Computer simulation of the performance of a solar desalination plant

Solar Energ.v Vol. 44, No. 4, pp. 193-205, 1990 0038-..092X/90 53.00+.00 Printed in the U.S.A. Copwight © 1990 Pergamon Pt'¢~ pie

COMPUTER SIMULATION OF THE PERFORMANCE OF A SOLAR DESALINATION PLANT

ALl M. EL-NASHAR* Water and Electricity Department, Abu Dhabi, United Arab Emirates

I. INTRODUCTION

Many areas in the Middle East and elsewhere have little Or no natural water supplies which can be used for human consumption and, therefore, depend heavily on water produced by desalination plants. These plants, usually coupled to electric power generating plants, are mostly located near large population centers with high electricity and water demands. Remote towns, villages, and small islands, which have a lower demand, receive their potable water supply from either small local desalination plants powered by trucked-in fuel, or transported from the nearest supply sources by a pipeline or tankers. Unreliability of the supply sources usually creates an cxceedingiy high cost of potable water at the consumption point.

The utilization of solar radiation as the energy source for desalination plants in remote areas seems to offer an alternative for supplying potable water at reasonable costs in areas with abundant solar radiation.

The design and performance prediction of such solar desalination plants are generally more complicated than desalination plants running on fossil fuels as the energy source. This is because the operating conditions of the solar desalination plant is highly variable and continuously changing depending on the prevailing weather conditions such as solar radiation and ambient air temperature which are continuously varying. The use of computer simulation to predict the operating conditions of the plant becomes an unavoidable ex- ereise in the design stage. This simulation involves the use of mathematical models to predict the performance of each component of the plant and then to develop a computer program which can integrate these models to predict the performance of such a plant.

This paper describes the mathematical model used to simulate the operational performance of a solar desalination plant which utilizes evacuated tube, flat plate collectors, multicffect-stack-type evaporators, and thermally stratified heat storage tanks. A plant of this type has been designed, built, and is currently in operation in Abu Dhabi, U.A.E.

Since many assumptions were made in the simulation model, the model has to be validated against

* ISES member. Address correspondence to Ali M. EI-Nashar, Water and

Electricity Dept., P.O. Box 219, Abu Dhabi, U.A.E.

actual measurements. The results of the simulation will be compared with data obtained from the Abu Dhabi plant.

2. SYSTEM DESCRIPTION

Figure I is a schematic diagram of the solar desalination system under investigation. The absorber area of the collectors may be allowed to vary from 500 to 20,000 square meters. The heat-collecting system uses a bypass line with a motorized on/of f valve. Another motorized valve is inserted in the accumulator hot water supply line. When the water temperature at the collector outlet drops below a set point, the collector bypass valve opens and the accumulator supply valve closes, thus recirculating the collector fluid for further heating. Once the outlet collector temperature reaches the set point, the bypass valve closes, and the accumulator supply valve opens to allow the hot water to charge the accumulator.

The collector fluid is pressurized by the heat collecting water pump which is turned on or off by an electric signal from the solar controller. The signal from this controller depends on the solar radiation as measured by a radiation sensor and on the water temperature at the bottom of the accumulator [1,2 ].

In this study, the accumulator is treated as a thermally stratified water tank with the temperature distribution inside the tank at any instant of time determined from the flow rates and temperatures of the inflow and outflow streams and from the temperature distribution inside the tank at an earlier instant.

The heating water supply to the evaporator is drawn from the top region of the accumulator, and the return flow is directed to the bottom region as shown in Fig. I. A three-way proportional control valve is placed in the evaporator hot water supply line in order to limit the heating water flow rate to the value corresponding to the maximum operating capacity of the evaporator, thus ensuring that this capacity is not exceeded. The evaporator capacity can be varied from 100 to 2,000 cubic meters per day ofdistillate. The maximum brine temperature in the evaporator may vary from 60°C to 80°C and the number of evaporator effects may range from 13 to 32.

The heating water pump is turned on or offby sig- nals from two temperature switches attached to the accumulator middle and upper regions. When the heating water pump is shutdown (i.e., the evaporator

193

194

5? [ ]

A. M. EL-NASHAR

Temperature probe

Temperature switch

~UL AIOA m a O l * l l ~ =(.~.~ fTSI E!

~ , . . . . ; , ', ,

~ , : q~

t4(AT CI~t.tCIlNG vA1(l l PUI4P

t t " - ' - I t " , i i i . ,¢ .al l t . .~ v a v ( l l 11 , ' I I I [ [

i m ~" - t, ' Ir ' a r q [ e

Fig. 1. Schematic of solar desalination system.

is not running), and the water temperature in the middle region of the accumulator reaches or exceeds the set point, the middle switch will turn the pump on. On the other hand, if the pump is running (i.e., the evaporator is working), but the water temperature in the top region of the accumulator drops below a second set point, the top switch will turn the pump off.

3. MATHEMATICAL MODEL

In this section we describe briefly the mathematical model used to simulate the operating performance of the major components of the solar desalination plant. The model is generally applicable for plants utilizing fiat-plate collectors, thermally stratified heat accu- mulators, and multieffect boiling evaporators. The model has been adapted so that it can be used to predict the performance of the Abu Dhabi solar desalination plant by using the specific design parameters of the collectors used which are designed by Sanyo Electric Co., and the multieffect stack evaporator used which was manufactured by Sasakura Engineering Co.

The model is used to predict the daily performance parameters of the plant at Abu Dhabi. The climatic data required for the model are essentially the solar radiation, the air temperature, and the seawater temperature and salinity. The sola~r radiation data may be available either as hourly data on horizontal or tilted surface, or as daily radiation on horizontal or tilted surface. The ambient air temperature may also be available on an hourly basis, or only the daily maximum, mean, and minimum values may be available. The model is designed in such a way that any of these types of data can be handled.

3.1 Solar radiation model To evaluate the amount of heat collected at each

hour of the day by the solar collectors, the hourly beam and diffuse components of the solar radiation on the absorber plate should first be estimated. Given the hourly total radiation on the absorber plate, the beam and diffuse components may be estimated by different

methods[3 ]. The method due to Bouguer and Ber- lage[4] was found to yield results very close to the measured values of beam and diffuse components in Abu Dhabi, hence was selected for use in this model. In this method, the beam and diffuse components were estimated in terms of the atmospheric transmissivity, P.

The atmospheric transmissivity is a parameter which indicates the degree of attenuation of beam radiation as it travels through the atmosphere. It is defined in terms of the beam radiation on a normal surface on earth and the corresponding extraterrestrial quantity, as well as the solar altitude angle, h, such that

I._z~ = pt / , i , (h) ( 1 ) Io

where I , and Io are the hourly normal beam radiation on the ground and outside the earth's atmosphere, respectively.

7r When the sun is at the zenith, h --- 5 ' the atmo-

spheric transmissivity is simply the ratio between the hourly beam radiation on a horizontal surface at the ground to the corresponding extraterrestrial value. As may be expected, the value of P varies continuously throughout the daylight period attaining its highest values during times of clear weather and having low values during cloudy or hazy periods.

Using the equations of Bouguer and Berlage, we may express the hourly beam and diffuse components of the total solar radiation on the absorber surface as

Hourly beam component:

Itb= IoPl/Si'(h)cos(O) (2)

Hourly diffuse component:

1 - p t / ~ , , ( h ~ l + c o s ( ~ ) !td = ~ l o s i n ( h ) 1 - 1.4 I n ( P ) 2 ( 3 )

Computer simulation of a solar desalination plant

where 0 is the incidence angle on the absorber plate and a0 is the tilt angle of the absorber plate relative to the ground plane. The total solar radiation on the absorber plate may therefore be expressed as the sum of the beam and diffuse components, thus

It =Itb +l ta (4)

Equations (2) and (3) enable the beam and diffuse components to be evaluated at any hour knowing the value of the atmospheric transmissivity at that hour. Normally, data on the total hourly radiation is directly measured and we are seeking the hourly beam and diffuse components. In this case an iterative procedure has tO be used to find the value of P which if substituted in eqns (2) and (3) would yield a total radiation equals, to within a preset tolerance level, the actual measured total radiation.

If the daily solar radiation on a horizontal surface is measured, then the hourly beam and diffuse components may be obtained from eqns 2 and 3 using a daily average atmospheric transmissivity. The value of this average transmissivity was obtained also by an iterative process in which the calculated hourly radiation, using eqns 2 and 3 for an assumed value of P, is in- tegrated over a 24-hour period and the result compared to the actual measured value. The iterative process is continued with progressively increasing values of P until the calculated and measured values of the daily solar radiation agrees to within a specified tolerance level.

3.2 Shadow effects on the collector absorber plate As the solar beam radiation impinges on the col-

lector, part ofthis radiation is intercepted on solid sur- faces other than the absorber plate. This results in shadows east on the absorber plate which causes a reduction in the amount of beam radiation falling on the absorber plane thus reducing the total radiation falling on the absorber plate,

195

Three shadow influences are incorporated in the computer simulation: (i) shadow influence projected by adjoined absorber plates; (ii) shadow influence projected by adjoined glass tubes; (iii) shadow influence projected by the header box of the collector.

These three shadow influences cause a reduction in the amount of beam radiation impinging on the absorber plate. The shadow area projected by each has to be calculated on an hour-by-hour basis, and the total shadow area has to be subtracted from the area of the absorber plate in order to calculate the plate area exposed to beam radiation.

The shadow area projected by the adjoining absorber plates, Ds, and by the adjoining glass tubes, Ds~, is demonstrated in Fig. 2, which shows two adjacent glass tubes in cross section. The shadow influence projected by the collector header box on the absorber plate is shown in Fig. 3. In this figure, Dsb represents the shadow length projected by header box of height H.

The three above-mentioned shadow lengths have already been derived using geometrical relationships for evacuated tube fiat plate-type collectors[ 3,5]. The resulting expressions are given below:

(a) Shadow by adjoined absorber plate (i) Case I (front shadow)

/ [cos(ac)tan(h~v) + s in(a , ) ] - L tan(h',v) Ds = (5)

cos(ac)tan(h~v) + sin(at)

(ii) Case II (back shadow)

*'[cos(ac)tan(h~v) - sin(at)] + L tan(hl-) Os =

cos(c~c)tan(hg,) - sin(at)

(b) Shadow by adjoined glass tubes (i) Case I (front shadow)

(6)

% •

;0:

Fig. 2. Shadows cast by adjoining absorber plates and glass tubes.

196 A. M. EL-NASHAR

Header box~~.

t / - ° - X . I / / \ , . .2~r ,

[b)

Fig. 3. Shadow influence projected by header box of collector.

D~

_e sin(.¢) + - - -L- - r 2 cos(h~v)

t a n ( h ~ ) [ L - ~ cos(a¢)]


(ii) Case II (back shadow)

(7)

shadow area ( 1 ), At = Dsb" e shadow area (2), A2 = D,. [Lr - D,0] shadow area (3), A3 = [D, s - D,]. [Lr - D,b].

The area approved exposed to beam radiation is marked (4) in the figure and is given by

A4 = A - [At + A2 + A3]. (10)

It should be noted that areas ( 1 ) and (2) in Fig. 4 are completely shadowed by solid obstacles which do not transmit any radiation, whereas area (3), due to the adjacent glass tube, has an attenuated solar radiation due to the transmittance of three layers of glass through which each solar ray has to travel. For the purpose of this simulation, it is assumed that the daily average transmittance of the three glass layers is equal 0.7 [ 3,7 ]. This assumption is put forward by the collector manufacturer (Sanyo Electric Co.) and is based on detailed hourly computer simulations. Consequently, the hourly net beam radiation on the absorber plate may therefore be expressed as

I',~ = I,o[(e - D~g)( Lr-..~ D'b)

+ 0 .7(D,g- Ds)(LrADSb)] . ( l l )

The nettotalsolarradiation on the absorber plate can then beobtained byadding thebeamand diffuse components

l't = l',b + Ira (12)

where I', and I',b are, respectively, the hourly total and beam radiations corrected for the shadow influences.

Dsg

- -# sin(at) -t 2 cos(h~v)

tan(h~v)[ L - ~ cos(aD]


(8)

(c) Shadow by header box

Dsb = H sin(TN) (9) tan(hN)

(See Nomenclature for symbol definitions.) Figure 4 shows the areas which are exposed to

shadow on a single absorber plate due to the adjacent absorber plate, glass tube, and header box. This figure represents a plan view of an absorber plate. The area marked ( 1 ) represents the shadow area due to the collector header box. The area marked ( 1 ) represents the shadow area due to the collector header box. The area marked (2) is that caused by the adjacent absorber plate and that marked (3) is due to the adjacent glass tube. With reference to Fig. 4, we may therefore write total area of absorber plate, A = Lr" e

3.3 Ambient temperature model A model is used to estimate the hourly ambient

temperatures if the input data consisting of daily maximum, daily mean, and daily minimum temperatures are used. The model which was constructed depends on the fact that the minimum ambient temperature in the Abu Dhabi region occurs each day close to sunrise while the daily maximum takes place around 14:30 hour in the afternoon. The hourly ambient temperature was found to follow the trend shown in Fig. 5. In this figure, temperatures above the mean value are plotted as ( T - T=~,)/( T=~ - Tmi,) whereas temperatures below the mean are plotted as (Tm~, - T ) / ( T ~

f Lt i

Fig. 4. Shadow areas on the collector absorber plate.

Computer simulation of a

- Train). The abscissa in Fig. 5 represents the solar time which is related to the standard time by the equation:

t f [ ~ + E , ] + - v - L ~ L (13) 15

where

t = solar time, hr ts = standard time, hr L = local longitude, degrees

Lo = principal meridean longitude, degrees E, = equation of time, hr.

The sunrise time is calculated by the formula[10]:

[cos -t [-tan(~). tan(~)l ] ls, = 12.0 - [ ~- (14)

In this equation, the sunrise time is expressed in hours and the latitude and declination angles, • and 6, respectively, are in degrees.

For the purpose ofthis simulation, the curve shown in Fig. 5 was fitted to polynomial equations of second degree.

3.4 Effect o f dust accumulation Dust accumulation on the collector glass tubes

causes a drop in the collector performance which has to be considered in the performance simulation. The effect of dust accumulation is incorporated in the computer simulation by including its effect on the transmissivity of the glass tubes. The variation of the transmissivity of the glass tube with the extent of dust accumulation has been the subject of extensive measurements at the solar desalination plant in Abu Dhabi. Based on these measurements [ 3,8 ], it was found that dust accumulation has a seasonal variation as shown in Fig. 6. This figure shows the transmissivity of the glass tubes at the end of one month from the day they

1.0

0

- I . 0 0:00

T : HOURLY AMBIENT TEMP. (r)

T,,,~ : DALLY MEAN TEMP. (~')

T,,~. : DALLY MAXIMUM TEMP. 0")

T,,~ :DALLY MINIMUM TEMP. (~') MAX. TEMP. h

$Ugt 1$( 14:30 SuI4str 24:00

SOl.All I I n [

Fig. 5. A m b i e n t temperature model .

solar desalination plant 197

have been cleaned with a water jet. When the glass tubes are perfectly clean, the transmissivity reaches its highest value of 0.98, but subsequently drops down to its lowest value at the end of the month.

The end-of-month transmissivity can be seen to vary from month to month depending on the season of the year. The way the transmissivity varies during a particular month was assumed to be exponential [ 8 ]:

r - r , = e_O.O, ~ (15) 7- 0 - - T m

where r is the transmissivity of the glass tube N days after last cleaning and r0 is the transmissivity of the clean glass tube immediately after cleaning, and rm is the transmissivity one month after cleaning. Point "a" in Fig. 6 represents the transmissivity of the clean glass tube and point "b" gives the transmissivity at the end of one month.

For the purpose of the present simulation, the curve shown in Fig. 6 was divided into twelve monthly seg- ments with each segment fitted to a second-degree polynomial of the form

r...~.~ = A ( i ) . N 2 + B ( i ) . N + C(i) TO

i = 1 - - . 1 2 (16)

where A(i), B(i), and C(i) are constants the value of which depend on the month in question and were obtained from least square fitting of the experimental data.

Equations (15) and (16) are used together to estimate the transmissivity of the glass tube at any particular day of the year given the days during which the glass tubes were cleaned. This is carded out as follows: the constants A, B, and C for the month in question are first obtained and introduced into eqn (16) to get the transmissivity at the end of one month. This value of transmissivity is then substituted in eqn (15) to obtain the transmissivity for a particular day knowing the value of N. The transmissivity for a particular day is then multiplied by the hourly solar radiation on the absorber plate to obtain the actual radiation on the absorber plate. We can then write

It - r "I t (17)

where I~' is the actual hourly radiation on the absorber plate, I; is the radiation on the absorber plate for a completely transparent glass tube, and r is the transmissivity of the glass tube for a particular day.

3.5 Heat collection amount The amount of heat collected by the solar collectors

during each hour of the year was estimated from the relationship

0.~ -- A~ . ,7~ " ~7 (18)

198 A.M. EL-NASHAR

1.0 LU 0.96 a ~ Uter deaninl;

\

r~ o.g At en¢ of mot th

o

Pr

E o.a 03

~ 0 7 JAN FEB MAR APR

\? J

MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

Fig. 6. Dust influence model (clean once a month at least).

where (2c is the hourly heat collected, kcai/h, Ac is the total collector absorber area, m 2 and ~1¢ is the efficiency of the collector. The collector efficiency was expressed by

nc = a + b x + c . x z (19)

where

½[T, + T2] - To X =

17

The heat collected may also be expressed in terms of the collector mass flow rate and the inlet and outlet water temperatures, thus:

0.~ = t h ~ . c p . [ T 2 - Tt] = I~ .A¢ .~¢ .

This equation is used to estimate the collector outlet temperature at any hour during the day given the amount of heat collected calculated by multiplying the net radiation on the absorber plate and the total collector area.

Not all the amount of heat collected by the solar collectors is effectively utilized by the plant; part ofthis heat is lost by the transmission piping system, part is lost by the heat accumulator, and part by the evaporator. Each of these losses were calculated separately on an hour-by-hour basis[ 3 ].

3.6 Solar controller

A solar controller is used to control the operation of the heat collection pump. The solar controller eval- uates the solar radiation levels at which the pump should start if it is not running or at which it should stop if it is running. These radiation levels are generally dependent on the temperature difference between the collector inlet water and the ambient air, (7"1 - T,). The actual relationship between the startup and shutdown radiation levels and this temperature difference actually depend on the weather conditions for the site under consideration and on the heat collecting system

itself[ 3,7 ]. Based on measured data that utilized evacuated glass tube collectors, the collector manufacturer (Sanyo) has recommended the following formulas:

(i) Heat collection pump startup condition

I s> 5.0[T~ - T,] - 25.0

(ii) Heat collection pump shutdown condition

I c < 5.0[T, - 7"=] - 10.0

where Is and le are, respectively, the solar radiation levels at which the controller will send a stanup or shutdown signal to the pump.

3.7 Tempera ture distribution on the

heat accumulator

In order to simulate the operating conditions of the solar plant, the temperature distribution inside the heat accumulator must be determined as accurately as pos- sible. The evaporator normally starts automatically by a signal from a thermostat at the center of the accumulator and is shut down when the supply temperature at the top of the accumulator drops below another set point. During operation, the distillate production of the evaporator is dependent on the evaporator supply temperature (temperature of the top layers of the heat accumulator) while the amount of heat collected by the solar collector is strongly influenced by the collector supply temperature (temperature of the bottom layers of the heat accumulator). Consequently, the temperature distribution in the heat accumulator will generally influence the performance of the entire plant.

The heat accumulator considered for the present simulation consists of a single vertical cylinder of height L filled with distilled water which acts as the heat car- tying medium. The water is considered to be thermally stratified with minimal mixing at the top and bottom layers. The accumulator was modelled by dividing the tank into 1000 equal elements. By considering a heat balance on a single element, the following equation was obtained:


OT p~c, ~ t = -the, T ; x - A.UI T - r . l

/ 02T\ + (2o

where T is the water temperature of an element, Ta is the ambient air temperature, x is the vertical distance measured upward along the axis of the tank, A is the tank cross-sectional area, As is the surface area of the tank per unit height, p is the water density, Cp is the specific heat of water, k is the thermal conductivity of water, rh is the net mass flow rate through the element, and U is the overall heat transfer coefficient from the water to the ambient air.

Initial condition: T = To(x) for 0 < x < L

Boundary conditions: OT - - = 0 for x = 0 and x = L dx T = Th2 for x = o ( when evaporator is on )

T = Tz for x = L (when heat collecting pump is on)

The initial condition specifies the temperature distribution To(x) in the accumulator at the start of the simulation period. The first boundary condition describes the condition of no heat transfer across the bottom and top tank insulation. The second boundary condition states that the temperature at the bottom of the accumulator should equal the return temperature of the heating water from the evaporator. The third boundary condition asserts that the temperature at the top of the accumulator is equal to that of the collector return water.

Equation 20 was cast into finite difference form using the Crank-Nicoison method[9]. The governing equation, in finite difference form, was then applied to each individual water element, and a set of linear simultaneous equations in the unknown element temperatures were solved to obtain the temperature of each element at the end of a time interval ~t in terms of the _ temperatures at the beginning of the interval.

3.8 The M E S evaporator As mentioned above, the seawater evaporator used

in the simulation is a horizontal-tube, thin-film, multieffect distiller called multieffect stack (MES) evaporator. This type of evaporator was chosen because of its relatively low specific heat consumption (high performance ratio) and its ability to sustain large load fluctuations due to variations in solar radiation.

The evaporator consumes both thermal and electrical energy during operation. Two performance in- dices are commonly used in seawater evaporators which indicate its thermal energy consumption: the performance ratio, PR, and the specific thermal energy consumption, q. The specific thermal energy consumption is defined as the amount of heat supplied to the evaporator per unit of distillate produced, kcal/

199

kg. The performance ratio of the evaporator, PR, is inversely proportional to the specific thermal energy consumption, q, by the relationship:

PR = hfg (21) q

where big is the latent heat of vaporization ( =526 kcal/ kg). The performance ratio is strongly dependent on the number of effects. For MES evaporators, the relationship between PR and the number in the evaporator of effects, n, may be expressed as[3,7]:

PR = - ( l . 875 ) (10 -Z)n 2 + 1.15n - 1.625

for 7 < n < 1 3

PR = - ( 2 . 5 ) ( 10-3)n 2 + 0.625n + 2.15

for 1 3 < n < 3 2 .

The electrical power consumption depends essentially on the rated capacity of the evaporator. For MES evaporators of the design used at the Abu Dhabi solar plant, the power consumption was calculated from the empirical relations [ 3,7 ]:

P = - (1 .25 ) (10 -5 )C 2 + 0.14C + 6.06

for C < 500

P = - ( 4 . 4 8 ) ( 10-5)C 2 + 0 .18C + 4.47

for 500 < C < 1000

P = - ( 6 . 0 0 ) ( 10-2 )C 2 + 0 .1C + 32.9

for C > I000

where P is the electrical power consumption in kW and C is the evaporator capacity in m~/d.

The part load distillate production is dependent upon the heating water flow rate (to the evaporator), the heating water temperature, the sea water flow rate (to the evaporator condenser) and the seawater temperature. The heating water and seawater flow rates are usually maintained constant during operation and these flow rates are provided as input parameters in the computer simulation. The seawater temperatures are also provided as monthly average values. The heating water temperature is obtained as output from the heat accumulator model discussed in the previous section.

The four parameters mentioned above affect the average overall heat transfer coefficient for the evaporator which, in turn, affect the distillate production rate. The overall heat transfer coefficient during evap- oration and condensation is strongly dependent on the temperature at which these processes take place. Since the evaporator operates at varying heating and sea water temperatures, the average overall heat transfer coefficient has to be evaluated at each operating condition. This is achieved by applying a correction factor to the value of the average heat transfer coefficient at the rated evaporator capacity. The average overall heat transfer

200 A. M. EL-NASHAR

coefficient, U, for any operating condition was calculated from the equation:

a C .:[ (22)

where C and Cu are the evaporator distillate production at any operating condition and at the design condition, respectively; c is a correction factor determined from Fig, 7 for the first effect vapor temperature T,~ and the last effect vapor temperature T,,, and a and b are con- slants. This equation is based on actual heat transfer measurements at the solar plant [1,2,5 ]. At the design condition, the overall heat transfer coefficient can be obtained from eqn 22 by substituting C = Ca, thus

Ua = (a + b) c(T..) + c(T..)

We can then express the relationship between the first and last effect temperatures in terms of fT for any operating condition as follows:

T,, = T¢,, + n [ f T + BPE]. (24)

The effective temperature difference at any operating condition ~T, may be expressed in terms of the corresponding value at the design condition fT*, by the empirical relation [ 3 ]:

c u~ fT . . . . . fiT*.

c~ u

Substituting this expression for fT in eqn 24 we get

[ C Ua 6T* ] T,, = To, + L ~ ' T " + BPE . (25)

Let us now introduce an effective temperature difference per single effect, fiT* at the rated capacity (design condition) as

fT* = ( I ) [T*~ - T * , - BPE .n] (23)

where BPE is an average boiling point elevation of the brine in all effects. T*t and T,. are the first and last effect temperatures at the design condition, fT* represents an average driving force for heat transfer in the evaporators. The term BPE. n represents a drop in the total driving force ( Te*t - T * ) due to the fact that the vapor inside each effect is slightly superheated (actually the degree of superheat is equal to BPE) and will have to lose this superhea$ before it starts to condense. By rearrangement, this equation can be written in the form

T*~ = T**, + h i l T * + BPE].

1.5

z

u _,.,.

1,0

o ~ 0.$ u

/ / f

/ - f

/

0 0 Z0 30 40 S0 $0 70 It0

TEnPt|A~'QtI[ OF I[ve, eOIAl'Olt, T o[:

Fig. 7. Correction f a c t o r for the evaporator overall heat transfer coefficient.

The last effect temperature may be obtained from the equation

T,, = T~w + [0.9 m,,,cpl + 1.2 (26)

where T~, and rh,w are the sea water temperature and flow rate and Q, is the heat input rate to the evaporator. This equation is based on a heat balance on the evaporator condenser and assumes that the condenser heat load constitutes 90% of the heat input to the evaporator with the balance of 10% representing vent and heat losses from the evaporator. It is also assumed in this equation that the temperature difference between the last effect and the condenser is 1.2"C.

The heat input rate may be expressed in terms of the heating water inlet and outlet temperatures as

Q, = mhcp[Thl- T~,]

(27)

For a particular evaporator production, the heat input rate may be expressed in terms of the performance ratio as follows:

~ = Ch~ PR " (28)

The calculation procedure incorporated in the evaporator model aims at calculating the hourly evaporator parameters given the heating water inlet temperature and flow rate, and the seawater temperature and flow rate. The most prominent performance parameter is, of course, the hourly distillate production. Equations (21)-(28) are used in an iterative manner to achieve this aim. The procedure may be summarized as follows. A first approximation to the capacity, C, is made. Using this value of C, the heat supplied is calculated from Equation (28) and the first effect temperature is calculated from eqn (27). The final effect temperature is then calculated from eqn (25) after the average overall


heat transfer coefficient is estimated from eqn (22). Using this value of final effect temperature in eqn (26), the value of the heat supplied is calculated from eqn (26) and checked against the previous calculated value. The evaporator capacity is then changed until the heat supplied calculated in one iteration agrees, to within a small tolerance, with the previous value.

4. COMPUTATIONAL PROCEDURE

A flow chart of the computational procedure used in the simulation program is shown in Fig. 8. The input data to the program consists of system data contained in three separate files: "System Data # !," "System Data #2," and "Basic Evaporator Performance Data." The two system data files contain input data such as collector area, tilt angle of absorber plate, heat accumulator capacity, etc. The evaporator performance data file contains information such as the effect of the different operating parameters such as the heating water temperature and flow rate, feed water temperature and flow rate, and condenser seawater temperature and flow rate on the evaporator product flow rate and specific heat consumption.

The initial condition of the solar desalination plant at the beginning of the simulation period has to be specified. This includes the temperature distribution in the heat accumulator. The extent of dust accumulation during the simulation period is also specified by indicating the days during which the collector field was cleaned.

The input meteorological data is contained in a separate file containing information on the solar radiation and ambient air temperature.

Once these input data are read by the program, ex- ecution of the heat collection calculations starts. This involves calculating the solar declination and equation of time which are estimated once for each day. The rest of the calculations are carried out on an hourly basis. For each hour of the day, the solar altitude, solar azimuth, hourly beam and diffuse radiation on the absorber plate, heat collection amount, heat loss from piping heat accumulator, temperature distribution in the heat accumulator, and evaporator production rate are estimated.

5. RESULTS

In order to validate the computer simulation, a comparison is made between the simulation results with those obtained from the Abu Dhabi solar desalination plant. For this purpose, the hourly solar radiation data measured at the plant site was actually used in the simulation. The specifications of the solar plant is given in Table 1. The plant consists of a solar collector field of vacuum tube flat plate collectors having a total absorber area of 1862 square meters, a heat accumulator having a capacity of 300 cubic meters, and an MES evaporator with a rated capacity of 130 cubic meter per day of distillate.

For the purpose of this comparison, the hourly total radiation data measured at the solar plant was actually

201

~Sy Input I stem Data No. 1 J [

~y ,n~t I stem Data No. 2 I

I K ,n~t I I L=atio. Oat~. =o. [

I Basic Performance

o~ Evaporator I

Daily Loop > J I

~M ,nput I ateorological Oata J

[ Oost'n"o. . I

Solar Declination Hourly Equation of Time Loop etc.

I Solar Altitude I Solar Azimuth

I Hoorly direct norm= I Solar Radiation Hourly Diffuse Radiation on H. Surface

Shadow of Adjacent Absorber J Plate, etc.

J no ned Surface Magn ficat on [ ¢

I Solar Radiation o~ I Absorber Plate

Heat Collection Amount Heat Loss from Piping, etc.

I v=:w::v0 C:,l ½

I Temp. Distribution in Accumulator [

'l

I

I I Solar RadlJtion Model Ambient TenD. Model

I

1 [Output Monthly and[

Fig. 8. Flow chart of solar desalination plant computer simulation program.

202 A. M. EL-NASHAR

Table !. Specifications of the Abu Dhabi solar plant

Solar Collectors Type Collector area Tilt angle

Heat Accumulator Capacity Heat storage fluid Configuration Surface area

Evaporator Design capacity Maximum brive temp. No. of effects Performance ratio

Evacuated tube, fiat plate 1862 square meters 21 degrees due south

300 cubic meter distilled water three tanks connected in series 481.75 square meters

130.0 cubic meters per day 68.0 C 18 13.0

. J used in the simulation program. The daily solar radiation on a horizontal surface during January 1985 is shown in Fig. 9. This month was selected because of the relatively large variability in the solar radiation since this month was characterized by frequent overcast skies in Abu Dhabi.

Figure 10 shows the daily amount of heat collected and supplied to the heat accumulator during January 1985. The agreement between the measured and calculated values of the daily heat collected seems to be quite good. The variation in the daily amount of heat collected seems to follow the change in the solar radiation.

The measured and calculated values of the daily distillate production during January 1985 is shown in Fig. 11. Again, the agreement is generally satisfactory except for the data of January 6 for which the calculated distillate production is substantially higher than the measured value. The reason for this discrepancy seems to be due to the fact that during this particular day, the evaporator shutdown temperature setpoint for the simulation and the actual plant were different. For the simulation, the setpoint was 63.3°C whereas in the plant, the setpoint was actually 66.5°C. Because of this difference in the setpoint, the evaporator was shutdown at 19:30 according to the simulation results, while in the real plant the shutdown time was recorded to be 11:30 on that day (January 6).

Table 2 shows the simulation results by day for 140

January 1985 and a comparison between the calculated and measured values of a number of prominent per- 120

10o s

2 840

1 J A N U A R Y 1S8S 2 0

o I I 10 20 30 0

DAy NUMBER

~ - MEASURED ... . . . . . . CALCULATED

: it - -

I . . 0

x

d

G 3 w

! . 1

0 1 10 20 30

DAY

Fig. 10. Comparison between measured values and calculated values o f heat collection amount (January 1985).

formance parameters. In this table (2c is the daily amount of heat collected by the collectors after the shadow and dust effects were accounted for. (~o represents the daily amount of heat supplied to the accumulator which is estimated by subtracting the calculated heat loss from the transmission piping from the amount of heat collected by the collectors. (~e is the daily net (effective) amount of heat collected after subtracting the piping and accumulator heat losses from the heat absorbed by the collectors. (2s is the daily heat supplied to the evaporator which may be higher or lower than the net amount of heat collected. For example, when (~ is larger than (~e, the accumulator thermal energy content will decrease by an amount equals ((~ - (~e).

The daily number of hours during which the evaporator was running, te, is shown to vary widely from day to day. On January 7, for example, the evaporator

MEASURED ......... CALCULATED

I/;, :fii i/ ll /: /Ait t)I/YJ LJ-

...... V 10 20 30

DAY NUMBER

Fig. 9. Daily solar radiation on a horizontal surface in Abu Fig. 11. Comparison between measured values and calculated Dhabi during January 1985. values of product water (January. 1985).

Computer simulation of a solar desalination plant 203

Table 2. Results of the simulation for January 1985 and comparison between the measured and calculated values of major performance parameters

* * * * * SIMULATION I]F SOLNI OE"S~LII~TION PLANT * * * * *

i

N H H, T i CI.~AN ; ~, O. (kcal /m.~d) ( k c a l / m 2 = l C" ( k c i l / d l ( k e e l / d )

l 3980 5250 18.6 CL 0.98 4620000 3980000 2 3800 4940 80 .0 * 0 . 9 8 q450000 3910000 2 3440 4380 22.5 * 0.98 3870000 3380000 4 2970 3700 2 1 . 4 * 0 . 9 8 3030000 2580000 5 3690 4770 19.7 • 0,97 ~050000 3~30000 6 2270 2760 19.8 • 0.97 1809000 1399000 7 3230 4100 19.1 * 0.97 3430000 8900000 8 4170 5460 19.0 * 0.97 4700000 4060000 9 3630 4690 18.9 " 0 .97 3920000 3350000

I0 4050 5260 19.0 * 0.97 4620000 ~l~OO00 11 3560 45~0 18.9 • 0.97 4620~00 3930000 12 3980 5160 18.5 * 0 . 9 7 46~0000 4010000 13 3930 5050 18.2 * 0 . 9 7 4~0000 41~0OO0 14 3310 4140 18.~ • 0.97 4/~?.0090 3~4Q000 15 3470 4340 E0,5 * 0 . 9 7 46~.0000 3790000 16 2630 3~30 18.8 . 0.97 46~0000 2410000 17 4100 5270 20.5 * 0.97 4&?.O000 5030000 18 3320 4100 8 0 . 0 * 0 . 9 / 46~0000 3080000 1o 36@0 4520 19.1 . 0 .96 46~0000 3910000 20 4160 5300 L~O.I + 0 .96 ~6~0000 4970000 21 3610 4460 80 .6 * 0 .96 4620000 4000000 22 3880 4860 ~0 ,6 . 0 . 9 6 46~0000 39~0000 23 ~I~0 5830 ~ . 5 * 0 .96 4620000 4880000 2a 4!70 5~50 82.4 * 0 . 9 6 46~0000 4950000 25 3840 4750 ~ 2 . 0 * 0 .96 4620000 4360000 26 2340 8740 2 1 . 8 * 0 .96 4620000 1744000 27 3850 4760 21.7 * 0 .96 46~0000 4440000 28 4080 5090 80.9 * 0.96 4620000 4350000 29 4470 5600 21 .1 * 0 .96 4620000 5240000 30 4450 5560 21.9 CL 0.98 4620000 5470000 31 4420 5600 21.8 * 0.98 4620000 5490000

~LcuLATED 14490~ IL:~I0(X)0O

MEASURED 1 4 ~ 0 0 115100000

I I

b. t. o. C t. ,:w (kellld) (hrs) ( kc l l / d l ( l i t / d ) (hrs) {I ~h,'d:

3460000 6.'~ 4820000 11750'? EC.," ~3: 34400C)0 4. I 4290000 105600 2 t,.O G~'- 2980000 2.7 4240000 104200 2:.. C; ~l. ~ 2160000 l .~ 213000 506" ~ ~ ~ 2910000 5.0 229000.) 29800 ~.5 3 ~ 9590+)0 1.3 3750000 01500 I : . 5 ~."

2450000 3 ,0 0 0 .0 ~ ~ 3520000 6 .5 2650000 38700 l I .~ :.4=- ~40000 6.5 4370000 i 07100 24.0 827 3640000 6.5 3780000 92700 2 4 . 0 @-=7 2970000 4.5 3710000 90600 24,0 821 3530000 3 .2 1206000 28800 B.5 354 3540000 6 .9 2890000 43000 12.0 4 t, l 2910000 5.6 4590000 112200 24.0 81. ~ 3320000 5.9 3840000 94200 24.0 .~ : 6 1971000 2 . 0 3810000 92600 2 4 . 0 236 4570000 6 .2 234000 515000 2 .0 15.~ 2510000 5.9 2860000 43300 12.0 ~,% 3390000 6 . 5 4700000 1148o0 24.0 ~ : a.470000 6 . 7 4290000 105900 24.0 ~.~ 3500000 5.8 1594000 39400 %0 35 ~ 3340000 6 .9 3320000 5120~ 13.0 : . : I 4370000 7 . 2 5270000 126200 24 .0 .=.~" 4460000 ?.0 4810000 I17600 24.0 2~7 3820000 6.0 4510000 111300 24.0 ~;.:. 1319000 1.5 4100000 100300 24.0 2~,'. 4000000 5,9 120400 2690 1.0 1~:: 3780000 6.6 2950000 42900 11.5 :~C' 4700000 7.2 5410000 128700 24.0 2~.' 4950000 7. I 5090000 1~3100 2~.0 e:7 4980000 7.1 5020000 121600 24.0 ---_~

104700000 ~390000 5~3 .0

100300000 2340000 5 ~ . @

CLEAN *oecifies day in which collector field is cleaned C collector field cleaned during that day • collector field was nat cleaned during that day

was shut down due to the depletion of the thermal charge of the accumulator because of a low solar radiation level occurring the previous day (January 6). The evaporator was shown to be running for only few hours per day during other days of the month for the same reason (accumulator depletion).

From this table, one can also compare the calculated and measured monthly amounts of solar radiation falling on the absorber plates, heat input to the accumulator, heat supplied to the evaporator, and distillate production. Close agreement between the measured and calculated values of these monthly quantities can be observed.

The daily measured and calculated values of the evaporator heat supply for January 1985 is shown in Fig. 12. The number of hours per day during which the evaporator was running is shown in Fig. 13 which gives the daily hours during which the distillate pump was operating versus the day number.

The plane energy balance for January 1985 is shown in Fig. 13 which shows the heat transport quantities for each of the collector field, piping system, accumulator, and evaporator. Out of@ total solar irradiation of 269.8 Mkcal, the collectors were able to convert 152.3 Mkcal into thermal energy thus achieving an efficiency of 56.4 percent. Out ofthis 152.3 Mkcal collected, 20.9 Mkcal was lost through the transmission piping and the rest ( 131.4 Mkcai) was used to charge the accumulator. 10.5 Mkcal of heat were lost from the accumulator during the month. With the evaporator consuming 121.1 Mkcal during the month, the

accumulator was discharged (depleted) by an amount of 0.2 Mkcal in order to compensate for the shortfall in the net amount of heat supplied to the evaporator. In the evaporator, 4.0 Mkcal were lost and 117.1 Mkcal were rejected to sea water. The overall energy conver- sion efficiency of the plant (from solar irradiation to thermal energy for the evaporator) is thus estimated to be 121.1/269.8 = 0.45 (i.e., 45.0%).

6. CONCLUSIONS

The solar desalination system utilising the evacuated tube collectors and the multieffect-stack (MES) distiller

6 - - J a n u a r y 1 9 8 5 1D

1 m e a s u r e d

e e o o e o e e ca lcu la ted

o 1 I I I 1 5 10 1 5 2 0 25 3 0

DAY NUMBER

Fig. 12. Daily heat supplied to the evaporator dunng January 1985.

204 A. M. EL-NASHAR

Heat loss Oust toss ( 93.a Mkcal) (8.4 Mkcal)

,l Solar irradiation J

(269.8 Mkcal ) v[ Collector

field

Heat collected

(152'3kcal)

54~adin 9 loss

(15.3 M kcal)

Piping loss Accumulator lots (20.9 Mkcal) ( 10.5 Mkcai )

F Heart° I

PiPin9 C131.4Mkcall[ (.0.;~ Mkcal ) r121,1Mkcal]

Evaporator toss (4.0 M kcal )

Evaporator

IHtat rejtcted to

l (117.1~kcall

Fig. 13. Energy balance in the solar desalination plant for January 1985.

was successfully simulated to determine its performance under different design and operating conditions. The computer-simulation program was written to study the effects of the various system parameters such as the collector area, heat accumulator capacity, evaporator capacity, etc. The results of the simulation program were compared to the measured performance of the Abu Dhabi solar desalination plant. In order to validate the results of the simulation program, the daily performance of the plant was compared with the results of the simulation program for the month of January 1985. The hourly solar radiation data as measured at the solar plant were introduced as input to the simulation program.

A close agreement between the calculated and measured daily performance was generally observed. In particular, the daily trends in the amount of heat collected and the distillate production show an almost identical behavior.

Acknowledgment--The author expresses his gratitude to Dr. Darwish, M. K. AI-Gobaisi, Director General of Power and Desalination Plants, WED for his assistance and encourage- ment. The critical comments and suggestions from the re- viewers/editor of the Solar Energy Journal, are also gratefully acknowledged.

NOMENCLATURE: a

A A~

A t . " "A3 b

BPE C

cp c(T)

C

C#

19. D,, D~

constant cross-sectional area of accumulator tank, m 2 surface area per unit height of accumulator, m2/ m

shadow areas on absorber plate, m s constant boiling point elevation, °C constant specific heat at constant pressure, kcal/kg oC heat transfer coefficient correction factor at temp. T evaporator distillate production rate, lit/h, lit/day, m3/day distillate production rate at design conditions, liter/ h shadow length by adjoined absorber plate, m shadow length by adjoined glass tube, m shadow length by header box, m

Et equation of time, h h solar altitude, rad.

h~v solar altitude measured from the collector plane, tad.

hN solar altitude measured along a plane normal to axis of collector tubes, tad.

h/g latent heat of vaporization, kcal/kg °C H daily radiation on a vaporization, kcal/kg °C H, daily radiation on a tilted surface, kcal/m 2 d

I hourly radiation on a horizontal surface, kcal/m s h

I, hourly radiation on a tilted surface, kcal/m 2 h l,b hourly beam radiation on a tilted surface, kcal/

m2 h ha hourly diffuse radiation on a tilted surface, kcal/

ms h [o hourly extraterrestrial radiation on a normal sur-

face, kcal/m2 h I', hourly radiation on absorber plate for a completely

transparent glass tube, kcal/m2 h 17 actual hourly radiation falling on the absorber plate

kcal/mz h /, hourly radiation for heat collecting pump startup

condition, kcal/m2 h le hourly radiation for heat collecting pump shut-

down condition, kcal/m2 h k thermal conductivity of water, kcal/hm °C

KW daily amount of electricity consumption by all pumps KWh / d width of absorber plate, m

L pitch of absorber plate, m; also local longitude, dcg.

Lo principal mcridean longitude, dcg. n~ net mass flow rate through the accumulator, kg/

h tfih mass flow rate of beating water, kg/h rfi~ mass flow rate of sea water, kg/h rhc collector mass flow rate, kg/h n number of evaporator effects N day number P power consumption of MES evaporator, KW; also

atmospheric transmissivity PR performance ratio of MES evaporator (~o hourly or daily beat supplied to accumulator, kcal/

h, kcal/day (2b hourly or daily heat collected, kcal/h, kcal/day Qe hourly or daily effective heat collected, kcal/h al~er

subtracting piping and accumulator losses, kcal/ h, kcal/day

(), hourly or daily heat supplied to evaporator, kcal/ h, kcal/day

r radius t solar time, h


to ambient air temperature, *C t~ daily evaporator running time, h tp daily heat collection pump operating time, h t, standard time, h t= sunrise time, h T~ inlet collector temperature, *C 7"= outlet collector temperature, *C

T,, first effect vapor temperature, *C T~, last effect vapor temperature, *C 7",, inlet heating water temperature evaporator, °C 7",2 outlet heating water temperature from evaporator,

*C

205

Greek ao tilt angle of collector absorber plate relative to

ground, tad. ac tilt angle of absorber plate relative to collector

plane, rad. azimuth angle of collector, rad.

q, incidence angle of collector plane, deg. declination, deg.

~t small time period, h ~T effective temperature difference per single effect,

*C 6T* effective temperature difference per single effect at

design condition, *C 3' solar azimuth angle, rad.

3"s solar azimuth angle measured from line of maximum inclination on collector plane, rad.

rlc collector efficiency r transmissivity of glass tube

rm transmissivity ofglass tube one month after cleaning

ro transmissivity of glass tube immediately after cleaning

REFERENCES

1. A. M. EI-Nashar and A. E. EI-Baghdadi, Sea water Dis- tillation by solar energy, Desalination 61, 49-66 ( 1987 ).

2. A. M. EI-Nashar and K. Ishii, Abu Dhabi Solar Distillation Plant, Desalination 52, 217-234 ( 1985 ).

3. Eng. Adv. Assoc. of Japan and Water and Electridty De- partment (Abu Dhabi), Research and Development Co- operation on Solar Energy Desalination Plant, Final Re- port (March 31, 1986).

4. Eng. Adv. Assoc. of Japan, The Development of a Solar System for Desalination--Conceptual Design (March 31, 1983).

5. Waterand Electricity Department (Abu Dhabi),Theso- lar Desalination Plant Monthly Report (January. 1985).

6. Sasakura Eng. Co. Ltd., The solar desalination plant, Training Manual ( 1985 ).

7. Eng. Adv. Assoc. of Japan and Water and Electricity De- partment (Abu Dhabi), Research and Development Co- operation on Solar Energy Desalination Plant. Interim Report (March 31, 1986).

8. A. Sayigh et al.. Dust effect on solar flat surface devices in Kuwait Proc.. Int. Symp. on Thermal Applications of Solar Energy (April 7-10, 1985).

9. C. F. Gerald, Applied Numerical Analysis, 2nd ed., Ad- dison-Wesley Publishing Co. (1980).

10. J. A. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes, Wiley, New York ( 1980 ).

Documents

Computer simulation of the performance of a solar desalination plant