 # Lecture 7 – Axial flow turbines

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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

Axial flow turbines Working fluid is accelerated by the stator and decelerated by the rotor Boundary layer growth and separation does not limit stage loading as in axial compressor Pictured here are the aerodynamic pressure contours from a computational simulation of a 21 blade row high performance compressor. The compressor is part of General Electric's GE90 turbofan engine that powers the new Boeing 777 airplane. The Average Passage NASA (APNASA) code was utilized for the 3- dimensional Navier-Stokes flow simulation. The computed pressure contours enable engineers to understand compressor performance before building and testing expensive hardware. Expansion occurs in stator and in relative frame of rotor

Elementary theory Energy equation for control volumes (again):
Adiabatic expansion process (work extracted from system - sign convention for added work = +w) Rotor => -w = cp(T03-T02) <=> w = cp(T02-T03) Stator => 0 = cp(T02-T01) => T02= T01

How is the temperature drop related to the blade angles ?
We study change of angular momentum at mid of blade (as approximation)

Governing equations and assumptions
Relative and absolute refererence frames are related by: We only study designs where: Ca2=Ca3 C1=C3 You should know how to extend the equations!!! We repeat the derivation of theoretical work used for radial and axial compressors:

Principle of angular momentum
Stage work output w: Ca constant:

The degree of reaction increases as α3 is increased. Why!

Energy equation Combine derived equations => Energy equation:
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.

Dimensionless parameters
Blade loading coefficient, temperature drop coefficient: Degree of reaction: Exercise: show that this expression is equal to => when C3= C1

 can be related to the blade angles!
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:

 can be related to the blade angles!
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.

Dimensionless parameters
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

Dimensionless parameters
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

Two simple homework exercises
Exercise: show that the velocity triangles become symmetric for  = 0.5. Hint combine 7.1 and 7.9 Exercise: use the “current aircraft practice” rules to derive bounds for what would be considered conventional aircraft turbine designs. What will be the range for 3? Assume  = 0.5.

Turbine loss coefficients:
Nozzle (stator) loss coefficients: Nozzle (rotor) loss coefficients:

Problem 7.1

3D design - vortex theory
U varies with radius Cw velocity component at stator exit => static pressure increases with radius => higher C2 velocity at root Twist blades to take changing gas angles into account Vortex blading 3D optimized blading (design beyond free vortex design)

Keep blade angles from root to tip (unless rt/rr high) Cut cost Rankine cycle relatively insensitive to component losses

Choice of blade profile, pitch and chord
We want to find a blade that will minimize loss and perform the required deflection Losses are frequently separated in terms:

Choice of blade profile, pitch and chord
As for compressors - profile families are used for thickness distributions. For instance: T6, C7 (British types)

Choice of blade profile, pitch and chord
Velocity triangles determine gas angles not blade angles. arccos(o/s) should approximate outflow air angle: Cascade testing shows a rather large range of incidence angles for which both secondary and profile losses are relatively insensitive

Choice of blade profile, pitch and chord
Selection of pitch chord: Blade loss must be minimized (the greater the required deflection the smaller is the optimum s/c - with respect to λProfile loss) Aspect ratio h/c. Not critical. Too low value => secondary flow and tip clearence effects in large proportion. Too high => vibration problems likely. 3-4 typical. h/c < 1 too low. Effect on root fixing Pitch must not be too small to allow safe fixing to turbine disc rim