Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

NUMERIAL ANALYSIS IN ORDER TO OPTIMIZE THE GEOMETRICAL DIMENSIONS OF THE

SOLAR ENERGY STORAGE TANK CONSIDERING THERMALLY STRATIFIED AND

INCREASING TANK EFFICIENCY

ALIASGHAR OWLA IVELI1a, MAZYAR SHARIFZADEH BAEI

b, QADIR ESMAILI

c

abcIslamic Azad University, Ayatollah Amoli Branch

ABSTRACT

Due to continuous nature of solar energy, solar energy systems require a sub-system to accumulate and reserve energy. In the

present study, a thermal energy storage tank has been designed and optimized for supplying hot water for industrial section. At the first

step, assuming a Storage tank with full mixture, the area of collector, the volume of the storage tank and solar energy portion have been

calculated by TRANSYS software. In the following, the storage tank was simulated through computational fluid dynamics (CFD), using

commercial CFD code (ANSYS CFX). Implementing CFD results, the optimization of height to diameter ratio of the storage tank was

conducted to improve the quality of thermal stratification inside the tank. It is shown that optimizing the ratio of height to diameter of the

tank has significant impact on thermal stratification and not only improves the energy saving efficiency of the storage tank but also increases

the solar energy fraction in supplying required thermal load.

KEYWORDS: Thermal Energy Storage, Thermally Stratified, Thermocline, Solar Energy

Energy reserving is considered as a critical

technology in energy saving and protection. The advantages of

thermal energy reserving include benefits in heating and

cooling applications. One of the tools in energy reserving is

using the thermal storage tank. Such reservoirs have

applications mostly in solar systems as solar energy is

available only in specific hours of the day and is not always

accessible. Eventually, energy reservoir is an answer for

continuous clean and green energy supplement for societies.

For most of solar systems, water is considered as an ideal

material for reserving the extra income energy. Once water

with different temperature is reserved inside a tank, the warm

fluid with lower density tends upward in time due to

thermosyphonic movement and hence, the fluid inside the

reservoir is stratified based on temperature. Therefore, such

reservoirs are known as thermally stratified reservoirs. Some

very primitive numerical studies of thermal energy reservoirs

in dynamic mode are conducted by Cabelli et al. He solved the

conservation equations in direct axis coordination system, via

vortices-fluid function and via implicit finite difference. The

Cabeli method problem was that the displacement differential

terms were discretized by central difference methods so which

in high Reynolds numbers, the equations became unstable.

Iwamoto solved the very same equations by explicit finite

difference method(Iwamoto,2009). He investigated and

simulated the shape of many input and output flows and in

contrary with experimental observations, they concluded that

the input and output flows has no effects on reservoir

efficiency. In most of the previous studies, the uni-

dimensional and bi-dimensional analyses have not been

conducted simultaneously. In the present study it is intended to

investigate and simulate the solar water heating system with

its thermal energy reservoir, using climate and geographic data

of the Sari city in north of Iran, obtained by RETscreen

software and uni-dimensional model (TRANSYS software)

and bi-dimensional model (CFX), in order to supply the

percentage of hot water required in the factory that located in

Sari. In addition, in most of the simulations by CFD, the

effects of thermal insulations are either neglected or have been

inserted through the total heat transfer coefficient in the

equations. However, in the present paper, this value is added

as a bi-dimensional parameter to the simulated storage tank

and been coupled with flow equations. Besides, in most of the

previous studies, the reservoir has been assumed as designed,

while in the present paper, the tank and its sub-systems have

been designed elaborately and the effects of dimensions on the

efficiency and thermal stratification have been investigated.

DESCRIPTION OF INVESTIGATION

In the present study, an industrial scale solar water heating

reservoir, as shown in (fig. 1), is designed under conditions of

Sari city humid climate through elaborating three methods of

practical, analytical and numerical, so which each method,

using RETsecreen, TRANSYS and ANSYS CFX software

respectively, are effective in appropriate design steps.

Indian J.Sci.Res.1(2) : 599-610, 2014 - 599 -

Figure 1. General Plan Of A Typical Solar Water Heater System(Ferziger,2002)

At first, the climate data of the considered region is

obtained by RETscreen. Introducing the obtained climate data

into the TRANSYS software and implementing the solar water

heater model of the software, the mesh and system details, as

well as the optimized values of the dominant factors (storage

tank volume, collector’s area) are calculated. It is feasible to

obtain more optimized values via CFD analysis of flows inside

the hot water tank. For this purpose, the hot water reservoir is

simulated in ANSYS CFX or ANSYS Fluent via

computational fluid dynamics and finite element method. The

optimized ratio of height to diameter of the tank (here referred

as R), which brings the most efficient thermal stratification

inside the tank, is calculated and proved that by implementing

the optimized R value, more energy can be obtained in an

specific volume and collector’s area; in another term, the

storage tank’s volume or collector’s area can be

reduced.Energy balance of a water energy reservoir (or any

other fluid) in uniform temperature (referring to non-mixed

state or without stratification) is illustrated in (fig. 2) and

works in a limited temperature range, based on the equation

below:

(1)

ACKNOWLEDGEMENTS

is the accumulating rate of energy to the tank by

collector, is the energy emersion rate out of tank, Ts is the

output temperature from tank, U is general heat transfer index,

A is side area of the tank, Cp is the specific heat of the fluid in

constant pressure, and is the ambient temperature around

the tank.

Figure 2 . The Storage Tank In The State Of Full Mixture

As mentioned before, because water’s density is reduced when

temperature is increased, movement occurs in opposite

direction of gravity so which the fluid with lower temperature

places at lower sections of the storage tank, while the higher

( ) ( ) ( )asssus

sp TTUALQdt

dTmc ′−−−= &&

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

x

p

y

u

x

u

y

uv

x

uu

t

u

∂

∂−

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂2

2

2

2

µρ

temperature fluid tends upward. Since there is no barrier

between hot and cold fluid, there would be a zone in which the

temperature is changed from high to low and a severe gradient

of the temperature can be observed. This zone is knows as

thermocline which its various states are demonstrated in (fig.

3).

Figure 3. Thermocline Layer Thickness In Three Different State Inside An Energy Stoage Tank(Cristofari,2003)

In (fig.4), three pictures are shown. In(fig. 4a) the

full-mixed state is illustrated in which no thermocline can be

seen and the whole tank is isothermal.In (figure 4b) the

mixture of cold and hot fluid is low, while in(figure 4c),

conditions are so that the least mixture of cold and hot water

has been occurred and the thermocline region is thin.

DOMINANT EQUATIONS

Water is a Newton fluid and non-compressible

(however, in natural displacement term, the density cannot be

assumed constant). Therefore, Navier Stocks equations can be

applied for non-compressible fluid for flows inside the tank.

To obtain the temperature profile in bi-dimensional state,

dynamic and thermal equations are solved together; however

in uni-dimensional state, only one energy equation is implied

which is independent from moment and energy conservation

equations. The flows inside the tank can be within normal

flows or turbulent flows, based on Reynolds and Rayleigh

number. Hence, the equations are implied for turbulent state

and for normal flow, necessarily the turbulence terms are

omitted, whenever required. The dominant equations are

described as the following: the continuum equation is

generally as:

(2)

ACKNOWLEDGEMENTS

In which ( )3mkgρ is the fluid’s density and ( )smur

is the

velocity vector.

Since the fluid is non-compressible, the term ( )t∂∂ρ can be

omitted from equation (2), thus:

(3)

ACKNOWLEDGEMENTS

In which the u(m/s) and v(m/s) are horizontal and vertical

velocities respectively.

The momentum equation cab be described as:

( ) ( ) xBx

pugraddiv

tD

uD+

∂

∂−= µ

ρ

(4)

In which µ represents dynamic viscosity of the fluid, p

pressure and Bx expresses the volumetric forces applied to the

unit volume of the fluid in horizontal direction. Since no

horizontal forces are applied to the fluid, the volumetric force

term in equation (4) can be deleted. Assuming constant

properties of the water and being non-compressible and

implying continuum equation, the momentum equation in

horizontal direction would be as the following

(Anderson,1984):

(5)

( ) 0=+∂∂

udivt

rρ

ρ

0=∂∂

+∂∂

y

v

x

u

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

x

p

y

u

yx

u

xy

uv

x

uu

t

ueffeff ∂

∂−

∂∂

∂∂

+∂∂

∂∂

=

∂

∂+

∂

∂+

∂

∂)()( µµρ

( ) ( ) ( ) ( )0ρρµµρρρ −−∂

∂−

∂

∂

∂∂

+

∂

∂

∂∂

=∂∂

+∂∂

+∂∂

gy

p

y

v

yx

v

xvv

yvu

xv

t

( )00 TTT

p

−

∂

∂+=

ρρρ

( ) ( ) ( ) ( )

−

∂

∂−+

∂

∂−

∂

∂

∂

∂+

∂

∂

∂

∂=

∂

∂+

∂

∂+

∂

∂0

11TT

Tg

y

p

y

v

yx

v

xvv

yvu

xv

tp

ρρρ

µρ

µρ

p

tT

∂

∂−=

ρρ

β1

In turbulent state, equation (5) can be written as:

(6)

In the above equation, µeff is the efficient viscosity which is implemented in high Reynolds and turbulent flows. The momentum

equation is:

( ) ( ) yB

y

pvgraddiv

tD

vD+

∂∂

−= µρ

(7)

In which By is the volumetric force applied to the unit volume

of the fluid and is in vertical direction. The buoyancy force,

resulted from temperature difference, would cause the fluid to

moves upward. Therefore, a fluid flow would occur due to

temperature gradient which practically represents itself as

density field. Thus the volumetric force in equation (7) is the

buoyancy term or -g(ρ-ρ0). By expanding its terms, the

equation (8) would be obtained:

(8)

In which g is the gravity acceleration and the 0 index indicated

the values as a reference status. Thus, the reference density is

the same fluid density in the reference temperature. The

Boussinesq estimation, which is conventionally applied for

natural displacement problems, is also implemented here. This

estimation expresses that, except in a particular case, the fluid

should be assumed as non-compressible. The exceptional case

refers to changes of density respective to changes in

temperature which is framed by the following equation and is

used in buoyancy term(Zelzouli,2012):

(9) Replacing this equation and assuming

non-compressible fluid, the equation (9) can be written as:

(10)

The thermal expansion term ( )Kt 1β is defined as:

(11)

Replacing this definition in equation (10), there would be:

(12)

By increasing the temperature, the density is reduced, thus

according to equation (11), it can be observed that the thermal

expansion coefficient is positive. Assuming dynamic viscosity

to be constant and applying continuum equation, the

momentum equation in vertical direction can be stated as:

(13)

In turbulent state, this equation can be written as:

(14)

In which the µeff is the efficient viscosity. The fluid’s energy

consists of three parts, including internal energy, kinetic

energy and potential energy. The fluid’s movement inside the

reservoir is occurred by natural displacement and potential

force of input flow. Therefore the velocity values are small.

The maximum height of the storage tank is 5 meters. Thus, the

kinetic, potential and gravity energies of the fluid are

neglectable, comparing to internal energy of the fluid.

Consequently, the energy equation is limited to internal energy

equation. In super-viscos flows, a part of kinetic energy is

converted into heat, due to viscosity and friction between

internal layers of the fluid. However, since the water is not

( ) ( ) ( ) ( )[ ]01

TTgy

p

y

v

yx

v

xvv

yvu

xv

tt −+

∂∂

−

∂∂

∂∂

+

∂∂

∂∂

=∂∂

+∂∂

+∂∂

βρ

µρ

µρ

( )02

2

2

2

TTgy

p

y

v

x

v

y

vv

x

vu

t

vt −+

∂

∂−

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂βρµρ

( )0)()( TTgy

p

y

v

yx

v

xy

vv

x

vu

t

vteffeff −+

∂∂

−∂∂

∂∂

+∂∂

∂∂

=

∂∂

+∂∂

+∂∂

βρµµρ

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

( ) ( ) ( ) hpp

STgradkdivuTcdivt

Tc+=

+

∂

∂ρ

viscous and neglecting the viscosity loss and assuming non- compressibility, the energy equation is as the following

:

(15)

In which k is the heat transfer coefficient and cp is the specific

heat of the fluid in constant pressure. The parameter Sh

indicates the generation rate or heat difference rate in unit

volume. Assuming the heat transfer coefficient and specific

heat of fluid to be constant and omitting the heat generation

rate, Sh, the equation (15) can be redefined as:

∂

∂+

∂

∂=

∂∂

+∂∂

+∂∂

2

2

2

2

y

T

x

T

y

Tv

x

Tu

t

Tαρ (16)

In which pc

k

ρα = is the heat distribution factor. To obtain the energy equation for turbulent state, the equation can be written as:

)()(y

T

yx

T

xy

Tv

x

Tu

t

Teffeff ∂

∂

∂

∂+

∂

∂

∂

∂=

∂

∂+

∂

∂+

∂

∂αα (17)

In above equation, the heat distribution factor can be described

by the following equation and in most cases, the Prandtl

number turbulence value is assigned equal to 0.9:

Pr

Preff

tur

α =

Considering the explanations above and the fact that most

references have suggested K-ε model for flows similar to the

present study, in order to solve the turbulence equations, the

K-ε double equation model can be assumed applicable for the

present study. However, it is important to choose the most

appropriate version; so two versions of K-ε model have been

discussed in the following. In K-ε model, the criteria indicate

the ratio of average kinetic energy of the main fluid. Based on

the changes of losses of energy in great Eddy, according to the

turbulence criteria hypothesis in K-ε model, the velocity,

length and time criteria can be written based on kinetic

turbulence energy and loss rate as the following(Crof, 2007):

, ,

Displacement Equations in K-ε Model for Numerical Analysis

of the Fluid The general equations of K and ε which are used

in numerical analysis for fluid phase, are as the following. K is

the kinetic turbulence energy and ε is the energy loss rate

(Sanieenejad,2005):

Y MGbGkxi

k

k

t

xiDt

DK−−++

∂

∂+

∂

∂= ρε

σµµρ (18)

( )k

GGbGGkk

Cxi

kt

xiDt

DK ερεεε

εσε

µµρ

2

231 +++

∂

∂

+

∂

∂= (19)

In which the Gk is the turbulence energy generation indicator due to changes in average velocity.

xi

v ju juiGk ∂

∂−= ''ρ (20)

According to Boussinesq theorem, the Gk term can be

redefined as below:

stGk2µ=

In which S is the major value of strain tensor. The term Gb is

the turbulence kinetic energy generation indicator due to

gravity and temperature gradient. The Gb parameter can be

modeled by Eddy-Viscosity estimation in which the turbulent

flux of vibrant density is calculated respective to average

density gradient.

g iip

tGb ρ

ρσ

µ−=

For constant flows, the buoyancy terms can be obtained by

Boussinesq estimation as following (The applied model in the

present study also calculates the buoyancy flow by Boussinesq

estimation:

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

g iip

tT jT

t

tg iGb ρ

ρσ

µβ

σ

µ

=

In which the βT is volume expansion index respective to

thermal changes. Ym is the indicator of fluid compressibility

effects in high Mach numbers.

ACKNOWLEDGEMENTS

δK and δε are the Prandtl turbulence numbers for each K and ε

equations and C1ε, C2ε and C3ε are turbulence constants which

are presented in standard values as the following:

MODELING

To obtain climate data of Sary city, RETscreen software was

used. The correspondent simulation was conducted in

TRANSYS software and the results were imported into CFD

analysis. According the geographical longitude and latitude of

Sary city, the climate date was obtained via RETscreen. The

city of Sary has longitude of 53.06 and latitude of 36.33. A

solar system is designed to supply 50-60% of hot water

required (based on the other design parameters, which the

exact values are to be calculated in the following sections). In

addition, according to the amount of daily solar radiation,

obtained by RETscreen, the diagram of radiation intensity

respect to daily hours is presented in (Fig. 4). In this diagram,

three lines are demonstrated, representing annual incident

radiation, horizontal radiation and vertical radiation on

collector’s surface, on a daily basis. It should be noted that the

best angel for collector which absorbs the most radiation, is

the same latitude. Therefore, the collector’s angel was set to

360 respective to horizon.

Figure 4 . The Diagram Of Annual Incident Radiation, Horizontal Radiation And Vertical Radiation On Collector’s Surface

In addition, the data of sun set and sun rise hours can be extracted based on Sary city latitude, illustrated in(Fig. 5).

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

Figure 5. The Diagram Of Sun Set And Sun Rise And The Day Hours Through A Year, Based On Latitude Of The City Of

Sari

In the next step, the required data are introduced into the

TRANSYS software. The solar system mesh, corresponding to

figure 2 of the software, is presented in (Fig. 6).

Figure 6 . The TRANSYS layout, correspondent to( fig.2)

To introduce the data of tank data and collector’s area, it is

essential to calculate an optimized value, considering the

following conditions (these conditions are defined based on

the objectives of this study):

• The volume of the storage tank should not be

exceeded than 1.5 times or less than 50% of the total daily

consumption.

• The share of solar energy in heating the water up to

850C through the year should be more than 50% in average.

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

1Corresponding authur

• The volume of the storage tank and the area of the

collector should be so which in more than 80% days of a year,

no heater be required. However, it should be noted that water

temperature should not exceed than 1050C in the simulations,

because the simulation has been conducted for a single phase

flow.

According the conducted simulation in TRANSYS and

considering the above restrains, a tank with 64m3 volume,

30m/h flow rate and with 500m2 collector is required. Based

on this calculation, this storage tank is able to provide more

than 75% of required annul energy from solar energy.To

design an optimized mesh, many considerations should be

taken into account. In the present study, due to geometrical

considerations, a tetrahedron mesh can be used. In addition,

sensitive points are also important. In the present problem, the

points neighboring the walls are important due to non-slide

and non-sprint conditions and therefore, the mesh is designed

so which by getting close to the walls, the mesh shrinks. Other

sensitive points are those affected by inertial force of input

flow and high temperature gradient. In this problem, these

zones can vary, depending on the position of the inlets and

hatches. Under such circumstances, when the flow is entered

inside the tank, it possesses inertia. This inertia prevents the

flow to exit from upper outlets. The flow tends downward

initially and then moves toward the upper outlets. This change

in velocity direction results in velocity gradient in zones,

beneath the upper wall sections of the storage tank. Therefore

such zones should have the tiniest mesh. In addition to the

described zone, small meshes should be applied around

symmetrical axis of the tank, due to symmetrical properties.

Considering all the content above, the final mesh was designed

and shown in (Fig. 7).

Figure 8. The designed mesh of the problem’s geometry

The present investigation is a transient problem which should

be analyzed in time period appropriate to problem itself.

Implicit method has been used and to couple pressure and

speed, the “simple” algorithm has been implemented, while

for velocity interpolation, the Rhie-Chow technique of degree

four has been applied. For discretization, the high resolution

technique of the CFX software was used. Considering the

previous section discussion, the K-ε equations was set as RNG

version for turbulence flows and the Prandtl number of

turbulence was assigned as 0.9. Hydrostatic pressure was set

respective to the highest point of the tank as the reference

point and the buoyancy was set with proper setting through the

software, imposing them into the solution.

2.3. Defining a Criteria for Thermal Stratification

Chan et al. (Chan,1983) theoretically investigated the

efficiency of a thermal storage tank for heating and cooling a

building. They used the term thermal efficiency as the thermal

stratified criteria, which is defined as:

( ) ( )T iniT in

T initT avt−

−=η1

(21)

ACKNOWLEDGEMENTS

To calculate the indicated factor, a tank with water in Tini

temperature in the time of t=0 is assumed. Hot water with

temperature Tin is introduced into the tank. In this equation, t

represents time and Tav is the average temperature with

average mass function which is defined as the following,

assuming slight changes in water’s density:

( )∫∫

∀

∀=

d

dtTtTav

)(

In which, d� is the volumetric element of the tank. The

mentioned approach has been used by many other researchers

and therefore, this approach is valid and used in the next steps

of the design.

RESULTS

The main objective of the present study was to obtain the

optimum ratio of height to diameter of the storage tank. In

general, increasing the ratio of height to diameter increases the

thermal stratification. However, there exist two preventive

factors. First one is that due to dimensional limits, height

cannot be practically increased so much; and the second factor

is that by increasing the ratio of height to diameter, the side

area of the tank and eventually the contact surface of the

insulation to the ambient atmosphere would be increased and

thus the heat loss would be increased as well. In(Fig. 9)

to(Fig. 12) the temperature distribution in different ratios of

height to diameter of the storage tank (R), during reservoir

discharge, are shown.

Indian J.Sci.Res.1(2) : 599-610, 2014 - 606 -

Figure 9.Ttemperature distribution inside the tank for R=0.2

Figure 10 .Temperature distribution inside the tank for R=0.5

Figure 11. Temperature distribution inside the tank for R=3

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

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Figure 12. Temperature distribution inside the tank for R=10

As it can be observed in above figures, as the ratio of height to

diameter increases, the diagrams are sticking together from up

to down. The temperature measurement is conducted in

specified and defined spots. If the thickness of the thermocline

is increased, the number of the diagrams, between two

diagram batches, is increased. As indicated above, the greater

ratios of height to diameter of the storage tank results in

greater thermal stratification and eventually smaller thickness

of thermocline. As it can be seen, at the maximum value of

this ratio (which is 10), no diagrams can be seen between

indicated zone and therefore it can be concluded that

thermocline thickness is less than two successive measuring

spots. The temperature contours of the reservoir, during

discharge time, are shown in (Fig. 13) to (Fig. 15).

Figure 13. Temperature contour in the tank for R=0.5

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

ISSN : 2250-0138 (Online)

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Figure 14. Temperature contour in the tank for R=0.3

Figure 15. Temperature contour in the tank for R=10

In all counters, at first the storage tank is full of hot water with

final temperature. Then the tank discharge was initiated and in

three different times, the temperature contour is obtained. The

thickness of thermocline is calculated as the distance of two

colors from down to one color toward up, as shown in the

following figure. It should be noted that once the thickness of

the thermocline is divided by tank’s height, it becomes

definitive and can be used to compare the quality of thermal

stratification. As it can be observed, in a horizontal line the

temperature distribution is almost constant; however,

technically it should not be constant, due to heat transfer from

the walls and buoyancy effects and should have a parabolic

shape (a parabolic curve with its minimum value at the storage

tank central axis and increases as getting close to the walls).

Since the storage tank’s discharge is conducted very slowly

and the insulation materials has been chosen properly, the

parabolic curvature slope is very low, renders it as an almost

straight line.

Indian J.Sci.Res.1(2) : 599-610, 2014 - 609 -

Figure 16. Velocity contour at the time of 2 hours, for R=3

Figure 17 . Velocity contour at the time of 5 hours, for R=3

The velocity contours have been presented for two different

times. As it has been demonstrated in (Fig. 16) and (Fig. 17),

the hot water exists from upper outlet (positioned at the center)

and the same amount of cold water enters the tank from

bottom inlet (positioned at the center as well). The cold water

enters into the tank with a specific velocity and advances

upwards, as long as there is cold water. Once it reaches the

thermocline, due to buoyancy forces, the cold water’s advance

is fetched up. Thus, in velocity contours in initial times, in

which the hot water tank content is greater, the introducing

water cannot advances so much and the lower flame, applied

to the tank is short. However, in next times, this flame is

longer. For instance, if the tank content is only cold water,

entering from bottom inlet, only the inertial force stops the

advancement and depending on initial speed, the cold waters

advances as much as possible.

Indian J.Sci.Res.1(2) : 599-610, 2014

ISSN:0976-2876(Print)

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In the following, the η1 parameter is defined, in order to obtain

the optimum ratio of the height to diameter and investigate the

efficiency of thermal stratification of the storage tank,

illustrated in (Fig. 18).

Figure 18 . The η1 diagram in different ratios

In the figure 18, it can be observed that the optimum value of

R has been reduces to 6, due to increase in total heat transfer

coefficient. In the next step, the obtained R value is introduced

into TRANSYS software to investigate the effects of

optimization on the solar energy portion utilization, comparing

two states of with and without stratification. This effect has

been shown in (Fig. 19).

Figure 19 . Solar energy fraction, comparing two models: with and without thermally stratification.

As it can be observed in figure 19, if the obtained optimum R

value is applied, the annual solar energy fraction is increased

from 75% up to 95%. The difference in the amount of

exploitation, with and without strafication, is pretty obvious.

CONCLUSION

The main objective of the present study was to find the

optimum ratio of height to diameter of the storage tank. The

effects of storage tank height on thermal stratification was

discussed and proved that by optimizing this dominant

parameter, it is feasible to improve the value and quality of

thermal stratified inside the tank so which it can be used in

hours without accessible solar energy. In addition, optimizing

the storage tank design in the present study, the annual solar

energy portion is increased from 75% up to 95%, if optimized

R value is implemented in the design.

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Indian J.Sci.Res.1(2) : 599-610, 2014

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ISSN : 2250-0138 (Online)

1Corresponding authur

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