Theoretical Model

The cross-sectional view of the used model for numerical analysis is shown in Fig. 1.

Boundary layer equations were used to determine the temperature and velocity distributions in the flow field. The analysis was based on the unsteady, three-dimensional continuity, momentum and energy equations.

The assumptions are used as:

— The flow is unsteady, turbulent and three-dimensional,

— The thermal conductivity of the tube sheet material does not change with temperature

— The tube material is homogeneous and isotropic.

Three dimensional continuity, momentum and energy equations are solved numerically. The upwind and central difference method used for convections and diffusions, respectively [9].

The aim of using the obstacle is supplying hot water as long as possible in the upper part of the tank to usage. So, high thermal stratification would be achieved by using these obstacles to obtain higher degree of hot water from the tank. The obstacle’s schematic view is shown in figure 2. The details of these obstacle geometries are shown in figure 3. Table 1 indicates that the matches between obstacle type and tank.

d =0.02 m f1 = 0.04 m Vk=0.2 m/s

D= 1 m g = 0.2 m

f = 0.2 m Si = 0.2 m

The hot water entrance velocity is assumed as 0.2 as forced convective regions. The water temperatures are assumed 333, 320 and 285 K for water exit from the tank to usage, water in the tank and water coming from the main lines, respectively.

dl

1

T4

V

Figure 1 Cross-sectional view of the used tank model

Table 1 Obstacle types and tanks matches

Obstacle types

The obstacle placed tank models.

1

7,8

2

9,10

3

12

4

11

5

12

6

1,2,3,4,5,6

The dimensions of the obstacles in figure 3 are shown in Table 2.

Table 2 The dimensions of the obstacles

Obstacles number

a

S (m)

t (m)

r1 (m)

r2(m)

r3(m)

r4(m)

l (m)

r5

1

0.8

0.02

0.96

0.2

2

0.8

0.2

0.96

0.0

3

0.2

1.0

4

0.2

1.0

0.2

5

0.2

0.8

6

20o

0.02

0.8

2.1 Physical properties of fluid and boundary conditions

The thermodynamic properties of the water are considered in this study. The velocity and is assumed to be zero at the beginning. The operation pressure in the tank is taken1 atmosphere and the hot water temperature is assumed to be 320 K when the water usage started. The time between the water is started to be used and the water usage was finished is assumed as

calculation region. This time is taken as 30 minutes and the problem solved as unsteady.

Figure 3 The details of the obstacles in the tank.