** **

** **

**Design, Construction and
Testing of a Parabolic Solar Steam Generator**

Joshua FOLARANMI

*Department
of Mechanical Engineering, **Federal** **University** of Technology **Minna**, **Niger** State. **Nigeria*.

E-mail: folajo2008@yahoo.com

** **

** **

**Abstract**

This paper reports the design, construction and testing of a parabolic dish solar steam generator. Using concentrating collector, heat from the sun is concentrated on a black absorber located at the focus point of the reflector in which water is heated to a very high temperature to form steam. It also describes the sun tracking system unit by manual tilting of the lever at the base of the parabolic dish to capture solar energy. The whole arrangement is mounted on a hinged frame supported with a slotted lever for tilting the parabolic dish reflector to different angles so that the sun is always directed to the collector at different period of the day. On the average sunny and cloud free days, the test results gave high temperature above 200°C.

**Keywords**

Solar Energy, Sun, Heat, Steam, Water, Radiation, Temperature

**Introduction **

** **

*The sun and its Energy*

When solar energy is mentioned anytime, the sun readily
comes to mind, so it is justifiable to discuss in brief the physical and
chemical behaviours of the sun before its application to heating. The sun has
structure and characteristics, which determine the nature of the energy it
radiates into space. The sun is sphere of intensely hot gaseous matter with a
diameter of 1.39x10^{6}km and is on the average 1.5x10^{8}km
from the earth. The surface of the sun is at an effective temperature of about
5762K (5489°C). The temperature in the central interior regions is estimated at
between 8x10^{6}K to 40x10^{6}K and the density about 80 to 100
times that of water. The fusion reactions which is suggested to supply the
energy radiated by the sun is several, the one considered most important is a
process in which hydrogen combines to form helium [[1]].

A schematic of the structure of the sun shows that 90%
of the energy is generated in the region 0 to 0.23R (where R = radius of the sun)
and contains 40% of the mass of the sun. At a distance of 0.7R from the center,
the temperature drops to about 130,000K and density dropped to 0.07g/cm^{3}.
Here convection processes begin to become important and from 0.7 to 1.0R is
known as the convective zone. The upper layer of the convective zone is called
the photosphere. The edge of the photosphere is sharply defined, even though it
is of low density. It is essentially opaque as the gases it composed of are
strongly ionized and able to absorb and emit a continuous spectrum of
radiation. The photosphere is the source of most solar radiation [[2]].

Outside of the photosphere is a more or less transparent solar atmosphere, which is observable during total solar eclipse or by instrument that occult the solar disk. Above the photosphere is a layer of cooler gases several hundred miles deep called the reversing layer, outside of that is layer referred to as the chromospheres, with a depth of about 10,000 km. This is a gaseous layer with temperature higher than that of the photosphere and with lower density. Further out is the corona of very low density and high temperature.

The sun's energy which is nuclear energy released in fusion reaction reaches the earth as electromagnetic in the wavelength band of about 0.3µm with its peak spectral intensity near 0.5µm. The scale of the sun's thermometer reaction is such that, as far as the earth is concerned, the energy available is practically inexhaustible.

The intensity of solar radiation on a surface normal to
the sun’s rays beyond the earth's atmosphere at the mean earth-sun distance is
defined as the solar constant I_{sc}. Although there are recurrent small
variations in the sun's radiant output caused primarily by periodic changes in
the ultraviolet portion of the solar spectrum, the currently accepted value of
I_{sc} is 4353w/m^{2}. Because the earth orbit is slightly
elliptical and the extraterrestrial radiation intensity Io varies inversely as
the square of the earth-sun distance, Io ranges from a maximum of 1398w/m^{2
}on January 3, when the earth is closer to the sun, to a minimum of
1310w/m^{2} on July 6, when the earth-sun distance reaches its maximum.

Despite the variations, solar energy can be used in three processes:

a. Heliothermal- this is the system in which the incident radiation is absorbed and turned into heat.

b. Heliochemical- in which radiation between 0.3 and 1.0µm can cause chemical reactions, sustain growth of plants and animals and through photosynthesis convert exhaled carbon dioxide to breakable oxygen.

c. Helioelectrical – in which part of the radiation in the band between 0.33 and 1.2 µm can be converted directly into electricity by photovoltaic cells.

The incoming solar radiation suffers depletion in the following ways:

1. Absorption by the ozone in the upper atmosphere.

2. Scattering by dry air.

3. Absorption, scattering and diffuse reflection by suspended solid particles.

4. Absorption and scattering by thin cloud layers.

5. Absorption and scattering by water vapour.

*Availability of Solar Energy
in **Nigeria** *

To evaluate the economics and performance of system for the utilization of solar energy in a particular location, knowledge of the available solar radiation at that place is essential. Thus the utilization of solar energy, as with any other natural resource requires detailed information on availability.

The availability of solar radiation on the earth's
surface is a function of geographical zone. The regions lying between 15° and
35°latitude north and south respectively seem to be most favourably located.
They have relatively little rains and clouds so that over 90% of the incident
sunshine is direct radiation and the yearly sunshine hour is usually over 3000.
The next most favourable region is the equatorial belt from 15°S to 15°N which
receives about 2300hours of sunshine per year with very little seasonal
variation. The high humidity and frequent clouds in this belt generally result
in a high proportion of the solar radiation taking the form of scattered
radiation. Nigeria lying
approximately between 4°N and 13°N latitude is a geographically favourable zone
for harnessing solar energy. On average the yearly total solar energy incident
on a horizontal surface in Nigeria is 2300kwh/m^{2 }[[3]].

The earth is closest to the sun at a distance of about
1.45x10^{11}m and farthest from the sun at a distance of about 1.54x10^{11}m
[[4]].

The objectives of this research work are:

· to design and fabricate a parabolic dish solar steam generating machine which uses solar energy as its fuel;

· to carryout performance analysis of a parabolic dish collector to heat the water located at the focal point of the concentrator;

· to minimize heat loses on the reflectors and thereby improving high temperature concentration at the focal point.

*Theoretical Background*

The basic principle adopted in the construction of the parabolic dish solar steam generator is that when parallel rays of light from the sun close to and parallel to the principal axis are incident on a concave or parabolic shaped mirror, they converge or come together after reflection to a point F on the principal axis called the principal focus as shown in figure.

*Figure 1**. Parabolic Dish*

**Material and Method**

** **

The parabolic dish solar steam generator considered in this paper is made up of the following parts as shown in figure 2.

*Figure 2.** Representation of the
Parabolic Dish Solar Steam Generator*

* *

where:

{1} - Cold Water Storage Tank;

{2} - Galvanized Pipe for Cold Water;

{3} - Absorber;

{4} - Parabolic Dish Reflector;

{5} - Adjustable Mechanism;

{6} - Outlet Pipe for Steam.

The parts in the figure are as follows:

·
*Tank: *The storage tank is made of iron sheet or plastic and mounted on a
stand higher than the parabolic dish stand for storing cold water.

·
*Flexible pipe: *This is a pipe made of galvanized steel. It carries cold water from
the storage tank to the absorber.

·
*Absorber: *It is a metal container that carries water, painted black and
located at the focal point of the parabolic dish. When the sunlight rays are incident
on the reflective surfaces of the parabolic dish, they are reflected and converged
to the base of the absorber located at the focal point to heat up the water in
it and generate steam.

·
*Parabolic dish: *This is the concave dish made of wood and lined with an aluminium sheet.
Method of a given focus and directrix was employed in the construction of the
parabolic dish. The reflector plain mirror cut into shapes and fixed by glue to
the aluminium sheet which is in turn riveted to the wooden skeleton structure
serve as the reflecting surface of the parabolic dish that converges heat to
the base of the absorber.

·
*Adjustable mechanism: *Parabolic dish adjustable mechanism is made of metal to support the
weight of parabolic dish and absorber. The main function is to allow the parabolic
dish to align at various angles to capture the sunlight rays depending on the
movement and position of the sun.

·
*Outlet Hose: *This is a pipe made of galvanized steel and it is fixed at the top
of the absorber. It serves as the outlet for the steam generated in the
absorber to the generator.

**Design Analysis**

** **

*Design Specifications*

The construction of the parabolic dish solar steam generator was made taking into account following design specifications:

·
Diameter of the sun: 1.39x10^{6}km;

·
Average distance of the sun from
the earth: 1.5x10^{8}km;

·
Radius of the earth (r_{e}):
6400km;

· Effective temperature of the surface of the sun 5762K;

·
The sun's central interior region
temperature (estimation): 8x10^{6}K to 40x10^{6}K;

· Density of the sun: 80 to 100 times that of water;

·
Solar constant (Isc): 1353w/m^{2};

·
Extraterrestrial radiation (Io): 1398w/m^{2}
(maximum); 1310w/m^{2} (minimum);

· Geographical location of Nigeria.

o Latitude between 4°N and 13°N.

o Longitude between 3°E and 15°W

·
Nigeria land area (A) =
932768km^{2} [[5]]

·
On average yearly total solar
energy incident on a horizontal surface in Nigeria: 2300kwh/m^{2 }[5]

** **

*Design Equation*

Average distance of the sun from the earth = 1.5x10^{8}km

Consider a sphere of radius 1.5x10^{8}km with the sun at its
centre.

Let Ss = surface area of this imaginary sphere

A_{E} = cross sectional area of the earth

r_{s} = radius of the sphere

r_{e} = radius of the earth

Therefore,

A_{E} = πr_{e}^{2}
= 3.142(6.4x10^{6})^{2} = 1.287x10^{14} m^{2} (1)

Ss = 4πr_{s}^{2}
= 4x3.142 (1.5·10^{11})^{2} = 2.828·10^{23}m^{2 } (2)

Percentage sun’s output= [(A_{E}/Ss) x100} (3)

= {[(1.287x10^{14})/ (2.828x10^{23})]
x100}

= 0.0000000455%

This then means that the earth receives 0.0000000455% of sun's energy output.

The world's average annual energy consumption is
9.262x10^{23}kwh [[6]].

Hence, Nigeria would receive radiation at that rate:

Let R_{c }= extraterrestrial radiation

A = continental land area

I_{sc }= extraterrestrial solar constant

Therefore, _{}

R_{c}=I_{sc}A (4)

=1353·932768x10^{6}

=1.262·10^{15}w/m^{2}

Therefore, for a yearly average sunshine hour of 9hours/day

= 1.262·10^{15}x (366x9)

= 4.157·10^{18}wh/year

Assuming a clearness index of 50% since 47% of extraterrestrial radiation reaches the earth surface.

Terrestrial radiation in Nigeria's land area

= [(50/100)·4.157x10^{18}

= 2.079·10^{18}wh/year.

The part of solar radiation that reaches the surface of the earth without being scattered, absorbed or reflected is direct radiation and it is the most intense. The intensity of the direct radiation reaching the surface of the earth is a function of time of the day, latitude of location and declination angle (Awachie, 1982).

To calculate the direct radiation reaching the earth surface as a function of time of the day (t), for a location (γ) with the sun at declination (δ):

Let Z -Zenith Angle

γ -Latitude of location

δ -declination angle

t -hour angle of the sun

I_{Z }-Direct Normal Radiation

I_{SC}-Extraterrestrial solar radiation constant

I_{h }-Horizontal radiation.

S and C are climatographically determined constants. The Zenith angle is calculated thus:

Cos Z = sinγ sinδ + cos γ cosδ cos t (5)

= sin14° sin0° + cos14° cos0°_{ }cos0°

= 0.2192 x 0 + 0.97029 x 1 x 1

= 0.97029.

Z = cos^{ – 1} (0.97029) = 14°

The intensity of the solar radiation after passing through the atmosphere is calculated thus:

I_{Z} = I_{Sc}℮^{– C(sec Z)S}
= 1353 ℮^{–0.357 (1/cos14)0.678 }= 940w/m^{2 } (6)

This is the value of the direct radiation on a normal surface and it is the maximum value possible. In practice only systems using full tracking mechanisms can collect this radiation.

The value of radiation on a horizontal surface is calculated thus:

I_{h}= I_{Z} cosZ = 940 x
0.970295726 = 912w/m^{2 } (7)

*Energy Balance of the collector *

For a steady state situation, an energy balance on the absorber plate yields the following equations [[7]].

q_{u} = A_{p}I_{sc}
– q_{1} (8)

A_{p }– Area of absorber plate (m^{2})

*Solar Radiation *

** **The** **total solar
radiation falling on a horizontal surface is given by:

I = I_{Sc} _{} (9)

where:

I - Average horizontal daily terrestrial radiation for the period (usually 1 month)

I_{Sc} - Extraterrestrial
solar radiation

A, b- climatically constants for a particular location

Φ - Latitude, 0.33°N, a, b are 0.32 and 0.4 respectively

n - day of the year

N - Possible daily maximum number of insolation.

θ – Angle

τ – transmissivity of cover

N = _{}_{} (10)

where δ – declination angle and is given by

δ = 23.45 Sin _{} (11)

** **

*Efficiency*

Collector efficiency is given by

_{} (12)

where

I_{T} -the amount of solar radiation falling on
the collector

A_{C}- area of the collector (m^{2})

ŋ_{i }- instantaneous collector efficiency
(%)

q_{U }- rate of useful heat gain (w_{i})

** Heat Loss**

In term of overall coefficient (U_{i}) the heat
loss from the collector is given in [7].

q_{i}=U_{i}A_{p}(T_{pm}–T_{a}) (13)

Hence, the loss from the collector is the sum of the heat loss from the top, the bottom and the side, thus,

q_{T}=q_{t}+ q_{b}
+ q_{s }(14)

Each of the losses are defined by the equations below

q_{t} = U_{t} A_{p}
(T_{pm} – T_{a}) (15)

q_{b} = U_{b} A_{p}
(T_{pm} – T_{a}) (16)

q_{s} = U_{s} A_{p}
(T_{pm} – T_{a}) (17)

So, U_{T} = U_{t} + U_{b} + U_{s}

U_{T} is measure of all the losses. Therefore,
it is an important parameter; typical values range from 2 – 10w/m^{2}K [[8]].

For empirical relation:

Nu = _{} = _{} (18)

h –Heat transfer coefficient (w/m^{2}K)

Nu = 0.54_{} (19)

where hp-c = 0.54 _{} _{} (20)

where Gr – Grasshoff number and Pr – Prandtl number

For 10^{5} < Gr < 2·10^{7} [[9]]:

Gr = _{} or _{}^{ }(21)

dT=T_{pm}– T_{a} (22)

β=_{} (23)

where: μ –Dynamic viscosity (Ns/m^{2}); *v *– Kinetic
viscosity (m/s); ρ – Density (kg/m^{3}); T_{m }–Mean
temperature (K); L - characteristic length

h_{rp-c}=_{} (24)

where

ε_{c }– Emissivity
of transparency cover

ε_{p }– Emissivity of absorber surface
for long wave radiation

T_{c }– Temperature of
transparency cover (K)

h_{r,p-c }– Radiation heat
transfer coefficient between absorber plate and surrounding. (w/m^{2}K).

h_{rc-s}=_{} (25)

the top loss coefficient, U_{t} is given by

U_{t}=_{} (26)

where

R_{1}– Thermal
resistance between plate and cover (W/°C)

R_{2 }– Thermal
resistance between cover and surrounding (W/°C)

h_{w} – Wind heat
transfer coefficient (w/m^{2}K)

h_{p-c}- convective
heat transfer coefficient between absorber and transparency (w/m^{2}K)

h_{r,c – s} – Radiation heat
transfer coefficient between absorber plate and surrounding (w/m^{2}K).

However, for a single transparent glass cover that is partially transparent to infrared radiation, the net radiant energy transfer directly between the collector plate and the sky is

q_{p}–sky=_{} (27)

where

T_{p }– Absorber plate temperature
(K)

T_{sky }–Temperature of sky
(K)

_{}– Stefan-Boltzman constant (w/m^{2}K^{4})

(Assuming transmittance is independent of source temperature) (John and Anthony, 1986).

Bottom loss coefficient

_{}_{} _{} (28)

where

K_{m }–Thermal conductivity
of casing material (W/mK)

δ_{b }– Thickness of
absorber plate (m)

Side loss coefficient

_{} (29)

Thus,

_{} (30)

where _{} is assumed as average temperature drop for
L_{1} – L_{2.}

Equation (29) becomes,

U_{s} = _{} (31)

And

q_{s } (32)

where

L –Collector characteristic length (m)

L_{1}–Length of absorber
plate (m)

L_{2 }–Width of absorber
plate (m)

L_{3 }–Height of collector
(m)

T_{pm}–Mean absorber surface
temperature (K)

δ_{s }– Thickness of
side plate

** Incident Angle Modifier **

The effective transmittance product (τα)_{e}
of a solar collector can be described by

_{} (33)

The incident angle modifier, Kατ, is a correction factor which is a function of the incident angle between the direct solar beams and outward drawn normal to the plane of the collector aperture.

** Concentration Ratio **

Two definitions of concentration ratio (CR) are natural and
have been in use. To avoid confusion a subscript should be added whenever the
context does not clearly specify which definition is meant. The first
definition is strictly geometrical the ratio of aperture area, A_{a} to
receiver area, A_{r},

CR = _{} (34)

For ratio of intensity at aperture to that of receiver

CR_{flux} = _{} (35)

Since the angular radius of the sun is _{}, the
thermodynamic limit of tracking solar concentrator is about 2000 in two
dimensional line (focus) geometry, and about 40,000 in three dimensional line
(point focus) geometry that is _{}(Kreider and Kreith, 1980).

** Calculation for reflector Area**

The area of the reflector is obtained from all the quantity of heat to boil water to steam in relation to the design insulation.

Heat required boiling 1kg of water Q_{1}

_{ }Q_{1}
= M x C x ΔT (36)

= 1.0 x 4200 x (100 – 32)

= 285,600J

C –Specific heat capacity of water (Jkg^{–1}K^{–1})

Heat required vaporizing (˝) the water context of the pot

Q_{2}= M x L (37)

= 0.5 x 2.26 x 10^{6}

=1130000J

Heat loss due to free convection across the surface of the absorber:

From the top of the absorber is given by

P_{top} = _{}_{} (38)

Where a_{T} is base area of the absorber, h_{p} is
the height of the absorber and ΔT is the change in temperature.

ΔT = T_{S} – T_{a}

where

T_{s} –temperature of generating steam (K)

T_{a} –ambient temperature (K)

For turbulence at the hot bottom of the absorber

Nu = 0.14 ξ ^{0.33} (39)

Where ξ is obtain from the equation

_{} (40)

Absorber diameter da = 0.2m, h_{p} = 0.25m to be used for boiling
for this design

Rayleigh number ξ for the top is

ξ_{top} = 5.8 x 10^{7}
x d^{3}ΔT (41)

= 5.8 x 10^{7} x (0.2)^{3}
x (100 – 32)

= 3.1552 x 10^{7}

From equation (39)

N_{u }= 0.14(3.1552x10^{7})^{0.33}

= 41.764

N_{U} –Nusset Number (w)

From equation (38), heat loss at the absorber top is

P_{top }= _{}

where K = 0.027m^{-1}

=_{}

= 9.64w

Convective heat loss from the side of the pot:

The applied N_{u} for the vertical side of the pot due to
laminar condition is

N_{u}=0.56_{} (42)

The dimension of the side (r/d)

_{} (43)

_{}= 3944000

equation (42) becomes

N_{u }= _{}

= 0.56(44.564) = 24.96

heat loss from the side of the absorber

_{}_{} = 28.80w (44)

Total convective heat loss in (w)

_{} (45)

_{}

_{}

Converting heat from equations (36) and (37) to power over a period of 1 hour

_{}

Power needed for boiling outside

_{}_{}

applying the solar insolation and reflectance of the mirror for the
design, the effective solar beam I_{t }that is reflected to a focal
plane is

_{}

_{} _{}

Using a design factor of 1.5 to calculate area of the reflector needed

_{} (Duffie, 1990)

_{}

Calculation for the concentration ratio from equation (34)

_{} _{}

Where b is the reflector aperture radius

_{}

_{}_{}_{}

*Testing *

The testing of the parabolic dish solar steam generator was done in the month of January 2009 for three days. The whole set was placed in an open space in the sun from 9:00am in the morning to 5:00 pm in the evening each day for three days. Resistance thermometer placed at the focal point was used to obtain its maximum obtainable temperature. The results obtained for hourly reading of 8hours everyday are tabulated in tables 1-3.

**Results **

*Result on 27 ^{th} January, 2009*

Table 1. Variation of Temperature at Focus Point with Time on the First Day

Time |
Ambient Temperature (°C) |
Focal Point Temperature (°C) |

9am |
29 |
89 |

10am |
29 |
138 |

11am |
30 |
172 |

12pm |
30 |
208 |

1pm |
30 |
224 |

2pm |
33 |
228 |

3pm |
32 |
200 |

4pm |
31 |
183 |

5pm |
30 |
140 |

** **

** **

*Result on 28 ^{th} January, 2009*

Table 2. Variation of Temperature at Focal Point with Time on the Second Day

Time |
Ambient Temperature (°C) |
Focal Point Temperature (°C) |

9am |
29 |
94 |

10am |
29 |
120 |

11am |
30 |
155 |

12pm |
30 |
193 |

1pm |
30 |
217 |

2pm |
33 |
220 |

3pm |
32 |
198 |

4pm |
31 |
169 |

5pm |
30 |
125 |

** **

*Result on 29 ^{th} January, 2009*

Table 3: Variation of Temperature at Focal Point with Time on the Third Day

Time |
Ambient Temperature (°C) |
Focal Point Temperature (°C) |

9am |
30 |
98 |

10am |
30 |
102 |

11am |
30 |
132 |

12pm |
31 |
178 |

1pm |
31 |
210 |

2pm |
31 |
196 |

3pm |
32 |
180 |

4pm |
31 |
141 |

5pm |
30 |
102 |

** **

** **

**Discussion of Results**

** **

Based on the results obtained during the test of the parabolic dish solar steam generator, temperature above 200°C was recorded against the ambient temperature. The temperature at the focal point varied with time but however, a peak value was always reached. Variation of temperature with time was due to movement and position of the sun, the angle of inclination of the parabolic dish and the atmospheric condition. When 1kg of water was poured inside absorber boiling took place in less than 10 minutes.

**Conclusions **

** **

In conclusions, the need for the construction of a parabolic dish solar steam generator arose as an alternative to solve the thermal energy needs of the populace. This will also reduce the total dependency on fossil fuels and other non-renewable and exhaustible energy source which have be known to be depleted with ages to come as they are being used up. As such, deforestation and other environmental populations are reduced to a minimum.

The need to utilize the free abundant natural resource of energy which is freely in abundance requires no recurrent expenses as other source of energy. Thus, it is regarded as the cheapest source of fuel for man.

Based on the result obtained in tables 1-3 during the test, temperature above 200°C was obtained at base of the absorber. Water boiled faster using the generator than when using ordinary charcoal or kerosene stove. The parabolic dish solar steam generator is very efficient heating equipment.

** **

** **

**References**

** **

** **

2. Garg.H.P. Advances in Solar Energy Technology, Vol. 3 chapter 1, D. Reidel Publishing Co., Holland, 1987.

3. Ezeilo.C.C.O.”Sun Tables and Charts for Nigerian Institutes” Presented to National Solar Energy Forum. The Federal Polytechnic, Bida, Niger state, April 27-30, 1983.

4. El-Wakil M.M., Power Plant Technology International Edition, McGraw-Hill Book Company, New York, 1984.

5. Ojo O., Fundamentals of physics and
dynamic climatology 1^{st} edition SEDEC publishers, Lagos, 2001.