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Evaluation of the experimental data to determine the performance of a solar chimney power plant
Materials Today: Proceedings xxx (xxxx) xxx
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Evaluation of the experimental data to determine the performance of a solar chimney power plant Pramod Belkhode a, Chandrasshekhar Sakhale b, Ajay Bejalwar a a b
LIT, Nagpur, India PCE, Nagpur, India
a r t i c l e
i n f o
Article history: Received 30 July 2019 Received in revised form 29 August 2019 Accepted 2 September 2019 Available online xxxx Keywords: Solar Chimney Collector Turbine Optimization Experimental setup
a b s t r a c t Solar chimney power plants play an important role in the field of renewable energies. The present study undertaken is related to design a solar updraft tower with all the variable geometric parameter in consideration and to optimize the performance for solar chimney power plant by means of experimental data as well as computer simulation with the formulation an approximate mathematical model. The components of the solar chimney power plant include the collector sheets, chimney and turbo generator. Solar radiation is transferred to the collector plates, air under the solar collector is heated up which is sucked vertical chimney located at the centre of the vertical cylindrical shell. The updraft is formed which drives the turbine and generator to produce the electricity with low cost as compared to other methods. Ó 2019 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the First International Conference on Recent Advances in Materials and Manufacturing 2019.
1. Introduction Many developing countries have large number of resources of renewable energy such as solar energy, wind power, biomass and hydro energy. Many countries are approaching towards the renewable energy due to the environmental issues such as global warming. The renewable energy is less expensive than the fuel energy such as oil and gas. However the supply of renewable energy depends on the atmospheric condition. In the remote areas the concept of solar chimney power plant is most effective as compared to the costly distribution of electricity or alternative to the diesel generators. The capital investment of the hydropower, tidal power is high as compared to the power generated by the solar and wind energy. Solar power generation have the advantages of low maintenance, simple installation, silent operation and long life span. The present study undertaken was related to design a solar updraft tower with all the variable geometric parameter in consideration and to optimize the performance for solar updraft power plant by means of experimental data as well as computer simulation with the generation an exact mathematical model. The mathematical model formed with all the variables involved in the design of the solar updraft tower. These independent variables are grouped such as variables related to collector, variables related to the chimney, variables related to atmospheric condition and heating condition. The indices of each grouped pie terms predict
the performance of the dependent variables such speed and power produced by the turbine. Based on the mathematical model performance of the solar updraft is optimize by the optimization technique. 2. Literature review The aim of this work is to develop a mathematical model to determine the natural air flow inside a solar chimney using daily solar irradiance data on a horizontal plane at a site. The model starts by calculating the hourly solar absorbed by the solar chimney of varying height for a given time (day of the year, hour) [1]. The low pressure solar thermal converter appears to offer development potential for low-tech solar energy conversion [2]. The solar chimney model is verified by comparing the simulation of a smallscale plant with experimental data [3]. Velocity, electric power generation and the turbine efficiency also studying in this work [4]. The total illumination on a horizontal surface from the sun and sky has been determined for clear sky and completely overcast sky conditions [5]. The solar chimney power plant need warm air to create the updraft which spins the turbine. The blade of the turbine will rotate due to the warm air absorbed by the land. This can be effectively done by covering the collector area with the gravel. The PV solar plant unable to produce power during night unless assembled with battery system [6]. If the panel is cover with dust
https://doi.org/10.1016/j.matpr.2019.09.006 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the First International Conference on Recent Advances in Materials and Manufacturing 2019.
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
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P. Belkhode et al. / Materials Today: Proceedings xxx (xxxx) xxx
than the efficiency of the PV panel reduces. Few however have the ability to store enough energy during the day so that a supply can be continued during night when the solar radiation is negligible. The potential of solar electric power generation as a means to significantly reduce CO2 emissions is also detailed [7]. The analysis showed that chimney height is the most important physical variable for the solar chimney design [8]. 3. Experimentation The Solar chimney uses warm air for the generating power. The solar chimney power plant system consists of four important components—collector, chimney, energy storage layer and turbo generators at the base. Radiation is absorbed by the solar collector sheets warms up the air under the solar collector roof which is sucked towards the centre of the vertical turbine shell from the base [9]. Thus the updraft produce run the turbine and produce the solar power with the help of wind turbine is located at the chimney base [10] (Fig. 1). The variables affecting the phenomenon under consideration are collector materials, chimney height, chimney diameter, turbine blades and solar radiation. All dependent and independent parameters are converted in to dimensionless term. Table 1 shows dependent and independent variables with units and symbols. Experimental setup is designed and fabricated to execute the experimentation according to experimentation plan. The experimental setup basically consists of concrete base with angle structural frame to assemble the chimney, roof collector plates and turbine at the base of chimney. The site is selected on the basis of availability of wind velocity and proximity to open sky so that sun rays are available throughout the day time. The base of around 4500 mm diameter covered with brick joints of three bricks layers with concrete. The sand filled in the circular base of bricks act as heat reservoir. On the periphery of bricks circle eight angles of 600 mm height are erected, to locate the frame of collector and chimney. The MS angle frame is fabricated of 4500 mm diameter on which the collector sheets are mounted and having 600 mm diameter circular hole at centre for mounting the turbine and frame to
Fig. 1. Solar updraft tower.
hold the chimney pipe. This frame is mounted on the angles erected at the periphery of bricks joint. The different types of collector sheets were examined each time on the experimental setup to determine the effect of updraft produce. The Chimney pipe of diameter 150 mm and height 3600 mm and 4800 mm is placed one at a time and subsequently changed during the experimentation to predict the performance of the turbine. Aluminium sheets are used to cover the portion opened around the periphery of angles erected on bricks joint for trapping the air under the collector roof. Opening of 3600 mm length is kept on both sides for air movements from outside to inside of collector. The experimentation is carried out during the summer with the various instruments. The digital tachometer is used for measuring the turbine speed, digital thermometer is used for measurement of the air under collector and outside the chimney, pyranometer is used for solar radiation and digital anemometer is used for measuring the air velocity. Warm air produced by the collector flow into the chimney which converts into kinetic and potential energy. Due to rise in the temperature inside the collector changes the density of air which works as the driving forces. The differences in the densities of air due the temperature difference cause the pressure difference which is used to accelerate the air and thus converted into the kinetic energy. Warms air for the solar tower is produced by the greenhouse effect in air collector which is consisting of different collector materials located above the ground level. Air heat up and transfer its heat to the air flowing to the tower. Mechanical output in the form of rotational energy obtained from the warm air in the tower. Cold air flows in the solar collector which is heated by the solar radiation which is recorded in the range of 450–550 W.m2 with recorded temperature rises from 450–570 °C and the recorded the warm up air velocity in the range of 1.8 m.s1 to 2.0.s1 during the experimentation in the design experimental setup. This warms air produced the draft rotates the turbine and generated the electricity. The output of the generator is supplied to the electronic panel were alternating current is converted to the direct current which is supplied to glow the LED light located on the panel. The digital multi meter is used to measures the voltage and current. The average power outputs for warm air condition practically ranged between 3 W and 6 W for 12 feet height tower and between 6 W and 9 W for 15 feet height tower. The experimental setup designed with the collector material such as glass, acrylic sheets, polycarbonate and crystalline material with thickness range from 0.002 to 0.004 m and conductivity in the range of 0.16–0.8 W.m1 K. The collector plates are placed at the circular ring of the 4.5 m in diameter and 0.6 m above the ground with the small inclination of 0.15 rad. The chimney is of PVC material located at the centre of the collector plate of diameter 0.15 m with different height of 3.6 m and 4.8 m. Table 1 shows the description of all the independent and dependent variables of the experimental setup of solar updraft tower. The correlation for the independent variables and dependent variables such turbine power output and turbine speed is formulated by the mathematical model. Since the numbers of the independent variables are more thus these variables are grouped in the respective group to predicate the performance and to reduce the complexity and to obtain the simplicity in the behaviour of the event, the pi terms are reduced as suggested by Schenk Jr. The pi terms related to the independent variables like Collector material, solar chimney, Relative Humidity, Ambient condition, solar radiation are reduced to form a single new pi term. The Table 2 shows the new pi terms of independent variables in reduced form. Thus the total seventeen pi terms of independent variables are reduced to six new pi terms as shown in the table below.
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
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P. Belkhode et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 1 Identification of variables for solar updraft tower. S. N
Description of Variables
Type of variable
Symbol
Unit
Dimension
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19
Diameter of Collector Thermal conductivity of Collector Material Height of collector from ground level Thickness of covering collector material Inclination of collector Chimney Height Diameter of Chimney No. of blades Ambient Temperature Humidity Air velocity at inlet Air velocity at outlet Temperature inside the collector Heating time Heat Flux Air inlet area Acceleration due to gravity Turbine Speed Power generated
Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Dependent Dependent
Dc K Hgc Tcc hc Hch Dch Nb Ta Hu Vi Vo Tc Th Q Aoi g Ts Pd
m W/mK m m rad m m – 0C % m/s m/s 0C sec W/m2 m2 m/s2 rpm W
M0L1T0 M1L1T3h1 M0L1T0 M0L1T0 M0L0T0 M0L1T0 M0L1T0 M0L0T0 M0L0T0h1 M0L0T0 M0L1T1 M0L1T1 M0L0T0h1 M0L0T1 M1L0T3 M0L2T0 M0L1T2 M0L0T1 M1L2T3
Table 2 Grouped independent pie terms.
h
Sr No
Independent Dimensionless ratios
Nature of Physical Quantities
01 02 03 04 05 06
p1 = [(Hgc Tcc hc)/Dc2] p2 = [Hch Dch Nb/Dc2] p3 = [Hu] p4 = [(Ta To)(ViDc/g2) (VoDc/g2)] p5 = [(g1/2Th/Dc1/2)(Aoi/Dc2)] p6 = [(DcQ/K)]
Collector material Solar Chimney Relative Humidity Ambient Condition Heating duration Heat flux
Dependent dimensionless ratios or p terms 01 pD1 = [(Dc1/2N/g1/2)] 02 pD2 = [Po/KDc]
pD2 ¼ 7:1796x1019 Hgc Tccqc=Dc2
i3:9024
h i0:1755 Hch Dch Nb=Dc2 ½Hu0:2861 0:8756 ðTa ToÞ ViDc=g 2 VoDc=g 2 h i6:6344 g 1=2 Th=Dc1=2 Aoi=Dc2 ½ðDcQ =K Þ1:1456
ð2Þ
The theory of experimentation suggested by Schenk Jr. is used to formulate the mathematical model. The mathematical model in the exponential forms obtained using the experimental data and corresponding independent pie terms from p1 to p6 and dependent pie terms pD1 to pD2 referred in Table 2 formulated. The model for dependent term pD1 i.e. turbine speed is
It is seen that the Eq. (2) is a model of a pi term containing power developed, PD as a response variable. The absolute index of p5 is highest viz. 6.6344. The factor p5 is related to time for heating which is the most influencing term in this model. The value of this index is positive indicating heating time has strong impact on pD2 and pD2 is directly varying with respect to p5. The influence of the other independent pi terms present in this model is p1, having absolute index of 3.9024. The indices of p3, p4 and p6 are 0.2861, 0.8756 and 1.1456 respectively. The negative indices are indicating need for improvement. The negative indices indicating that pD2 varies inversely with respect to p3, p4, and p6.
pD1 ¼ 0:5705 Hgc Tccqc=Dc2
4. Optimization of models
h
h
2
i0:0424
Turbine Speed Power Developed
i0:9101
0:0474
Hch Dch Nb=Dc ½Hu h i0:3036 2 VoDc=g2 ðTa ToÞ ViDc=g h i0:6156 1=2 2 g1=2 Th=Dc ½ðDcQ =KÞ0:4977 Aoi=Dc
ð1Þ
It is seen that the Eq. (1) is a model of a pi term containing turbine speed, N as a response variable. The following primary conclusion drawn appears to be justified from the above model. The absolute index of p4 is highest viz. 0.3036. The factor p4 is related to ambient condition which is the most influencing term in this model. The value of this index is positive indicating ambient condition has strong impact on p01 and p01 is directly varying with respect to p4.) The influence of the other independent pi terms present in this model is p1, having absolute index of 0.9101. The indices of p3, p5 and p6 are 0.0424, 0.6156 and 0.4977 respectively. The negative indices are indicating need for improvement. The negative indices indicating that p01 varies inversely with respect to p1, p5, and p6. The model for dependent term pD1 i.e. power developed is
The models have been developed for the phenomenon. To find out the best set of independent variables, this will result in maximization of the objective function [11–13]. The two different models corresponding to the Turbine speed (Z1) and Power developed (Z2) is optimize to get the best set of the variables. There will be two objective functions corresponding to these models. The model for the turbine speed (Z1) and Power developed (Z2) needs to be maximized [14–16]. The models are in non-linear form; hence, they are to be converted into a linear form for optimization purpose. This is achieved by taking the log on both sides of the model. To maximize the linear function, we can use the linear programming technique as shown below: 4.1. Optimization of the models for turbine speed For the dependent p term (Z1),
ðZ1Þ ¼ K1 ðp1Þa1 ðp2Þb1 ðp3Þc1 ðp4Þd1 ðp5Þe1 ðp6Þf1 Taking log on both sides of the equation, we have,
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
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P. Belkhode et al. / Materials Today: Proceedings xxx (xxxx) xxx
LogðZ1Þ ¼ logK1 þ a1 logðp1Þ þ b1 logðp2Þ þ c1 logðp3Þ þ d1 logðp4Þ þ e1 logðp5Þ þ f1 logðp6Þ Let, Log(Z1) = Z, LogK1 = K10 , log(p1) = X1, log(p2) = X2, log(p3) = X3, log(p4) = X4, log(p5) = X5 and log(p6) = X6 then the linear model in the form of first degree polynomial can be written as under:
Z ¼ K10 þ a1 X1 þ b1 X2 þ c1 X3 þ d1 X4 þ e1 X5 þ f1 X6 Thus, the equation will be the objective function for the optimization or to be very specific for maximization for the purpose of formulation of the linear programming problem. The constraints can be the boundaries defined for the various independent p terms involved in the function. During the experimentation, the ranges for each independent Pi terms have been observed. These ranges will be the constraints for the problem. Thus, there will be two constraints for each independent variable as under. The maximum and minimum values of a dependent p term Z1 by p1max and p1min by then, the first two constraints for the problem will be obtained by taking log of the variables equate to the zero. Let the log of the limits be assign, as C1 and C2 i.e. C1 = log (p1max.) and C2 = log(p1min.). Constraints equation is as under 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C1 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C2 Similarly other constraints found as under: 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C3 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C4 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 C5 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 C6 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 C7 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 C8 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 C9 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 C10 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 C11 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 C12 After solving this linear programming problem, we get the maximum value of the Z and the set of values of the variables to achieve this maximum value. The values of the independent pi terms can then be obtained by finding the antilog of the values of Z, X1, X2, X3, X4, X5 and X6. The actual values of the multipliers and the variables are found and substituted in the above equations and the actual problem in this case can be stated as below [17–19]. This can now be solved as a linear programming problem using MS Solver available in MS Excel. Thus, the actual problem is to maximise Z, where Z = K10 + a1 * X1 + b1 * X2 + c1 * X3 + d1 * X4 + e1 * X5 + f1 * X6 Z = log(0.5705) 0.9101*log (p1) + 0.0424 * log(p2) + 0.0474 * log(p3) + 0.3036 * log(p4) 0.6156 * log(p5) 0.4977 * log(p6) Z = log(0.5705) + (0.9101 * X1) + (0.0424 * X2) + (0.0474*X3) + (0.3036 * X4) + (0.6156 * X5) + (0.4977 * X6) Subject to following constraints: 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 4.6060 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 4.9071 The other constraints can be likewise found as under: 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 1.1480 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 1.2730 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 0.6989
0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 0.7958 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 1.5178 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 1.2175 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 0.5494 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 0.5494 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 4.1392 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 3.4743 On solving the above problem with MS solver, X1 = 4.9070, X2 = 1.1480, X3 = 0.6989, X4 = 1.5178, X5 = 0.5494 and X6 = 3.4743 Thus, Z1 Max. = Antilog(2.7030) = 504.7392 and corresponding to this, the values of the Z1 Max the values of independent p terms are obtained by taking the antilog of X1, X2, X3, X4, X5 and X6. These values are 1.2385 105, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively. 4.2. Optimization of the models for power developed Similarly, Z2 Max. = Antilog(1.7794) = 60.1784 and corresponding to this, the values of the Z1 Max the values of independent p terms are obtained by taking the antilog of X1, X2, X3, X4, X5 and X6. These values are 1.2385 105, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively. 5. Result and discussion The output power from the solar updraft tower power plant is proportional to the air flow rate and temperature difference produced from the solar collector. The updraft can be raise by the rise of the chimney height which enhances its efficiency. The temperature variation can be raise with increasing the collector area which enhances its efficiency. Solar power increases with the increase in tower height due to increase in updraft as the pressure difference between the air inside the collector roof and atmospheric air increases. Similarly, the air mass flow rate increase with increase in collector roof diameter which further increases the kinetic energy required for rotating the turbine blades. 6. Conclusion The output of the plant is small due to the small size of the solar chimney power plant. The solar power plant cannot produce power as of coal power plant. Although, the output is low suitable for the remote areas with fuel as solar rays. The experimental investigation showed that the peaks of collector roof are always greater than the ambient temperature throughout the experimentation with a maximum difference of 10.1 °C. From the experimentation it is concluded that the solar rays transmits through plain glass as a collector roof material is about 80% beneath the roof collector is the better option than other materials to be used as collector roof compared to other Acrylic sheet, Polycarbonate sheet and Crystalline sheets which has poor transmission of solar rays through them. With the increased in chimney height of the Solar Updraft Tower from 3.6 m to 4.8 m, the increased in the power developed is 38.46%. Solar updraft tower is environmental friendly with a low initial cost with no operating cost. The Solar updraft tower is the simplest and can be applied in a great variety of circumstances which can be built on rooftops of residential buildings. The majority of the cost associated with solar updraft towers is the initial investment required with low maintenance cost with high reliability. Solar chimney power plant generates the power without noise and exhaust gases.
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
P. Belkhode et al. / Materials Today: Proceedings xxx (xxxx) xxx
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Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Evaluation of the experimental data to determine the performance of a solar chimney power plant Pramod Belkhode a, Chandrasshekhar Sakhale b, Ajay Bejalwar a a b
LIT, Nagpur, India PCE, Nagpur, India
a r t i c l e
i n f o
Article history: Received 30 July 2019 Received in revised form 29 August 2019 Accepted 2 September 2019 Available online xxxx Keywords: Solar Chimney Collector Turbine Optimization Experimental setup
a b s t r a c t Solar chimney power plants play an important role in the field of renewable energies. The present study undertaken is related to design a solar updraft tower with all the variable geometric parameter in consideration and to optimize the performance for solar chimney power plant by means of experimental data as well as computer simulation with the formulation an approximate mathematical model. The components of the solar chimney power plant include the collector sheets, chimney and turbo generator. Solar radiation is transferred to the collector plates, air under the solar collector is heated up which is sucked vertical chimney located at the centre of the vertical cylindrical shell. The updraft is formed which drives the turbine and generator to produce the electricity with low cost as compared to other methods. Ó 2019 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the First International Conference on Recent Advances in Materials and Manufacturing 2019.
1. Introduction Many developing countries have large number of resources of renewable energy such as solar energy, wind power, biomass and hydro energy. Many countries are approaching towards the renewable energy due to the environmental issues such as global warming. The renewable energy is less expensive than the fuel energy such as oil and gas. However the supply of renewable energy depends on the atmospheric condition. In the remote areas the concept of solar chimney power plant is most effective as compared to the costly distribution of electricity or alternative to the diesel generators. The capital investment of the hydropower, tidal power is high as compared to the power generated by the solar and wind energy. Solar power generation have the advantages of low maintenance, simple installation, silent operation and long life span. The present study undertaken was related to design a solar updraft tower with all the variable geometric parameter in consideration and to optimize the performance for solar updraft power plant by means of experimental data as well as computer simulation with the generation an exact mathematical model. The mathematical model formed with all the variables involved in the design of the solar updraft tower. These independent variables are grouped such as variables related to collector, variables related to the chimney, variables related to atmospheric condition and heating condition. The indices of each grouped pie terms predict
the performance of the dependent variables such speed and power produced by the turbine. Based on the mathematical model performance of the solar updraft is optimize by the optimization technique. 2. Literature review The aim of this work is to develop a mathematical model to determine the natural air flow inside a solar chimney using daily solar irradiance data on a horizontal plane at a site. The model starts by calculating the hourly solar absorbed by the solar chimney of varying height for a given time (day of the year, hour) [1]. The low pressure solar thermal converter appears to offer development potential for low-tech solar energy conversion [2]. The solar chimney model is verified by comparing the simulation of a smallscale plant with experimental data [3]. Velocity, electric power generation and the turbine efficiency also studying in this work [4]. The total illumination on a horizontal surface from the sun and sky has been determined for clear sky and completely overcast sky conditions [5]. The solar chimney power plant need warm air to create the updraft which spins the turbine. The blade of the turbine will rotate due to the warm air absorbed by the land. This can be effectively done by covering the collector area with the gravel. The PV solar plant unable to produce power during night unless assembled with battery system [6]. If the panel is cover with dust
https://doi.org/10.1016/j.matpr.2019.09.006 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the First International Conference on Recent Advances in Materials and Manufacturing 2019.
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than the efficiency of the PV panel reduces. Few however have the ability to store enough energy during the day so that a supply can be continued during night when the solar radiation is negligible. The potential of solar electric power generation as a means to significantly reduce CO2 emissions is also detailed [7]. The analysis showed that chimney height is the most important physical variable for the solar chimney design [8]. 3. Experimentation The Solar chimney uses warm air for the generating power. The solar chimney power plant system consists of four important components—collector, chimney, energy storage layer and turbo generators at the base. Radiation is absorbed by the solar collector sheets warms up the air under the solar collector roof which is sucked towards the centre of the vertical turbine shell from the base [9]. Thus the updraft produce run the turbine and produce the solar power with the help of wind turbine is located at the chimney base [10] (Fig. 1). The variables affecting the phenomenon under consideration are collector materials, chimney height, chimney diameter, turbine blades and solar radiation. All dependent and independent parameters are converted in to dimensionless term. Table 1 shows dependent and independent variables with units and symbols. Experimental setup is designed and fabricated to execute the experimentation according to experimentation plan. The experimental setup basically consists of concrete base with angle structural frame to assemble the chimney, roof collector plates and turbine at the base of chimney. The site is selected on the basis of availability of wind velocity and proximity to open sky so that sun rays are available throughout the day time. The base of around 4500 mm diameter covered with brick joints of three bricks layers with concrete. The sand filled in the circular base of bricks act as heat reservoir. On the periphery of bricks circle eight angles of 600 mm height are erected, to locate the frame of collector and chimney. The MS angle frame is fabricated of 4500 mm diameter on which the collector sheets are mounted and having 600 mm diameter circular hole at centre for mounting the turbine and frame to
Fig. 1. Solar updraft tower.
hold the chimney pipe. This frame is mounted on the angles erected at the periphery of bricks joint. The different types of collector sheets were examined each time on the experimental setup to determine the effect of updraft produce. The Chimney pipe of diameter 150 mm and height 3600 mm and 4800 mm is placed one at a time and subsequently changed during the experimentation to predict the performance of the turbine. Aluminium sheets are used to cover the portion opened around the periphery of angles erected on bricks joint for trapping the air under the collector roof. Opening of 3600 mm length is kept on both sides for air movements from outside to inside of collector. The experimentation is carried out during the summer with the various instruments. The digital tachometer is used for measuring the turbine speed, digital thermometer is used for measurement of the air under collector and outside the chimney, pyranometer is used for solar radiation and digital anemometer is used for measuring the air velocity. Warm air produced by the collector flow into the chimney which converts into kinetic and potential energy. Due to rise in the temperature inside the collector changes the density of air which works as the driving forces. The differences in the densities of air due the temperature difference cause the pressure difference which is used to accelerate the air and thus converted into the kinetic energy. Warms air for the solar tower is produced by the greenhouse effect in air collector which is consisting of different collector materials located above the ground level. Air heat up and transfer its heat to the air flowing to the tower. Mechanical output in the form of rotational energy obtained from the warm air in the tower. Cold air flows in the solar collector which is heated by the solar radiation which is recorded in the range of 450–550 W.m2 with recorded temperature rises from 450–570 °C and the recorded the warm up air velocity in the range of 1.8 m.s1 to 2.0.s1 during the experimentation in the design experimental setup. This warms air produced the draft rotates the turbine and generated the electricity. The output of the generator is supplied to the electronic panel were alternating current is converted to the direct current which is supplied to glow the LED light located on the panel. The digital multi meter is used to measures the voltage and current. The average power outputs for warm air condition practically ranged between 3 W and 6 W for 12 feet height tower and between 6 W and 9 W for 15 feet height tower. The experimental setup designed with the collector material such as glass, acrylic sheets, polycarbonate and crystalline material with thickness range from 0.002 to 0.004 m and conductivity in the range of 0.16–0.8 W.m1 K. The collector plates are placed at the circular ring of the 4.5 m in diameter and 0.6 m above the ground with the small inclination of 0.15 rad. The chimney is of PVC material located at the centre of the collector plate of diameter 0.15 m with different height of 3.6 m and 4.8 m. Table 1 shows the description of all the independent and dependent variables of the experimental setup of solar updraft tower. The correlation for the independent variables and dependent variables such turbine power output and turbine speed is formulated by the mathematical model. Since the numbers of the independent variables are more thus these variables are grouped in the respective group to predicate the performance and to reduce the complexity and to obtain the simplicity in the behaviour of the event, the pi terms are reduced as suggested by Schenk Jr. The pi terms related to the independent variables like Collector material, solar chimney, Relative Humidity, Ambient condition, solar radiation are reduced to form a single new pi term. The Table 2 shows the new pi terms of independent variables in reduced form. Thus the total seventeen pi terms of independent variables are reduced to six new pi terms as shown in the table below.
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
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P. Belkhode et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 1 Identification of variables for solar updraft tower. S. N
Description of Variables
Type of variable
Symbol
Unit
Dimension
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19
Diameter of Collector Thermal conductivity of Collector Material Height of collector from ground level Thickness of covering collector material Inclination of collector Chimney Height Diameter of Chimney No. of blades Ambient Temperature Humidity Air velocity at inlet Air velocity at outlet Temperature inside the collector Heating time Heat Flux Air inlet area Acceleration due to gravity Turbine Speed Power generated
Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Dependent Dependent
Dc K Hgc Tcc hc Hch Dch Nb Ta Hu Vi Vo Tc Th Q Aoi g Ts Pd
m W/mK m m rad m m – 0C % m/s m/s 0C sec W/m2 m2 m/s2 rpm W
M0L1T0 M1L1T3h1 M0L1T0 M0L1T0 M0L0T0 M0L1T0 M0L1T0 M0L0T0 M0L0T0h1 M0L0T0 M0L1T1 M0L1T1 M0L0T0h1 M0L0T1 M1L0T3 M0L2T0 M0L1T2 M0L0T1 M1L2T3
Table 2 Grouped independent pie terms.
h
Sr No
Independent Dimensionless ratios
Nature of Physical Quantities
01 02 03 04 05 06
p1 = [(Hgc Tcc hc)/Dc2] p2 = [Hch Dch Nb/Dc2] p3 = [Hu] p4 = [(Ta To)(ViDc/g2) (VoDc/g2)] p5 = [(g1/2Th/Dc1/2)(Aoi/Dc2)] p6 = [(DcQ/K)]
Collector material Solar Chimney Relative Humidity Ambient Condition Heating duration Heat flux
Dependent dimensionless ratios or p terms 01 pD1 = [(Dc1/2N/g1/2)] 02 pD2 = [Po/KDc]
pD2 ¼ 7:1796x1019 Hgc Tccqc=Dc2
i3:9024
h i0:1755 Hch Dch Nb=Dc2 ½Hu0:2861 0:8756 ðTa ToÞ ViDc=g 2 VoDc=g 2 h i6:6344 g 1=2 Th=Dc1=2 Aoi=Dc2 ½ðDcQ =K Þ1:1456
ð2Þ
The theory of experimentation suggested by Schenk Jr. is used to formulate the mathematical model. The mathematical model in the exponential forms obtained using the experimental data and corresponding independent pie terms from p1 to p6 and dependent pie terms pD1 to pD2 referred in Table 2 formulated. The model for dependent term pD1 i.e. turbine speed is
It is seen that the Eq. (2) is a model of a pi term containing power developed, PD as a response variable. The absolute index of p5 is highest viz. 6.6344. The factor p5 is related to time for heating which is the most influencing term in this model. The value of this index is positive indicating heating time has strong impact on pD2 and pD2 is directly varying with respect to p5. The influence of the other independent pi terms present in this model is p1, having absolute index of 3.9024. The indices of p3, p4 and p6 are 0.2861, 0.8756 and 1.1456 respectively. The negative indices are indicating need for improvement. The negative indices indicating that pD2 varies inversely with respect to p3, p4, and p6.
pD1 ¼ 0:5705 Hgc Tccqc=Dc2
4. Optimization of models
h
h
2
i0:0424
Turbine Speed Power Developed
i0:9101
0:0474
Hch Dch Nb=Dc ½Hu h i0:3036 2 VoDc=g2 ðTa ToÞ ViDc=g h i0:6156 1=2 2 g1=2 Th=Dc ½ðDcQ =KÞ0:4977 Aoi=Dc
ð1Þ
It is seen that the Eq. (1) is a model of a pi term containing turbine speed, N as a response variable. The following primary conclusion drawn appears to be justified from the above model. The absolute index of p4 is highest viz. 0.3036. The factor p4 is related to ambient condition which is the most influencing term in this model. The value of this index is positive indicating ambient condition has strong impact on p01 and p01 is directly varying with respect to p4.) The influence of the other independent pi terms present in this model is p1, having absolute index of 0.9101. The indices of p3, p5 and p6 are 0.0424, 0.6156 and 0.4977 respectively. The negative indices are indicating need for improvement. The negative indices indicating that p01 varies inversely with respect to p1, p5, and p6. The model for dependent term pD1 i.e. power developed is
The models have been developed for the phenomenon. To find out the best set of independent variables, this will result in maximization of the objective function [11–13]. The two different models corresponding to the Turbine speed (Z1) and Power developed (Z2) is optimize to get the best set of the variables. There will be two objective functions corresponding to these models. The model for the turbine speed (Z1) and Power developed (Z2) needs to be maximized [14–16]. The models are in non-linear form; hence, they are to be converted into a linear form for optimization purpose. This is achieved by taking the log on both sides of the model. To maximize the linear function, we can use the linear programming technique as shown below: 4.1. Optimization of the models for turbine speed For the dependent p term (Z1),
ðZ1Þ ¼ K1 ðp1Þa1 ðp2Þb1 ðp3Þc1 ðp4Þd1 ðp5Þe1 ðp6Þf1 Taking log on both sides of the equation, we have,
Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006
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LogðZ1Þ ¼ logK1 þ a1 logðp1Þ þ b1 logðp2Þ þ c1 logðp3Þ þ d1 logðp4Þ þ e1 logðp5Þ þ f1 logðp6Þ Let, Log(Z1) = Z, LogK1 = K10 , log(p1) = X1, log(p2) = X2, log(p3) = X3, log(p4) = X4, log(p5) = X5 and log(p6) = X6 then the linear model in the form of first degree polynomial can be written as under:
Z ¼ K10 þ a1 X1 þ b1 X2 þ c1 X3 þ d1 X4 þ e1 X5 þ f1 X6 Thus, the equation will be the objective function for the optimization or to be very specific for maximization for the purpose of formulation of the linear programming problem. The constraints can be the boundaries defined for the various independent p terms involved in the function. During the experimentation, the ranges for each independent Pi terms have been observed. These ranges will be the constraints for the problem. Thus, there will be two constraints for each independent variable as under. The maximum and minimum values of a dependent p term Z1 by p1max and p1min by then, the first two constraints for the problem will be obtained by taking log of the variables equate to the zero. Let the log of the limits be assign, as C1 and C2 i.e. C1 = log (p1max.) and C2 = log(p1min.). Constraints equation is as under 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C1 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C2 Similarly other constraints found as under: 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C3 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 C4 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 C5 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 C6 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 C7 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 C8 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 C9 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 C10 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 C11 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 C12 After solving this linear programming problem, we get the maximum value of the Z and the set of values of the variables to achieve this maximum value. The values of the independent pi terms can then be obtained by finding the antilog of the values of Z, X1, X2, X3, X4, X5 and X6. The actual values of the multipliers and the variables are found and substituted in the above equations and the actual problem in this case can be stated as below [17–19]. This can now be solved as a linear programming problem using MS Solver available in MS Excel. Thus, the actual problem is to maximise Z, where Z = K10 + a1 * X1 + b1 * X2 + c1 * X3 + d1 * X4 + e1 * X5 + f1 * X6 Z = log(0.5705) 0.9101*log (p1) + 0.0424 * log(p2) + 0.0474 * log(p3) + 0.3036 * log(p4) 0.6156 * log(p5) 0.4977 * log(p6) Z = log(0.5705) + (0.9101 * X1) + (0.0424 * X2) + (0.0474*X3) + (0.3036 * X4) + (0.6156 * X5) + (0.4977 * X6) Subject to following constraints: 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 4.6060 1*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 4.9071 The other constraints can be likewise found as under: 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 1.1480 0*X1 + 1*X2 + 0*X3 + 0*X4 + 0*X5 + 0*X6 1.2730 0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 0.6989
0*X1 + 0*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6 0.7958 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 1.5178 0*X1 + 0*X2 + 0*X3 + 1*X4 + 0*X5 + 0*X6 1.2175 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 0.5494 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 0*X6 0.5494 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 4.1392 0*X1 + 0*X2 + 0*X3 + 0*X4 + 0*X5 + 1*X6 3.4743 On solving the above problem with MS solver, X1 = 4.9070, X2 = 1.1480, X3 = 0.6989, X4 = 1.5178, X5 = 0.5494 and X6 = 3.4743 Thus, Z1 Max. = Antilog(2.7030) = 504.7392 and corresponding to this, the values of the Z1 Max the values of independent p terms are obtained by taking the antilog of X1, X2, X3, X4, X5 and X6. These values are 1.2385 105, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively. 4.2. Optimization of the models for power developed Similarly, Z2 Max. = Antilog(1.7794) = 60.1784 and corresponding to this, the values of the Z1 Max the values of independent p terms are obtained by taking the antilog of X1, X2, X3, X4, X5 and X6. These values are 1.2385 105, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively. 5. Result and discussion The output power from the solar updraft tower power plant is proportional to the air flow rate and temperature difference produced from the solar collector. The updraft can be raise by the rise of the chimney height which enhances its efficiency. The temperature variation can be raise with increasing the collector area which enhances its efficiency. Solar power increases with the increase in tower height due to increase in updraft as the pressure difference between the air inside the collector roof and atmospheric air increases. Similarly, the air mass flow rate increase with increase in collector roof diameter which further increases the kinetic energy required for rotating the turbine blades. 6. Conclusion The output of the plant is small due to the small size of the solar chimney power plant. The solar power plant cannot produce power as of coal power plant. Although, the output is low suitable for the remote areas with fuel as solar rays. The experimental investigation showed that the peaks of collector roof are always greater than the ambient temperature throughout the experimentation with a maximum difference of 10.1 °C. From the experimentation it is concluded that the solar rays transmits through plain glass as a collector roof material is about 80% beneath the roof collector is the better option than other materials to be used as collector roof compared to other Acrylic sheet, Polycarbonate sheet and Crystalline sheets which has poor transmission of solar rays through them. With the increased in chimney height of the Solar Updraft Tower from 3.6 m to 4.8 m, the increased in the power developed is 38.46%. Solar updraft tower is environmental friendly with a low initial cost with no operating cost. The Solar updraft tower is the simplest and can be applied in a great variety of circumstances which can be built on rooftops of residential buildings. The majority of the cost associated with solar updraft towers is the initial investment required with low maintenance cost with high reliability. Solar chimney power plant generates the power without noise and exhaust gases.
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Please cite this article as: P. Belkhode, C. Sakhale and A. Bejalwar, Evaluation of the experimental data to determine the performance of a solar chimney power plant, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.006