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The direction of the air flows gives us DownDraft (DD), and UpDraft (UD) and CrossDraft (CD). In all three the fire is at the bottom. There is also a "Top-Lit UpDraft" (TLUD) gasifier. AVUD is a type of traditional UpDraft, but it is "Another Variation" specific for micro-gasification.
The purpose and the cleanliness of the gases give us gasifiers for heat only (with burning the tars as in TLUDs and AVUDs) and for power as in the operation of internal combustion (IC) engines that can spin electricity generators or move vehicles or turn pumps (with gases either created without tars or with the tars removed as in large DD gasifiers). CHP (Combined Heat and Power) means that after the electro-mechanical power is made, the remaining heat is put to some use.
Sizes of gasifiers are in relative terms with rather overlapping categories. Confusion can occur because "energy" can be electrical (kWe), mechanical (HP), or thermal (kWth or BTU), or megaJoules, etc... "Power" is energy per specified unit of time. Energy should be expressed as "per hour" to show the power concentration, and kilowatts of electrical output is really kwe-hr.