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)
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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
ISSN:0976-2876(Print)
ISSN : 2250-0138 (Online)
1Corresponding authur
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