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This method makes use of the behavior of a single airfoil in an infinite room, i.e. the airfoil is not influenced by other airfoils. This is true if the solidity l/t is smaller than one.
The design described here is based on the relation between aerodynamic or hydrodynamic profile data and design parameter cast into the Euler equation.
The circumferential force Fu based on the profile properties reads as:
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whereas if it is derived from the force balance it reads as:
.
By equalizing both force descriptions one gets the following equation, which co-relates the profile properties lift coefficient cL and solidity l/t with the design point data (Y, n, m):
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The meaning of the variables is given in the following table:
YImp |
specific work of the impeller |
l/t |
solidity (chord length/pitch) |
b |
width of the profile |
cu |
absolute circumferential velocity component |
cm |
absolute meridional velocity component |
β∞ |
average rel. flow angle |
w∞ |
average rel. velocity |
cL |
lift coefficient |
α |
angle of attack |
δ |
angle between resulting force and lift force |