The choice of a parabolic dish

Écrit par Rohan NOWAK et Waldan GIRARD le . Publié dans How to distill using solar energy ?

We realized we would be obliged to use a parabolic dish instead of a solar oven when we saw how fast the artisan we met got the water to boil. Our predecessors had tried to adapt their solar oven for distilling, but found that the heat transferred to the water wasn’t sufficient to bring the water to a rapid boil. On top of that, the time and cost of construction of such a system were too great. We decided to orient out research towards the solar dish and recycling satellite dishes.

a)Average power provided by a gas burner

We evaluated the heat flow transferred to water by a gas burner to compare it to that from a solar dish, the goal being to choose the size of the satellite dishes we would recycle, since their diameter varies between 50cm and 2m.

 

Experiment: Measure the heat flow provided by a traditional gas burner

Protocol:

-              Fill pressure cooker up with 6L of room temperature water

-              Heat using gas burner on full power

-              Time how long the water takes to boil

 

Observations: The water boils in 17min

That leads to:  

With cwater = 4.18 J.g-1.K-1, the calorific value of water per unit of mass

That’s why  

Conclusion: This heat flow is high, compared to the solar constant or solar flux above the earth’s atmosphere which is 1361 W.m-2. The solar flux on the ground will necessarily be lower so even with an efficiency of 100%, it seems that a dish with the biggest diameter as possible is necessary.

b) Power provided by the solar dish

The purchased solar dish we have in Tours and in Marrakech has a diameter of 1.50m. The heat flow of a gas burner doesn’t vary very much between different trials whereas the heat flow from a solar dish varies according to the sunshine. Therefore we tried to determine the efficiency of our device for a certain amount of sunshine, assuming the efficiency of heat transfer is independent of the amount of sunlight it receives.

 Protocol:

-          Place the same pressure cooker containing 6.0L of water on the central support of the solar dish and close it while measuring the temperature of the water

-          Orient the dish so as it is facing the sun on the horizontal axis and adjust it vertically so as the patch of light where the sun rays converge is under the pressure cooker

-          Measure the angle of incidence of the sun rays and the inclination of the dish with respect to the horizontal axis

-          Time how long the water takes to boil

 

Measurements taken on 21 Jan 2016 at 11:15:

Dt = 52 min / qi= 20°C / qf = 100°C

Angle of incidence of the sun rays arays=33° and inclination of the dish adish=44°

 

Conclusion:

The power provided by a solar dish in January is considerably lower than that from a gas burner. However, January isn’t the period during which the Moroccans distill their floral waters; they distill during flowering time, which is from April to June. So as to estimate how long the water would take to boil, or how much heat is transferred to the water, in that period of the year we evaluated the efficiency of our device under the experimental conditions in January.

Thanks to an internet site, we were able to get the maximum solar flux  at ground level according to the day of the year. On the 21 Jan at 12:00 the solar flux was of 681 W/m² and at its highest the sun was 38°.

 

It’s important to note that the sun rays don’t hit the dish parallel to its optical axis, but with a 13° inclination (b=90-adish-arays).

 

So the total solar surface recuperated is decreased: S’=Scosb=0,97S. We only lose 3% of the total surface, and that allowed us to make our device more stable, as will be explained later.

 

 

 

 

 

Therefore the solar power recuperated by the dish is:

 

A.N.:  = 1172 W = 1.17 kW.

 

Previously, we discovered that the water recuperated 0.64 kW. Therefore, the efficiency of our device is 55%. What happened to the missing 0.53 kW?

First hypothesis: The first hypothesis we made was about the mirror paper: it absorbs a certain percentage of the light received. This coefficient of absorption probably also depends on the wavelength of the light that is used.

 Experiment

-          Measure the incoming power of an HE-Ne laser (633 nm) 

-          Measure the power reflected by the mirror paper for different angles

 

Conclusion: The coefficient of reflection (R) is 0.90 for a 10° angle

 

Second hypothesis: The pressure cooker doesn’t absorb all the light received, even when painted black.

 

Experiment: Using a radiometer, we measured its albedo, which means the percentage of light sent back by light scattering.

 

Conclusion: 9% (±1%) of the light is scattered, so the pressure cooker only absorbs (91±1)% of the light received, its coefficient of absorption is a= 0,91.

 

Therefore, we have explained that regardless of the incident flow on the dish, the power absorbed by the pressure cooker is Pabs = aRPsolar = 0.82 Psolar. That explains a loss of 18% but not of 49%.

 

Third hypothesis: The pressure cooker, when heated, will lose energy by radiation, and also by convection and conduction, because it isn’t at the same temperature as its environment.

The diagram below sums up all the heat transfers that take place:

 


Knowing these different losses, we wanted to establish a model enabling us to evaluate the time that is required to bring a certain volume of water to a boil with a given amount of sunshine. We won’t take into account the losses by conduction as the contact between the stand and the pressure cooker is small (even if they might not be negligible).

 

- Loss of heat due to thermal radiation 

- ε is the emissivity of the stainless steel covered in black. With the hypothesis of the black body, ε=α=0.91 

- σ = 5.6696.10-8 is the Boltzmann constant

- Tcooker is the temperature at the surface of the metal (in K)

- s is the surface area for heat exchange between the pressure cooker and the air (in m²)

It is important to note that these losses depend on the temperature, which varies.

 

- Loss of heat due to natural convection

- s is the surface area for heat exchange between the pressure cooker and the air (in m²)

- Tair is the temperature of the surrounding air (in K)

- h is the heat exchange coefficient of the air. It depends on the temperature, the viscosity, the conductivity, the diffusivity, the density of the air… etc. In our case, we took the maximal value of h (10 W/m².K) that we found on internet so that we don’t minimize the losses.

Once again, these losses depend on the temperature of the pressure cooker, which varies.

 

If we only consider these losses, the conservation of energy can be expressed as follows:

Pwater/cocotte= PABS – (PRAD + PCONV)

 

This leads to a nonlinear first order differential equation. We solved it using the Euler method.

Knowing the initial temperature of the water, bit by bit we can determine the time taken to bring the water to a boil using a small increment operator

 

Table 2: Theoretical estimation of the time to bring water to a boil

 

t (in s)

t (in min)

T ( in K)

 

 

 

0

0.0

293

 

a

0.91

20

0.3

293.7

 

R

0.9

40

0.7

294.4

 

q (in °)

13

60

1.0

295.1

 

D (in m)

1.5

80

1.3

295.8

 

d (in m)

0.25

100

1.7

296.5

 

H (in m)

0.175

120

2.0

297.1

 

S (in m²)

1.76625

140

2.3

297.8

 

s' (in m²)

0.2355

160

2.7

298.5

 

Tout (in K)

293

180

3.0

299.2

 

dt (in s)

20

200

3.3

299.9

 

m (in g)

6000

220

3.7

300.5

 

h (W/m².K)

10

240

4.0

301.2

 

F (W/m²)

681

260

4.3

301.9

 

Pabs (in W)

960

280

4.7

302.5

 

mAl (in g)

2500

2840

47.3

372.4

 

caluminium  (J.g-1.K-1)

0.897

2860

47.7

372.8

 

 

 

2880

48.0

373.3

 

 

 

Using this technique and our hypotheses, we determined that the water should have boiled in 48 min and not 52min, which is a difference of about 8%. When we started the experiment at 11:00am the solar flux wasn’t at its maximum since the height of the sun was 33° and not 38°, which was the theoretical maximum height for that day. We didn’t take into account the losses by conduction or by forced convection (wind)… Therefore there is room for improvement of our model.

 

Thus for our subsequent trips to Morocco we had available two different methods for estimating by the time it would take to bring 20°C water to a boil:

-          Either by assuming that the efficiency will always be the same (50%). Since the instantaneous losses are proportional to the temperature of the water or to its temperature to the power of 4 and not to the solar flux, the efficiency will increase with increasing sunshine.

-          Or by using the model above.

-           

Table 3: Theoretical estimation of the power of the parabolic dish and heating times

 

 

End of March

Beginning of May

Solar flux (W/m²)

990

1080

Solar power (kW)

1,72

1,87

Average heat transferred to the water  (kW)

0.95

1.03 (50% compared to a gas burner)

Heating time (min) for 2.5L* for an efficiency of 55%

9

8

Heating time for 1.5L* with the theoretical model

 

8

7

Distillation time for 0.75L* (min)

29

27

: Quantities used for our distillations.

 

Calculation of the time taken to heat water from 20 to 100°C:   

Calculation of the time of distillation:  with Lvap,  = 2257 J/g   

 

In conclusion, we can note that in the season during which the solar dish is destined to be used, it only provides 50% of the power that a gas burner provides. Nevertheless, our system showed potential because it uses a renewable source of energy that is free and clean of greenhouse gases.