This is a tough and dull paragraph. But also the basis of an Imbert gas generator. Therefore an important paragraph. I will not explain how the formulas have come about. For that you need to study the literature. This is only a summary.
We start with the most important formula, which is nevertheless difficult to find in literature: the calculation of the quantity of required gas. The dimensions of all important components of the whole gasifier unit are based on this. This is it:
G = V x n x 0.5 x 0.48 x 0.72 [l/s]
G is the needed quantity of gas in liters per second
V is the engine displacement in liters
n is the rpm
0.5 is the four stroke factor
0.48 is the mixture composition (1: 1.1)
0.72 is the filling degree of the engine (assumption)
60 for the conversion to seconds
Example: G = 2.32 x 2,750 x 0.5 x 0.48 x 0.72 = 18.4 [liter cold gas per second]
This quantity of gas is sucked by the engine every second. These are the numbers which I have used for my Volvo: 2,320 cc and 2,750 rpm, a little under 3,000. It is better to dimension the generator too small than too large. A generator which generally is used under its nominal capacity, can produce tar. Certainly when slow driving in town or on long idling.
Next calculation is the determination of the diameter of the restriction. We assume thereby a superficial gas speed through the restriction of 2.5 [m/s]. I foresee now glaring looks, but you will encounter this number in the literature also, study therefore!
d = square root from (4/pi x G/Vi)
d is the restriction diameter
pi is 3.142
G is quantity of cold gas per second
Vi is the superficial velocity being: 2.5 [m/s] = 25 [dm/s] for an Imbert
Example: d = square root from ((4/3,142) x (18,4/25)) = 0.97 [dm] = 97 [mm]
This is an important dimension, because it determines all other dimensions of the hearth. These measures can be calculated, but I will not bother you with that. They depend entirely on which type of Imbert you want to build. For this reason I refer to the tables in the literature. With the restriction diameter you can read the remaining dimensions in the tables.
For a simple Imbert with V-hearth use the tables in the “Handbook or biomass downdraft gasifier systems”. Tables for gasifiers with effective primary air pre-heating can be found in FAO 72. And as the attentive student notices, the literature is not always uniform. That is not a big problem, certainly not if you ensure that nozzles and restriction are interchangeable. Nozzles that are adjustable in length and a height adjustable restriction by means of shims.
Tubing diameters depend on the gas quantity, but also on the temperature. In most tubing, we want a laminar flow (< 5 m/s). In some tubing we need a turbulent flow(> 6 m/s). Unfortunately turbulence raises the pressure drop in the system and reduces the filling degree and with that, engine power output.
To determine the tubing diameter, we first calculate the gas flow in liters per second. “We had that number already?!” you will notice; indeed, the quantity of cold gas. But since the gas is hot, an increase of volume occurs. We recalculate this flow using a conversion in Kelvin. 0 degrees Celsius are 273 Kelvin. 350 degrees Celsius are 273 + 350 = 623 Kelvin. 18.4 [l/s] at 350 degrees becomes:
(623/273) x 18.4 = 42.0 [l/s]
See, that asks for a wider tube! Those 350 degrees is the temperature of the gas which comes out of the generator of the Volvo. Because the gas has internally exchanged energy with primary air by effective double heat exchangers, this temperature is rather low. Without heat exchangers, the temperature would be 600 to 700 degrees. So pay attention, which type of Imbert you want to use.
In the tube after the generator, we want a turbulent gas stream, to avoid settling of dust particles in the tube. Take 10 [m/s] =100 [dm/s]
Diameter pipe D = gas flow/gas speed = 42.0/100 = 0.42 [dm2] = 4,200 [mm2]
Pipe diameter d = square root ((4 x 4,200) /pi) = 73 [mm]
76.1 is x 1.5 [mm] or 3” is existing tube and fits very well.
After the filtering we want a laminar flow to avoid much resistance and power loss. So, up to 5 [m/s]. In practice you use the same size tubing in the whole system; in my situation, 76.1 x 1.5 mm. Downstream the gas decreases in temperature, shrinks and automatically a lower speed is obtained. Better a too wide than a too tight tube.
In the “Handbook or biomass downdraft gasifier systems” a chapter has been dedicated to the cyclone. Also the website of Bill Pentz is very instructive. Take into account that a slim cyclone removes also a large part of the fine dust. A too generous sized cyclone has less resistance, but only removes the coarse particles. Take an entrance speed in the cyclone of 25 to 30 meters per second, taking the temperature of the gas into account. Calculation of the entrance diameter is the same as before on tubing diameters. The remaining dimensions can be calculated or derived from the above mentioned documents.
For the glass-fibre filter surface area is a formula:
Af = 1.5 x V [m2]
Af is filter surface area in [m2]
V engine displacement in [litre]
For the Volvo:
Af = 1.5 x 2.32 = 3.5 [m2]
I must admit that it has become less: 2.8 [m2].
Also for the total cooling area there is a directive. With “total cooling area” I mean all surfaces which are in contact with the open air, therefore also the tubing. The filter barrel has been insulated, therefore that does not count. Of course, the cooler itself has the most surface area. The directive is:
Ak = V x n x 1.25 [m2]
Ak is the cooling area in [m2]
V engine displacement in [litres]
n is the rpm divided by thousand
For the Volvo:
Ak = 2.32 x 2.75 x 1.25 = 8.0 [m2]
In practice it is difficult to realise. For this reason I have chosen for a cyclone, an apparatus which not only filters, but because of the very high gas speeds and the high gas temperatures, cools extraordinarily well with a relatively small surface. The gas tube, coming from the filter barrel, is finned, so that the out coming gases of approximately 100 degrees Centigrade are cooled down to 40 degrees over a length of only 70 cm, so it is under the dew point. Water condenses in the tube before it heads under the trunk towards the engine. An additional advantage is that possible mineral deposits are rinsed to the cooler.
The cooler itself can best be made of thin walled stainless steel tubes with a diameter of 15 to 25 mm. Gas always goes up in the cooler. Or up by two third of the tubes and down by a third. Up, because of the earlier-mentioned flush effect. The condensate rinses down along the tube wall, also cleaning the dry part. The reason for two third up and one third down is the warmer, expanded gas going in. While being cooled, the volume shrinks and less tubes are needed for the same gas speed. A slight turbulent flow is best for heat exchanging.