Lieblein method

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Lieblein method

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This is method shall be used when the pressure difference to be generated is comparably high and demands for a high solidity, i.e. a high number of blades. In this case the aerodynamic behavior of each individual blade cannot be determined by investigations on an single blade but is dependent on the whole blade cascade.

Lieblein carried out systematic wind tunnel investigations on the swirl change properties of the profiles of the NACA 65 series. The meaning of the used entities is given in the following table

γ

stagger angle

l/t

solidity (chord length/pitch)

β

Angle of relative flow

βB

Blade angle (of the equivalent circular skeleton line)

φ

camber angle

u

circumferential velocity

w

Relative velocity

i

Incidence angle: i = βB1 - β1

δ

Deviation angle: δ = βB1 - β2

Three limitations apply for this approach:

The maximum relative thickness must be d/l < 0.1.

The Reynolds-Number must be Rel > 2·105.

The solidity l/t must be on all spans: 0.4 <= l/t <= 2.0.

Lieblein derived design diagrams for the following parameter

Incidence i

Deviation δ

The basic approach is as follows: with the specified solidity the skeleton length is calculated. With the relative flow angle β1 (from cu-specification) and the solidity l/t the incidence is determined using Lieblein's design diagrams. The same is done with respect to the deviation. Now the the blade angles at leading and trailing edge are known. Note: The blade angles are applied to the equivalent circular skeleton line with the radius:

.

From the blade angles the stagger angle can be determined by:

.

The dimensionless skeleton line used for the generation of the NACA 65 series profile is described by the following equation:

,

with cfl the theoretical lift coefficient:

.

Since this skeleton line is perpendicular at the very beginning (LE) and end (TE) to the chord line, blade angles at these locations derived be tangent angles are not reasonable. This is the reason for applying the equivalent circular skeleton line for the determination of βB1 and βB2.