Stage Vector Diagram

Question 1

What are 3 design conditions for the velocity vector diagram?

Answer 1

• incoming flow tangential to the camber line
  in the relative coordinate system
• relative system rotates with u=f(r) in radial direction
• outcoming flow tangential to the camber line in the relative coordinate system

Question 1

Which coordinate systems need to be considered?

Answer 1

• Fixed coordinate system for absolute flow
• Rotating coordinate system for relative flow

Question 2

What is the goal of having a meanline?

Answer 2

The goal is to have a general coordinate system which can be used for all kinds of flow channel geometries
- the m-coordinate represents the main flow direction of the local mass flow
- the u-coordinate represents the rotational movement or the swirl of the flow
- the n-coordinate only describes secondary and tertiary flow phenomena

Question 3

Why do we need a stator in a turbine stage?

Answer 3

• Flow acceleration results in a
  pressure drop due to nozzle principle
  gz+∫dp/ρ(p)+c^2/2 = const
• Increase of swirl to increase potential
  work extraction in the rotor stage
• Preparation of the inlet flow for the
  rotor stage

Question 4

Why do we need a stator in a compressor stage?

Answer 4

• Flow deceleration results in a pressure rise
  due to diffusor principle
  gz+∫dp/ρ(p)+c^2/2 = const
• Reduction of angular flow momentum to
  reduce loses due to shear movement in
  boundary layers
• Preparation of the inlet flow for the next stage

Question 5

How are forces on the airfoil generated?

Answer 5

• Pressure and shear forces result from the flow around the airfoil
• These surface forces result in a resultant force which can be
  divided in axis parallel and rotational parallel forces or camber normal and camber parallel forces
• Forces from nS airfoils result in a
  torque on the driveshaft

Question 6

What is the relation between twist and distance to propeller core?

Answer 6

The closer to the propeller core, the more twisted the rotor blades are

Question 7

Why is an airfoil generally twisted?

Answer 7

• Rotational speed increases with increasing radius: u = ω ∗ r
• Relative incoming flow less steep
  towards tip
• Camber line is twisted towards
  machine axis closer to the hub
• Magnitude of the relative speed
  increases towards the tip of the airfoil

Question 8

What are the differences between compressor and turbine stage?

Answer 8

• Stator after rotor (C) vs. Rotor after stator (T)
• Indexing 1,2,3 (C) vs. Indexing 0,1,2 (T)
• Pressure side is leading (C) vs. Suction side is leading (T)
• Resulting force vector in negative Φ-direction (C) vs. Resulting force vector in positive Φ-direction (T)