An Experimental Study of an Evacuated Tube Solar Collector Using the Response Surface Methodology (RSM)

An Experimental Study of an Evacuated Tube Solar Collector Using the Response Surface Methodology (RSM)

Abdelmadjid BensahaFatiha Benkouider SMA. Bekkouche Abdelkader Abdellaoui Toufik Chergui Abdelwahab Benseddik 

Unité de Recherche Appliquée en Energies Renouvelables (URAER), Centre de Développement des Energies Renouvelables, CDER, 47133, Ghardaïa, Algérie

Laboratoire des Télécommunications, Signaux et Systèmes (LTSS), Université Amar Telidji de Laghouat, BP G37, route de Ghardaia, Laghouat, Algérie

Université Paris Est-Créteil, Université paris XII, France

Corresponding Author Email: 
bensaha.madjid@gmail.com
Page: 
148-153
|
DOI: 
https://doi.org/10.18280/mmc_b.882-414
Received: 
26 June 2019
|
Accepted: 
6 November 2019
|
Published: 
30 December 2019
| Citation

OPEN ACCESS

Abstract: 

The purpose of this study is to investigate experimentally the performance of a solar hot water system with evacuated tube solar collector to obtain optimum process parameters by user-specified design. In these study parameters as solar radiation and fluid flow are optimized with the consideration of responses as outlet fluid temperature and bottom water temperature using the Response Surface Methodology (RSM). As a result, the optimal independent variables in the determined intervals are as follows: solar radiation is 850 w/m2 and fluid flow is 1, 36641 l/min; under these favorable conditions, the outlet fluid temperature can reach a maximum value of 75.9954 ° C whereas the bottom water temperature in the storage tank may attain a maximum value of 65.1443 ° C. It was found from the experimental design and ANOVA using the STATGRAPHICS Centurion (VERSION 18) program, that the solar radiation is the major parameter that influences of a solar hot water system performance.

Keywords: 

experimental study, evacuated tube solar collector, response surface methodology

1. Introduction

A solar water heating system is the conversion of sunlight into heat for water heating using a solar thermal collector such as flat plate systems, evacuated tube systems and thermosyphon systems. These systems are widely used in residential sector and some industrial applications.

In this study, we are interested in a heat pipe evacuated tube collector (HP-ETC) made up of a heat U-pipe inside a vacuum tube. The vacuum envelope reduces convection and conduction losses, so the collectors can operate at higher temperatures than flat plate collectors or thermosyphon collectors. The product IMEXSol 200L is intended for the production of domestic hot water using solar energy by heating a heat transfer fluid in a closed circuit. Vacuum tubes absorb solar radiation to turn it into heat. The heat is transported by a heat transfer fluid through the U-pipe in the vacuum tubes to a 200-liter storage tank through a coil finally to transfer heat collected by the solar collector to water inside the storage tank.

Hayek et al. [1] The authors investigated and compared the overall performance of two types of solar collectors (water in glass collector and heat pipe evacuated tube collector) under Eastern Mediterranean climatic conditions. They concluded that the heat pipe evacuated tube collector performs better than water in glass collector. In another work, Ayompe and Duffy [2] presented an analysis of a solar water heater system with a 3 m2 heat pipe evacuated tube collector using data from a field trial in Dublin, Ireland.

Azimi et al. [3] studied the performance of evacuated tube solar collector in different climatic conditions in Iran using TRNSYS 16 software; they also improved instantaneous sensor yield using genetic algorithm in MATLAB software.

Laurence et al. [4] evaluated the performance of an evacuated tube solar hot water system installed on a domestic house of 5 persons in Dublin, they found that the system produced 1216 kW h of useful heating energy with a system efficiency of 62.8%.

Kabeel et al. [5] designed a modified coaxial heat pipes to improve the thermal performance of evacuated tube solar collector, the results show that the thermal efficiency can reach a maximum value of 67% at a mass flow rate of 0.009 kg/s.

Elsheniti et al. [6] presented the thermal performance of a heat-pipe evacuated-tube solar collector at a high inlet temperature by predicting the thermal efficiency as a function of operating parameters such as fluid flow, inlet temperature and number of evacuated tubes.

Evaluation of the overall performance of solar collectors is usually carried out experimentally using proven procedures according to international standards [7-10] and many correlations have been developed for the purpose of predicting the overall efficiency under various climatic conditions.

The response surface methodology (RSM) is a widely used mathematical and statistical method for modeling and analyzing a process in which the response of interest is affected by various variables [11] and the objective of this method is to optimize the response [12]. The parameters that affect the process are called dependent variables, while the responses are called dependent variables [13].

The RSM method was used in many fields such as  optimizing the performance of thermal efficiency of the evacuated tube solar collector [14], optimizing parabolic mirror position in a solar cooker [15,16], optimizing extraction of plant materials [17], Optimization of hydrogen production [18] and the parameters of solar Drying [19, 20].

Our literature review shows that no one has used the response surface methodology in the domain of solar domestic hot water system, especially when combining the operating parameters to optimize the system. Accordingly, the present study focused on modeling the effect of the solar radiation and fluid flow (as independent variables) on the outlet fluid temperature and bottom water temperature in the vertical storage tank (as dependent variables) in a process of domestic hot water. The modeling was based on the Response Surfaces Methodology. The experiments were designed according to the user-specified design plan with two factors, each at five different levels.

2. Materials and Methods

2.1 Experimental of a Solar Hot Water System

An experimental set-up was designed and installed on the workshop rooftop in the Applied Research Unit in Renewable Energies in Ghardaia region- Algeria. Figure 1 shows all the kit components of the product IMEXSol200L with a solar collector made up of 12 evacuated tubes and a vertical storage tank. The experimental set-up is a closed loop circuit with the required components and measurement tools as sketched in figure 1.

A vacuum solar collector consists of a series of 12 transparent glass tubes, the length of the tubes is 1.73 m and their diameter is 4 cm. In each tube there is an absorber for capturing solar radiation and a U-pipe type heat exchanger to allow the transfer of thermal energy. Vacuum sensors can reach high temperatures (150° C). The vacuum created inside the tubes makes it possible to reduce significantly the losses during rise in temperature.

The solar collector consists of 12 U-pipe collectors filled with a heat transfer liquid, which transports the calories captured by the solar collector to the hot water storage tank; this transport is carried out via a forced pipe (the solar pump). The solar collector is oriented towards the South and inclined by 32 °.

The regulator of RESOL type is an electronic device that controls the flow of heat transfer fluid through a solar pump that circulates the fluid within the closed circuit between the solar collector and the tank. The role of this control system is the adjustment and the control of the solar station (R1) and electric auxiliary station (R2). In this work, the operation of R2 was cancelled.

The storage tank is equipped with several automatic control and protection means such as a thermostatic control, protection for high and medium temperatures and pressure protection (P / T valve and check valve), equipped with a supplementary electric heating element (auxiliary heater R2) for safety. The storage tank transmits the calories provided by the heat transfer liquid to the water (through the exchanger located at the bottom of the tank).

Figure 1. The product IMEXSol 200L installed in Ghardaïa region

The ImexSol 200L system consists of four probes: thermistors S1 and S4which measure the temperature of the heat transfer liquid at the inlet and outlet of the solar collector respectively; S2 and S3which measure the water temperature in the lower and upper level of the tank respectively.

The regulator calculates the temperature difference between thermistors S1 and S2, if this difference is greater than+1°C,the solar pump (R1) is switched on; by contrast, the solar pump is switched off when the outlet fluid temperature is higher than the bottom water temperature by the predefined deactivation value of 0.5°C (DTF).

2.2 Method adapted for statistical analysis

The response surface methodology (RSM) has been ‎proven to be a powerful tool for determining the effects of ‎each factor and the interactions among them, thereby ‎allowing for effective process optimization [21]. The response ‎surface procedures involve experimental strategy, ‎mathematical methods, and statistical inference, which, ‎when combined, enable users to make an efficient empirical ‎exploration of the system in which they are interested [22].‎

RSM can be applied to any system that has the following ‎key elements: (1) a criterion of effectiveness, measurable on ‎a continuous scale (extraction time), and (2) quantifiable ‎independent variables (both controllable and uncontrollable) ‎that affect the system’s performance (such as the extraction ‎process, solvent, and drying method). Given these conditions, ‎RSM offers techniques for finding the optimum response of ‎the system in an efficient manner [22]. The major advantage ‎of RSM is that the amount of data needed for evaluation, ‎analysis and optimization significantly reduces the number ‎of experiments required. RSM is a faster and more ‎economical method for collecting research results than the ‎classic one-variable at a time or full-factor experimentation ‎‎[16].‎

The STATGRAPHICS Centurion software (VERSION 18) ‎has been used for this purpose. RSM generates the table for ‎the experimental design plan specified by the user. This ‎experimental strategy has been widely used in production / ‎process development.‎

To study the effect of the operational parameters of solar ‎water heating system, two operating parameters were favored ‎and selected: solar radiation (between 250 and 850 w / m2) ‎and heat transfer fluid flow (between 0.6 and 3 l / min). After ‎choosing the operating parameters that are the most ‎influential and because of a large possible range of variation ‎of each parameter, it was convenient to carry out a statistical ‎study to identify, at the least cost of experimentation, the ‎domain of exploitation of the parameters. Thus, during the ‎present study, the surface response method was adopted; it is ‎a user-specified design plan with two factors, each with five ‎different levels.‎

The experimental design is presented in Table 1. The aim is ‎to obtain samples adapted to the 25-point experimental ‎design given in Table 2. The relationship between the ‎independent variables, solar radiation (x1), and the flow of the ‎heat transfer fluid (x2) is expressed mathematically in the ‎form of a polynomial model, which gave the following two ‎responses: the outlet fluid temperature Y1 and the bottom ‎water temperature Y2 according to these variables. A ‎second-order polynomial equation is presented in the ‎following general form:‎

$Y_{k}=a_{0}+\sum_{i=1}^{2} a_{i} x_{i}+\sum_{i=1}^{2} a_{i} x_{i}^{2}+\sum_{i=1}^{2} \sum_{j=1}^{2} a_{i j} x_{i} x_{j}$          (1)

Table 1. The levels of the variables utilized in this study for the user-specified design

variables

Levels of the user-specified design

x1 (w/m2)

250

400

550

700

850

x2 (l/min)

0.6

1.2

1.8

2.4

3

Table 2. Conditions and experimental design results based on the plan of the user-specified design at five levels

N

Factors values

Responses values

x1 (w/m2)

x2 (l/min)

Y1 (°C)

Y2 (°C)

Observed values

Predicted values

Observed values

Predicted values

1

250

0,6

46,5

47,6914

38,8

38,8257

2

400

0,6

57,2

56,2931

46,4

45,4051

3

550

0,6

65,5

63,8777

52,0

51,6503

4

700

0,6

70,8

70,4451

57,8

57,5611

5

850

0,6

75,7

75,9954

62,7

63,1377

6

250

1,2

46,0

46,5766

41,3

42,3217

7

400

1,2

53,9

54,5183

47,1

48,5051

8

550

1,2

60,7

61,4429

52,9

54,3543

9

700

1,2

66,4

67,3503

58,4

59,8691

10

850

1,2

70,9

72,2406

63,5

65,0497

11

250

1,8

46,6

45,4103

44,9

43,3577

12

400

1,8

53,4

52,692

51,5

49,1451

13

550

1,8

59,9

58,9566

57,8

54,5983

14

700

1,8

64,9

64,204

63,3

59,7171

15

850

1,8

69,2

68,4343

67,8

64,5017

16

250

2,4

44,2

44,1926

40,4

41,9337

17

400

2,4

49,0

50,8143

43,8

47,3251

18

550

2,4

56,4

56,4189

49,8

52,3823

19

700

2,4

61,1

61,0063

55,3

57,1051

20

850

2,4

64,8

64,5766

59,2

61,4937

21

250

3

44,3

42,9234

40,0

38,0497

22

400

3

47,6

48,8851

42,7

43,0451

23

550

3

53,5

53,8297

48,5

47,7063

24

700

3

57,7

57,7571

53,0

52,0331

25

850

3

61,0

60,6674

56,2

56,0257

3. Results and Discussions

3.1 Responses surface analysis and interpretation

The experimental data were employed to calculate the coefficients of the quadratic equation. Table 3 summarizes the results concerning the analysis of the variance (ANOVA) for the responses and the coefficients of the mathematical models.

The coefficient of determination R2 represents the proportion of variation of the response attributed to the model rather than the random error. It has been suggested that a good fit of models should have R2 not less than 90%. When R2 is close to unity, the empirical models are adapted to fit the experimental data.

Based on these results, an empirical relationship between system responses and independent variables has been established for domestic hot water and then expressed by second-order polynomial equations as follows:

$Y_{1}=31.06+0.08 x_{1}+0.1 x_{2}-0.071 x_{1}^{2}$

$-0.0073 x_{1} x_{2}$          (2)

$Y_{2}=20.5+0.05 x_{1}+13.08 x_{2}-0.0000074 x_{1}^{2}$

$-3.42 x_{2}^{2}-0.0044 x_{1} x_{2}$          (3)

The response surface analysis (RSA) of the data in Table 3 shows that the relationship between the responses and the independent variables (solar radiation and fluid flow) is quadratic, with a good regression coefficient (99.0237% for (Y1, R2) and 94.6654% for (Y2, R2). This indicates that there was good agreement between the experimental data and the two predicted responses.

The results show that the models used in this study were able to identify the optimal operating condition of this solar system dedicated to heating sanitary water. Figure 2 describes the correlation between the value of the observed response and that of the predicted response by the mathematical model; it shows a good correlation between the responses of the system obtained experimentally and those predicted by the mathematical models proposed from equations 2 and 3.

Figure 2. Linear correlation between calculated and measured system responses

Table 3. Analysis of variance (ANOVA), linear, interaction and quadratic terms for each response variable and the prediction model coefficients

 

Source

Coefficients

Sum of Squares

DDL

Mean of squares

F-value

p-Value prob>F

Outlet fluid temperature

x1

0,0764368

1656,6

1

1656,6

1569,75

0,0000

x2

0,10381

315,5

1

315,5

298,97

0,0000

x12

-0,0000226032

18,105

1

18,105

17,16

0,0006

x22

-0,0714286

0,0463

1

0,0463

0,04

0,8363

x1 x2

-0,00733333

43,56

1

43,56

41,28

0,0000

Residual

 

20,051

19

1,05531

-

-

R2(%)

99,0237

 

 

 

 

 

Adj-R2(adjusted for d.f.)

98,7668 %

 

 

 

 

 

the standard deviation of the residue

1,02728

 

 

 

 

 

Mean Sequare Error

0,737646

 

 

 

 

 

Durbin-Watson test

1,53068

 

 

 

 

 

 

x1

0,0513314

1397,1

1

1397,1

300,18

0,0000

x2

13,0767

48,6

1

48,6

10,44

0,0044

x12

-0,00000742857

1,9556

1

1,9556

0,42

0,5246

x22

-3,41667

105,90

1

105,90

22,75

0,0001

x1 x2

-0,0044

15,681

1

15,681

3,37

0,0821

Residual

 

88,430

19

4,6542

-

-

R2(%)

94,6654

 

 

 

 

 

Adj-R2(adjusted for d.f.) (%)

93,2616

 

 

 

 

 

The standard deviation of the residue

2,15736

 

 

 

 

 

Mean Sequare Error

1,55589

 

 

 

 

 

Durbin-Watson test

0,767507

 

 

 

 

 

Figure 3. Response surfaces (a, b) and isopleth curves (c,d)

However, it is clear that the experimental results of the responses Y1 and Y2 and the predicted values obtained using equations 2 and 3 are not significantly different (Figure 2).

On the other hand, from equations 2 and 3, we can obtain the 3D response surfaces and the isopleth curves shown in Figures (3) (a-b) and (3) (c-d) respectively. These figures illustrate the effect of solar radiation (x1) and the fluid flow (x2) on the outlet fluid temperature in the solar collector and the bottom water temperature in the storage tank (Y1 and Y2).

We can see from Figure 3 that Y1 is proportional to x1 and inversely proportional to x2. However, Y2 is proportional to x1 and x2 around the mean level. As can be seen in figure 3 (a and c) that for lower or higher x2 values, both responses increase as solar radiation increases.

3.2 Optimization of parameters

According to the above analysis, solar radiation is the most important variable, so that the optimization of solar radiation always corresponds to the maximum value of the interval. Optimization of the variables is given in Table 4. So, it can be seen from this table that the optimal independent variables are as follows: the solar radiation is 850 w / m2 and the fluid flow is 1.36641 l/min. Under these appropriate conditions, the temperature of the oulet fluid temperature can reach amaximum value of 75.9954 °C while the bottom water temperature in the vertical storage tank can reach the maximum value of 65.1443 °C.

Table 4. The levels of the variables used in this study for user-specified design in the response surface methodology

Levels

Optimal values of independent variables

Responses

Solar radiation

(w/m2)

Fluid flow

(l/min)

Outlet fluid

temperature (°C)

Bottom water

temperature (°C)

x1

x2

Y1

Y1

Low

250

0.6

46,5

38,8

High

850

3

61

56,2

Optimum

850

1,36641

75,9954

65,1443

4. Conclusion

An experimental set-up was installed under optimal design conditions of the response surface methodology to investigate the influence of the above parameters on domestic solar hot water. From the quadratic models of the response surfaces, it was found that the outlet fluid temperature and the bottom water temperature in the storage tank were significantly affected by solar radiation. The optimized parameters are presented as follows: Solar radiation is 850 w / m2, and fluid flow is 1.36641 l / min, under these optimal conditions, outlet fluid temperature is 75.9954 °C while the bottom water temperature is 65.1443 ° C.

Acknowledgment

This work was performed in the Unité de Recherche Appliquée en Energies Renouvelables (URAER), Centre de Développement des Energies Renouvelables, CDER, Ghardaïa, Algérie.

The authors would like to thank the personelle for their support in materials as well as all the collaborators of this work.

Nomenclature

x1

Solar radiation (w/m2)

x2

‎heat transfer fluid (l/min)

Y1

Y2

Outlet fluid temperature (°C)

Bottom water temperature (°C)

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