet
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diffuser is simply a 12.7 mm (0.5 in) standard steel-coupling, flush welded to the tank surface.
3. Experiments Performance tests were made for two specially-designed domestic EWHs, having an equal storage capacity of 50 l, but of different dimensions. Heater A has a cylindrical storage tank of height H=0.4 m with an internal diameter D=0.4 m (i.e. an aspect ratio of 1), while the tank of heater B is 0.634 m height and 0.317 m inside diameter, yielding an aspect ratio of 2. Both storage tanks were made from the same 2 mm thick galvanized steel sheet and were insulated on the lateral surface and top and bottom with the same thickness of fiberglass mats. A typical test heater is shown schematically in Fig. 2. Each heater has two inlets for incoming cold water located at the same level 4 cm from the bottom of the tank (zi) and two outlets for hot water draw located also at the same level but 4 cm from the top of the tank (H-zo). Inlet (1) and outlet (2) are of conventional design and are normal to the tank bottom while inlet (3) and outlet (4) have the modified design and configuration as explained above. Both test heaters A and B are equipped with the necessary valve-arrangement and associated plumbing to switch from the conventional inlet–outlet combination to the
Fig. 2. Schematic of test heater.
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improved one. The flow rate of the incoming cold water, and consequently the flow rate of hot water draw, was adjusted by using control valves attached at the outlet ports, while keeping the inlet valves fully opened during testing. The draw-off rate was measured using a calibrated catch tank and a stopwatch. Much care was taken in adjusting the opening of the outlet control valve so that the accuracy of the measured flow rate was always within 0.1 l/min or better. Nevertheless, cold water inflow was supplied from a large constant-head elevated tank to ensure steady flow conditions. Experiments were carried out for two draw-off rates of 5 and 10 l/min. The water flowrate is the same at the inlet and outlet ports as long the storage tank behaves as an open system during the experiment. Three heating elements, having a nominal power rating of 1200 W, but of different heights equal to 13, 28 and 33.4 cm, were used to initially heat the water inside the storage tanks of test heaters A and B. The shortest heating element (No. 1) is typical to the second one (No. 2) of height 28 cm, but it was formed to have an inverted Ushape [see Fig. 1(a)] of 13 cm height, which is approximately half the original height. These heating elements were welded to three identical brass flanges, so that they can be easily interchanged and installed at the central opening in the tank bottom of either heaters A or B. Transient temperature distributions for the water inside the storage tank of each EWH were measured using nine copper-constantan thermocouples made of wires 0.315 mm in diameter. The thermocouple probes was inserted vertically from a sealed opening in the tank top and close to its axis as shown in Fig. 2. The junctions of the thermocouples were located at the centres of nine equal volumes of the storage water. For conventional and improved designs, these temperature measurements were employed in determining the characteristics of thermal stratification inside the storage tanks of both heaters A and B during the hot/cold water discharging/charging processes. Two more pairs of thermocouples were placed in the inlet and outlet ports for continuously monitoring the inflow and outflow water temperatures. These two temperatures, in conjunction with water draw-off rate, were used to evaluate the amount of energy delivered out of the heater storage tank. Temperature signals were collected from the test heater by a data logger interfaced to a personal computer. Regardless of the water flowrate, water-temperature data inside the tank were sampled at 30-s intervals. Calibration of the thermocouples showed that the overall accuracy of the measurements was within 0.2 C. Flow visualization experiments were also made to study the characteristics of the incoming cold-water stream when it was introduced either from the conventional inlet or the improved one. Experiments were conducted in a steel tank sized 707070 cm3 and having a 6060 cm2 glass window on the front side. Initially, the tank was filled with clear hot-water having a uniform temperature of 70 C. In contrast, the inflow cold water was separately maintained at the uniform temperature of 25 C in the constant-head elevated tank and was colored with black dye to facilitate the observation of the flow pattern and its characteristics. Visualization of flow was performed by introducing the colored cold-water into the rectangular tank through either the conventional inlet or the modified one. Photographic flow visualization records were also made using a 35 mm single-lens reflex camera for later inspection.
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4. Test procedure and discharging efficiency The basic sequence of the present test procedure is similar to the procedure of Collector and System Testing Group of the European Community [18,19] except for some minor differences in details to simulate the actual operation of a domestic EWH. Before the start of the experiment, water was allowed to discharge from the storage tank of a particular EWH while carefully controlling the draw-off rate (v) to the desired value of 5 or 10 l/min either through the conventional or the improved inlet-outlet ports. Then, the valve of the outlet port was closed, so that the storage tank becomes full with cold water at a uniform temperature (Ti) before activating the heating element. After 150 min, the electrical heater was turned off and the initial temperature distribution inside the storage tank was recorded. Immediately, the valve of the outlet port was opened to discharge an amount of water (Vo) equivalent to three tank volumes (3Vst) while simultaneously charging the storage tank, at the same rate, with cold water (Vi) at temperature (Ti). During this discharging/charging process with Vo ¼ Vi ¼ V, the outflow and inflow temperatures (To, Ti) as well as the temperature of the nine thermocouples inside the storage tank (T1, . . . Tj, . . . T9) were monitored and recorded for subsequent data processing. Of course, the duration of each test depends on water volumetric flowrate but, in general, it could be said that each test lasts three times the mean residence time (3tres) necessary to fully charge the storage tank with an equal water volume at a given volumetric flowrate: tres ¼ Vst =v
ð1Þ
Although the temperature data were recorded as a function of time (t), these data can be expressed in terms of the withdrawn volume (V) since for a constant volumetric flowrate V ¼ tv. Accordingly, the temperature history To(V) of the water leaving the EWH can be easily related to the withdrawn volume (V) and it is called ‘‘The draw-off temperature profile’’, To(t) [19]. Also, it may be expressed in dimensionless form as: ðVÞ ¼ ðTo ðVÞ Ti Þ=ðTo ðV ¼ 0Þ Ti Þ;
ð2Þ
where ðVÞ is the draw-off profile. Note that To ðV ¼ 0Þ is actually the highest temperature of water initially present in the heater tank and at the entrance of the outlet port of either design at t=0. The initial temperature distribution inside the storage tank, which was recorded immediately before drawing off the hot water, is employed in computing the initial energy stored in the tank relative to the temperature of the cold water Ti: Est ðt ¼ V ¼ oÞ ¼
9 X Vcp j Tj Vj Ti j¼1
ð3Þ
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where and cp are the density and specific heat of the water sub-volume Vj of the tank j-th layer. The total number of layers are nine corresponding to the number of thermocouples in the tank. In writing Eq. (3), it is assumed that the temperature measured by each thermocouple Tj prevails over the entire sub-volume Vj. Eq. (3) was also used to compute the water stored energy relative to Ti at any time t. On the other hand, the amount of useful energy delivered by the water leaving the storage tank up to a certain time t can be calculated by: ðt EðtÞ ¼ vcp ðTo ðtÞ Ti Þdt ð4Þ 0
on the basis of the same volumetric flowrate at the inlet and outlet ports and incorporating the measured temperatures of the water inflow and outflow. Employing Eq. (1), however, the delivered energy could be expressed in terms of the dimensionless time ¼ t=tres , which is also equal to ðV=Vst Þ, as follows: ð Eð Þ ¼ Vst cp ðTo ð Þ Ti Þd ð5Þ 0
where the upper limit of is 3. It is important to evaluate the effect of the proposed design improvements on the thermal stratification inside the heater tank during the discharging process and, in turn, on the performance of EWHs A and B. This is assessed by computing the discharging efficiency, which is defined as the ratio of the net thermal energy delivered in the first mean residence time 0 4 4 1 (i.e. after pumping through one tank volume of cold water V=Vst) to the initial thermal energy stored in the heater tank. Hence, the discharging efficiency dis could be expressed as : dis ¼ Eð ¼ 1Þ=Est ð ¼ 0Þ
ð6Þ
after using Eqs. (3) and (5). It should be mentioned that the discharging efficiency dis is the same as the storage efficiency defined by Mavros et al. [18], but it is the opposite to the figure of merit (FOM) proposed by Wildin and Truman [20], the storage efficiency utilized by Yoo and Pak [21], and the charging efficiency employed by Hahne and Chen [22] as a measure of the performance of the hot-water charging process. In fact, fluid mixing is unavoidable during hot-water discharging. So that, the discharging efficiency varies between two limiting values. The upper limit is dis=100%, corresponding to a perfectly-stratified tank in which the cold water inflow is continuously pushing the hot water up in an ideal plug flow manner without any mixing or disturbance. The other limiting case is the perfect mixing of the cold and hot fluids in the tank throughout the discharging process. For this unstratified case, with water initially isothermal in the tank, it can be easily proved that dis is equal to 63.2% after withdrawing one tank volume of water, V=Vst, [19,21]. By increasing the volume of the water draw, the discharging efficiency increases
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correspondingly but with a slower rate, approaching the value of 95% for V=3Vst. Achieving nearly the upper limit of discharging efficiency after pumping through one tank volume is the aim of the present design improvements, which means effective use of the thermal energy stored in the heater tank and, in turn, significant savings in the electricity consumption.
5. Results and discussion Twenty four experiments were conducted during the course of this study to investigate the effects of storage tank aspect ratio H/D, heating element relative height h/H, discharging flow rate v, the design and configuration of inlet and outlet ports on the performance characteristics of such 50 l, popular size EWHs. Also, the transient temperature distributions of water inside the heater tank were examined to reveal the affects of these parameters on the thermal stratification of the storage water and how it affects the heater performance. These distributions are presented in terms of the dimensionless height (z/H) and temperature T* defined by: T ðz; tÞ ¼ ðTðz; tÞ Ti Þ=ðTo ðt ¼ 0Þ Ti Þ
ð7Þ
where T(z, t) is the temperature of the storage water at height z and given time t. The initial (t ¼ 0) temperature distributions of storage water inside EWHs A and B after a heating period of 150 min are shown in Fig. 3, on an average basis, and are parameterized by the heating element relative height, h/H. Clearly, the temperature of water in the upper half of any tank is almost uniform in contrast to those in the lower halves of tanks A and B which are seen to depend remarkably on the tanks aspect ratio (H/D) and on the element relative height (h/H). Thus, more uniform
Fig. 3. Initial temperature distributions of water inside test heaters A and B using heating elements 1, 2 and 3.
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temperature inside the storage tank, which is highly desirable, could initially be obtained by using storage tanks of high aspect-ratios and equipped with short heating elements. For the extreme case of heater B (H/D=2) with heating element No. 1 (h/H=0.205), however, part of the slight variation in the temperature distribution in the region adjacent to the tank bottom is attributed to the conduction heat loss through the metal pipework and the supporting rods of the EWH since both act as cooling fins. Experiments were conducted for different days of different ambient temperatures. Therefore, heat losses due to the fin effect are expected to vary, resulting in variations in the initial (t=0) readings of the thermocouples. In general, the initial temperature distributions at t=0 of a particular EWH A or B, energized with a certain heating element 1, 2 or 3, are almost the same except for the first thermocouple since it is close to the tank bottom. The transient temperature distributions (t > 0) of storage water in EWHs A and B during hot/cold water discharging/charging process as at a rate of 5 l/min are shown in Figs. 4 and 5, respectively, for both conventional (a, c) and improved (b, d)
Fig. 4. Transient temperature distributions for the water during discharging at 5 l/min from heater A (H/D=1) with (a, c) conventional or (b, d) improved design and heating elements Nos. 1 and 2.
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Fig. 5. Transient temperature distributions for the water during discharging at 5 l/min from heater B (H/D=2) with (a, c) conventional or (b, d) improved design and heating elements Nos. 1 and 2.
designs with heating elements Nos. 1 and 2. For the sake of brevity, the results of heating element No. 3 are not presented since they are similar in behaviour and close to those of heating element No. 2. In general, the transient temperature-distributions are seen to be significantly dependent on the inlet/outlet configuration and design as well as on the storage tanks aspect ratio H/D. Although the temperature distributions for the improved design EWHs A and B are similar in character see Figs. 4(b and d) and 5(b and d), there are quantitative differences among them, and also they differ from the corresponding distributions for the conventional design. However, the temperature distributions for the conventional design EWHs A and B exhibit different characteristics as illustrated in Figs. 4(a and c) and 5(a and c). Attention may first be turned to the transient temperature distributions shown in Figs. 4(a and c) and 5(a and c) for the conventional design with short and long pipes inserted vertically from the bottom of the storage tank as inlet and an outlet diffusers, respectively. Obviously, the temperature distributions for heater A are quite
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different from those of heater B. Also, it is noticeable in Fig. 4(a and c) that heater A has a well-mixed tank, i.e. uniform temperature, at any time > 0.1. In contrast, the temperature distributions of heater B show a relatively strong thermal stratification along with a thick thermocline region due to the presence of a large circulation in the lower half of the tank as can be identified in Fig. 5(a and c). However, the size of this circulation gets larger and stronger when element No. 1 is used in heating the storage water. This is attributed to the inverted U-shaped element, which evidently influences the flow and mixing, resulting in smaller temperature gradients. Such a flow behaviour could be explained with the aid of flow-visualization tests which showed that the simple vertical-pipe inlet diffuser produces severe mixing and entrainment between the inflow cold water and the hot water in the tank due to the jet-like flow of the incoming water. For a flow rate of 5 l/min and water height of the order of 40 cm ( HA), the mixing region occupies most of the test tank and thus water mixing is greatly enhanced, resulting in a well-mixed tank. On the other hand, when the height of the hot water is of the order of 60 cm ( HB), the flow pattern in the test tank resembles a mushroom-shape submerged jet, while the circulation region shrinks in size to occupy only most of the tanks lower half. Attention may now be turned to the transient temperature-distributions of the improved design EWHs shown in Figs. 4(b and d) and 5(b and d). For this design, the inflow diffuser is simply a short horizontal-pipe with a wedged-cut in its lower half and is fixed near the tanks bottom, while the outflow port is directly above and parallel to the inflow port but far as possible on the tanks lateral surface. Therefore, the cold inflow water is directed towards the bottom of the tank and tends to stay there since it has a negatively buoyant force relative to the storage hot water. This reduces mixing with the upper layers and results in a stable stratification with a relatively thin thermocline region separating the hot top layers and cold bottom ones. As seen in Figs. 4(b and d) and 5(b and d), the decrease in the temperature of the bottom layers is initially faster due to the smaller thickness of the mixing zone. These thermofluid characteristics are more apparent in Fig. 5(b and d) for heater B of aspect ratio 2 as the outlet port is relatively away from the mixing zone at the inlet. The flow visualization study has indicated that the flow behaviour of the cold water downstream of the wedged inlet diffuser is close to that of an offset wall-jet so, creating a small circulation zone at the tanks lowermost region, which causes limited mixing between the incoming cold-water and the storage hot-water. Consequently, moderate thermal stratification is initially developed which gets stronger with time as more cold water is charged up to =0.3–0.4 for heater A and =0.5–0.6 for heater B; see Figs. 4(b and d) and 5(b and d). This is accompanied by a substantial difference in the temperature of water in the uppermost and lowermost layers in the tank along with a continuous upward movement for the thermocline region. With further increase in the dimensionless time , thermal stratification decays and the thermocline region fades away until the temperature of the water in the tank becomes uniform but decreasing steadily to approach the inlet one. These characteristics are more pronounced in Fig. 5(b and d) for heater B of the higher aspect ratio. Further inspection of Figs. 4(b and d) and 5(b and d) reveals that the relative height (z/H) of the circulation region at the bottom of heater A tank is greater than the
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corresponding one with heater B. In fact, the actual height (z) of the circulation zone in both tanks is almost the same, since it depends only on the design of the inlet diffuser, while the height of heater A (40 cm) is almost two-thirds that of heater B (63.4 cm). However, it is obvious from these figures that the height of this circulation region was also affected by employing heating element No. 1 due to its inverted U-shape, which enhances the water mixing and increases the thickness of the thermocline. The draw-off temperature-profiles for the previously considered cases are plotted in Figs. 6 and 7 for EWHs A and B, respectively. Also superimposed on these figures are the initial temperature-distributions, which represent the draw-off profiles under
Fig. 6. Draw-off temperature profiles of water discharging at 5 l/min from heater A (H/D=1) with conventional or improved design and heating elements Nos. 1 and 2.
Fig. 7. Draw-off temperature profiles of water discharging at 5 l/min from heater B (H/D=2) with conventional or improved design and heating elements Nos. 1 and 2.
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the conditions of an ideal plug flow, to fairly assess the effects of design improvements on the performances of such EWHs. For the conventional design, examination of Figs. 6 and 7 reveals that heaters A and B perform in a markedly different fashion. As is expected, the draw-off profiles for heater A display the classical shape that is characteristic of a perfectly-mixed tank over the experiment duration =0–3. On the other hand, the draw-off profiles for heater B show a different behaviour by comparison. In the interval of < 0:5 for element No. 1 and < 0:7 for element No. 2, the draw-off profiles resemble those of flow through a double-pipe heat-exchanger before they drop sharply and then continue to decrease, but with a slow rate for > 1:2. In general, the profiles for both heaters A and B have long ‘‘tails’’, which means that appreciable amounts of hot water are trapped in the side corners and, hence, such a conventional design is less efficient in terms of energy delivery during the first mean residence-time, i.e. 0 4 4 1. The draw-off profiles of improved design EWHs are quite different from those of the conventional design. As shown in Figs. 6 and 7, the temperature profiles of water out from EWHs A and B display a profile that is close to the ideal plug flow case. This is clearly evident for heater B (H/D=2) compared to heater A (H/D=1). In other words, heater B is capable of delivering a greater volume of hot water at nearly constant temperature than heater A. This is the desired characteristic which motivated the present study. The second set of experiments is similar to the first one, except that the draw-off rate is doubled to 10 l/min. For brevity, representative transient temperature distributions from this set of experiments are plotted in Figs. 8 and 9 for EWHs A and B and employing heating-element No. 2. The corresponding draw-off profiles are presented in Fig. 10. To place the effect of doubling water draw in perspective, these temperature distributions should be compared with those of draw rate 5 l/min shown in Figs. 4 and 5. For heater A (H/D=1) with the conventional design, it is seen in Fig. 8(a) that the transient temperature-distributions are almost uniform for
Fig. 8. Transient temperature distributions for the water during discharging at 10 l/min from heater A (H/D=1) with (a) conventional or (b) improved design and heating element No. 2.
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Fig. 9. Transient temperature distributions of water during discharging at 10 l/min from heater B (H/ D=2) with (a) conventional or (b) improved design and heating element No. 2.
5 0:2, indicating a fully mixed tank. By examining and comparing Figs. 8(a) and 4(c), however, it is seen that the transient temperature-distributions for v=10 l/min are at higher values than the corresponding distributions for v=5 l/min at any time > 0:1. This warming up is a consequence of better mixing inside the tank of the EWH since the momentum of the inlet flow jet for v=10 l/min is much greater than the one for v=5 l/min. Turning to heater B (H/D= 2) with the conventional design, inspection of Figs. 9(a) and 5(c) reveals that doubling the charge rate gives rise to a greater mixing intensity of the cold water emerging from the inlet diffuser so that a fully mixed tank is left after each withdrawal. Also the comparison between the draw-off profiles illustrated in Figs. 10(b) and 7(b) confirms that for v =10 l/min water mixing is much vigorous due to the inertia of the incoming cold water and, in turn, mixing extends far from the inlet to include the whole tank for this case. Therefore, the draw-off profile in Fig. 10(b) seems to be close to the profile of Fig. 10(a) instead of the profile shown in Fig. 7(b). A further exploration of the effect of doubling water draw-off rate to 10 l/min can be made by comparing Figs. 8(b) and 9(b) with Figs. 4(d) and 5(d) for v=5 l/min, where the transient temperature-distributions are shown for improved design heaters A and B, respectively. The comparison reveals that with doubling the flow rate, the thermocline gets thicker, while the mixing region in the neighborhood of the tank bottom is increased in size by almost 50%. This is due to the increase in water mixing downstream of the inlet diffuser. In contrast to the conventional design, mixing is not so vigorous and, in turn, the temperatures in the mixing region exhibit an appreciable departure from uniformity for < 0:9. Such a behaviour is attributed to the damping effect of the improved design inlet-diffuser. For heater A of aspect ratio 1, it can be noticed that the thermocline is much thicker and degrades faster when v=10 l/min since the mixing region occupies two-thirds of the tank volume. This means that such EWHs should be designed with higher aspect-ratios for better
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thermal performances. The draw-off profiles shown in Fig. 10 confirm this conclusion. As is obvious, heater B (H/D=2) delivers more hot water than heater A (H/ D=1) in the first mean residence time 0 4 st ð¼ V=Vst Þ 4 1. Nevertheless, almost 70% of this amount of hot water ð0 < < 0:7Þ exhibits a nearly constant temperature, which is of prime concern for the users of such heaters. To quantify the effects of design improvements on the performance of conventional design EWHs, Fig. 11 has been prepared. The figure consists of two graphs; the first one (a) is for test heater A of aspect ratio 1 while the second (b) is for heater B of aspect ratio 2. In each graph, the discharging efficiency dis is plotted versus the heating-elements relative height (h/H) for the considered draw-off rates v=5 and 10 l/ min. To distinguish between the different sets of results, the data for improved
Fig. 10. Draw-off temperature profiles for water discharging at 10 l/min from heaters A and B with the conventional or improved design and heating element No. 2.
Fig. 11. Comparisons among the discharge-efficiency results for improved and conventional design heaters A and B under different test conditions.
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design (dark symbols) are represented by lines, while data for conventional design (open symbols) are fitted with dashed lines. However, the effect of aspect ratio on the performance of such heaters can be deduced by comparing the efficiency values reported in Fig. 11(a) and (b) under similar test conditions. An overview of the results in Fig. 11 shows that the proposed design improvements are successful in enhancing the thermal performance, as indicated by the higher values for discharging efficiency (dark symbols). Regardless of the heater design, it is generally seen that the discharging efficiency increases with increasing tanks aspect-ratio, but it decreases with increasing draw rate. These trends are, in line with the experimental information for thermal-energy-storage tanks, as deduced from trendwise comparisons with the available literature (e.g. [7,10–12,14–16,20]. From a careful examination of Fig. 11, several significant flow-related effects can be identified. First, the discharging efficiency of the conventional design is more or less constant and independent of the heating-elements relative height, h/H. This is due to the vigorous mixing between the inflow cold water and the storage hot water. For the draw rate of 5 l/min, therefore, the discharging efficiency is of the order of 68% (well-mixed tank) for heater A (H/D=1) but increases slightly to around 73% for heater B of higher aspect ratio (H/D=2) since flow mixing does not extend far in the vertical direction from the inlet port and, thus, relatively strong stratification is developed, as discussed before. With doubling the draw rate to 10 l/min, the discharging efficiency for both heaters A and B drops to around 60%, which is close to the perfectly-mixed limit of 63.2%. This is due to better mixing by the charging-jets induced entrainment, which becomes more vigorous with increasing flow rate. Hence, it can be concluded that conventional design EWHs are less efficient in terms of energy delivery during the first mean residence-time, 4 1. Secondly, the increase in the discharging efficiency for improved design EWHs is, however, comparatively small ( < 11%) as the aspect ratio is doubled from 1 to 2. These small differences in the efficiency values are reflective of the slight differences in the flow fields with heaters A and B. This means that the proposed simple design and configuration for the inlet and outlet ports are successful in restraining the extent of the mixing region and in confining it to the lowermost layers of the heater tank. Nevertheless, the noticeable decrease in the discharging efficiency of heater A (H/D=1) activated by element No. 1 (h/H=0.325) is attributed to the element shape (inverted U) which gives rise to better mixing and, in turn, increases the relative height of the mixing region. In contrast to heater A, the use of element No. 1 (h/ H=0.205) resulted in a slight decrease in the discharging efficiency of heater B since HB (63.4 cm)=1.58 HA (40 cm), Fig. 11(b), which overshadows the increase in the height of the mixing region. Finally, it is important to point out that the efficiency data shown in Fig. 11 highlight the major role of thermal stratification in determining the performance of such heaters. This is particularly true if the flow characteristics inside the heater tank facilitate the development of a thermocline region and consequently the existence of thermal stratification. With the conventional design and discharge rate v=5 l/min, for example, a better thermal stratification was observed in the tank of heater B (H/ D=2) that resulted in efficiency values ( 73%) higher than those ( 68%) of heater
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A (H/D=1) which always had a well-mixed tank. In contrast, improved design heaters lead to a stronger thermal stratification and, hence, higher discharging efficiency values (see Fig. 11) for both draw-off rates of 5 and 10 l/min. Accordingly, the discharging efficiency could be used with great confidence to assess thermal stratification inside the storage tanks of such type of EWHs.
6. Conclusions An experimental investigation of the thermal performance of an improved design for storage-type domestic EWHs was carried out. The performance, in terms of water draw-off temperature profile and discharging efficiency, was compared with that of conventional comparable design units of, 50 l tank capacity and 1200 W power rating. The results showed that the design improvements are very effective in enhancing the performances of such small capacity heaters as they could provide more hot water at almost constant temperature compared to conventional design EWHs. Moreover, the transient temperature-distributions in the storage water during hot/cold water discharging/charging process indicated the effectiveness of the horizontal wedged-pipe inlet in promoting thermal stratification inside such small size tanks, this had a direct impact on the heater performance as indicated by the higher discharging efficiency values. Further, better thermal stratification was obtained with increasing tank aspect-ratio and decreasing draw-off rate, which is consistent with the experimental information available in the literature concerning thermal energy storage tanks. Finally, this improved design for storage-type EWHs is still simple to adopt as it only requires minor modifications to be made to existing models for EWHs.
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