Abstract
The effect of a cylindrical baffle on heat transfer to an immersed heat exchanger is investigated in initially thermally stratified tanks. The heat exchanger is located in the annular region created by the baffle and the tank wall. Three different cases of initial thermal stratification are explored, and in each case, experiments are conducted with and without the baffle in the stratified tank and in a comparable isothermal tank with the same initial energy, enabling exploration of the role of the baffle in a stratified tank and the role of stratification in tanks with or without the baffle. The baffle maintains the high initial temperature of the upper zone of the stratified tank for 10–16 min, as cool plumes that form on the heat exchanger are confined to the annular baffle region until they exit at the bottom of the tank. Regardless of stratification, the baffle always improves heat transfer to the immersed heat exchanger. In the isothermal tanks, the baffle increases total energy extracted in the first 30 min of discharge by over 20%. In stratified tanks, the baffle increases total energy extracted in 30 min of discharge by 9–16%. Initially, improvement in heat transfer in stratified tanks is due to the higher driving temperature differences around the heat exchanger. Later, after all the water from the hot zone has entered and flowed through the baffle, the tank is basically isothermal, and velocity increases as the fluid temperature drops, maintaining rates of heat transfer higher than that in the tank without the baffle. Stratification improves heat transfer in tanks without a baffle because, by design, the driving temperature difference between the heat exchanger wall and the surrounding fluid is considerably higher. However, in tanks with the baffle, stratification has only a modest positive effect on heat transfer to the immersed heat exchanger.
Introduction
The impacts of excessive greenhouse gas emissions on our climate have already arrived and will get worse before they get better. To avoid outright global catastrophe, we must make a rapid and dramatic shift to renewable and sustainable energy resources [1]. This shift cannot be made by relying on a single technology or focusing on a single energy sector; it must include a wide array of technologies in all sectors. Reducing emissions from thermal loads in buildings is no exception. Meeting those loads with heat pumps, electric water heaters, and so on, running on low-carbon electricity can reduce building emissions, but that approach does not apply equally well in all settings. Moreover, the environmental consequences of solar photovoltaics, wind, and batteries grow when we try to replace more and more energy services with low-carbon electricity (i.e., transportation, building thermal loads, thermal processes in manufacturing, etc.) [2,3]. Solar thermal hot water systems can provide an elegant alternative, as they capture diffuse and intermittent solar energy, store it, and use it to meet the similarly low-quality energy demands of space heating and domestic hot water. Thus, our lab continues to pursue development of more efficient and effective solar thermal storage systems.
It is well established that stratification in the solar storage tank can improve overall system performance, often quantified by annual solar fraction [4,5]. Enhancing stratification decreases the temperature of the water that leaves the storage tank and flows to the solar collector, resulting in the largest possible gains in the collector. It can also improve heat transfer to heat exchangers immersed in the tank, increasing the temperature of water available to meet thermal loads. Strategic placement of immersed heat exchangers in the tank can maximize a driving temperature difference for heat transfer and/or create useful thermal zones in the tank [6]. As such, they are often employed in “combistores” (tanks designed to meet multiple thermal loads simultaneously) [7–9]. Immersed heat exchangers can also simplify a system by eliminating the need for a pump or a pressurized tank when the heat exchanger working fluid is pressurized water from the main water supply.
When immersed heat exchangers are made from highly conductive materials, the dominant resistance to heat transfer between the heat exchanger working fluid and the storage fluid is the natural convection heat transfer between the heat exchanger outer wall and the storage fluid. Two mechanisms can increase that convective heat transfer: increasing the driving temperature between the heat exchanger wall and storage fluid, usually done by increasing thermal stratification in the tank or increasing the velocity of the recirculating tank fluid as it flows around the heat exchanger. Strategically placed barriers in the storage tank—baffles and shrouds—can be used to control the flow field in the tank with the goal of improving heat transfer to immersed heat exchangers by one or both of those mechanisms. However, many baffles and shrouds investigated have not successfully improved heat transfer generally because designs chosen to improve stratification had the unintended consequence of dramatically reducing fluid velocity [10–12]. Others showed benefits of baffle-shrouds through simulations but used geometries that are not applicable to solar storage tanks [13–15].
However, work at the University of Minnesota Solar Lab demonstrated the benefits of a cylindrical baffle that creates an annular region with the tank wall, within which a coiled heat exchanger is located [12,16]. With this design, as shown in Fig. 1, water from the top of the tank enters the baffle region and flows over the heat exchanger. The cool plumes that form on the heat exchanger are confined to that annular region, only exiting at the bottom of the baffle region, located toward the bottom of the tank. In these initial studies, we found that the baffle created a flow field with higher fluid velocities around the heat exchanger, resulting in improved heat transfer to the heat exchanger when the baffle was in place. Though the baffle did not create significant thermal stratification (), it did maintain thermal stratification in an initially thermally stratified tank [16].
Subsequent investigations by the Lafayette College Solar Lab into the baffle geometry [17,18], the width of the annular region [19], and the heat exchanger pitch [20] have refined and optimized the design of the cylindrical baffle and immersed heat exchanger for discharging an initially isothermal hot water storage tank. All experiments have shown the consistent benefit of the cylindrical baffle, with all baffle experiments outperforming experiments conducted without the baffle. Through both experiments [17] and simulations [18], we showed that a straight baffle design outperformed more complicated designs in which the annular width below the heat exchanger was smaller than that around the heat exchanger. The straight design allowed for the highest velocities across the heat exchanger and, thus, the most significant improvements to heat transfer. A subsequent experimental optimization of the baffle diameter [19] determined that narrowing the annular region created by the baffle and the tank wall resulted in slight improvements in heat transfer due to slight increases in thermal stratification. The narrowest baffle region investigated has a width of 1.5 times the heat exchanger diameter, or 1.5, so that width was used in subsequent studies. Because the baffle region width of 1.5 leaves only a tiny 2 mm gap between the heat exchanger and the tank and baffle walls, it was the smallest considered.
Most recently, we explored the effect the pitch of the coils of the immersed heat exchanger have on heat transfer in an initially isothermal tank [20]. Experiments were conducted with heat exchangers of pitches varying from 2 to 12, both with and without a straight baffle. All cases with the baffle outperformed all cases without the baffle. In the tank with no baffle, the heat transfer improves with the increasing heat exchanger pitch. In contrast, with the baffle in place, the heat exchanger pitch has very minimal effect on heat transfer. The performance of the heat exchanger with a pitch of 3 slightly outperformed those with pitches of 2, 4, and 6, but overall the baffle significantly reduced the effect of the pitch on heat transfer especially for pitches of 6 and smaller. We attributed this finding to a direct tradeoff between the temperature of the water around the heat exchanger and the velocity of that water as it flows past the heat exchanger. As pitch increased from 2 to 6, the driving temperature difference increased, but the velocity of the plumes decreased.
In this study, we take the optimized parameters of the past studies—a straight baffle region of width 1.5 and a heat exchanger with a pitch of 3—and explore the performance of the system when the tank is initially thermally stratified. The first experimental study on the utility of a cylindrical baffle [16] included a brief exploration of the performance of an initially thermally stratified tank. We found that the baffle maintained the existing thermal stratification and, thus, high temperatures approaching the heat exchanger for 15 min. However, that study did not include comparisons of heat transfer with and without the baffle in place or comparisons to an isothermal tank. Moreover, while many studies have explored generating and maintaining thermal stratification [4,5,21,22], none investigated the combined effects of the cylindrical baffle and thermal stratification. In this work, we examine three variations of initial thermal stratification. For each case, we conduct experiments with and without the baffle. We also conduct experiments in an isothermal tank with the same initial energy, again with and without a baffle. These sets of four experiments for each of the three stratification cases will provide insights into the combined effects of the cylindrical baffle and thermal stratification on heat transfer to an immersed heat exchanger.
Methods
The experimental apparatus and procedure used in this study are largely the same as those used in the prior work from our lab [17,19,20]. In the prior work, we varied the baffle and heat exchanger design, while in this work, we vary only the initial condition of the storage fluid temperature. We refer readers to Nicodemus et al. [17] for a more detailed explanation of the experimental method.
Experimental Apparatus.
The 300 L, well-insulated () experimental tank is depicted in cross-sectional view in Fig. 2. The baffle is constructed from a 3 mm thick polycarbonate sheet, rolled into a cylinder with a radius of 282 mm, creating an annular region 1.5 times the diameter of the heat exchanger, or 1.5. The baffle length, , is 871 mm, and the baffle sits on legs so that it extends from mm to m, where is the distance from the bottom of the tank. Tank dimensions are shown in Fig. 2.
The heat exchanger, made from a 10 m long copper tube with an outer diameter, , of 9.5 mm, and an inner diameter, , of 8 mm, is sized to ensure that storage side natural convection is the dominant thermal resistance. It is formed into a coil with a radius of 290 mm and a pitch 28.5 mm (three times tube diameter or 3), resulting in 5.5 loops. The heat exchanger shape is maintained by four polycarbonate spacers that also secure the heat exchanger at the top of the tank and center the baffle in the tank. For both experiments with and without the baffle, the center of the copper tube is 0.75 from the tank wall. In experiments with the baffle, this puts the heat exchanger in center of the annular region between the tank wall and the baffle.
Procedure.
The nominal initial conditions for the three stratification cases are shown in Fig. 3. In case 1, the upper 60% of the tank is nominally 60 , while the lower 40% is 40 . In Case 2, which has a smaller cold zone relative to Case 1, the upper 80% is initially 60 and the lower 20% is initially 40 . In Case 3, which has a smaller temperature difference relative to Case 1, the upper 60% is initially 60 and the lower 40% is initially 50 . Experiments in the stratified tanks are run with and without the baffle. As previously described, each stratification case has a corresponding isothermal case. The initial temperatures of these corresponding isothermal experiments are such that the initial energy in the isothermal tank is the same as or very close to the initial energy in the stratified tank for each case. In other words, the average tank temperature is the same or nearly the same for isothermal and stratified experiments within each set of four experiments.
Achieving the desired initial conditions consistently required considerable effort. The lab is designed to reliably produce water at two temperatures—a “hot” temperature (61 ) that historically was used to fill fully charged isothermal tanks and a “cold” temperature (20 ) to serve as the working fluid in the heat exchanger. Both water delivery systems employ storage tanks and thus have a considerable thermal mass that makes it impossible to quickly change temperature set points. Therefore, to achieve the moderate temperatures desired in the lower zone of the stratified tanks, we employed buoyancy-driven mixing. The tank was filled in stages through a port at the bottom of the tank. First, hot (61 ) water was added to the tank until the tank was 60% full (Cases 1 and 3) or 80% full (Case 2). Next, a layer of cold (20 ) water was added below it, followed by another layer of hot water below that. The layer of cold water above the second layer of hot water resulted in gentle buoyancy-driven mixing of the two lower layers, creating a single cool layer in the bottom portion of the tank. The relative proportions of the cold layer and second hot layer were determined to achieve the desired temperatures in the bottom zone of the stratified tanks. In the isothermal cases, setup was simpler. Because there was no need for water at 61 , the hot water delivery system could be given a lower temperature set point of 58 . After the tank was filled with this water, it was allowed to cool until it reached the desired initial temperature.
Because of this challenging setup for stratified cases, the initial conditions in the tank are slightly different from the nominal conditions, as described in Table 1. However, we worked very hard to ensure consistency between experiments in these conditions to allow for meaningful comparisons. Specifically, the following parameters are highly consistent: (1) the total energy in the tank is consistent within each case; (2) in stratified tanks, the initial temperature of the top portion of the tank, , is consistent within and across all cases; and (3) in stratified tanks, the initial temperature of the bottom portion of the tank, , is close to consistent within each case and also between Cases 1 and 2, as presented in Table 1.
() | () | () | () | (kg/s) | |
---|---|---|---|---|---|
Case 1: Nominally 60% at 60 and 40% at 40 | |||||
Stratified with baffle | 50.0 | ||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – | |||
Case 2: Nominally 80% at 60 and 20% at 40 | |||||
Stratified with baffle | |||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – | |||
Case 3: Nominally 60% at 60 and 40% at 50 | |||||
Stratified with baffle | |||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – |
() | () | () | () | (kg/s) | |
---|---|---|---|---|---|
Case 1: Nominally 60% at 60 and 40% at 40 | |||||
Stratified with baffle | 50.0 | ||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – | |||
Case 2: Nominally 80% at 60 and 20% at 40 | |||||
Stratified with baffle | |||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – | |||
Case 3: Nominally 60% at 60 and 40% at 50 | |||||
Stratified with baffle | |||||
Isothermal with baffle | – | – | |||
Stratified without baffle | |||||
Isothermal without baffle | – | – |
Note: Initial conditions include the average temperature of the tank, , and, for stratified tanks, the average temperature in the top portion of the tank, , and the bottom portion of the tank, , all at the start of the experiment. The ranges provided for and are the standard deviation in the measured data over the experimental duration.
The heat exchanger working fluid is water with a nominal constant inlet temperature, , of and nominal flowrate, , of (). The constant temperature water is produced by a chiller in series with three insulated water tanks. When the mains water temperatures are below the cold water inlet temperature (), the chiller is not necessary and four 4500 W electric heating elements in the first two tanks generate the constant temperature water. They are separately controlled by a labview data acquisition and control program. The third tank adds volume, supporting more consistent operating conditions. If the mains water temperature is above , the chiller pre-cools the water to before it is reheated by the hot water tanks.
Despite these considerable efforts, the operating conditions can and do vary. We run multiple experiments in each configuration. To eliminate the possibility that variations in operating conditions affect results, we only consider experiments in which remained between and and was generally between and for the duration of the experiment. For each type of experiment, we ran trials until we had three experiments with consistent initial conditions (as described earlier) and operating conditions that met the conditions described here. Those three experiments demonstrated excellent repeatability in all types of experiments. The experiment that provided the most consistency in initial and operating conditions within and across cases was selected for each type, and the data are listed in Table 1. Table 1 includes the mean and standard deviation for operating conditions and over the experimental duration.
Tank temperature is monitored with 25 thermocouples (type-T, ), located in the tank as shown in Fig. 2. The heat exchanger wall temperature is measured with five thermocouples affixed to the outside wall of the heat exchanger. Heat exchanger inlet and outlet temperatures are each measured with three type-T thermocouples connected in parallel to reduce the error (), while the mass flowrate is measured with a Coriolis flowmeter (Micro Motion Elite, uncertainty). The data sampling rate is 1 Hz, and minute averages of that data are reported here. Experiments end after 60 min.
Data Analysis
In our previous papers [17–20], we used several types of metrics to describe tank performance results, including the rate of heat transfer from the storage fluid to the working fluid, fractional energy discharge, heat exchanger outlet temperature, heat exchanger effectiveness, and Nusselt–Rayleigh correlations. In all cases, the results were consistent across metrics. In this study, we have three stratification cases each with four experiments, resulting in many types of comparisons and a more complex discussion of results. Thus, for the sake of clarity and brevity, we present just two metrics: the heat transfer rate, , and the cumulative energy extracted, . Stratification plots (i.e., storage fluid temperature versus height plots at various times), the temperature of fluid surrounding the heat exchanger (), and the estimated velocity of fluid flowing over the heat exchanger are used to explain those results.
To understand the mechanisms that influence system performance—that is, the reasons for improvements—we turn to the temperature of the water surrounding the heat exchanger and the velocity of the storage water as it flows over the heat exchanger. The temperature of the water surrounding the heat exchanger, , is calculated by averaging the temperature measurements from thermocouples at with vertical locations between or just above the heat exchanger coils. It is a useful metric to understand system performance, as it is the temperature that drives the heat transfer between the storage water and the outer wall of the heat exchanger.
The velocity of the fluid as it flows around the heat exchanger is not directly measured. However, we estimate velocities in that region by using a mixed convection analysis described in detail in prior works [17,19,20] and summarized here. Though the flow field in the tank is entirely buoyancy driven, recirculation results in velocities beyond that which would develop due to pure natural convection in an unbounded domain, resulting in buoyancy-driven “mixed” convection. The mixed convection is calculated from the measured data. The pure natural convection Nusselt number () is estimated from Morgan’s 1975 correlation for natural convection to/from a cylinder in an unbounded domain [23]. Knowing and , we isolate the forced convection Nusselt number, . The Reynolds number, , is determined from Hilpert’s 1933 correlation for forced convection for a cylinder in cross-flow [24]. Finally, solving for the velocity, , from provides an estimate of the additional generated velocity around the heat exchanger that would account for the observed heat transfer. The validity of this approach has been verified through comparisons to computational fluid dynamics simulations [18]. The average absolute uncertainty in the velocity estimates is m/s (95% confidence level).
Results and Discussion
Figures 4 and 5 show the transient heat transfer rates and total energy extracted, respectively, plotted against time for the sets of experiments in () case 1, () case 2, and () case 3. In these and all subsequent figures with data from multiple experiments, experiments with an initially thermally stratified tank are plotted with circles and experiments with an initially isothermal tank are plotted with diamonds. Experiments with the baffle in place are represented by filled markers, while experiments without the baffle are represented by open markers. The four types of experiments for each case are plotted on a single figure. In addition, the total energy extracted by the heat exchanger during the first 30 min of discharge for all experiments is listed in Table 2. Table 2 also includes comparisons that highlight the impacts of the baffle and/or stratification on heat transfer.
Case 1 | Case 2 | Case 3 | |
---|---|---|---|
Data | |||
Stratified with baffle | 11.4 mJ | 12.8 mJ | 12.6 mJ |
Isothermal with baffle | 11.1 mJ | 12.5 mJ | 12.7 mJ |
Stratified without baffle | 10.4 mJ | 11.4 mJ | 10.8 mJ |
Isothermal without baffle | 8.9 mJ | 10.3 mJ | 10.4 mJ |
Comparisons: Percent change | |||
Effect of baffle in stratified tank | 9.2% | 11.9% | 16.6% |
Effect of baffle in isothermal tank | 24.3% | 21.9% | 22.1% |
Effect of stratification in tank with baffle | 2.8% | 2.1% | % |
Effect of stratification in tank without baffle | 17.0% | 11.1% | 3.4% |
Combined effect of stratification and baffle | 27.8% | 24.4% | 20.6% |
Case 1 | Case 2 | Case 3 | |
---|---|---|---|
Data | |||
Stratified with baffle | 11.4 mJ | 12.8 mJ | 12.6 mJ |
Isothermal with baffle | 11.1 mJ | 12.5 mJ | 12.7 mJ |
Stratified without baffle | 10.4 mJ | 11.4 mJ | 10.8 mJ |
Isothermal without baffle | 8.9 mJ | 10.3 mJ | 10.4 mJ |
Comparisons: Percent change | |||
Effect of baffle in stratified tank | 9.2% | 11.9% | 16.6% |
Effect of baffle in isothermal tank | 24.3% | 21.9% | 22.1% |
Effect of stratification in tank with baffle | 2.8% | 2.1% | % |
Effect of stratification in tank without baffle | 17.0% | 11.1% | 3.4% |
Combined effect of stratification and baffle | 27.8% | 24.4% | 20.6% |
Note: The effect of the baffle and/or stratification is also listed.
Analysis of the data in Figs. 4 and 5 and Table 2 provides some interesting results. First, in both the initially thermally stratified tanks and in the initially isothermal tanks, the presence of the baffle significantly improves heat transfer. That benefit on total energy extracted increases with time, as shown in Fig. 5. While this effect has been well documented in isothermal tanks [16,17,19,20], this study is the first to show that the benefit applies in stratified tanks as well. It is worth noting that the benefit is smaller in the stratified tanks than in the isothermal tanks. Indeed, in the stratified tank, the total energy extracted after 30 min in experiments with the baffle versus without is 9.2%, 11.9%, and 16.6% higher for cases 1, 2, and 3, respectively. In comparison, for experiments using the isothermal tanks, that same metric is 24.3%, 21.9%, and 22.1% higher with the baffle for cases 1, 2, and 3, respectively. The type of stratification affects heat transfer as well. In case 3, which has a smaller temperature difference than the others and is thus more like an isothermal tank, the benefit of the baffle is more pronounced. The data in Fig. 5 and Table 2 show that total energy extracted is very similar for the two experiments with the baffle in place (i.e., stratification has only a small effect), whereas stratification clearly improves heat transfer in tanks without the baffle. Thus, the greater benefit of the baffle in isothermal tanks relative to stratified tanks is largely due to the lower heat transfer in isothermal tanks compared to stratified tanks when no baffle is in place.
While the baffle improves the rate of heat transfer in all cases studied, the role of stratification is more complicated. In a tank with no baffle, stratification increases total energy extracted in the first 30 min by 17.0%, 11.1%, and 3.4% in cases 1, 2, and 3, respectively. In contrast, the results with a baffle show that the presence of the baffle reduces the importance of stratification in heat exchanger performance. With the baffle in place, total energy extracted is very similar at all times, as shown in Fig. 5. For example, the amount of energy extracted after 30 min from the stratified tank relative to the isothermal tank is 2.8% and 2.1% higher for cases 1 and 2, respectively. For case 3, the total energy extracted after 30 min is actually 1.2% lower in the stratified tank compared to the isothermal tank. This result may be due to the fact that the average temperature of the isothermal tank was higher than that of the stratified tank, resulting in a slightly higher initial tank energy. Still, case 1 has the higher degree of stratification either in terms of volume (case 1 versus case 2) or temperature (case 1 versus case 3), and it also generates the largest increase in heat transfer relative to the corresponding isothermal case. So, greater stratification has a small benefit on heat transfer with the baffle in place. Regardless, a very interesting result here is that when the baffle is in the tank, stratification has only a small affect on heat transfer to the immersed heat exchanger. However, the biggest improvements shown in Table 2 are those due to the combined effects of stratification and the baffle. Total energy extracted after 30 min in experiments with the baffle in a stratified tank were 27.8%, 24.4%, and 20.6% higher than their comparable experiments in an isothermal tank without a baffle, for cases 1, 2, and 3, respectively. Moreover, while stratification has only a modest affect on heat transfer to the immersed heat exchanger, it is still desirable in solar thermal storage tanks. In addition to having hotter water at the top of the tank, stratified tanks have colder water at the bottom of the tank, which increases the amount of energy gain possible during charging from the solar thermal panels.
Conditions in the tank affect heat transfer via two mechanisms: the temperature of the fluid surrounding the heat exchanger and the velocity of the storage fluid as it flows over the heat exchanger. We present a detailed analysis of how these mechanisms affect heat transfer in case 1 experiments, followed by a summary of how cases 2 and 3 differ. Temperature profiles are shown in Fig. 6 for case 1 experiments for a stratified tank with and without a baffle. These figures show centerline temperatures versus height in the tank at , 3, 6, 9, 12, 15, 20, 30, and 60 min. Figure 6(a) shows how temperatures in the tank change with time when the baffle is in place. The initial temperatures show a hot upper portion and cooler lower portion. As energy is extracted from the tank, the upper most temperature readings stay around 60 for about 12 min, though the size of the hot zone decreases. Water flows into the baffle region from the top of the tank, is cooled by the heat exchanger, and exits the baffle region at the bottom of the tank. As such, it keeps the temperatures of the hot and cool zone relatively steady, but with time, the size of the hot zone shrinks as the cool zone grows. Eventually, all the hot water flows over the heat exchanger and through the baffle region. At this point, the tank transitions from a stratified operation to an isothermal operation with the tank cooling uniformly. Once the tank is behaving like the initially isothermal experiments with the baffle, the baffle does maintain around a 2.5 temperature difference between the top and bottom of the tank. In contrast, Fig. 6(b) shows centerline temperatures versus height in the tank when no baffle is present in an initially stratified tank. In this case, as energy discharge progresses, the cool plumes that form on the heat exchanger mix with the water in the hot zone and largely do not initially affect the cool zone. The hot zone cools uniformly until it is the same temperature as the cool zone below, at which point the tank is isothermal and cools uniformly for the rest of the experiment.
The temperature profiles demonstrate that stratification and the presence of a baffle clearly affect the temperature of the fluid surrounding the heat exchanger. This temperature is shown directly in Fig. 7 for all three cases. Focusing on case 1, Fig. 7(a) shows that for approximately the first 20 min, is considerably higher in both stratified experiments than in corresponding isothermal experiments with or without the baffle, which of course is the nature of stratification. This results in a higher driving temperature difference for heat transfer. The figure also shows that is also initially higher in both experiments without the baffle relative to their corresponding experiments with the baffle in either a stratified or isothermal tank. is an average of the temperature measurements around the heat exchanger, including near the lower coils. When the baffle is in place, the cool plumes are confined to the annular baffle region and thus have a greater cooling effect on the temperatures around the heat exchanger, which explains the initially higher for experiments without a baffle. As time progresses, the baffle maintains the high temperature of the hot zone, as described earlier, resulting in a relatively constant for about 16 min. In contrast, in the stratified tank without the baffle, rapidly cools, falling below that of the baffle case at min, because without the baffle, the upper hot zone cools uniformly, as described earlier. While it is not surprising that stratification increases —that is, the goal of stratification after all—it is interesting to note the effect that the baffle has on , in particular that it maintains a higher temperature for longer.
Figure 8 shows the velocity in all types of experiments for the three stratification cases. In case 1, velocity is low for all experiments other than the isothermal tank with a baffle for the first 10–15 min of discharge. The isothermal tank with the baffle has a considerably higher fluid velocity throughout the experiment, which explains why it has one of the highest rates of heat transfer (Fig. 4(a)), despite having a much lower (Fig. 7(a)). The low velocity of the fluid flowing around the heat exchanger has been well established for experiments without a baffle and is again demonstrated here. However, in past studies, the baffle always increased velocity [16,17,19,20], but in this case, it only does so in the isothermal tank. In the stratified tank for case 1, the velocity is about as low with the baffle as without. As described in our past work, the baffle increases the fluid velocity by confining the plumes to the narrow annular region. However, when the tank is stratified, there is no easy exit for the plumes descending through the baffle region, as they impinge on the cool layer of water in the bottom portion of the tank. Because the plumes are no longer negatively buoyant at that point, they need to displace the layer of colder water in the bottom half of the tank. Thus, thermal stratification prevents the baffle from having the same benefit on velocity as it does in the isothermal tank. The velocities in the case 1 experiments are initially low in both stratified experiments, so heat transfer at that time is primarily affected by . Indeed, relative trends between the two stratified experiments in the data for and mirror each other (Figs. 4(a) and 7(a))—both are initially higher in the stratified tank without the baffle, but after about 4 min, both and are higher in the stratified tank with the baffle. After 16 min, the entire hot upper zone has been slowly pushed into the baffle region (Fig. 6(a)), resulting in a tank that is isothermal and that behaves much like the initially isothermal tank, with lower and higher velocity.
In general, and velocity affect heat transfer in the same ways in cases 2 and 3, though there are a few modest differences. In these cases, the cool plumes that formed in the baffle region in the stratified cases were still slowed by the barrier created by the layer of cold water at the bottom of the tank. However, because case 2 had a smaller cold zone and case 3 had a smaller temperature difference, the effect on velocity was not as strong. Figure 8 shows that while the velocity in the stratified tank with the baffle was initially much lower than that in the isothermal tank with the baffle, it was higher than either experiment without a baffle for both cases 2 and 3. Because of these higher velocities, the warm water from the hot zone moved through the baffle region faster, and the tanks reached a largely isothermal state after 10 min (case 2) and 9 min (case 3), compared to 16 min of stratification for case 1.
Conclusions
The effects of an annular baffle and thermal stratification on heat transfer to an immersed copper coil heat exchanger situated in the annular region between the baffle wall and the wall of the hot water tank are investigated for three stratification cases. In each case, experiments with and without the baffle are conducted in initially stratified tanks and in corresponding isothermal tanks with the same initial tank energy. The baffle maintains the high initial temperature of the upper zone of the stratified tank for 10–16 min, as cool plumes that form on the heat exchanger are confined to the annular baffle region until they exit at the bottom of the tank in the cool zone. In contrast, without the baffle, the upper hot zone cools uniformly as the cool plumes cause mixing of the entire upper zone.
Regardless of stratification, the cylindrical baffle always improves heat transfer to the immersed heat exchanger. In the isothermal tanks, the baffle increases total energy extracted in the first 30 min of discharge by over 20%. As in prior works [16–20], this improved heat transfer is attributed to increased velocity of the fluid flowing over the heat exchanger. In stratified tanks, the cylindrical baffle increases total energy extracted in 30 min of discharge by 9.2%, 11.9%, and 16.6% for cases 1, 2, and 3, respectively. Clearly, the impact of the baffle in stratified tanks is less than that in isothermal tanks, but is still quite considerable. In this case, the improvement in heat transfer is attributed primarily to the higher driving temperature differences around the heat exchanger until all the water from the hot zone has entered and flowed through the baffle region. After that point, the tank is basically isothermal, and the surrounding fluid temperatures drop and the velocity increases, maintaining rates of heat transfer higher than that in the tank without the baffle.
Stratification improves heat transfer in tanks without a baffle because, by design, the driving temperature difference between the heat exchanger wall and the surrounding fluid is considerably higher. However, in tanks with the annular baffle, stratification has only a modest effect on heat transfer to the immersed heat exchanger relative to the corresponding isothermal experiment for all cases. Adding stratification to a tank with the baffle initially results in a higher driving temperature difference, but a much lower velocity of the fluid around the heat exchanger, as the cool plumes now impinge on cool water, where they no longer have the same negative buoyancy to drive the flow field. Thus, the plumes must displace the layer of cold water in the bottom zone of the tank before they can exit the baffle. Once all the hot water from the top zone of the tank has moved over the heat exchanger and through the baffle, the velocity increases even as the driving temperature difference rapidly falls, and the tank behaves like the isothermal tank. In short, the baffle always generates one benefit to heat transfer—either an increased driving temperature difference in the stratified tank or increased velocity when the tank is isothermal.
This work demonstrates that the benefit of the annular baffle on heat transfer to an immersed copper coil heat exchanger situated within the annular region between the tank and baffle walls extends to tanks with varying degrees of initial thermal stratification. Future work will investigate systems with simultaneous charging and discharging to assess performance of the annular baffle combined with charging devices designed to generate and maintain thermal stratification.
Acknowledgment
We are grateful for the various forms of funding from Lafayette College to support undergraduate student researchers as well as to purchase equipment. The Excel Scholars program provided funding for Joseph Noreika and Tingyu Zhou to participate in this research during the summers of 2021 and 2022, respectively. The Engineering Division’s Clare Booth Luce scholars program provided the funding for Manaka Gomi to participate in this project in the summer of 2022. Funding for laboratory equipment came from Lafayette College via the Engineering Studies Program and the Engineering Division.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.
Nomenclature
- =
heat exchanger inner diameter, mm
- =
radial coordinate, measured from the center of the tank, mm
- =
time, min
- =
velocity of the storage fluid over the heat exchanger, m s
- =
vertical coordinate, measured from the bottom of the tank, mm
- =
mass flowrate,
- =
heat exchanger outer diameter, mm
- =
cumulative energy extracted from the storage tank, J
- =
heat transfer rate, W
- =
specific heat, J kg C
- =
length of the baffle, mm
- =
initial volume-averaged storage temperature at the bottom of the tank,
- =
heat exchanger inlet temperature,
- =
heat exchanger outlet temperature,
- =
initial volume-averaged storage temperature,
- =
initial volume-averaged storage temperature at the top of the tank,
- =
temperature of the storage fluid surrounding the heat exchanger,
- =
Nusselt number for the mixed (M), natural (N), and forced (F) convection components
- =
Reynolds number