Lecture 7 – Axial flow turbines Discussion on design task 1 Elementary axial turbine theory Velocity triangles Degree of reaction Blade loading coefficient, flow coefficient Problem 7.1 Some turbine design aspects Choice of blade profile, pitch and chord
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Stage work output w:
We have a relation between temperature drop and blade angles!!! :
Exercise: derive the correct expression when 3 is small enough to allow 3 to be pointing in the direction of rotation.
Blade loading coefficient, temperature drop coefficient:
Degree of reaction:
Exercise: show that this expression is equal to =>
when C3= C1
C3 = C1 =>
Relative to the rotor the flow does no work (in the relative frame the blade is fixed). Thus T0,relative is constant =>
Exercise: Verify this by using the definition of the relative total temperature:
Plugging in results in definition of =>
The parameter quantifies relative amount of ”expansion” in rotor. Thus, equation 7.7 relates blade angles to the relative amount of expansion. Aircraft turbine designs are typically 50% degree of reaction designs.
Finally, the flow coefficient:
Current aircraft practice (according to C.R.S):
Aircraft practice => relatively high values on flow and stage loading coefficients limit efficiencies
Using the flow coefficient in 7.6 and 7.7 we obtain:
The above equations and 7.1 can be used to obtain the gas and blade angles as a function of the dimensionless parameters
Nozzle (stator) loss coefficients:
Nozzle (rotor) loss coefficients:
3D optimized blading (design beyond free vortex design)