Experiments on stratified chilled-water tanks

Transcription

1 International Journal of Refrigeration 22 (1999) Experiments on stratified chilled-water tanks J.E.B. Nelson 1, A.R. Balakrishnan, S. Srinivasa Murthy* Indian Institute of Technology, Madras, Chennai , India Received 16 September 1997; received in revised form 27 August 1998; accepted 24 September 1998 Abstract This paper presents experimental studies on thermal stratification in chilled-water storage systems. A fibreglass storage tank in static and dynamic modes of operation is used. The parameters varied are aspect ratio, flow rates, initial temperature difference and thickness of insulation. Emphasis is given to the effects of mixing at the inlet, leading to the definition of the mixing coefficient. The thermocline decay increases with the value of mixing coefficient, which is expressed as a function of Reynolds number and Richardson number Elsevier Science Ltd and IIR. All rights reserved. Keywords: Thermal storage; Chilled water; Stratification; Convection; Reservoir; Design Expériences menées avec des reservoirs d accumulation d eau glacée àstratification Resumé Cette communication présente des études expérimentales sur la stratification thermique dans des systèmes d accumulation d eau glacée. On a utilisé un reservoir en fibre de verre en mode de fonctionnement statique ou dynamique. Les paramètres variables sont : le rapport de forme, les vitesses d écoulement, la différence de température initiale et l épaisseur de l isolation. Les auteurs soulignent les effets de mélanges à l entrée : cette dernière permet de calculer le coefficient de mélange. La déterioration de la limite thermique s accentue avec l accroissement du coefficient de mélange exprimé en termes de nombre de Reynolds et nombre de Richardson Elsevier Science Ltd and IIR. All rights reserved. Mots clés :Accumulation thermique ; Eau glacée ; Stratification ; Convection ; Reservoir ; Conception Nomenclature C m heat capacity of the tank water mixing with the inlet stream (kj K 1 ) C i heat capacity of the inlet stream (kj K 1 ) C p specific heat of water (kj kg 1 K 1 ) * Corresponding author. Tel.: ; fax: address: ssmurthy@iitm.ernet.in (S.S. Murthy) 1 Present address: Department of Mechanical Engineering, Regional Engineering College, Warangal , India /99/$ Elsevier Science Ltd and IIR. All rights reserved. PII: S (98) D diameter of the storage tank (m) H cooling capacity defined in Eq. (1) (kj) k f thermal conductivity of the water (W m 1 K 1 ) k w thermal conductivity of the wall material (W m 1 K 1 ) L length of the storage tank (m) m mass of water (kg) PCR percent cold recoverable, defined in Eq. (1) Q c charge flow rate (m 3 s 1 ) Q d discharge flow rate (m 3 s 1 ) Re Reynolds number (Dvr/m) Ri Richardson number (gbdtl/v 2 )

2 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 1. Schematic illustration of the storage tank. Fig. 1. Schéma du réservoir. t time (h) T f temperature of water in the tank ( C) T 1 initial temperature of the chilled water ( C) T 2 initial temperature of the warm water ( C) v bulk velocity of flow (m s 1 ) x axial coordinate (m) X dimensionless length (x/l) Z mixing coefficient Greek symbols DT initial temperature difference, T 2 T 1 ( C) b coefficient of thermal expansion of water (K 1 ) d wall thickness of the storage tank (m) r density of water (kg m 3 ) m absolute viscosity of water (N s m 2 ) h c charge efficiency discharge efficiency h d 1. Introduction A thermal storage integrated into the cooling system of a building helps in reducing the peak demand and energy consumption, particularly when energy costs during peak periods are much higher than those in off-peak periods. Energy storage systems can thus contribute significantly to the overall economy. The cooling capacity may be stored as ice or chilled water. Thermal storage systems that separate warm and chilled water by means of gravitational stratification are being suggested in the cooling of buildings, because they can easily be retrofitted into existing chilled-water systems. The performance of a stratified storage depends upon the ability to store warm and chilled water with little incursion of temperatures during its storage. The interfacial zone between the warm and chilled water in the storage tank, where there is a large temperature gradient, is called the thermocline, and its thickness should be as small as possible. The increase in thermocline thickness with time is a measure of stratification decay in the chilled-water storage system and leads to the loss of cooling capacity. Stratification in a storage tank depends mainly on the volume of the tank; the size, location and design of the inlets and outlets; and the flow rates of entering and leaving streams. The available cooling capacity of the chilled water degrades owing to disturbance to the thermocline caused by: 1. heat gains from the ambient; 2. thermal diffusion from warm water to chilled water; 3. axial conduction in the tank wall in the vertical direction; and 4. mixing induced by charging and discharging of water. Stratified chilled-water storage systems have been studied by some researchers. Wildin [1] confirmed through his experiments that it is possible to establish a distinct and relatively thin thermocline even at a very low value of Richardson number. He also concluded that the temperature distribution in the tank fluid is largely one-dimensional after the formation of thermoclines. Wildin and Truman [2,3]

3 218 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 2. Schematic illustration of the test rig. Fig. 2. Schéma du banc d essai. conducted experiments to understand the factors influencing the performance of storage systems, using naturally stratified, diaphragm-type and multi-tank systems. Among these, they observed the performance of the naturally stratified storage systems to be the best. Al-Marafie [4], in his experiments on a 7.5 m 3 chilled-water storage, concluded that the extraction efficiency is reduced owing to hydrodynamic disturbances. He achieved a high extraction efficiency of 90% using a distributor by selecting a proper number and size of holes in the distributor header, to maximize the pressure drop through the exit hole and achieve equal flow through all the holes. Suri et al. [5] performed experiments on two equal sized 7.5 m 3 fibreglass storage tanks connected in series to provide a cooling capacity of 125 kw h. They concluded that the cool storage system offered a significant saving of power during peak periods and a reduction in cooling cost of over 25%. Wildin [6] carried out experiments on cool storage systems fitted with radial diffusers and observed that the mixing taking place at the inlet of the diffuser depends on the inlet Reynolds number and Froude number. He optimized the performance of the diffuser based on the inlet Froude number. Fiorino [7,8] described how a stratified storage helps in achieving energy conservation in addition to shifting of the cooling electrical demand from peak daytime periods to offpeak night and weekend periods. The main objective of the study of Bahnfleth and Joyce [9] was to identify the design and operating procedures to achieve energy conservation. Their studies showed that thermal storage benefits large multi-chiller systems and district cooling systems. Ghaddar and Al-Marafie [10] presented numerical and experimental studies on the influence of finite wall thickness on stratification during charging of solar thermal storage tanks. They used a two-dimensional spectral element model. The temperatures predicted by their model were

4 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) uniform at low flow rates, but varies largely at high flow rates. Even though much has been published on stratified heat storages, no systematic parametric study has been done in the case of cool storages. In this paper, the experimental results of parametric studies affecting the thermal stratification in cool storages are presented. The degradation of thermoclines and thus a loss of available cooling capacity in the dynamic mode of operation are largely due to mixing taking place in the storage tank between the inlet stream and the stored water. The degree of mixing is a function of inlet jet velocity, temperature difference between the inlet stream of water and stored water in the tank, and the thermophysical properties of the fluid. Quantification of the effect of mixing is done in many cases by using some empirical relationships to match the experimental temperature profiles. In this study, the mixing parameter is quantified as a function of two dimensionless parameters, namely the Reynolds number and the Richardson number. 2. Experimental studies Fig. 3. Thermocouple locations in the storage tank. Fig. 3. Emplacements des thermocouples dans le reservoir. compared with experimental data and with a onedimensional plug flow model. They concluded that thermocline degradation is mainly due to the conducting wall. They also found that the radial temperature distribution is nearly Experiments were conducted on cylindrical storage tanks of different aspect ratios from 2 to 3.5 in steps of 0.5, having a diameter of 540 mm and a wall thickness of 5 mm. The material of the tank is fibreglass, which has a thermal conductivity of 0.14 W m 1 K 1. The exterior insulation used was Styrofoam (polystyrene foam) having a material thermal conductivity of 0.04 W m 1 K 1. The bottom of the storage tank is made of 3 mm thick steel plate insulated with fibreglass on the water side and with 20 mm thick Styrofoam on the ambient side. The lateral surface and the top of the storage tank are also insulated with Styrofoam to minimize the heat gain from the ambient. Schematic diagrams of the storage tank and the experimental set-up are shown in Figs. 1 and 2, respectively. An array of copper constantan thermocouples is used to measure the temperature distribution in the body at various radial and axial locations, as shown in Fig. 3. A thermostatically controlled chiller was used to supply chilled water at the desired constant temperature to the storage tank. The inlet and outlet of water to the storage tank take place through the diffusers. Fig. 4 shows the details of the linear diffuser used in the present experiments. The static experiments were carried out first by filling the storage tank completely with warm water at the desired uniform temperature, and then pumping chilled water through the diffuser at the bottom of the storage tank to replace half of the warm water by volume. During this process the charging flow rate is chosen to cause as little hydrodynamic disturbance as possible. The tank is left idle in this mode of operation. The temperature distribution at various instants of time are plotted. The charge cycle is achieved by filling the tank originally

5 220 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 4. Details of the linear diffuser. Fig. 4. Détail du diffuseur linéaire. with warm water and then charging chilled water from the chiller into the storage tank through the bottom diffuser until all the warm water is completely replaced by the chilled water. The discharge cycle is achieved by withdrawing the chilled water through the bottom of the storage tank (the tank is charged with chilled water initially), at the same rate as the return water is admitted into the tank through the top diffuser. A part of the discharged quantity is by-passed from entering the load (fan coil unit); the quantity of water passed through the load and the by-passed (not shown in Fig. 2) quantity are both mixed thoroughly and admitted into the tank through the top diffuser. The return water temperature is regulated by controlling the quantities of water passed through the load and by-passed. The diffusers at the top and bottom of the storage tank help in admitting and withdrawing the water with as little hydrodynamic disturbance as possible. These diffusers at the top and bottom alternate as inlet and outlet during charge and discharge cycles. 3. Results and discussion 3.1. Parametric studies Thermoclines are plotted for both static and dynamic (charge and discharge cycles) modes of operation. The parameter values and ranges are: Inner diameter of the tank 540 mm Tank wall thickness 5 mm Aspect ratio 2 to 3.5 Thickness of insulation 10 and 20 mm Initial temperature difference 10 to 15 C During the experiments the ambient temperature varied in the range from 29 to 32 C Static mode In this mode of operation, the available cooling capacity of the bottom layers of chilled water is degraded due to heat

6 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 5. Temperature profiles in static mode. Fig. 5. Profil des températures en mode de fonctionnement statique. Fig. 6. Effect of insulation thickness on stratification in the static mode. Fig. 6. Influence de l épaisseur de l isolation sur la stratification en mode de fonctionnement statique.

7 222 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 7. Effect of initial temperature difference on stratification in the static mode. Fig. 7. Effet de la différence de température initiale sur la stratification en mode de fonctionnement statique. gain from the ambient, heat conduction across the thermocline and axial wall conduction. The warming up of the tank wall in contact with the bottom layers of chilled water due to axial conduction induces convection currents leading to degradation of thermoclines. The thermal degradation due to axial wall conduction depends upon the thermal conductivity ratio of the stored fluid and tank wall material and L/d. A tank with a high thermal Fig. 8. Effect of aspect ratio on stratification in the static mode. Fig. 8. Influence du rapport de forme sur la stratification en mode de fonctionnement statique.

8 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 9. Temperature profiles during a charge cycle at the inlet temperature of 13 C ^ 0.5 C. Fig. 9. Profil des températures pendant un cycle de charge à une température d entrée de13 C ^ 0,5 C. conductivity ratio and a large L/d contributes to increased thermal stratification. Fig. 5 shows the typical transient temperature profiles in the storage tank, indicating the degradation of available cooling capacity. The topmost layers of warm water heat up more owing to heat transfer from the top surface of the tank. The available cooling capacity of the bottom layers of chilled water is also degraded owing to heat exchange from Fig. 10. Effect of temperature difference on stratification during a charge cycle. Fig. 10. Effet de la température sur la stratification pendant un cycle de charge.

9 224 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 11. Effect of flow rate on stratification during a charge cycle. Fig. 11. Effet de la vitesse d écoulement sur la stratification pendant un cycle de charge. the environment, axial wall conduction through the tank wall, and thermal diffusion within the tank fluid. These effects result in the rapid increase in temperature of the bottom layers of chilled water. The thermal degradation due to heat conduction across the thermocline depends on the temperature gradient across the thermocline. The bottom layers of chilled water and top layers of warm water heat up by 4 C and 3 C, respectively, after a time interval of 6 h Fig. 12. Effect of aspect ratio on stratification during a charge cycle. Fig. 12. Effet du rapport de forme sur la stratification pendant un cycle de charge.

10 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 13. Temperature profiles during a discharge cycle. Fig. 13. Profils de température pendant un cycle de décharge. (Fig. 5). Thus the available cooling capacity of the storage system is degraded because of the increase in temperature of the chilled water. The stratification behaviour of the storage tank with different thicknesses of insulation is shown in Fig. 6. The temperature profiles plotted for a time interval of 4 h show that the bottom and top layers of water increase in temperature by 1 C and 0.6 C, respectively, in the storage tank with 20 mm thick insulation. The corresponding increases in the case of a storage tank with 10 mm insulation are 2 C and 2.4 C. When the thickness of insulation is 20 mm, the bottom layers heat up slightly more than the top layers. This is due to heat conduction across the thermocline and axial conduction. However, the decrease in thermal degradation due to heat gain from ambient decreases with increasing thickness of insulation. Hence thermal stratification improves with the increase in thickness of the insulation. The axial variation in the temperature of the water body is plotted for two different initial temperature differences in Fig. 7. The stability of the thermoclines increases with increase in the initial temperature difference (DT) between warm and chilled water layers, owing to increased density difference. However, thermal degradation due to axial wall conduction and thermal diffusion increases with DT. A close examination of the temperature profiles in Fig. 7 shows that the bottom layers of chilled water heat up more in the storage tank when DT is increased from 10 to 15 C. Fig. 8 shows the temperature profiles in two storage tanks having the same diameter and wall thickness, but different lengths yielding different aspect ratios. The bottom layers of chilled water and top layers of warm water are initially at a higher temperature in the storage tank with an aspect ratio of 3. At the end of 7 h the temperature distribution in the water body is nearly the same in both storage tanks. This shows that the thermal degradation increases with decreasing aspect ratio. This is due to the increase in axial wall conduction with decreasing L/d ratio. The L/d ratio decreases with decreasing aspect ratio. Thermal degradation due to axial wall conduction is higher in the storage tank with an aspect ratio of 2. Therefore, the thermocline degradation is faster at lower values of aspect ratio Charge cycle Fig. 9 presents the temperature profiles in a stratified storage tank during a charge cycle. The chilled water at a temperature of 12.5 C is charged through the bottom diffuser into the tank at the same rate as the warm water is displaced through the top of the storage tank. The thermocline forms at the bottom and slowly moves up to the top as charging is continued. During charging, the available cooling capacity of the charged water degrades due to mixing of the charge with the stored water. This is in addition to the thermal diffusion, axial wall conduction and heat gains from the ambient. Hydrodynamic disturbances caused by the high jet velocity of the inlet stream cause mixing of warm and chilled water. The thermal degradation due to mixing reduces with decreasing charge flow rate. Therefore, at very low charge flow rates, the thermal degradation is mainly a result of a combination of heat gain from ambient,

11 226 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 14. Temperature profiles during a discharge cycle. Fig. 14. Profils de température pendant un cycle de décharge. thermal diffusion and axial wall conduction. The temperature profile drawn at the completion of the charging cycle shows that the temperature of the stored fluid is slightly higher, by about 1 C, than the temperature of charging. Fig. 10 shows the temperature profiles for a constant flow rate at two different initial temperature differences of 14 and 8 C. The tanks are charged with chilled water at a temperature of about 9 C. The chilled water temperatures below the Fig. 15. Effect of temperature difference on stratification during a discharge cycle. Fig. 15. Effet de la température sur la stratification pendant un cycle de décharge.

12 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 16. Effect of flow rate on stratification during a discharge cycle. Fig. 16. Effet de la vitesse d écoulement sur la stratification pendant un cycle de décharge. thermocline are 10 C and 11.5 C, respectively, after 1 h in the above storage tanks. The degree of thermal stratification decreases with the decrease in initial temperature difference. Thus, the thermocline zone broadens with decreasing initial temperature difference during charging. This is because the stability of thermoclines decreases with decreasing initial temperature differences. With the increase in the density difference between the incoming stream and the stored Fig. 17. Effect of aspect ratio on stratification during a discharge cycle. Fig. 17. Effet du rapport de forme sur la stratification pendant un cycle de décharge.

13 228 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 18. Effect of aspect ratio on PCR. Fig. 18. Effet du rapport de forme sur le pourcentage de froid récupéré (PCR). water, the flow is dominated by the density difference rather than the inertial force and hence stratification increases with increasing temperature difference. The mixing also decreases with the increase in initial temperature difference. The effect of flow rate on thermal stratification in a stratified storage tank is shown by drawing the temperature for two different charge rates in Fig. 11. These temperature profiles correspond to a condition when the tanks are charged to the same cooling capacity. The time for charging a given volume of water decreases with the increase in flow rate. The thermal degradation due to thermal diffusion, axial wall conduction and heat gain from ambient decreases with increasing flow rate as they are all rate processes. But still a higher rise in temperature of stored water is observed at higher flow rate. This is obviously due to increased mixing of the inlet water stream with the stored water. The mixing coefficient increases with increase in the flow rate. The increase in inertial forces, due to increased inlet velocity at higher rates of charging, disturb the gravity current flow. This results in increased temperature at the end of charging, leading to the loss in cooling capacity. Fig. 12 shows the effect of aspect ratio on thermal stratification in a charge cycle. The initial temperature distribution, diameter and wall thickness and charging rate are the same in both storage tanks. The tanks are charged with a flow rate of m 3 s 1. The transient temperature profiles drawn for two time intervals of 0.5 and 1 h show that the thermocline thickness is larger at any time in the storage tank with an aspect ratio of 2.5. Hence thermal stratification increases with aspect ratio, when all the other parameters are kept constant. The tanks considered here have the same diameters but different lengths. With the increase in distance between the inlet and outlet of the tank the mixing coefficient also decreases. So, thermal stratification increases with increase in the aspect ratio of the storage tank Discharge cycle In a discharge cycle, the storage tank initially filled with chilled water is discharged through the bottom diffuser and returned to the tank through the diffuser at the top, after it is passed through the load. The thermocline forms at the top initially and slowly moves down to the bottom at the end of a discharge cycle. The thermocline broadens with time. The discharge temperature increases with time as seen from Fig. 13. The effect of axial wall conduction is not significant due to the large L/d ratio and also the low thermal conductivity of fibreglass. The heat gain from ambient is also less owing to the low thermal conductivity of the tank wall material and an insulation of lower conductance (Styrofoam) on the exterior surfaces of the storage tank. The thermal degradation here is mainly due to thermal diffusion in the tank and mixing. Fig. 14 shows the temperature profiles in the tank. At the end of 1.5 h, the discharge temperature increases by 1.5 C. At large flow rates the increase in the discharge temperature is mainly due to increased mixing, since the effects of the other factors controlling the thermal degradation reduce significantly owing to a reduction in discharge time. The flow rates through the tank, the initial temperature

14 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 19. Effect of flow rate on PCR. Fig. 19. Effet de la vitesse d écoulement sur le PCR. difference, insulation of the tank and the material of the storage tank contribute significantly in controlling the thermal degradation. The stability of the thermocline decreases with initial temperature difference and this leads to mixing of warm return water with the stored chilled water in the tank. The hydrodynamic disturbances, however small they may be, cause mixing in the storage tank. Fig. 15 is a plot of temperature profiles which shows that the discharge temperature increases with decreasing initial temperature difference. For an initial temperature difference Fig. 20. Effect of temperature difference on PCR. Fig. 20. Effet de la température sur le PCR.

15 230 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 21. Effect of initial temperature difference on charge/discharge efficiency. Fig. 21. Effet de la différence de température initiale sur le rendement pendant des cycles de charge et de décharge. of 10 C and 12 C, the discharge temperature increases by 2.5 C and 1.5 C, respectively, at the end of a time interval of 1.5 h. The thermal stability of the thermoclines decreases as a consequence of the decrease in density difference at low values of initial temperature difference. Even a small hydrodynamic disturbance leads to mixing in the storage tank. Therefore mixing increases with decrease in initial temperature difference. Thus thermal degradation increases with decrease in initial temperature difference. The effect of flow rate during a discharge cycle is shown in Fig. 16. The discharge temperature increases by 1.5 Cata discharge rate of m 3 s 1 and by 2.25 C ata Fig. 22. Effect of flow rate on charge and discharge efficiency. Fig. 22. Effet de la vitesse d écoulement sur le rendement pendant des cycles de charge et de décharge.

16 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 23. Validation of experimental and numerical data. Fig. 23. Validation des données expérimentales et numériques. discharge rate of m 3 s 1 after a time interval of 1 h. The degree of mixing increases with an increase in the flow rate, due to increased inlet jet velocity. Hence the discharge temperature increases with flow rate. Therefore, the available cooling capacity degrades owing to increased hydrodynamic disturbances at higher flow rates. Fig. 17 shows the effect of aspect ratio on thermal stratification in a discharge cycle, when the diameters of the storage tanks are the same. The discharge temperatures at the end of 1 h for storage tanks with L/D of 3.5 and 2.5 are 6 and 10 C, respectively. The effect of axial wall conduction increases with decrease of aspect ratio. The degree of mixing increases with the decrease in length of the storage tank. Thus, stratification decay increases with the decrease in aspect ratio of the storage tank. A well designed stratified cool storage tank is expected to retain the charged cooling capacity with negligible thermal degradation. The storage time is normally 6 to 12 h between the charge and discharge cycles in the case of stratified cool storages. During a discharge cycle the chilled water from the tank is passed through the load and the warm return water from the load admitted through the top of the storage tank. Thermal degradation of chilled water remaining in the storage tank due to the admission of return warm water is a performance parameter of the stratified storage system. The cooling capacity of the storage tank at any time is calculated by summing up the energy of all the fluid elements in the storage tank, the temperature of which does not rise by more than 20% of the initial temperature difference (DT). This is based on the assumption that the fluid elements having a temperature of T j ˆ T 1 0.2DT or lower are only useful for our purpose. A performance parameter is required to compare the stratified cool storage systems. Percent cold recoverable (PCR) is defined as the ratio of the total cooling capacity of all the water elements whose temperature at any time is either equal to or less than T j,to the cooling capacity of the stored water initially. This is similar to the definition used for stratified heat storages by Abdolly and Rapp [11]. Thus the percent cold recoverable is: PCR ˆ H t =H 0 1 where H 0 is the cooling capacity available at time 0 and H t is the cooling capacity available at any time t, given by H t ˆ X 2 j H j where H j ˆ m j C p T j T 1 H j ˆ 0 if T j T 1 if T j T 1 = T 2 T 1 0:2 = T 2 T 1 0:2 Subscript j refers to the cylindrical volume element. The PCR reflects the loss in available cooling capacity due to diffusion, mixing and axial wall conduction. The rate of heat gain from the walls and the heat transfer through the thermocline are the same for tanks with the same diameter, irrespective of their lengths. The axial wall conduction and

17 232 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) Fig. 24. Variation of mixing coefficient with Re/Ri. Fig. 24. Variation du coefficient de mélange avec le rapport Re/Ri. mixing decrease with increasing length of the storage tank. The surface area of the storage tank and the volume of chilled water stored increase with increase in the length of the storage tank. The duration of the discharge cycle decreases with the decrease in aspect ratio. The net effect of all these leads to a small increase in PCR with the decrease in aspect ratio, as shown in Fig. 18. As the flow rate decreases, the cycle time increases. This Fig. 25. Temperature profiles in tanks of the same mixing coefficient. Fig. 25. Profils de température dans des reservoirs avec le même coefficient de mélange.

18 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) results in heat transfer through the thermocline. The contribution of the axial wall conduction and heat gain from ambient to thermal degradation is not much compared with the thermal diffusion, owing to the large L/d ratio and low thermal conductivity of the tank wall material. Since thermal diffusion is a rate process, the thermal degradation increases with increase in cycle time. The contribution of this is more than the decrease in thermal degradation due to reduced mixing. Hence PCR values are low at low flow rates as seen in Fig. 19. The water layers mix even under a slight hydrodynamic disturbance and hence PCR increases with initial temperature difference, as shown in Fig. 20. The charge efficiency (h c ) is defined as the ratio of the cooling capacity stored in the storage tank at the end of the charge cycle to the cooling capacity supplied. The discharge efficiency (h d ) is defined as the ratio of the cooling capacity delivered to the load during the discharge cycle to the cooling capacity available in the storage tank at the beginning of the discharge cycle. Both charge and discharge efficiencies increase with initial temperature difference, as seen in Fig. 21. This is due to a decrease in thermal stability of the thermoclines with decreasing temperature difference. The charge and discharge efficiencies increase with flow rate as shown in Fig. 22. Increased flow rates enhance mixing. The thermal degradation due to other mechanisms such as conduction through the thermocline, axial wall conduction and heat transfer from ambient are all rate processes and hence decrease with decreasing cycle time. The cycle time increases with decrease in flow rate. So the thermal degradation due to heat transfer from ambient, conduction across the thermocline and axial wall conduction increases with decrease in flow rates. However, the thermal degradation due to mixing decreases with flow rate. The effect of the increase in cycle time on thermal degradation outweighs the reduction in the same owing to reduced mixing at low flow rates. Hence both charge and discharge efficiencies increase with increasing flow rate, as seen in the above figure Mixing coefficients The stream of water entering the storage tank causes mixing in a region close to the inlet, even at very low velocities. The mixing thus produced influences formation of the thermocline. The resulting temperature of the mixed water mass in this region depends upon the depth to which the inlet stream penetrates. Therefore the cooling capacity available at the end of charging is less than the amount of cooling supplied to the storage tank. Similarly, the cooling capacity supplied to the application during discharge will be less than the amount stored in the storage tank. Thus mixing causes loss of cooling capacity both during charging and discharging. It depends on the inlet jet velocity, the temperature difference between the warm and chilled water, and the distance between the inlet and outlet. Quantification of mixing is a difficult task. In a few models published in the literature [12 14], the effect of mixing is accounted for by using empirical constants. In the present work this is accomplished by defining a mixing coefficient, Z, which represents the ratio of the sum of the heat capacities of the tank water in the mixing region and the inlet stream mixing with it to the heat capacity of tank water in the mixing region. Thus, Z ˆ C m C i =Cm 3 Z ˆ 1 corresponds to the condition that the inlet stream and the stored fluid do not mix with each other. This is similar to a piston displacing the fluid in a cylinder and hence this is also sometimes called piston flow. As Z increases, the inlet stream entering at any given time interval mixes with the stored water and this results in a loss of available energy of the inlet stream. Experiments have been carried out by varying the aspect ratios, initial temperature differences and flow rates. A numerical model developed by the authors [15] was used to predict the transient temperature distribution in the storage tank to match the results of the experiments, by adjusting the value of Z in the numerical model. The Reynolds number based on the average velocity of flow and the Richardson number are calculated from the experimental data. A correlation is obtained for Z in terms of Re/ Ri. The correlation is used for calculating the value of Z in the experiments conducted further by the authors with both linear and radial diffusers. The calculated value of Z is used to predict the temperature distribution in the tank at various intervals of time. The agreement between the predicted and experimental data is found to be reasonably good as shown in the Fig. 23 for the linear diffuser used in this experimental programme. The mixing increases with decrease in height of the tank and initial temperature difference. It also increases with the inlet velocity. The mixing coefficients expressed as a function of two dimensionless numbers, namely the Richardson and Reynolds numbers (which account for the effects of all the above parameters contributing to the stratification decay), are as follows: Z ˆ 1: Re=Ri 0:67 4 where Re ˆ Dvr=m Ri ˆ gbdtl=v 2 The variation of Z with Re/Ri is shown in Fig. 24. Storage tanks having different aspect ratios, flow rates and whose mixing coefficients are the same have nearly the same temperature distribution, as seen in Fig. 25. This confirms that the mixing at the inlet in the tanks is only a function of Reynolds and Richardson numbers. From Eq. (4) it is clear that, for a given DT, the dimensions of the storage tank (L and D) and the inlet stream

19 234 J.E.B. Nelson et al. / International Journal of Refrigeration 22 (1999) velocity (v) at the diffuser can be selected to minimize the value of Z as close to 1 as possible, so that a high degree of thermal stratification is obtained. 4. Conclusions The aspect ratio (L/D) is an important parameter in deciding the performance of a stratified storage system. Performance improves with L/D. However, the improvement is not significant beyond L/D of about 3. A storage tank wall of larger length-to-wall-thickness ratio results in good thermal stratification. Thermal stratification does not improve much for length-to-wallthickness ratios greater than 200 for any tank. The mixing coefficient is expressed as a function of two dimensionless numbers, Re and Ri. This eliminates the usage of adjustable empirical constants used hitherto in earlier models for predicting the temperature profiles. The percent cold recoverable (PCR) in a discharge cycle increases with increasing initial temperature difference (DT), aspect ratio and flow rate. The charge and discharge efficiencies increase with increase in flow rate and increase in initial temperature difference. References [1] Wildin MW. Use of thermally stratified water tanks to store cooling capacity. In: Solar engineering, Proc Sixth Annual Conf. Las Vegas (NV): ASME, 8 12 April 1984, p [2] Wildin MW, Truman CR. Performance of stratified vertical cylindrical thermal storage tanks part I (scale model tank). ASHRAE Trans 1989;95(Part 1): [3] Wildin MW. Performance of stratified cylindrical thermal storage tanks part II (prototype tank). ASHRAE Trans 1989;95(Part 1): [4] Al-Marafie AM. Stratification behaviour in chilled water storage tank. Int J Refrig 1987;10: [5] Suri RK, Al-Marafie AM, Maheswari GP, Juwayhel AL. Experimental investigation of chilled water storage technique for power shaving. Int J Energy Engng 1988;2: [6] Wildin MW. Diffuser design for naturally stratified thermal storage. ASHRAE Trans 1990;96(Part 1B): [7] Fiorino DP. Case study of a large naturally stratified, chilled water thermal energy storage system. ASHRAE Trans 1991;97(Part 2): [8] Fiorino DP. Energy conservation with thermally stratified chilled-water storage. ASHRAE Trans 1994;100(Part 1): [9] Bahnfleth WP, Joyce WS. Energy use in a district cooling system with stratified chilled water storage. ASHRAE Trans 1994;100(Part 1): [10] Ghaddar NK, Al-Marafie AM. Study of charging of stratified storage tanks with finite wall thickness. Int J Energy Res 1997;21: [11] Abdolly MA, Rapp D. Theoretical and experimental numerical studies of stratified thermocline storage hot water. Energy Conversion Management 1982;23: [12] Cole RL, Bellinger FO. Thermally stratified tanks. ASHRAE Trans 1988;94(Part 2): [13] Oppel FJ, Ghajar AJ, Moretti PM. A numerical and experimental study of stratified thermal storage. ASHRAE Trans 1986;92(Part 2A): [14] Al-Najem NM, Al-Marafie AMR, Ezuddin KY. Analytical and experimental investigation of thermal stratification in storage tanks. Int J Energy Res 1993;17: [15] Nelson JEB, Balakrishnan AR, Srinivasa Murthy S. Parametric studies on thermally stratified chilled water storages. Appl Thermal Engng (in press).