Session 3. Solar agricultural dryer design procedures and rules of thumb
Step 1. (5 minutes)
Step 2. (1 hour)
Step 3. (20 minutes)
Step 4. (20 minutes)
Step 5. (15 minutes)
TECHNICAL DESIGN INFORMATION FOR SOLAR DRYERS
A. How to find Percent moisture content (wet basis):
M = percent moisture
10 kg of fresh fruit which weigh 6 kg when dry.
w = 10 kg
B. Energy Balance for Drying
The Energy Balance is an equation which expresses the following idea mathematically:
The energy available from the quantity and temperature of air going through the dryer should be equal to the energy needed to evaporate the amount of water to be removed from the crop.
The formula is: macp(Ti-Tf)=mwL
ma = mass (or weigh) of drying air
C. How to figure how much water (mw) must be removed from your crop:
Mw= mass (weight of water to be removed
wi = initial mass (weight) of crop to be dried
Mi & Mf = initial and desired final % moisture of the crop
How much water must be removed from 100 kg of groundnuts in reducing from initial moisture of 26% to final moisture of 14%?
D. Two Constants:
Latent heat of vaporization of water (L):
Amount of energy needed to vaporize (evaporate) each unit (gram, pound, etc.) of water from the crop.
For free water (in open pan), it's about 2,400 KJ* /kg For water from crops, it's more
and varies a bit with temperature
* KJ = kilo joules
Specific heat capacity of air (Cp):
Varies a bit with humidity and temperature.
E. How to figure volume (V) of air from weight:
Air is usually quantified as volume at atmospheric pressure (P) and temperature (t).
The formula: PV = maRt
P = Pressure (in kilopascals - kPa)
The Rule of Thumb is:
1 kg air at 35°C and normal pressure = 0.9 m³ or use psychrometric chart
* * *
Useful Solar Dryer Formulae:
THE PSYCHROMETRIC CHART
The upper curve of the chart is for saturated air and is label led wet-bulb and dewpoint temperature. (The word "dewpoint" arose from the observation that dew forms on grass when the grass cools, by radiaiton to the sky, to a temperature equal to or less than the wet-bulb temperature of the air above it.)
The other curves on the psychrometric chart that are similar in shape to the wet-bulb line are lines of constant relative humidity (in X). By definition, relative humidity is a ratio: the partial pressure of the water vapor at a given temperature - the saturation pressure of the water vapor at the same temperature. The scale at the left side of the chart gives the pressures.
The straight lines sloping gently downward to the right are lines of constant wet-bulb temperatures. The intersection of a dry-bulb and a wet-bulb line gives the state of the air for a given moisture content and relative humidity. The lines of constant wet-bulb temperature also give values of constant enthalpy (total heat content), measured in heat units per unit weight of dry air.
Other lines sloping more steeply to the right give the specific volume of dry air, the volume occupied by one kilogram of dry air under the indicated conditions.
In examining a psychrometric chart, note that:
* Processes in which air is heated or cooled without change in moisture content give horizontal lines. Heating along such lines will decrease the relative humidity, while cooling will increase it.
* The wet-bulb temperature lines, sloping downward to the right, are lines of adiabatic cooling (where there is no change in heat content). These lines typify drying processes in which air is passed over the surface of wet material and is cooled by evaporation of water from the material. Lines of constant total heat parallel these wet-bulb tines.
* Although no processes follow the lines giving the specific volume of dry air, these lines show that at any given dry-bulb temperature, the density of air decreases as either the temperature or the relative humidity rises.
DESIGN RULES OF THUMB FOR SOLAR DRYERS
A. Assorted considerations for solar agricultural dryer designs:
* 1 kg of air at 35°C @ 0.9 m³
* For grain drying, make beds no more than l5 cm thick, giving a maximum loading rate of 9Okg/M² (requires stirring).
* Tropical-monsoon insolation of 5-25 MJ* /M² per day. Use 15 MJ/M² per day for estimate (approximately 14,000 BTUs or 3,500 kcal).
* Typical conservative day long efficiency of stationary collection: -25%
(That is, the energy delivered as heated air to the drying crop is 25% of the energy in the sunlight striking a horizontal surface of equal area to the dryer's collector.)
* MJ = Mega Joule or 1 million joules.
B. Collector size:
Making the collector equal to three times the tray area gives a high drying rate dryer.
C. Dryer capacity:
In the tropics, figure on about 180 M of air to remove 1 kg of water.
Figure about 3/4 M² of collector area to remove 1 kg of water per day (i.e., dry 1.5 kg fresh fruits or 5.25 kg grain per day).
D. Dryer temperature:
1. Depends upon insolation, collection area and vent size.
2. Is very sensitive to vent size (cutting vent size by one half increases delta t by about three times (up to some limit).
3. Doubling area of collector increases it by about one half.
4. Raising temperature from 20 to 35°C can triple the water capacity of the air.
E. Dryer air flow rate:
1. Doubling vent area doubles the air flow rate (but drops delta by about 3/4).
F. Required moisture contents of crops/approximate values:
G. Figuring how much air you need for drying:
There are two methods: using the psychrometric chart or using the energy balance equation.
Method #1. Using the Psychrometric Chart
You want to dry 1 kg. of rice from initial moisture of 22X to final moisture of 14%. Assume ambient air temperature is 30°C at 80X humidity and you pre-heat the air to 45 for drying.
The path A-B represents the heating process. Note that in moving the temperature to 8, the humidity drops to 35%.
The path B-C represents the change in the air as it passes through the dryer, cooling and picking up moisture from the rice. Initially (because rice is quite wet), air gets to C. At the end of the process, it only reaches D. As the rice gets dryer, you find points C & D from the table* of equiibrium moisture contents (it's similar for all crops). In this case, the air's humidity ratio rose by about 0.005. (That's how much water the air carried away.)
* Moisture level at which rice will stabilize if exposed to the specified temperatures and humidity conditions.
The amount of water to be extracted from 1 kg of rice in this case can be figured using the equation found in Part C of Attachment A.
From the definition of humidity ratio (weight of water vapor in the air - the weight of dry gases in the same air), it follows that the mass of air needed (ma) in this case, where humidity ratio rose by 0.005, is:
We can transform this weight to volume with the equation from Part E of Attachment A:
PV = ma RT
P = 101.3 (normal sea level)
Method #2. Using Energy Balance Equation (See Example)
We have calculated above that the amount of water to be removed (Mw) = 0.093 kg.
We know the two constants:
1. Latent heat of vaporization (L) = 2,800 KJ/kg
Assuming initial temperature (Ti) = 45°C and final temperature is a mean value of 32°C, we can substitute in the energy balance equation to get ma:
We can transfer that to M³ using our rule of thumb (1 kg @ 0.9 M³) or PV = MaRT and we get about 17.3 M³ of air.
You will notice that this result is not identical to the 16.5 M³ calculated above using the psychrometric chart. However, the result is close enough for design work.
H. To figure air flow rate:
Say we want to dry 1,000 kg of rice. We've figured it takes 17 M³/kg, so that's 17,000 M total. If we want this to flow in 30 hours (say, four 7-1/2 hour solar days), that's:
17,000/30 or 566-2/3 M³/hr. or 9.44 M³/min.
I. To figure area of solar collector needed:
You must determine:
1. Mass of water to be evaporated (Mw)
For 1,000 kgs. of rice, we calculated that we must remove 93 kg. of water. We know L = 2,800 KJ/kg. So the heat required is 93 x 2,800 = 260,400 KJ (260.4 MJ)*
* MJ = Megajoule (1,000,000 joules or 1,000 kilojoules)
This heat must come from the available solar energy.
Tropical monsoon insolation is highly variable, depending upon cloudiness: from 5 to 25 MJ/M² per day.
Use 15 MJ/M² per day as a conservative average in absence of data.
Assuming 15 MJ/M² per day and 25% efficiency of the collector yields 3.75 MJ/M² per day or 15 MJ/M² in four days.
So, the total area of collector required is:
J. How to figure vent area. using two methods:
If you have the required flow rate figured (See Section H.), use this formula:
Assume air flow calculations showed a flow rate of 9.4 M³/min required to dry our 1,000 kg or rice in four days (review Section H.). Then checking data sources, assume that 'he desired temperature of the drying rice is 62 C and that the ambient temperature is 30°C. So delta temperature (change in air temperature in the dryer) is 62° - 30° = 32°. Assume a height Of 4m for the dryer. Substitute in the equation:
If you have an aperture (collector) area and some idea of solar intensity, use this formula:
Assume that a maximum of 15% of the total daily radiation falls in the hottest mid-day hour. This is 0.15 x 25 MJ = 3.75 MJ/hr M² = 896 Kcal/ hr. m² *
* 1 MJ/m² = 239 Kcal/m² = 88 BTu/m²
Using the aperture area found in Section I, it's 17.5 m². Let Δt = 32ºC and h = 4M as above.
Always assume a high insolation rate so your vents will be large enough to prevent over-heating, even under the most intense sun conditions. You can always close the vent to some degree, if necessary.
Then, substituting the formula:
Note: This is the maximum vent area you would ever need. With a lower insolation rate of 15 MJ/day, 2 the vent area could be cut down to about 2,600 CM².
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