## Temperature distributions according to the velocities

The cold water enters and exit pipes in radial direction are in the same axis as symmetrical condition. So, higher percentage of the cold water entering to the tank would be directed towards to cold water exit channel (T-i) from the tank. At the end, the cold water can not produce a lot of vortex inside the tank and destroying effects into thermal stratification inside the tank would be decreased. The hot water exit channel (T3) is generally located at the top of the tank. So, the hot water can be supplied as long as possible because of the positions of the hot water exit channel.

2. Discussion

The effect of the cold water velocity into the thermal stratification has been presented to obtain higher thermal stratification. So, the water velocity has varied between 0.1 to 1 m/s for finding optimum velocity in order to obtain better stratification. Figure from 2-1 to 2-12 represent the temperature distributions of the tank with and without the obstacle with different water velocities. This work is the initial work to investigate optimum velocity to try in experimental set­up.

In order to take the optimum thermal stratification, firstly smooth tank is considered as in figure 2-1 to 2-6 for different velocities. There is a little thermal stratification at the upper part of the tank in smooth tank but this temperature differences is not very high enough. The better thermal stratification has obtained in figure 2-5 has 0.8 m/s water velocity in smooth tank models. The hot water (T2) and cold water (T4) has contact in all axial cross-sectional area when they enter the tank. The rotations of the hot and cold water velocity vectors occur. The hot water stratification has been destroyed by cold water in this condition. In order to keep higher thermal stratification, the axial contact area between cold and hot water must be decreased and cold water mustn’t be directed towards upper part of the tank. Therefore, the obstacle is placed into the tank to decrease contact area.

The thermal stratification area and thickness are higher in tank with obstacle rather than tank without obstacle. T3 and T-i temperature distributions according to the tank model must be considered for choosing the tank model has better performance of thermal stratification. The T1 must be lower and T3 must be higher value as possible as to get better stratifications.

T-i and T3 values have presented in figure 3 for smooth tank for several water velocities. Both of these temperatures are increased with the increase of the water velocities. The differences of these two temperatures are 2 oC at 0.1 m/s velocity and 5 oC for 1.0 m/s.

SHAPE * MERGEFORMAT

Vk=0.8 m/s, V?=1 m/s, Si= 200 mm, di= 200 mm

Vk=1 m/s, V?=1 m/s, Si= 200 mm, di= 200 mm

Figure 2. z-r Temperature distribution inside the tank in the z-r plane

The temperature differences of T1 and T3 values are presented in figure 4 for tank with obstacle for different velocities. The temperature differences are also increased with the increase of the velocity. But, this increment is higher than the smooth tank. This difference is 27 oC at 0.1 m/s velocity and 34 oC for 1.0 m/s. The differences id increased from 7 to 13.5 times rather than smooth tank. This is proved that the use of the obstacle is necessary to get the higher thermal stratification.

The best velocity is found as the Vk=0.8 m/s for all investigated cases. The temperature differences between T1 and T3 is 4.887 K and 30.928 K for smooth and obstacle placed tank for Vk=0.8 m/s.

In figure 5, T1 and T3, T2 and T3, T1 and T4, T3 and T4, T2 and T1 temperature distribution are

presented for different velocities for smooth tank. The temperature differences are very small for this type as 2.5 oC. T1-T3 has increased with the increase of the water velocity. This is desirable thing for thermal stratification. If (T2-T3) is high this will help the increase of the performance of the heater and storage tank. This value is also decreased with the water velocity. (T1-T4) is desired to be as small as possible. This value is nearly 20^25 oC for smooth tank. This is not as small as desired. This value has also decreased with the water velocity.

The temperature difference (T3 and T4) is desired to be high. This value is nearly 22^23 oC for smooth tank as seen in figure 5. This value has increased with the water velocity increment. (T1 — T4) is also desired to have small values. This value is nearly 4^7 oC for smooth tank. This is good value for this condition. This value increased while the velocity increases.

The different temperature differences versus by water velocity has presented in figure 6. The very helpful parameter to supply high water to usage is the (T2-T1). This value is higher 1.5 to 2 times in obstacle placed tank rather than smooth tank. The difference between T3 and T4 is higher 1.5 times in obstacle placed tank than smooth tank. The higher value of this parameter is very important for solar energy heating systems. T3 and T1 temperature differences are also desired to be high for solar energy heat storage tank and evaluate the efficiency of the water heater by solar. This difference is 33 % higher in obstacle placed tank as seen in figure 6. This value is increased with the increase of the water velocity in obstacle placed tank and this value is decreased in smooth tank. The temperature difference between T2 and T3 is desired to be lower for obtaining the higher thermal stratification. This value is nearly 20 oC and 15 oC for smooth and obstacle placed tank, respectively. This is the advantage of the obstacle. The temperature differences of water between the water return to the storage tank and water

coming from the main line is important to improve heat efficiency of the storage tank. This value is desired to be as low as possible. This value is nearly 5 oC for obstacle placed tank. This value is also the same in smooth tank but it increases with water velocity. This increment is lower in obstacle placed tank.

320 318 ^316 ^314 >-312 310 308

0, 1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Vk [mis]

Figure 6. T3 and T1 temperature distribution for non obstacle tank

5. Conclusions

The numerical analysis of the effects of water flow rate into the thermal stratifications in the cylindrical hot water storage tank has been presented. The optimum water velocity value has been found to obtain higher thermal stratifications. The water velocity Vk=0.8 m/s is found to be better velocity to obtain higher thermal stratifications for the tank with and without obstacle.

T3-T1 temperature differences are important parameters to evaluate the thermal stratification. This value is very close as 3^5 oC for smooth pipe and 27^34 oC for tank with obstacle. As a result, the tank with obstacle has nearly 7^13.5 times higher thermal stratification compared to the smooth one. This value has increased with the increment of the water velocity for both types. T3 — T1 value has 4.887 and 30.928 K for smooth and obstacle placed type tank.

The temperature difference between T2-T3 is desired to be high to improve heat storage tank and heater performance. This value has decreased with the increment of water velocity.

T3-T4 is very important parameter to determine thermal stratification. This value has changed between 22^33 oC for smooth tank and between 33^39 oC for obstacle placed tank. This value is 33% higher in obstacle placed tank rather than smooth tank. This is the advantage of using obstacle in the tank. This value has increased with the increment of water velocity for both types.

T1-T4 is desired to be low. This value is nearly 20^25 C and 4^7 oC for the tank with and without obstacle, respectively. Using obstacle has improved this value. This value has not highly changed with both velocities.

T2-T1 is 1.5^2 times higher in obstacle placed tank. This value has not highly changed with the water velocity.

T2-T3 is desired to be low to obtain higher thermal stratification. This value is nearly 20 oC and 15 oC for the tank with and without obstacle, respectively. This is a very important advantage of using obstacle in the tank. This value has decreased with the increase of water velocity. This is undesirable condition for thermal stratification.

Acknowledgement

It is the pleasure of the authors to acknowledge TUBITAK for their sponsorship and collaboration with the University of the Notre Dame.