Table of Contents

## Abstract

Solar updraft tower 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 updraft power plant by means of experimental data as well as computer simulation with the generation an exact 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. Electricity produce from the solar updraft plant is lower cost as compared to the other methods.

Keywords: Solar Chimney, collector, turbine, optimization, experimental setup.

## Introduction

Many developing countries have large number of renewable energy resources such as solar energy, wind power, biomass and hydro energy. Developing countries are approaching towards the renewable energy due to the environmental issues such as global warming and pollution. These countries are implementing the policies for the development of renewable energy. The consumption of oil and natural gas can be optimized by proper utilizing the renewable energy sources. 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 expensive distribution of electricity grid 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 solar chimney power plant need warm air to create the updraft which spins the turbine. The spinning of the turbine is continues due to the collected warm air absorbed by the land during the sun shining. This can be effective done by covering the collector area with the gravel. Solar power produce by the PV solar plant cannot provide power during night unless equipped with storage system. The efficiency of the PV panel reduces as the panel is covered with the dust. Solar chimney power plant produces power at the low running cost and high reliability. Few however have the ability to store sufficient energy during the day so that a supply can be maintained during night as well, when the solar radiation is negligible. 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 variables related to 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.

## Experimentation

The Solar chimney uses warm air for the power generation. The solar chimney power plant system consists of four major components—collector, chimney, energy storage layer and turbo generators at the base. Solar radiation is absorbed by the collector plates warms up the air under the solar collector which is sucked towards the centre of the vertical turbine shell from the base. Thus the draft produce drives the turbine and generate the solar power. The wind turbine is located at the bottom of the chimney.

Figure 1: Solar updraft tower

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 locate the Chimney and collector sheets as well as to locate turbine at the bottom 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. This circular base of bricks is filled with sand, which will 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 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 3600mm and 4800 mm is placed one at a time and subsequently changed during the experimentation to predict the performance of the turbine. The lower base of the solar tower or the pipe is fitted with a vertical Wind turbine equipped with blades.

Aluminium sheets are used to cover the portion opened around the periphery of angles erected on bricks joint to trap the air inside the collector. Opening of 3600mm length is kept on both sides for air movements from outside to inside of collector.

Figure 2: Model of solar updraft tower

The experimentation is carried out during the summer with the various instruments. Figure 2 show the experimental setup. 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 W/m2 to 550 W/m2 with recorded temperature rises from 450C to 570C and the recorded the warm up air velocity in the range of 1.8 m/s to 2.0 m/s 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 watts to 6 watts for 12 feet height tower and between 6 watts to 9 watts 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 W/m K to 0.8 W/m 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 0.15m with different height of 3.6m and 4.8m. 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.

Table 1: Identification of variables for solar updraft tower

S.N

Description of Variables

Type of variable

Symbol

Unit

Dimension

01

Diameter of Collector

Independent

Dc

m

M0L1T0

02

Thermal conductivity of Collector Material

Independent

K

W/mK

M1L1T-3(-1

03

Height of collector from ground level

Independent

Hgc

m

M0L1T0

04

Thickness of covering collector material

Independent

Tcc

m

M0L1T0

05

Inclination of collector

Independent

(c

rad

M0L0T0

06

Chimney Height

Independent

Hch

m

M0L1T0

07

Diameter of Chimney

Independent

Dch

m

M0L1T0

08

No. of blades

Independent

Nb

—

M0L0T0

09

Ambient Temperature

Independent

Ta

0C

M0L0T0(1

10

Humidity

Independent

Hu

%

M0L0T0

11

Air velocity at inlet

Independent

Vi

m/s

M0L1T-1

12

Air velocity at outlet

Independent

Vo

m/s

M0L1T-1

13

Temperature inside the collector

Independent

Tc

0C

M0L0T0(1

14

Heating time

Independent

Th

sec

M0L0T1

15

Heat Flux

Independent

Q

W/m2

M1L0T-3

16

Air inlet area

Independent

Aoi

m2

M0L2T0

17

Acceleration due to gravity

Independent

g

m/s2

M0L1T-2

18

Turbine Speed

Dependent

Ts

rpm

M0L0T-1

19

Power generated

Dependent

Pd

W

M1L2T-3

Table 2: Grouped Independent pie terms

SrNo

Independent Dimensionless ratios

Nature of Physical Quantities

01

(1= [(Hgc Tcc (c)/Dc2]

Collector material

02

(2= [Hch Dch Nb/Dc2]

Solar Chimney

03

(3= [Hu]

Relative Humidity

04

(4= [ (Ta To)(ViDc/g2) (VoDc/g2)]

Ambient Condition

05

(5= [(g1/2Th/Dc1/2)(Aoi/Dc2)]

Heating duration

06

(6= [(DcQ/K)]

Heat flux

Dependent Dimensionless ratios or ( terms

01

(D1 =[(Dc1/2 N/g1/2)]

Turbine Speed

02

(D2 = [Po/KDc]

### Power Developed

The theory of experimentation suggested by H 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 (1 to (6 and dependent pie terms (D1 to (D2 referred in table 2 formulated.

The model for dependent term (D1 i.e. turbine speed is

[image: image3.png] QUOTE

(D1 = 0.5705 x [Hgc Tcc (c)/Dc2] – 0.9101 x [Hch Dch Nb/Dc2 ]0.0424 x [Hu]0.0474 x [(Ta To)(ViDc/g2) (VoDc/g2)]0.3036 x [(g1/2Th/Dc1/2)(Aoi/Dc2)]-0.6156 x [(DcQ/K)]-0.4977 (1)

It is seen that the equation 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 π4 is highest viz.0.3036. The factor π4 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 π01 and π01 is directly varying with respect to π4. ) The influence of the other independent pi terms present in this model is π1, having absolute index of -0.9101. The indices of π3, π5 and π6 are 0.0424,-0.6156 and -0.4977 respectively. The negative indices are indicating need for improvement. The negative indices indicating that π01 varies inversely with respect to π1, π5, and π6.

The model for dependent term (D1 i.e. power developed is

[image: image5.png] QUOTE

(D2 =7.1796×10-19 x[Hgc Tcc (c)/Dc2] -3.9024 x [Hch Dch Nb/Dc2 ]0.1755 x [Hu]0.2861 x [(Ta To)(ViDc/g2) (VoDc/g2)]0.8756 x [(g1/2Th/Dc1/2)(Aoi/Dc2)]6.6344 x [(DcQ/K)]-1.1456 (2)

It is seen that the equation 2 is a model of a pi term containing power developed, PD as a response variable. The absolute index of π5 is highest viz. 6.6344. The factor π5 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 πD2 and πD2 is directly varying with respect to π5. The influence of the other independent pi terms present in this model is π1, having absolute index of -3.9024. The indices of π3, π4 and π6 are 0.2861,0.8756 and -1.1456 respectively. The negative indices are indicating need for improvement. The negative indices indicating that πD2 varies inversely with respect to π3, π4, and π6.

### Optimization of Models

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. 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. 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:

3.1 Optimization of the models for Turbine Speed:

For the dependent (term(Z1),

(Z1)= K1*((1) a1*((2) b1*((3) c1*((4) d1*( (5) e1*( (6) f1

Taking log on both sides of the equation, we have,

Log(Z1)=logK1+ a1*log((1)+b1* log((2)+c1* log((3)+ d1* log((4)+ e1* log((5)+ f1* log((6)

Let, Log(Z1)=Z, LogK1=K1’, log((1)=X1, log((2)=X2, log((3)=X3, log((4)=X4, log((5)=X5 and log((6)=X6 then the linear model in the form of first degree polynomial can be written as under:

Z= K1’ + a1*X1 +b1*X2 +c1*X3 +d1*X4 +e1*X5 +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 ( 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 ( term Z1 by (1max and (1 min by then, the first two constraints for the problem will be obtained by taking log of the varibles equate to the zero

Let the log of the limits be assign, as C1 and C2 i.e. C1=log((1max.) and C2=log((1min.). 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. 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=K1’ + a1*X1 +b1*X2 +c1*X3 +d1*X4 +e1*X5 +f1*X6

Z=log (0.5705) – 0.9101*log ((1) + 0.0424*log((2) + 0.0474* log((3) +0.3036* log((4) -0.6156* log((5) -0.4977 * log((6)

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 ( terms are obtained by taking the antilog of X1, X2, X3,X4,X5 and X6. These values are 1.2385×10-5, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively.

3.2 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 ( terms are obtained by taking the antilog of X1, X2, X3,X4,X5 and X6. These values are 1.2385×10-5, 0.07111, 0.2, 32.9520, 3.5433 and 2981.25 respectively.

## 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.

## Conclusion

The output of the plant was moderately because it was a smaller solar chimney plant. Solar updraft tower has 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 generate the power without noise and exhaust gases.

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