MIXING MODEL FOR THERMAL ENERGY STORAGE WATER TANK OF MULTI- CONNECTED MIXING TYPE H. Kitano, T. Iwata, Y. Ishikawa Mie University 577 Kurimamachiya, Tsu, Mie 54-857 JAPAN Tel: 8-5--44 kitano@arch.mie-u.ac.jp S. Ichose Chubu Electric Power Co., Inc. Higashishmachi, Higasi, Nagoya, Aichi 4-88 JAPAN K. Sagara Osaka University - Yamadaoka, Suita, Osaka 55-87 JAPAN. INTRODUCTION Water thermal storage tank of multi-connected mixg type is one of the most popular thermal storage tanks Japan and is troduced AHSRAE handbook as a labyrth tank (ASHRAE, 5). The water storage tanks use effectively spaces between footg beams of buildg base, therefore the construction cost of tanks is relatively low. The thermal energy storage tank is generally consistg of more than 5 tanks connected series with connectg holes due to hibit the mixg of lower temperature water (e.g. chilled water from refrigerator) and higher temperature water (e.g. return water from AHU). In each tank of multi-connected mixg type, tank water is well mixed and water temperature is uniform. However, this is an ideal case and practice there are some unused water mass for thermal storage due to short-circuit stream the tank. The performance of thermal storage tank is reduced by the short-circuit stream the tank. And the put conditions and connectg holes arrangement and its size have also a great effect on the mixg behavior the tank. Therefore, the connectg holes are designed to be well mixed water each tank dependg on flow rate. In this paper, a mixg model for the thermal storage tank of multi-connected mixg type is presented. A past model wide general use for a simulation of thermal storage system is based on the assumption that water each tank is perfectly mixed (Nakahara et al., 88). The performance of thermal storage tank may be overestimated by usg this model. In the mixg model presented this paper, the vertical temperature distribution each tank is taken to consideration. And an existence of unused water mass for thermal storage the tank can be found by system simulations usg the mixg model. The mixg model is based on the mixg mode for temperaturestratified thermal storage tank and is applicable to the thermal storage tank of both temperature-stratified type and multi-connected mixg type. Some experiments were conducted usg an experimental storage tank. The experimental tank is / scale model to general actual tank. The calculated results by usg the mixg model are compared with the experimental results.. MODELING OF MIXING BEHAVIORE IN TANK The mixg model presented this paper, is based on the mixg model for the temperature-stratified thermal storage tank (Kitano et al., ). It is assumed that vertical one-dimensional diffusive and convective heat transfer is considered and flow water from let pipe or connectg hole is mixed with the tank water a region accordg
to put conditions and vertical temperature distribution the tank (Figure ). T Temperature z-axis Height from bottom of the tank L st z,h z eq q l -axis l m l m q Mixg region Φ z-axis d e, z,h l -axis Figure : Concept of the mixg model Ω Equation () is the governg equation of the mixg model this paper. Tst Tst Tst Φ = κ U st + ( T Tst ) () t z z A where U st : velocity horizontal cross section of the tank [m/s], T st : water temperature the tank [ C], κ : thermal diffusivity of water thermal storage tank [m /s], T : flow water temperature from connectg hole or let pipe [ C], Φ : flow rate per unit vertical depth the mixg region [m /s], t : time [s], z : height from the bottom of tank [m] and A st : horizontal sectional area of the tank. Ω is flow rate per unit vertical depth [m /s] and the tegrated value of Ω or Φ from to L st is equal to flow rate, q. And Φ and Ω is formalized as equation () and equation (5) and D equation () is expressed by equation (4). Ω has a maximum when z is equal to the distance from the tank bottom to the position where the tank water temperature is equal to the let water temperature, z eq. D = q L st L st = Φ d z = ( z l ) ( z z ) st Ω d z eq m eq q ( z, h lm < z < ) D Φ = lm ( ) ( ) () lm z + lm q ( < z < z, h + lm ) D lm z l l (4) + m + lm eq m ( z l ) ( z z ) d z ( z l ) eq m eq + eq m ( z ) d z ( z z) d e, 4, h Ω π d e, 4 = q (5) where l m is a distance from the the centroid of flow to the bottom of tank, l m is a distance from the the centroid of flow to the water surface the tank, z,h is the distance of centroid of flow from the tank bottom [m] and d e, is the apparent diameter of virtual let pipe [m]. The depth of mixg region is divided to two parts and these depths are calculated by equation () obtaed as an experimental equation. The experimental equation is obtaed from experimental results of temperature-stratified thermal storage tank under various conditions..5 l.8 Ar d j =, () m j = ( ) j ()
Δ ρ j Ar j = g d ( =, ) ρr, j u j (7) where Ar and Ar are the Archimedes number, which are defed by equation (7) usg flow velocity, u, from let pipe or connectg holes, the reference density of tank water, ρ r, and ρ r,, and the difference between the density of flow water and the reference density of tank water, Δρ and Δρ. Ar, ρ r, and Δρ are variables concerned with the lower part of mixg region, and Ar, ρ r,, and Δρ.are variables concerned with the upper part of mixg region. The reference density of tank water is determed accordg to the followg procedure: It is presupposed that the vertical water jet flows to the tank from the centroid of flow toward the bottom of tank or the water surface the tank, and water density of the jet is equal to put water density to the tank and the velocity of jet at l j = is also equal to the one of put water. And the vertical velocity of this water jet at the distance from flow centroid, l j, is assumed to be expressed by the followg equation (8). ρ u p j = ρ u + j l ( ) j ( ρ ρ ) g d l j ( =, ) j (8) where l j is the vertical distance from the flow centroid [m], ρ is the flow water density [kg/m ], ρ is tank water density at which the vertical distance from the flow centroid is l j [m], u pj is the vertical velocity of water jet [m/s], g is the acceleration of gravity [m/s ] and u is the flow velocity [m/s]. The vertical position where the water jet reaches is obtaed by usg equation (8). The reference temperature is defed that the water temperature at the depth where the jet reaches, and the reference density the tank is defed as the density of water at the reference temperature. When the water jet reaches to the bottom or water surface of the tank, the reference density is the water density at the bottom or water surface of the tank. The distribution of flow to the mixg region, Φ, is determed as follows. The flow rate per unit depth, Φ, is expressed by quadratic functions and it has the maximum value at the position where the water temperature is equal to the flow water temperature. And the distribution rate of flow water is equal to zero at both ends of the mixg region. When the mixg region is beyond the water surface or the bottom of tank, the distribution of flow water is truncated at the water surface or the bottom of tank. The flow rate distribution of flow, Ω, is determed as follows. It is assumed that flow from the tank has uniform velocity cross section of virtual let pipe. And the diameter of virtual let pipe is determed accordg to the flow velocity, the diameter of let pipe and let Archimedes number by usg the followg experimental equation..4 e, =.4 d Ar d () Δ ρ Ar = g d ρ u () where d is the diameter of let pipe [m], d e, is the apparent diameter of virtual let pipe [m] and Ar is an let Archimedes number defed by equation (). ρ r, is the reference density of tank water and Δρ is the difference between the reference density of tank water and the density of the tank water at the same vertical position of let pipe center. The reference density of tank water is the higher density of tank water at the lower and upper end of flow region. The let Archimedes number is dependent on the apparent diameter of let pipe, therefore, the apparent diameter is obtaed by iterative calculations. r, 4. COMPARISON OF EXPERIMENTAL RESULTS WITH CALCULATED RESULTS Experiments ware conducted usg scale model tanks to clarify the mixg behavior the multi-connected mixg type thermal storage tank and to verify the mixg model. The experimental tanks are shown figure. The experimental tank consist of four tanks connected series, and is designed as approximately / scale model of actual thermal storage tank. The experiments are conducted by usg the experimental tank with two pattern of
connectg holes arrangement. One is the arrangement which connectg holes are placed at the lower part of the tank series, and the other is the arrangement which connectg holes are set alternately lower and upper part the tank. In the experiments, vertical temperature distribution each tank, connectg holes and let pipe are measured. The position of the thermocouple stalled is shown figure. Table shows the experimental conditions which results are presented this paper. No. Duration of experiment [h] Input water temperature [ C] Table : Experimental conditions Initial temperature [ C] [m /h] Archimedes number* Connectg holes arrangement type. 5.7 -. 7..8.87.5 5. -. 7..7.55 Type A 4..4 -.5 8.7..7 4..7-8. 4... 5.5.8 -. 5..8.4 Type B 5.8.8-7. (. -. h).8 -.4 (. - 5.8 h)..4.44 Type A * : This Archimedes number is defed as the followg equation. In the equation, ρ is water density at itial temperature the tank, Δρ is the density difference between ρ and water density at average put water temperature while elapsed time is from.5 to.5 hours, u c is water flow velocity at the connectg hole and d c is the diameter of the connectg holes. Δ ρ Ar = g dc ρ u c,75 4 4 4 4,7,5,5,5,855 5 ( st tank ) ( nd tank ) ( rd tank ) ( 4th tank ) ( Buffer tank ) pipe 5 55 55 Partition wall 85, pipe Connectg hole 58 7 : Thermocouple 4 7 (a) Horizontal section of the tank pipe Partition wall Connectg hole pipe Connectg hole 5 ( Buffer tank ) 5 5 4 ( st tank ) ( nd tank ) ( rd tank ) ( 4th tank ) The case of connectg holes settg near bottom series (connectg holes arrangement : Type A) pipe Partition wall Connectg hole pipe Connectg hole 5 ( Buffer tank ) 5 5 4 ( st tank ) ( nd tank ) ( rd tank ) ( 4th tank ) The case of connectg holes settg upper and lower alternately (connectg holes arrangement : Type B) (b) Vertical section of the tank Figure : Experimental tank
The equations of the mixg model are solved by an explicit fite differential method. The tank water is vertically divided to and time clement is. seconds. In this calculation, the vertical temperature distributions the tank were calculated by usg the itial temperature the tank and the put conditions measured durg each experiment. Calculated results Experimental results 7 5 7 5......5.4... The st tank The nd tank The rd tank The 4th tank.h.h.h.h Water Temperature the tank [ o C] Vertical temperature profile the tank (a) Experiment No. 8 4..5.4... The st tank The nd tank The rd tank The 4th tank.5h.5h.h.h..5..5 8 8 8 8 Water Temperature the tank [ o C] Vertical temperature profile the tank (b) Experiment No. 8 4 8.... 4...5.4... The st tank The nd tank The rd tank The 4th tank.h.h.h.h 8 Water Temperature the tank [ o C] 4.h 8 8 8 Vertical temperature profile the tank (c) Experiment No. Figure : Comparison of the experimental results and the calculated results the case that connectg holes arrangement is Type A (refer to figure )
Calculated results Experimental results 7 5 7 5 7 5 Flowrate......5.4... The st tank The nd tank The rd tank The 4th tank.h.h.h.h 8 8 8 8 Water Temperature the tank [ o C] Vertical temperature profile the tank (a) Experiment No. 4 7 5..5..5..5.4... The st tank The nd tank The rd tank The 4th tank.5h.h.5h.h 7 7 7 7 Water Temperature the tank [ o C] Vertical temperature profile the tank (b) Experiment No. 5 Figure 4: Comparison of the experimental results and the calculated results the case that connectg holes arrangement is Type B Calculated results Experimental results 5 7 5 7 5 7 5.... 4. 5...5.4... The st tank The nd tank The rd tank The 4th tank.h.h 4.h 5.h 8 8 7 8 7 8 7 Water temperature the tank [ o C] Vertical temperature profile the tank Figure 5: Comparison of the experimental results and the calculated results the case that connectg holes arrangement is Type A ( Experiment No. )
Figure shows experimental results and calculated results the case that the connectg holes arrangement is Type A (refer to figure ). Left figure shows the let water temperature to the st tank and flow rate, and right figure shows the temperature distribution change each tanks. In the case that put water temperature was lower than tank water temperature, it was found that water the upper part of the experimental tanks (the nd and rd tank figure (a)) was not mixed well with the flow water from the connectg holes and remaed high temperature. The tank water this region is not used for the thermal storage and therefore heat capacity of the thermal storage tank is decreased. When the Archimedes number was higher (figure (b)) or flow water temperature was higher than tank water temperature (figure (c)), water each tank was mixed well. There were some differences the temperature gradient at stratified region and the position of stratification figure (a). These results show a necessity of a few corrections for the experimental equation (equation (4)). However, the calculated results on temperature profiles the tanks agree with the experimental results. Figure 4 shows the experimental results and calculated results the case that the connectg holes arrangement is Type B (refer to figure ). In this connectg holes arrangement, the water each tank was mixed well with the flow water even if the Archimedes number was relatively high as figure 4(a). The calculated water temperature at the upper part of the st tank was lower than the measured temperature the experiment No.4. It was also found that the calculated results agree with the experimental results under the conditions of this connectg holes arrangement. Figure 5 shows the results under the conditions that the flow water temperature was changed from lower to higher than the tank water. Under the conditions which Archimedes number was relatively high and the connectg holes were arranged near bottom series, most of tank water was not effectively used for thermal storage the nd tank and the rd tank shown figure 5. It is found that the calculated results were also agreement with the experimental results under this put condition. 5. CONCLUSION In this paper, a mixg model which can be applied to multi-connected mixg type thermal storage tank is presented. And the experiments carried the model tank which consists of four tanks connected series. When the connectg holes were set at the bottom of tank partition series, the upper part of each tank was not used effectively for thermal storage. When the connectg holes were arranged upper and lower alternately, the tank water tended to be mixed well even if velocity of flow was relatively low. And the temperature profiles the tank calculated by usg the mixg model were compared with the results of experiments. It was found that the calculated results by usg the mixg model agreed with the experimental results. REFERENCES ASHRAE Handbook HVAC Applications (5), American Society of Heatg, Refrigeratg and Air Conditiong Engeers, p.4. Nakahara, N. and Sagara, K. (88). Water Thermal Storage Tank, Part Basic Design Concept and Storage Estimation for Multi-connected Complete Mixg Tanks, ASHRAE Trans., Vol.4, Part, 7-4. Kitano, H., Iwata, T. & Sagara, K. (). Study on Modified Mixg Model of Temperature-stratified Thermal Storage Tank under Variable Input Conditions. Proc. FUTURESTOCK, Warsaw, 5-.