7/30/2019 steam2

1/5

Investigation of a Flow Coefficient for Predicting a Natural Circulation of Water in a Built-in-storageSolar Water Heater

Pachern Jansa, Supachart Chungpaibulpatana, and Bundit Limmeechokchai

Abstract - This paper describes an investigation of an overall flow coefficient K f for predicting thermosyphon flow rate of water circulating in abuilt-in-storage (BIS) solar water heater. Firstly, a set of mathematical equations for solving storage tank temperatures of the BIS solar water heater has been developed based on the energy balances on three main components: absorber plate, collector channel and storage tank. The

thermosyphon flow rate of water in the system is then modeled and an overall flow coefficient K f is introduced in the flow model as a system performance parameter, which must be determined from experimental tests on the actual system. Procedure to determine the value of K f hasalso been established. Consistent results have been satisfactorily obtained from several tests conducted on the system with different conditionsof flow restrictions and under prevailing sky conditions. The investigation has shown that the overall flow coefficient K f introduced in the flowmodel can be considered to be a parameter used for simulating the performance of BIS solar water heater.

Keywords - Solar water heater, Built-in-storage, Thermosyphon, Thermal diode, Overall flow coefficient, System modeling, Simulation.

1. INTRODUCTION

A passive solar water heater operated with naturalcirculation is often called the thermosyphon solar water heater.Especially when a collector and storage is integrated in the same

unit, it is known in a name as a built-in-storage (BIS) solar water heater. The system mainly consists of an inclined tank, in which thewalls of the tank are thermally insulated except front wall, which is

painted with black matte from outside and covered with glass sheet[6]. Different developments are suggested by researchers toimprove the performance of the BIS solar water heater such asusing an insulation cover during night-time [5] and using atransparent insulation [1]. Another modification of BIS solar water heater which utilizes a reflector to minimize radiation losses is also

presented [2]. The BIS solar water heater with a baffle plate placed between collector and storage tank is also proposed to reduce heatlosses through the aperture area [4]. For a problem of convectionlosses during the night, a light plastic as a thermal diode is used tofix on an insulated baffle plate of a trapezoidal cross section tank to

prevent reverse circulation [3].As far as manufacturing is concerned, the trapezoidal

cross section tank might be difficult to construct. Also, a light plastic plate using as a thermal diode might not be durable and noteasy to change when damaged. A simple rectangular tank with acommercial check-valve as a thermal diode was therefore designed and constructed in order to conduct experimental tests [11].

A flow rate of water circulation is important to determinethe thermal performance of a solar water heater. A thermosyphonflow rate occurred by a natural circulation of water in the BIS solar water heater is very difficult to measure. Thus, the main purpose of this study is to investigate an overall flow coefficient for predictingthe thermosyphon flow rate of the constructed BIS solar water heater. A simulation model for predicting the storage tank temperature of the constructed BIS solar water heater has beendeveloped. To verify the developed BIS system simulation model,the predicted results from the simulation are compared with thoseobtained from the experimental tests.

__________________________

Pachern Jansa is with the mechanical engineeringdepartment, Sripatum University, 61 Phaholythin Rd., Jatujak,Bangkok 10900, Thailand. Phone: (+662) 579-1111 ext. 1202; Fax:(+662) 579-1111 ext. 1202 e-mail: p_jansa@hotmail.com ,corresponding author

Supachart Chungpaibulpatana is with SirindhornInternational Institute of Technology, ThammasatUniversity,P.O.Box 22, Thammasat Rangsit Post Office,

Klongluang, Patumthani 12121, Thailand. e-mail;supachar@siit.tu.ac.th Bundit Limmeechokchai is with Sirindhorn International

Institute of Technology, Thammasat University,P.O.Box 22,Thammasat Rangsit Post Office, Klongluang, Patumthani 12121,Thailand. e-mail; bundit@siit.tu.ac.th

2. MATHEMATICAL MODEL FORMULATION

The thermal performance of the developed built-in-storage solar water heater can be described by the energy balanceson three main components, i.e. the absorber plate, the water in the

collector channel and the water in the storage tank as shown in Fig.1 and 2.

Fig.1 Schematic diagram of the three main components and the position of temperature measurement

(a) Enlarged schematic diagram of the three main components for an elementary portion y

(b) Heat transferred network connecting the three main componentsFig. 2 Main components of the built-in-storage solar water heater

for model formulation.

Absorbed solar radiation, ( )eIT

T f

d

Ambient, T a

T p

L

mT s

H

1

23

j-1 j

j+1

n-1n

y

Portion =

Glass cover Absorber plate

Collector channel

Storage

1sf U

1osU

1

of U

1

t U

1

f h

T a

pT

T a

I T

f T

sT

T a

QuQu + Qu, y

Qu

Qu + Qu, y

Q c

Qs

Glass cover

Absorber plate

Water in collector channel

Water in storage

Storage casing withinsulation

Insulated partition

pT

f T

sT

I T

Flow

Flow

f h

t U

7/30/2019 steam2

2/5

2.1 ABSORBER PLATE

The energy balance on the absorber plate, the heatcapacity of which is assumed to be negligible, can be described by

Q A Q TL = Q p-c or

( ) ( ) ( )e T t p a f p f I U T T h T T = (1)

where Q A = absorbed total solar radiation on the absorber plate(W/m 2), QTL = total heat losses from the top of the absorber plate tothe ambient air (W/m 2), Q p-c = total heat transfer from the absorber

plate to the water in collector channel (W/m 2), ( )e = effectivetransmittance-absorptance product of the collector, I T = total solar irradiance falling on the collector surface (W/m 2), U t = overall toploss coefficient between the absorber plate and ambient temperaturetaken into account the effect of glass cover (W/m 2K), T p = averagetemperature of the absorber plate ( C), T a = ambient temperature(C), h f = convective heat transfer coefficient between the absorber and water in the channel (W/m 2K), and T f = average temperature of water in the channel ( C). From eq. (1), one gets

pT =

( ) e t f f t a

f t

I h T U T

h U

+ +

+ (2)

The effective transmittance-absorbtance product can beapproximated by [7], [8]

( ) e = 1.01 g p (3)

where g = transmittance of glass cover, and p = absorptance of absorber plate.

The overall top loss coefficient can be calculated by thefollowing equation [7], [8].

U t =

( )* **

-1

-

1 p a

p

eT T C v N f T

N h

+

+

* * *2 *2

2 -1 0.133-1

( )( ) ( 0.00591 ) - p

g

p a p a

N f

p v

T T T T Nh N

+ ++ ++

+ +(4)

where N = number of glass cover, * pT = absolute absorber plate

temperature (K), *aT = absolute ambient temperature (K), g =

emittance of glass cover, p = emittance of absorber plate, =Stefan-Boltzmann constant (5.6697 x 10 -8 W/m 2K 4), hv = wind heattransfer coefficient = 5.7 + 3.8 vwind (W/m

2C, [Duffie and Beckman,1980 [7], where vwind = wind speed across the front cover of thecollector, (m/s), e = 0.43(1-100/ * pT ), f = (1 + 0.089 hv -

0.1166 hv p)(1 + 0.07866 N ), and C = 520(1-0.000051 2) for 0 < <

70, = collector tilt angle (degree). Note that U t is calculated based on projected area of the absorber plate [7], [8].The convective heat transfer coefficient between the

absorber and water in the collector channel can be calculated for theinclined plate facing downward with approximately constant heatflux as follows [9]:

h f = e Nu k w / y (5)

where e Nu = average Nusselt number = 0.56(Gr e Pr e cos )1/4

< 88 ; 10 5 < Gr e Pr e cos < 10 11, Gr e = g (T p T f )L3 / , g =gravitational constant (m/s 2), = density of water (kg/m 3), =thermal expansion coefficient of water (K -1), = viscosity of water (kg/m-s), k w = thermal conductivity of water (W/mK), y = lengthof the portion (m). Note that all properties of water except , usingto calculated the average Nusselt number, are evaluated at areference temperature T ref1 = T p - 0.25( T p - T f ); is evaluated at atemperature of T ref2 = T f + 0.5( T p T f ).

2.2 COLLECTOR CHANNEL

The energy balance of the water in the collector channelfor each portion dy at any instant is described by the followingequation.

cQ = p c c s c a uQ Q Q Q or

f

f pf

dT dC

dt = ( ) ( ) f p f sf f sh T T U T T

2( )( )

pf f

of f a

mC dT d U T T

B B dy

&(6)

where Qc = total energy stored in the water in the collector channel at any instant (W/m 2), Qc-s = energy transfer between water in the collector channel and the storage tank by passing through theinsulated partition (W/m 2), Qc-a = energy loss from the collector channel to the ambient air (W/m 2), Qu = useful energy in the water flowing out from the collector channel (W/m 2), f = density of thewater in the collector channel (kg/m 3), d = collector channel depth(m), B = width of collector channel (m), C pf = specific heat of water in the collector channel (kJ/kgK), m& = mass flow rate of water flowing through the system (kg/s), T

f = water temperature in the

collector channel ( C), T s = water temperature in the storage tank (C), and U sf = heat transfer coefficient between water in thechannel and the storage tank (W/m 2K) = k sf /lsf , where k sf = heatconductivity of the insulated partition and lsf = thickness of theinsulated partition, U of = heat losses coefficient from water in thecollector channel through the side insulation wall to the ambient air (W/m 2K) = k of /lof , where k of = heat conductivity of the wallinsulation partition and lof = thickness of the wall insulation. After substituting an expression of T p into eq. (6) one has

f

f pf

dT dC

dt =

[( ) ( )] f e T t f a

f t

h I U T T

h U

+

2( ) ( )( )sf f s of f a

d U T T U T T B

pf f mC dT

B dy

&

(7)

Since the partial differential form of eq. (7) is not easy tosolve analytically, a finite difference numerical method is used [10].If the collector channel is represented by n portions along its flowdirection as shown in Fig. 1. The temperature of the jth portion at thenext time step t can be written as follows:

j

t t

f T + =

[( ) ( )]{ j

j

t t t t t

f e T t f at

f t t t t

f pf f t

h I U T T t T

dC h U

+

+

2( ) ( )( )

j j j

t t t t

sf f s of f a

d U T T U T T

B

1( )}

j j

t pf t t

f f

t m C T T B y

& (8)

where t f T = water temperature in the collector channel at time t

(C), t t f T + = water temperature in the collector channel at time t+ t

(C), t sT = water temperature in the storage tank at time t (C),t

aT =

ambient temperature at time t (C), t f = density of the water in the

collector channel at time t (kg/m 3), t pf C = specific heat of water in

the collector channel at time t (kJ/kgK), t T I = total solar irradiance

falling on the collector surface at time t (W/m 2), t f h = convection

heat transfer coefficient between the absorber and water in thechannel at time t (W/m 2K), t t U = overall top loss coefficient

between the absorber plate and ambient temperature taken intoaccount the effect of glass cover at time t (W/m 2K), and t m& = massflow rate of water flowing through the system at time t (kg/s).

7/30/2019 steam2

3/5

Note that, for the bottom and the top end portions of thecollector channel, there is an additional heat loss from the water through the end side to the ambient air. Hence the 3 rd heat loss termon the right hand side of eq. (8) must be replaced by

1 2( ) ( )

j

t t

of f aU d T T y B

+

.

2.3 STORAGE TANK

The energy balance for an elementary portion dy of thewater in the storage tank can be described by the followingequation.

sQ = u c s s aQ Q Q + or

ss ps

dT HC

dt = ( - ) ps s sf f s

mC dT U T T

B dy+

&(9)

where Qs = total energy stored in the storage at any instant (W/m2),

Qs-a = energy loss from the storage to the ambient air (W/m2), s =

density of the water in the storage tank (kg/m 3), H = storage tank depth (m), C ps = specific heat of water in the storage tank (kJ/kgK),U os = heat loss coefficient between the storage tank and ambient

(W/m2

K); U os = k os/los, where k os = heat conductivity of tank wallinsulation (W/mK) and los = thickness of tank wall insulation (m).As shown in Fig. 1, the temperature at the next period of time for the jth node can be written as

j

t t

sT + =

-1[ ( - )

j j j

t

pst t t

s s st t

s ps j

t m C t T T T

HC B y

+

&

2( - ) - (1 )( - )]

j j j

t t t t

sf f s os s a

H U T T U T T

B+ + (10)

where t t sT + = water temperature in the storage tank at time t + t

(C), t s = density of water in of storage tank at time t (kg/m3), t psC =

specific heat of water in the storage tank at the time t (kJ/kgK). Note that, for the bottom and the top end portions of the storage,there is an additional heat loss from the water through the end sideto the ambient air. Hence the 3 rd heat loss term on the right hand side of eq. (10) must be replaced by

2(1 )( )

j

t t

os s a

H H U T T

B y+ +

.

2.4 THERMOSYPHON FLOW RATE

a) Thermosyphon Head

The thermosyphon built-in-storage solar water heater and its density-head diagram can be shown in Fig. 3. The thermosyphonhead at any instant is created by the difference between the total

pressure head along the path 123 and that along the path 143.

Fig. 3 The density head diagram of the system.

The thermosyphon head (H T) is described by

HT =2 3 4 3

1 2 1 4

- -gdh gdh gdh gdh + (11)

where h = the vertical height (m). Since the temperaturevariation of water inside the system is small, the water temperature

is assumed to be linearly dependent on its density i.e. T = C g,where C is a constant. The thermosyphon head can then beexpressed as:

HT = C 1(h2-h1)(T mb-T sb) + C 1(h3-h2)(T fm-T sb)- C 1(h4-h1)(T sm-T sb) C 1(h3-h4)(T mt -T sb) (12)

where C 1 = constant, T fm = average temperature of the water in thecollector channel ( C), T sm = average temperature of the water in thestorage tank ( C), T mb = average temperature of the water at the

bottom, ( T sb+T fb)/2, ( C), T mt = average temperature of the water atthe top, ( T ft +T st )/2, ( C), T sb = temperature of the water at the

bottom of the storage ( C), T fb = temperature of the water at the bottom of the collector channel ( C), T ft = temperature of the water at the top of the collector channel ( C), T st = temperature of thewater at the top of the storage ( C).

b) Friction Head

The total friction head that occurs in the built-in-storagesolar water heater due to the friction of water flowing through theentrance, exit, distributor and check-valve in the flow circuit can bedescribed by:

HF = C 2V 2

= 32

C m& (13)

where C 2, C 3 = constant, V = velocity of flow (m/s). Note thatthe friction due to the viscosity of water along the collector channelis relatively small in comparison with the above-mentioned friction.However it can be assumed that this small effect is already included in eq (13).

c) Mass Flow Rate

Equating eqs. (12) and (13), the mass flow rate in passingthrough the collector channel can be obtained as;

23C m& = C 1{(h2-h1)(T mb-T sb) + ( h3-h2)(T fm-T sb)

(h4-h1)(T sm-T sb) ( h3-h4)(T mt -T sb)} (14)

or m& = K f {(h2-h1)(T mb-T sb) + ( h3-h2)(T fm-T sb) (h4-h1)(T sm-T sb) ( h3-h4)(T mt -T sb)}

(1/2) (15)where K f = the overall flow coefficient due to the friction alongthe water flow passage through distributor, inlet and outlet hole of the collector channel and check valve (kg s -1{m K} -1/2).

3. SYSTEM SIMULATION PROCEDURE

Table 1 Simulation parameter.Parameter ValueInclination angle of the system, 15 * Latitude of test location, Lat 15

(north)Collector width, B (m) 1.1 * Collector length, L (m) 1.7 * Average channel depth of the collector passage, d (m)

0.0425 *

Wall insulation thickness, los (m) 0.03*

Insulated partition thickness, lsf (m) 0.035*

Wall insulation heat conductivity, k os (W/mK) 0.07**

Insulated partition heat conductivity, k sf (W/mK) 0.15**

Number of glass cover, N 1Transmittance of glass cover, g 0.88

**

Emittance of glass cover, g 0.88**

Emittance of absorber plate, p 0.95**

Absorptance of absorber plate, p 0.8**

Water volume in storage tank, s (liters) 273*

Heights (h 2 h 1) and (h 3 h 4) in Fig. 3.4 (m) 0.10*

Heights (h 3 h 2) and (h 4 h 1) in Fig. 3.4 (m) 0.46*

* Obtained from measurement** Obtained from manufacturers specifications

2

1

3

4

h1h2

h4h3

Head, h

TemperatureDensity

1

2

3

4

7/30/2019 steam2

4/5

A finite difference method has been used to solve themathematical model of the constructed BIS system by dividing thesystem into several portions along the length of the system asshown in Fig. 1. For the simulation the BIS system was divided into17 portions along the length of the collector. The parameters of thesystem used in the simulation are listed in Table 1 and thesimulation procedure can be described by Fig. 4.

Fig. 4 Flow chart of simulation program.

4. DETERMINATION OF OVERALL FLOW COEFFICIENT, K F

4.1 DETERMINATION PROCEDURE

The overall flow coefficient K f , which appears in eq. (15)

and must be known so that the thermosyphon mass flow rate, m&

,of the water circulating in the system can be predicted by thesimulation. K f is the overall effects of all frictions occurred alongthe water flowing passage throughout the system. A trial and error

procedure is proposed to determine the value of K f from theexperimental data obtained from the tests on the system. Severalvalues of K f are guessed systematically and input to the simulation

program. For each value of K f , the program predicts the averagetemperature of the water in the storage tank, T sm, at any timeinterval of interest in accordance with the given meteorological dataobserved from the experimental test. These simulated values of T sm are compared with their corresponding values of T sm observed fromthe experiment. Their errors are estimated and the standard errors of estimate (SEE) of T sm is then calculated by

SEE =

2

, ,exp1( )

1

i i

nt t

sm cal smi

T T

n

=

(C) (21)

where ,t

sm calT = average temperature of the water in the storage

resulted from simulation at any time t (C), ,expt

smT = average

temperature of the water in the storage resulted from experiment atany time t ( C), n = number of the data. Finally the value of K f that

produces the minimum value of SEE is therefore selected for thesystem under the considered condition.

The water in the collector channel flows upward duringthe heating period and, if provision for preventing reversethermosyphon flow is not installed in the system, the water would flow downward in the collector channel during the night or coolingdown period. Hence the value of the overall flow coefficient K f during the heating may differ from that during the cooling sincedifferent friction resistances can be expected from the oppositedirection of flow through any passage. Hence K f is considered fromtwo parts of data of each experimental test run, i.e. K f for theheating period and K f for the cooling period. For the heating period,K f is suggested to determine from the days with high solar radiationintensity, say about 20 MJ/m 2. Note that with such a high insolationday it is ascertained that the water flow exists in the system with arate high enough to give accurate results of K f .

The value of K f for the heating period is determined usingthe experimental data over the period which the thermosyphonhead, H T, calculated by eq. (12) is found to be positive valuewhereas K f for the cooling period is determined from the period when the thermosyphon head is negative. As, in each test, thesystem cooling down period occurred in the evening after thedaytime heating up period, K f for the heating period is determined first and then the accepted value of K f for the heating period will beused to determine K f for the cooling period.

4.2 DETERMINATION RESULTS AND DISCUSSION

The three different operational cases can be described asfollows:

Case 1: The check-valve in the flow passage was forced open throughout the test i.e. reverse circulation may occur at night.

Case 2: The check-valve was allowed to work freelythroughout the test. The valve opening is dependent on the pressure

difference between each side of the valve lid.Case 3: The check-valve was allowed to work freely

during the day but forced close at night i.e. no reverse circulation atnight may occur.

The best values of K f obtained using the above mentioned determination procedure for both heating and cooling periods of several experimental test runs are shown in Table 2 and sampleresults showing the simulated storage tank temperatures, T sm,cal incomparison with those T sm,exp are given in Fig. 5, Fig. 6, and Fig. 7.

In Table 2, it is found that K f for heating period of Case 1is higher than those of Case 2 and Case 3. As K f is directly related with the mass flow rate of water circulating in the system, this meanthat the flow rate in Case 1 was higher than the other two cases.

Note that with higher K f , the resistance to flow is less resulting in

higher flow rate. This can be explained by the fact that, in Case 1,the check-valve installed in the flow passage was forced to fullyopen throughout the day (and the night as well). The resistance toflow was therefore less than those of the other two cases in whichthe check-valve was allowed to work freely, i.e. the valve wasusually partly opened depending on the driving forced created bydifferential pressures of water located at both sides of the valve. Thevalve was then very rare in the full opening position. Similar resultswere also found in the case of cooling at night in which relativelyvery high reverse flow was shown in Case 1 in comparison withthose in the other two cases. Note that, in Case 3 in which thecheck-valve was forced close, the value of K f obtained from thenight was not zero as it must be in reality. However the obtained value was very small and actually very close to zero. The smalldiscrepancy may be explained by the errors in experimentalmeasurements. It should also be noted here that the value of K f for night-time period was found quite low for Case 2 indicating that theinstalled check-valve could significantly stop the reversecirculation.

Input a data file the meteorologicaldata of interest ( I T , T a , and wind )

Start

Input System Parameters , B, L, d, l os ,lsf , k sf , k os , N, g , g , p , p ,and s

Check If t > n time

Calculate U sf , U os, jt U by eq. (3.4), j f h by eq. (3.5)

and j p

T by eq. (3.2)

Calculate t m& by eq. (3.15)

Calculate j

t t f T

+and

j

t t sT

+ by eq. (3.8) and (3.10)

Stop

Input initial system temperatures ( T fi , T si)

Input No. of time period for simulation(n time )

t = 1

Yes

No

Store , f h m& , HT, , , , ,, , , f bottom f middle f top s bottomT T T T

, ,, ,s middle s top fmT T T , and smT in Output File

7/30/2019 steam2

5/5

5. CONCLUSIONS

A mathematical model has been formulated for simulatingthe transient storage tank temperature of the developed BIS solar water heater operated under varying weather conditions of solar irradiance, ambient temperature and wind speed. A submodel for estimating the thermosyphon flow rate along the flow circuit

between the collector channel and storage tank has also been proposed. An overall flow coefficient K f has been introduced in thesubmodel to reflect the overall effects of various frictions occurring

along the water flow passage. Procedure for determining the valueof K f from the experimental test conducted on the BIS system has

been described.Using experimental data obtained from various test runs

on the BIS system under different operations of check-valve, thevalues of K f determined according to the above-mentioned

procedure have been successfully found to be consistent, that ishigher K f which results in higher flow rate is obtained when thecheck-valve is forced fully open. Hence the overall flow coefficientK f can be used as a performance parameter for the BIS system.

ACKNOWLEDGEMENTS

The author is grateful to Sripatum University and theEnergy Policy and Planing Office--EPPO (formally called the

Thailand National Energy Policy Office--NEPO) for their kind contribution in providing partial financial support.

REFERENCES

[1] M. Arulanantham, K. S. Reddy and N. D. Kaushika (1998),Solar gain characteristics of absorber parallel transparentinsulation materials. Energy Conversion and Management 39,1519-1527

[2] G.N. Tiwari Doung Duc Hong and R.K. Goyal (1998), A lowcost solar water heater suitable for rural, as well as urban,areas of Vietnam. Energy Conversion and Management 39,953-962

[3] A.A. Mohamad (1997), Integrated solar collector-storage tank system with thermal diode. Solar Energy 61, 211-218.

[4] I.N. Kaptan and A. Kilic (1996), A theoretical and experimental investigation of a novel built-in-storage solar water heater. Solar Energy 57, 393-400

[5] S.C. Kaushik, Rakesh Kumar, H.P. Garg, and J. Prakash(1994), Transient analysis of a triangular built-in-storage solar water heater under winter conditions. Heat Recovery Systems& CHP 14, 337-341

[6] M.S. Sodha, J.K. Nayak, S.C. Kaushik, S.P. Sabberwal, and M.A.S. Malik (1979), Performance of a collector/storage solar water heater. Energy Conversion and Management 19, 41-47

[7] John A. Duffie and William A. Beckman (1980), Solar Engineering of Thermal Processes (First Edition). John Wiley& Sons, Inc.

[8] John A. Duffie and William A. Beckman (1991), Solar Engineering of Thermal Processes (Second Edition). JohnWiley & Sons, Inc.

[9] J. P. Holman (1997), Heat Transfer. McGraw-Hill, Inc.[10] G.Y. Saunier, Ph. Bouix, Supachart Chungpaibulpatana, and

Thada Vitagsabootr (1985), A test procedure for thermosyphon solar water heaters. Solar Thermal Componentand System Testing: Proceedings of the Fourth Asian Schoolon Solar Energy Harnessing 12-20 December 1985 at AIT,Bangkok, 163-177

[11] P. Jansa, S. Chungpaibulpatana, and B. Limmeechokchai(2003), Development of a built-in-storage solar water heater for remote areas. Proceedings of the 2 nd Regional conferenceon Energy Technology Towards a Clean Environment, TheJoint Graduate School of Energy and Environment on 12-14February 2003 at Phuket, Thailand, 422-428

Fig.5 Simulation results in comparison with experimental results on9/10/2002

Fig.6 Simulation results in comparison with experimental results on15/11/2002

Fig.7 Simulation results in comparison with experimental results on12/7/200

Table 2 Best values of the overall flow coefficient K f obtained for three different operations of check-valve.

0

100

200

300

400

500

600

700

800

900

1000

6 : 0

0

7 : 3

0

9 : 0

0

1 0 : 3

0

1 2 : 0

0

1 3 : 3

0

1 5 : 0

0

1 6 : 3

0

1 8 : 0

0

1 9 : 3

0

2 1 : 0

0

2 2 : 3

0

0 : 0

0

1 : 3

0

3 : 0

0

4 : 3

0

6 : 0

0

0

10

20

30

40

50

60

70

80

90

100

v w i n d

( x 1 0 - 1

m / s ) , T e m p e r a

t u r e

( C )

I T

Time

IT

Tsm,exp

Tsm,cal

Ta

vwind

0

100

200

300

400

500

600

700

800

900

1000

6 : 0

0

7 : 3

0

9 : 0

0

1 0 : 3

0

1 2 : 0 0

1 3 : 3 0

1 5 : 0 0

1 6 : 3 0

1 8 : 0 0

1 9 : 3 0

2 1 : 0

0

2 2 : 3 0

0 : 0

0

1 : 3

0

3 : 0

0

4 : 3

0

6 : 0

00

10

20

30

40

50

60

70

80

90

100

v w i n d

( x 1 0 - 1

m / s ) , T e m

p e r a

t u r e

( C )

I T

Time

IT

Tsm,exp

Tsm,cal

Tavwind

0

100

200

300

400

500

600

700

800

900

1000

6 : 0

0

7 : 3

0

9 : 0

0

1 0 : 3

0

1 2 : 0

0

1 3 : 3

0

1 5 : 0

0

1 6 : 3

0

1 8 : 0

0

1 9 : 3

0

2 1 : 0

0

2 2 : 3

0

0 : 0

0

1 : 3

0

3 : 0

0

4 : 3

0

6 : 0

0

0

10

20

30

40

50

60

70

80

90

100

v w i n d

( x 1 0 - 1

m / s ) , T e m p e r a

t u r e

( C )

I T

Time

IT

Tsm,exp

Tsm,cal

Ta

vwind