Experimental and theoretical study on temperature distribution of adding coal cinder to bottom of salt gradient solar pond

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ScienceDirect Solar Energy 110 (2014) 756–767 www.elsevier.com/locate/solener

Experimental and theoretical study on temperature distribution of adding coal cinder to bottom of salt gradient solar pond Hua Wang a,⇑, Jianing Zou b, J.L. Cortina c, J. Kizito d a

School of Mechanical and Power Engineering, Henan Polytechnic University, 2001 Century Avenue, Jiaozuo 454003, Henan, PR China b Mordern Education Center, Henan Polytechnic University (HPU), Jiaozuo, Henan, PR China c Department of Chemical Engineering, Universitat Polite`cnica de Catalunya-Barcelona Tech (UPC), Barcelona, Spain d Department of Mechanical, Engineering College, North Carolina Agricultural & Technology University (NCAT), Greensboro, NC, USA Received 23 March 2014; received in revised form 12 October 2014; accepted 14 October 2014

Communicated by: Associate Editor Aliakbar Akbarzadeh

Abstract A higher Low Convective Zone (LCZ) temperature is important for the Salt Gradient Solar Pond (SGSP) thermal engineering application, which is bound to bring a more extensive application. For this purpose, we studied on adding a layer of coal cinder at bottom of LCZ of solar pond, here coal cinder is the burning residues of coal. Temperature development of adding coal cinder at bottom of SGSP has been experimentally and theoretically studied. One dimensional transient numerical model was used to estimate the temperature development in SGSP. The outdoor experiments were used to qualitatively study the temperature evolution of different bottom treatments and porous materials influence, and also used to validate the mathematics model present in this paper. The results show that adding coal cinder at bottom of SGSP leads to a higher LCZ temperature than the traditional bottom treatment. Good consistency has been achieved in the simulation results and the experimental results. Finally, in order to estimate the effect of coal cinder used in large-scale solar pond, a numerical simulation was given and compared to the similar research. The results of this paper show that it can obviously increase LCZ temperature by adding coal cinder at bottom of LCZ, and as a cheap material with perfect thermal performance, it is suitable to be applied in practical SGSP. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Solar pond; Porous material; Coal cinder; Temperature

1. Introduction Solar pond is an artificial pond that acts as a solar energy trap and provides thermal energy. Normally, it consists of three zones: two convective zones, the Upper Convective Zone (UCZ) and the Lower Convective Zone (LCZ) and a Non-convective Zone (NCZ) which separates the two said zones. Usually, UCZ is filled with fresh water, NCZ is salinity gradient, and LCZ is nearly saturated salt ⇑ Corresponding author. Tel.: +86 15039138423.

E-mail address: [email protected] (H. Wang). http://dx.doi.org/10.1016/j.solener.2014.10.018 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

water. Due to the capability of solar pond to capture and store solar energy, solar ponds appear to have significant potential for solar thermal energy storage (Karakilcik et al., 2006), and there are many research reports on transient and steady state modeling of solar ponds (Date et al., 2013; Sua´rez et al., 2014; Boudhiaf and Baccar, 2014). Solar ponds combine solar energy collection with longterm storage and can provide reliable thermal energy at temperature ranging from 50 to 90 °C (Busquets et al., 2012). However, the thermal performance of the solar ponds depends on the turbidity of the pond fluid, the season and the climatic condition, the construction and

H. Wang et al. / Solar Energy 110 (2014) 756–767

757

Nomenclature a, b A C H h h(x) I k Pr q(x) Qi,t Ra RS rt T t Ta Taver Tg Ups Upw

the modified constant related to local climate, and for Dalian city, a = 0.36 and b = 0.23 area for absorption of solar radiation (m2) the specific heat (kJ/kg °C1) the month averaged daily radiation on the horizontal surface (kJ/m2) solar energy penetration the solar radiation attenuation function in brine water the global solar radiation on the horizontal surface per hour (kJ /m2 h) the coefficient of heat conductivity (W/m°C1) Prandtl number the solar radiation intensity reach the depth of x (W/m2) the heat absorbed by the ith layer at time t (kJ) thermal Rayleigh number Ra = agDTd3/kTt solute Rayleigh number RS = bgDSd3/kSt the rate of hourly radiation to daily total amount of radiation the temperature (°C) time (h) ambient temperature (°C) the daily average temperature (°C) ground temperature (°C) the coefficient of heat loss from the surface to surroundings (W/m2 °C1) the coefficient of heat loss from the side wall to surroundings. (W/m2 °C1)

its maintenance, etc. (Karakilcik et al., 2006; Velmurugan and Srithar, 2007). Maintenance of the clarity of the water and the proper depth of the gradient zone is essential for increasing the bottom temperature (Velmurugan and Srithar, 2007; Hull, 1990). For the actual solar pond, Puyasena et al. (2003) achieved a maximum temperature of 63 °C in a 39,000 m2 saltpan solar pond; in a 50 m2 saltpan, Sun and Zhou (2003) got a maximum temperature of 60 °C. Zhen Nie et al. (2011) have obtained the maximum temperature of 39.1 °C in a 2500 m2 solar pond in zabuye salt lake. It indicated that for the applied salt gradient solar pond, it is difficult to attain a high temperature. So, in order to get more useful heat, it is meaningful to increase the LCZ temperature of the normal actual solar pond. This is exactly the main objective of the present study. To increase the temperature of the storage zone, various methods have been presented by many researchers, such as plane mirror (Aboul-Enein et al., 2004), mobile cover (Ibrahim and El-Reidy, 1996), baffle plates (El-Sebaii, 2005) and honeycomb surface insulation system (Arulanantham et al., 1997) which have been used to improve the performance of the pond. All these researches

Upg x DT Dx

the coefficient of heat loss from the solar pond to ground (W/m2 °C1) depth, distance from surface of the solar pond (m) the daily max temperature difference (°C) depth step (m)

Greek symbols a thermal expansion coefficient (°C1) b saline expansion coefficient (m3/kg) d declination angle (rad) e porosity l extinction coefficient (m1) q density (kg/m3) s ratio of diffusivities (Lewis number) s = ks/kT t kinematic viscosity (m2/s) u the local latitude (rad) x the time angle (in radians) xs the sunset angle (in radians) Subscripts: a air e effective f fluid (salt water) g ground s solid (porous material) t time

have proved useful for increasing the LCZ temperature for small or mini solar ponds. But most of these methods are unsuitable for the actual solar ponds for reason of the economic or the devices feasibility. Al-Juwayhel and El-Refaee (1998) firstly provide the concept that adding rockbed on the bottom of LCZ, and they numerically studied the thermal performance of a combined packed bed solar pond system, and the results showed that the storage temperature remarkably increased when low thermal diffusivity rocks are used in the packed bed. In order to increase the quality of heat in LCZ, we have proposed to add a layer of coal cinder at bottom of LCZ of solar pond mainly based on the following reasons (Hua et al., 2009). It is well-known that the material with a lower diffusivity coefficient tends to have a better-insulated effect, and the thermal diffusivity of most of the porous materials is much lower. Coal cinder is a normal porous media and low-cost industrial byproduct. It is the burned or partly burned residues of coal. Another important reason for selecting this material is that, just like painting the solar pond bottom black, the dark color increases the absorption of the solar radiation energy.

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H. Wang et al. / Solar Energy 110 (2014) 756–767

In a solar pond with a porous material bed (PB), due to the LCZ temperature increasing and quick localized heating effect of porous material, we need to pay attention to the stability of the interface of LCZ and NCZ. The porous media to add on bottom of LCZ has been shown to effect the stability of the pond and heat loss at the base of the pond (Hill and Carr, 2013). Some reports show that the addition of porous material can stabilize the fluid-porous material system (Hadim and Burmeister, 1992; Horng et al., 2006; Karim et al., 2010). While Hill and Carr (2013) found that there exits a critical value for the proportion of porous material to the total LCZ to attain the maximum LCZ temperature. This paper experimentally and numerically studies the influence of coal cinder on LCZ temperature. A series small solar pond experiments and experimental solar pond with area of 2.8  2.3 m2 and depth of 0.8 m are carried out to investigate the temperature rise effect of coal cinder and also compare with the numerical results. A one-dimensional model gives a temperature distribution, and the boundary condition is considered according to the experimental solar pond, with the actual measured data of solar radiation and ambient temperature as boundary conditions to simulate. The purpose of this paper is to experimentally and numerically validate the effect of adding coal cinder at bottom of LCZ. The small experiments were used to show the results qualitatively and validate the numerical model. The effect of this material used in large-scale solar pond was estimated by numerical model. 2. Experiments 2.1. Experimental method 2.1.1. Small experimental solar pond Four plastic tanks with an area of 0.4  0.25 m2, and a depth of 0.3 m have been used for experiment. The tanks are all placed on a 0.04 m thick thermal insulated board which is the high density board with polystyrene resin as the main material. The test of the blank bottom without any addition of any material was conducted to compare the effects of adding porous materials. The same method for perfusion is used for each plastic tank: the lower zone is 0.16 m thick brine (solution of NaCl) with the salinity of 120 kg/m3 and the upper layer is 0.10 m thick freshwater. Then, stand it for one week to let salt diffuse upward to form the salt gradient zone. The turbidity of the saturated brine is 6.8 ntu, and fresh water is 2.1 ntu. During the experimental period, freshwater is used to add to the surface to make up the loss from evaporation. Before coal cinder is added to solar pond, we must do some pretreatments on them, include (i) crush and screening to the expected particle size, (ii) clean to remove ash and dust, (iii) remove the light-color and low density ones to avoid them floating in NCZ and the low absorptivity of radiation.

2.1.2. Experimental solar pond A solar pond with a surface area of 2.3  2.8 m2 and 0.8 m depth was constructed on seashore of Dalian city (39°280 N, 121°310 E). The walls of the solar pond are mainly constructed by bricks, and the exterior of the walls are evenly daubed with cement paste, 6 cm polystyrene board was used for thermal insulation purpose. There is 0.10 m reinforced concrete under the bottom polystyrene board. The total thickness of the side wall is 0.20 m. Fig. 1 shows the completed solar pond. The saturated salt water with initial salinity of 30% and turbidity of 10 ntu were used to fill the LCZ, which was 0.40 m deep. Seawater with a turbidity of 1.2 ntu dissolved different proportion of salt was used to fill the gradient zone (NCZ), and the total thickness of the NCZ was 0.35 m which decreases from 25% at the bottom to 5% to the top at 5%/7 cm of the salt gradient. UCZ with a thickness of 5 cm was filled with freshwater. To compensate for the surface evaporation loss, freshwater was regularly replenished in the surface. Fig. 2 shows the schematic diagram of the experimental solar pond. As is shown in Fig. 2, coal cinder with a thickness of 10 cm was added at the bottom of LCZ. It is the residue of the coal combustion with the average particle diameter after treatment of no bigger than 1 cm. It is evenly spread at the bottom of the storage layer of the solar pond and the porosity of the mixing zone of the coal cinder and saturated salt water was 50%. 2.1.3. Instrumentation and analytical measurements TBQ-2 radiometer was used to determine the transient solar radiation intensity, with the accuracy of ±1 W/m2. Several corrosion-resisted temperature sensors with accuracy of ±0.1 °C were used to measure temperature development in solar pond and atmosphere. PC-2 recorder was used to record the temperature and solar radiation data. The digital turbidity meter WGZ-1 with accuracy ±0.1 ntu was used to determine the turbidity of the water. Fig. 3 shows some of the measure devices. 2.2. Experimental results and discussion 2.2.1. Influence of bottom treatment What material to use for the liner is one of the major issues in the design and installation of man made solar

Fig. 1. The conducted solar pond.

H. Wang et al. / Solar Energy 110 (2014) 756–767

Solar Energy

0.05 m

UCZ (fresh water)

NCZ (salt water)

LCZ (saturated brine)

1

0.35 m

4

0.40 m

1

2

3

1. Insulated wall 2. Insulated bottom 3. Ground 4. Coal cinder and bittern layer Fig. 2. Experimental solar pond combined coal cinder bottom layer.

1 2

3

Note: 1. Signal wire

2. Recorder

3. TBQ-2 radiometer

Fig. 3. Measured instruments.

ponds (Silvaa and Almanza, 2009). In the reported literatures, in order to increase the absorption factor of the solar pond bottom, most researchers adopted the method by darkening the color bottom. In order to show the difference proposed in this paper over the other methods, As shown in Table 1, three plastic tanks which described above were used: one plastic tank whose bottom is left treated (Case A), one plastic tank whose bottom surface has no porous material and is only covered with black plastic, which is

759

equivalent to a dark bottom surface (Case B), and one plastic tank whose bottom is covered with a thin layer of coal cinder (Case C). The saline perfusion methods were the same as those described in Section 2.1.1. Fig. 4 shows experimental results of nearly 10 h. For the highest temperature, the temperature of Case C which is the one covered with coal cinder at the bottom is 65.5 °C at about 13:00 pm, which is 12 °C and 14 °C higher than Case A in the blank experiment and Case B with black plastic covered bottom respectively. The experimental results show that the effect to increase LCZ temperature of SGSP is obvious when the coal cinder is added to the bed of the SGSP, and certainly, due to the material’s high absorption of radiation, black covered bottom layer is better than the traditional blank bottom. Sua´rez et al. (2014) have found that models based on laboratory-scale observations can be utilized to understand the expected performance of large-scale solar ponds, and boundary effects, light radiation and turbidity are the main factors that result in differences between small and large-scale pond performance. In this study, the experiments have been performed outdoor, so the light radiation is seem to large-scale ones, and the other two factors of boundary conditions and turbidity are seem to other small scale experiments, therefore they should be reliable to get a qualitative conclusion. 2.2.2. Influence of porous materials The above experiments indicate that the bottom temperature of the pool could be obviously increased by adding a layer of coal cinder to LCZ, and it is certainly better than the traditional styles of both the blank and black bottom ones. In order to compare the effects of different adding materials and then a long-term positive effect of this method, as shown in Fig. 5, two kinds of materials: coal cinder and pebbles were selected to study. Parallel experiments were carried out in small plastic tanks. The coal cinder was collected and screened from a nearby boiler room, while pebbles are collected from the beach. Three other experiments which included blank one (Case D) which means a general one and without any treatment on bottom, pebble-covered bottom (Case E) and coal cinder covered bottom (Case F) were carried out for 20 days and the detailed parameters are showed in Table 2. The measurement points are as those above. During the experimental period, the freshwater was replenished at surface to make up the loss from evaporation. Because there are no other thermal insulated treatments except for the

Table 1 Parameters related to the three experiments. Case

A

B

C

Total thickness Nonconnective zone Lower zone

26 cm 10 cm fresh water 16 cm saturated salt water

26 cm 10 cm fresh water 16 cm saturated salt water

Bottom layer

Nothing

Covered with a piece of black plastic

26 cm 10 cm fresh water 16 cm mixing layer: saturated salt water and 2 cm coal cinder Nothing

H. Wang et al. / Solar Energy 110 (2014) 756–767

o

Temperature ( C)

760 70 65 60 55 50 45 40 35 30 25 20 15 8:00

coal cinder

black plastics

blank test

9:12

10:24

11:36

12:48

14:00

15:12

16:24

Time Fig. 4. Temperature evolution of different bottom disposal styles.

4 cm thickness insulated board below the test tank, plus the limited depth of the test pool, the temperature variation of the test pool is more dependent on the solar radiation. That is to say, under the experimental conditions, there is almost no heat storage ability during the night. Therefore, the measurement time was generally less than 24 h. Pebbles are all oval-shaped and 2 cm thick at bottom of the experimental tanks which the thickness of mixing layer is 20% of the total LCZ. The choose of this thickness of coal cinder was based on the opinion that to state issues clarity, and Hill and Carr (2013) have found that approximately 60% of porous material in the LCZ appears to optimize the maximum LCZ temperature. The porosity of the porous medium layer of the mixing zone formed by salt water and coal cinder and the porosity of that formed by salt water and pebble is 50% and 32% respectively. Fig. 6(a)–(c) gives the temperature experimental results of the 1st, 5th and 10th days. The three curves in Fig. 6(a)–(c) are temperature measurement results of Case D (blank one), Case E (pebble one), Case F (coal cinder one) and atmospheric temperature. From Fig. 6(a)–(c), we can see that, the initial temperature of every morning is close to the atmospheric temperature, and the small pool

with coal cinder covered bottom has the highest temperature among the three cases. The daily highest temperature difference between Case F and Case D for these four days (the 1st, 5th, 10th and days) are 5.4 °C, 6.7 °C, and 7.4 °C respectively. This result seems to show temperature difference tends to increase with time, but this does not mean that the coal cinder’s positive effect for temperature increasing will be enhanced with the immersion time in brine. There are other factors influencing the bottom temperature of the solar pond in addition to the pond bottom layer treatment, such as the atmospheric temperature and the solar radiation. This means that the average solar radiation has increased. The experimental results showed in Figs. 4 and 6 suggested us that the coal cinder’s positive thermal effect of increasing LCZ temperature may be enhanced with the larger input of the solar radiation energy. So, we can also deduce that the porous characteristics of the coal cinder results in a more uniform heat diffusion, thereby obtains an more effective thermal apply and heat transfer. 3. Simulation 3.1. Non-convective zone stability of the experimental solar pond With the effect of increasing LCZ temperature, inevitably, it may have the potential effect to destruct the stability of NCZ. However, in any case of with and without porous material conditions, if we only focus on NCZ, it must obey the thermodynamic stability relationship between thermal gradient and density gradient. As known, NCZ is a typical heat and salt double convective system that means that in the interior of the gradient layer, temperature gradient can result in unstable which can lead to local mixing. In order to prevent these conditions, the stability of this zone must be considered. NCZ stability depends on the interaction relation between thermal and saline Rayleigh number

Fig. 5. The materials used in the parallel test (coal cinder and pebble).

Table 2 Parameters related to the three experiments. Case Non-convective zone Lower zone

10 cm fresh water Salt water PB

D (blank one)

E

F

10 cm fresh water 10 cm saturated salt water Nothing

10 cm fresh water 10 cm saturated salt water 2 cm thickness pebble

10 cm saturated salt water 2 cm thickness coal cinder

H. Wang et al. / Solar Energy 110 (2014) 756–767

parameters of the two experiments involved in this paper. All the original values have been got or calculated according to the real data. The meanings and expression of the parameters in Table 3 can be found in Nomenclature. From Table 3 we can see that the stability number of Ra/RS is all rather small, and they are all below the critical stability conditions gave in the research reports (Giestas et al., 1996; Zangrando and Bertram, 1985; Wang et al., 2011). So it means that NCZ are under stable state in the conditions in the experiments of this study.

55

o

Temperature ( C)

50 45

coal cinder pebble

blank test

40 35

ambient

30 25 20 15 6:00

8:24

10:48

13:12

15:36

18:00

Time

3.2. Modeling

(a) The temperature curves for the first day 55

o

Temperature ( C)

50

coal cinder

45

pebble

40 blank test

35 30 25

ambient

20 15 6:44

9:48

12:48

15:48

18:48

21:52

0:52

3:52

6:52

Time

(b) The temperature curves for the 5th day 55 coal cinder pebble

45

o

Temperature ( C)

50

40

blank test

35 30

ambient

20 9:00

12:00

15:00

A one dimension transient heat transfer model developed to simulate the transient temperature distribution in the solar pond. The present model is a similar version of the one used by Karakilcik et al. (2006) which developed from Kayalı et al. (1998). We consider the temperature is same in every certain horizontal level and the heat loss through the wall and bottom were considered. Some other hypotheses were made as follows: The solar radiation reaching the upper surface of porous bed is completely absorbed within the depth of the porous material particle size. Conductivity and specific heat of salt and water mixture are considered as functions of temperature and salinity. The difference between this model and the traditional model of SGSP is the increase of the solar radiation attenuation function and the effective thermal physical property parameters of this porous media layer. As is shown in Fig. 7, the solar pond is divided into n layers with six zones from the surface of water to pond bottom. The energy balance equations of each area are as following: Qi;tþ1 ¼ Qsolar þ Qiþ1;t  Qi1;t  Qloss

25

15 6:00

761

18:00

21:00

0:00

Time

(c) The temperature curves for the 10th day Fig. 6. Temperature development with adding different porous materials.

(Giestas et al., 1996; Zangrando and Bertram, 1985; Wang et al., 2011; Karim et al., 2011; Busquets et al., 2012; Hill and Carr, 2013). In order to determine the stability of NCZ in this study’s experimental ponds, Table 3 gives the

ð1Þ

The differential form of the energy balance equation of each zone is as follows: A: The first layer, which is the water surface:   @T kA qCADx ðT iþ1  T i Þ ¼ Ae ½qðxÞ  qðx þ DxÞ þ @t Dx  U ps AðT i  T a Þ  U pw A0 ðT i  T a Þ

ð2Þ

where Ae is the effective area for absorption of solar radiation; A is the solar pond surface area; Ups and Upw are

Table 3 Parameters of the experiment related to the non-convective zone stability. Experiment

a (°C1) 4

b (m3kg1)

d (m)

kT (m2 s1) 7

kS (m2 s1) 9

t (m2 s1) 9

E1 E2

5.4  10 5.5  104

0.0056 0.0056

0.1 0.35

1.58  10 1.56  107

2.52  10 2.26  109

8.1  10 8.9  107

E1 E2

DS (kg/m3) 220 220

DT (°C) 28 25

s 0.0159 0.0145

Ra 1.16  109 4.16  1010

RS 5.93  1011 2.57  1013

Ra/RS 0.00195 0.00162

Note: E1 refers to the small experiment; E2 refers to the experiment conducted in the 2.3  2.8 m2 solar pond, which is introduced in Section 4.2.

Pr 5.13 5.71

762

H. Wang et al. / Solar Energy 110 (2014) 756–767 A UCZ

NCZ

B

1

2 3

Δx

C e ¼ eC f þ ð1  eÞC s

ð6Þ

qe ¼ eqf þ ð1  eÞqs

ð7Þ

F: The last layer of the porous medium zone. Little solar radiation can reach this layer and the heat mainly comes from the top zone, so the energy balance equation is:   @T keA qe C e ADx ðT iþ1  T i Þ ¼ Ae h n q 0 þ @t Dx

C

D LCZ E PB

 U pw A0 ðT i  T a Þ  U pg AðT i  T g Þ

F

Fig. 7. Energy balance for every zone in solar pond with porous bed.

coefficient of heat loss from the surface and from the side wall to the surrounding environment. B, C and D: The zones between water surface and the porous medium layer:   @T keA qCADx ðT iþ1  T i Þ ¼ Ae ½qðxÞ  qðx þ DxÞ þ @t Dx keA  ðT i  T i1 Þ  U pw A0 ðT i  T a Þ ð3Þ Dx Though these zones follow the same equations form, the working medium of each layer is different, so the effective thermal conductivity of ke in each layer is also different: In the upper convective zone B, due to the convection, the effective thermal conductivity is regarded as 3 times of the thermal conductivity of the water: ke = 3k; since the salt gradient layer is stable, no convection occurs, and heat exchange only happens by conduction, so, in the area of C, ke = k; likewise, in the lower convective zone where there is only saturated salt water, ke = 1.5k. The selection of the above effective conductivity coefficients ke is similar to literature (El-Sebaii, 2005). E: The zone of the (PB) porous medium layer. The energy balance equation is similar to the above conditions. And the energy balance equation in this zone can be written as follows:   @T keA keA qe C e ADx ðT iþ1  T i Þ  ðT i ¼ Ae h j q 0 þ @t Dx Dx  T i1 Þ  U pw A0 ðT i  T a Þ

ð4Þ

where hj = l  elx; q0 is the intensity of the solar radiation reaching the surface of the porous medium; in this zone, the effective thermal conductivity of ke is calculated by Eq. (5), similarly, the effective density qe and the specific heat Ce are given as Eqs. (6) and (7), and this simple equivalent weight methods for the thermal properties of the mixing layer of PB are also used by Al-Juwayhel and El-Refaee (1998): k e ¼ ek f þ ð1  eÞk s

ð5Þ

ð8Þ

where hn is the solar radiation transmission of this layer; Upg is the heat loss coefficient from the solar pond to ground. 3.3. Parameters Finite difference method has used to solve the above governing equations. The main numerical computation parameters are as following: time step, Dt = 0.05 h; total layers, N = 26; depth step, Dx = 0.01 m. The properties of the salt water are calculated using the following relations as discussed by Wang and Akbarzadeh (1982): k ¼ 3:6  ½0:5553  0:0008133  sðiÞ þ 0:0008  ðT ðiÞ  20Þ ð9Þ where s(i) is the salinity of the ith layer, and T(i) is the temperature of the ith layer. Salinity is calculated by this equation: sðiÞ ¼ ð1  998=qðiÞÞ=0:65

ð10Þ

where the q(i) is the density of the ith layer, and the value as follows: qðiÞ ¼ 1000;

ði ¼ 1 : 10Þ

qðiÞ ¼ 1200;

ði ¼ 11 : N Þ

ð11Þ

Similarly, the special heat of the salt water of each layer C(i) was also considered as a function of temperature and salinity: CðiÞ ¼ 4180  4:396  sðiÞ  qðiÞ þ 0:0048  s2 ðiÞ  q2 ðiÞ ð12Þ 3.4. Solar radiation and ambient temperature If the Measured data are available, which refers to solar radiation and ambient temperature, and then they are substituted for the model as thermal source and boundary conditions. However, for some special reasons, if the data are unavailable, then Eqs. (13) and (19) are used to estimate the solar radiation and ambient temperature (Zhang, 1990): p cos x  cos xs I ¼ H  rt ¼ H  ða þ b cos xÞ ð13Þ 24 sin xs  xs

H. Wang et al. / Solar Energy 110 (2014) 756–767

where for Dalian city, a = 0.36 and b = 0.23; x and xs are time angle and sunset angle (in radians); H can be expressed as follows:   n H ¼ H 0 a0 þ b0 ð14Þ LD    24  3:6Gsc 2p  n H0 ¼ 1 þ 0:033 cos 365 p  ½cos u cos d sin xs þ xs sin u sin d

ð15Þ

where Gsc is the solar constant, and Gsc = 1353 W/m2. H0 is average daily solar irradiation on horizontal plane out of extra atmosphere (kJ/m2) in the month; n is the actual hours of the daily sunshine; LD is the astronomy hours of the daily sunshine: LD ¼ 2 arccosð tan u tan dÞ=15

ð16Þ

d and x can be calculated by the Cooper Equation: d ¼ 23:45  sinð360  ð284 þ nÞ=365Þ

ð17Þ

x ¼ 2pðt  12Þ=24

ð18Þ

n is the number of days in date order of a year, and t is the local time. Atmospheric temperature at t hour according to the following equation: p T a ðtÞ ¼ T aver þ 0:489DT  cos ðt  15:05Þ 12 p ð19Þ þ 0:062DT  cos ðt  1:17Þ 6 where Taver is the daily average temperature, DT is the daily max temperature difference, if the daily maximum and minimum temperature were Tmax and Tmin respectively, then, DT ¼ T max  T min . The sunrise time and sunshine duration each day is determined according to the following equations. t ¼ 12  xr =15

ð20Þ

where xr is the sunrise time angle, and is calculated by this equation: xr ¼ arccosð tan u tan dÞ

ð21Þ

4. Simulation results and discussion 4.1. For the small solar ponds The governing equations and boundary conditions introduced above have been used to the simulation of the temperature development of the solar pond. The measured solar radiation data used as the source term and ambient temperature data were used as the boundary temperature conditions. In this part, the experimental results of the 5th day and the 10th day have been used to compare to the simulation results. Physical properties of the added materials are given in Table 4.

763

Table 4 Thermal performance of the material. Materials

Density (kg/m3)

Thermal conductivity (W/m°C1)

Special heat (kJ/kg°C1)

Coal cinder Pebble

1690 2240

0.3 0.65

1.5 0.92

Other parameters according to the actual situations: the extinction coefficient of salt water: l = 0.7; coefficient of thermal conductivity of insulation board at the bottom: Upg = 0.03 W/m°C1; for the blank experiment, 70% of the solar radiation arriving at the bottom is absorbed. And here, Ups = 26.25 W/m2°C1, Upw = 0.36 W/m2°C1, Tg = 10 °C. As is shown in Fig. 8, the calculated results are compared with the experimental results; Fig. 9 shows change of the solar radiation intensity with time for the 5th and the 10th days. The results in Fig. 9 show that the experimental and numerical curves have the same trends and good consistency. In addition to Fig. 8(b) in the case of the coal cinder, the temperature of the calculated and experimental results in other cases are very close at the highest temperature at noon, but the calculation value and the experimental results are slightly different in the morning and in the afternoon, especially in the afternoon during which the predicted temperature decreased rapidly. This maybe because the effective thermal conductivity is simplified, and the convective thermal contact heat resistance between solid and porous media is not taken into consideration, therefore, the results cannot accurately reflect the continuous heat conduction. In a word, the model is accurate enough to predict the bed temperature of the solar pond with porous media. For the 5th day, the standard deviation of the measured data and the calculated value in the case of the coal cinder, pebbles and blank experiment are respectively 1.65, 1.44 and 1.13; for the 10th day, they are respectively 1.57, 1.39 and 1.28. 4.2. For the 2.3  2.8 m2 experimental solar pond This experimental solar pond was operated in June. The solar radiation intensity, the ambient temperature and the temperature inside the solar pond had been measured every minute during the experimental period. The temperature sensor is placed in the center of the pond, respectively 5 cm, 10 cm, 15 cm and 25 cm above the bottom. The experimental measurement period is 28 days. The simulation equations and boundary conditions are same as which are presented in Section 4.1, expect that the coefficient of heat loss from solar pond to ground and heat loss through wall are both 0.36 W/m°C1. Fig. 10 shows the experimental and numerical results for 670 h from June 1st to June 28th. The upper three curves in Fig. 10 are the average experimental and numerical temperature for the points 0.2 m above the bottom, of which the

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(b) Temperature curves for the 10th day Fig. 8. Experimental and numerical temperature evolution comparison between coal cinder and pebble bed. Subscripts: ‘C’ refers to coal cinder, ‘P’ refers to pebble, ‘0’ refers to the blank experiment ‘e’ represents experimental results, ‘n’ represents numerical results. ‘Ta’ refers to ambient temperature.

(a) Solar radiation the 5th day

(b) Solar radiation the 10th day

Fig. 9. Solar radiation profiles for Fig. 8.

numerical results reflect the conditions both with and without the coal cinder. The ambient temperature is also given in Fig. 10, and the solar radiation intensity on the horizontal plane is given in Fig. 11. The numerical results in Fig. 10

are all calculated according to the measured solar radiation and ambient temperature. However, from Fig. 10, we can see that, for some special reasons, the measurement was not wholly continuous, for example, the experimental

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Time(h) Fig. 10. Comparison for mean temperature evolution of 0.20 m distance from bottom (calculated results for both with and without coal cinder adding at bottom, experimental data, and also the ambient air temperature).

coal cinder has low thermal diffusion than other solid materials, so temperature will not significantly decrease during night. In fact, it is equal to adding storage layer to the bottom of SGSP, producing the effect of solar energy absorption and temperature enhancement. 4.3. Estimation in large-scale solar pond

Fig. 11. Hourly mean solar radiation during experimental period (31 May to 28 June).

results achieved between 500 and 600 h. Then, for this short term, Eqs. (13) and (19) were used to estimate solar radiation and ambient temperature. From Fig. 10, we can see that the experimental temperature results are slightly smaller than the numerical ones, but, overall, they tally with each other which demonstrate the correctness of the equations. For the numerical results, 10.8 °C temperature differences between the conditions with and the condition without coal cinder is predicted, while the actual difference between the experimental results for which coal cinder is added and the numerical result for which no coal cinder is added at all is 8.5 °C. This may be caused by the different thermal physical properties between the mixture of salt water and coal cinder and the salt water. As we all known, the special heat of salt water is bigger than that of the former, so under the same ambient conditions, the porous medium zone formed by the mixture of salt water and coal cinder would reach a higher temperature. On the other hand, due to its porous characteristic,

According to the above experiment and numerical research, it is rather reliable simulating model which is presented in this paper. In order to compare with other similar research, we have simulated the temperature development in large-scale solar pond with coal cinder added, and use the parameter conditions as Al-Juwayhel (Al-Juwayhel and El-Refaee, 1998) have done. The main parameters used in simulation are listed in Table 5. Due to the large-scale area, we have neglected the heat loss from the lateral walls. The numerical results of temperature developments for conditions of with and without adding coal cinder in LCZ was presented in Fig. 12. For the first year, the max Table 5 Main calculation parameters for the simulation. Properties

Descriptions

Size

UCZ:0.3 m, NCZ: 1.3 m, LCZ: 1.4 m, PB layer: 30% depth of LCZ 28 months, started from April 1st The heat loss coefficient from LCZ to ground 0.8 W/m2°C1 Constant as 10 °C

Period Heat loss Ground soil Temperature Salinity Extinction coefficient Step Initial temperature

UCZ: freshwater; LCZ: 30% (wt); NCZ: 5% linearly downward increased to 30% l = 0.6 m1 Space step: Dz = 0.01 m; time step: Dt = 0.05 h Equal to the atmosphere temperature

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LCZ temperature with coal cinder added conditions is 84 °C and occurs on the August 30th, and 75 °C on September 5th for without adding coal cinder condition. This may because the heat Capacity of water is bigger than coal cinder solid. LCZ temperature here is about 5 °C smaller than the result of Al-Juwayhel (Al-Juwayhel and El-Refaee, 1998) where they used bakelite as the porous material. Fig. 12 mainly indicates such informations: (i) it is obvious that an evidence increase is obtained under the condition of adding coal cinder in LCZ; (ii) it can also be found that the day on which solar pond without coal cinder reaches the maximum temperature is a little delayed than with coal cinder condition; (iii) during the temperature increasing period, the temperature between the two conditions is nearly constant, but for the temperature decreasing period, the temperature difference is rather small. The last two tendencies are a little different with the results of Al-Juwayhel (Al-Juwayhel and El-Refaee, 1998), yet we think that this may be caused by the good thermal stability of water which has a bigger heat capacity than other solid materials. 5. Conclusions Experiments and simulations study revealed that the introduction of coal cinder can obviously increase the temperature of solar pond. The results showed that adding porous medium, such as coal cinder, is better than the traditional bottom style. And also, Coal cinder, compared with pebble, can obviously increase the temperature. The measured temperature of the pond paved with pebble increased most rapidly and also declined most fast at night. The pebble may probably be seen as a typical kind of rock material. The positive effect of coal cinder in this study mainly results from the high absorption of the material

for the solar radiation, the heat transfer enhancement effect, and also the perfect thermal physical characteristics, such as the proper special heat and lower thermal diffusivity. In conclusion, the method involved in this paper which is aimed to increase LCZ temperature of SGSP, is easy to be implemented, and the porous material of coal cinder is cheap with broad sources. It is suitable to be applied in large SGSP. A higher LCZ temperature will be positive for the SGSP’s thermal engineering application, and it is bound to bring an extensive application and higher heat transfer efficiency. For porous material as coal cinder, due to the solar irradiation attenuation, its physical thermal property to increase the temperature of LCZ may be not fully exercised. So there should be an optimal thickness of PB, and a detailed investigation of influence of porous material on stability of NCZ will be the future research issues. Acknowledgments The authors thank Prof. Aliakbar Akbarzadeh for useful discussions and suggestions. This work has been carried out with the financial support of the National Natural Science Foundation of China (U1404520) and Henan Province characteristic specialty for Thermal and Power Engineering. References Aboul-Enein, S., El-Sebaii, A.A., Ramadan, M.R.I., Khallaf, A.M., 2004. Parametric study of a shadow solar-pond under the batch mode of heat extraction. Appl. Energy 78, 159–177. Al-Juwayhel, F., El-Refaee, M.M., 1998. Thermal performance of a combined packed bed-solar pond system-a numerical study. Appl. Therm. Eng. 18, 1207–1223. Arulanantham, M., Avanti, P., Kaushika, N.D., 1997. Solar pond with honeycomb surface insulation system. Tech. Note Rev. Energy 12 (4), 435–443.

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