1. Lecture 8 – Axial turbines 2 + radial compressors 2
Turbine stress considerations
The cooled turbine
Simplified 3D axisymmetric inviscid flow
Free vortex design method
Radial compressors 2
Diffuser and vaneless space
Compressor maps

2. Choice of blade profile, pitch and chord
Annulus area
Rotor blade stresses:
centrifugal stress:
gas bending stresses reduce as cube of chord:
centrifugal bending stress
Source for fatigue failure
Combination steady/ fluctuating
A complete stress analysis would require thermal stresses to be computed.
Modern turbines can actually withstand values close to the double.
Steady stress/Creep

3. The cooled turbine Cooled turbine
application of coolant to the nozzle and rotor blades (disc and blade roots have always been cooled). This may reduce blade temperatures with K.
blades are either:
cast - conventional, directionally solidified, single crystal blade
forged

4. The cooled turbine Typical cooling distribution for stage:
Distribution required for operation at 1500 K

5. The cooled turbine - methods
Air cooling is divided into the following methods
external cooling
Film cooling
Transpiration cooling
internal cooling
Techniques to cool
rotor blade

6. The cooled turbine - methods
Stator cooling
Jet impingement cools the hot leading edge surface of the blade.
Spent air leave through slots in the blade surface or in the trailing edge
Techniques to cool
stator blade

7. 3D axi-symmetric flow (inviscid)
Allow radial velocity components.
Derive relation in radial direction
Balance inertia, FI, and pressure forces (viscous forces are neglected)
Derived results can be used to interpret results from CFD and measurements
2D approach (circumferential coordinate z is omitted)

8. 3D flow (inviscid)
Pressure forces FP balancing the inertia forces in the radial direction are:
Equating pressure forces and inertia forces yields:

9. 3D flow
For many design situations rs can be assumed to be large and thus αs small. These approximations give the radial equilibrium equation:
The above equation will be used to derive an energy relation.

10. 3D flow
The stagnation enthalpy at any radius is (neglecting radial components):
The radial variation is therefore:
We have the thermodynamic relation: which produces:

11. 3D flow
We now have:
If we neglect the radial variation of entropy we get the vortex energy equation:

12. Theory 8.1 – The free vortex design method
Use:
and design for:
constant specific work at all radii
maintain Ca constant across the annulus
Thus Cwr must be kept constant to fulfill our design assumption.
This condition is called the free vortex condition
Designs based on free vortex principle sometimes yields a marked variation of degree of reaction with radius

13. Design methods (Λ m = 0.50)
For low root tip ratios a high degree of reaction is required in the mid to ensure positive reaction in the root
Free vortex blading (n = -1) gives the lowest degree of reaction in the root region!

14. Free vortex design - turbines
We have shown that if we assume
constant specific work at all radii, i.e. h0 constant over annulus (dh0/dr=0)
maintain Ca constant across the annulus (dCa/dr=0)
We get
Cwr must then be kept constant to satisfy the radial equilibrium equation
Thus we have Cw r = Ca tanα r r = constant. But Ca constant => tanα r r = constant, which leads to the radial variations:

15. Radial compressor 2 - General characteristics
Suitable for handling small volume flows
Engines with mass flows in this range will have very small geometrical areas at the back of an axial compressor when operating at a pressure ratio of around 20.
Typical for turboshaft or turboprop engines with output power below 10MW
Axial compressor cross section area may only be one half or a third of the radial machine
Better at resisting FOD (for instance bird strikes)
Less susceptible to fouling (dirt deposits on blade causing performance degradation)
Operate over wider range of mass flow at a particular speed

16. Development trends
Pressure ratios over 8 possible for one stage (in production – titanium alloys)
Efficiency has increased around % per year the last 20 years

17. Axial centrifugal combination - T700
The Sikorsky UH-60A Black Hawk, first flown in October 1974, is a light transport helicopter used for air assault, air cavalry, and aeromedical evacuation units.
In October 1989, the engines were upgraded to two General Electric T700-GE-701C 1890 shp turboshaft engines, and an improved durability gear box was added, resulting in a model designation change from UH-60A to UH-60L. The T700-GE-701C has better high altitude and hot weather performance, greater lifting capacity, and improved corrosion protection, in comparison with the two previous T700 gas turbines.

18. The vaneless space - diffuser
Use Cw and guessed
Cr => C => T => M, Mr
Perform check on area (stagnation properties
constant):

19. The diffuser
Boundary layer growth and risk of separation makes stagnation process difficult
Diffuser design will be a compromise between minimizing length and retaining attached flow

20. Shrouds Removes losses in clearance. Not used in gas turbines
Add additional mass
Unacceptable for high rotational speed where high stresses are produced

21. Non-dimensional numbers - maps
We state that:
based on the observation that we can not think of any more variables on which P02 and ηc depends.

22. Non-dimensional parameters
Nine independent parameters
Four primary variables
mass, length, time and temperature
9 - 4 = 5 independent non-dimensional parameters
According to pi teorem.

23. Non-dimensional numbers
Several ways to form non-dimensional numbers exist. The following is the most frequently used formulation:

24. Non-dimensional numbers
For a given design and working fluid we obtain:
Compressors normally operate at such high Reynolds numbers that they become independent of Re!!!

25. Non-dimensional numbers
We arrive at the following expressions:
Compressors normally operate at such high Reynolds numbers that they become independent of Re!!!

26. Compressor maps
Data is usually collected in diagrams called compressor maps
What is meant by surge
What happens at right-hand extremities of rotational speed lines

27. Surge What will happen in point D if mass flow drops infinitesimally
Delivery pressure drops
If pressure of air downstream of compressor does not drop quickly enough flow may reverse its direction
Thus, onset of surge depends on characteristics of compressor and components downstream
Surge can lead to mechanical failure

28. Choke What happens for increasing mass flow? Increasing mass flow
Decreasing density
Eventually M = 1 in some section in impeller (frequently throat of diffuser

29. Overall turbine performance
Typical turbine map
Designed to choke in stator
Mass flow capacity becomes independent of rotational speed in choking condition
Variation in mass flow capacity below choking pressure ratio decreases with number of stages
Relatively large tolerance to incidence angle variation on profile and secondary losses give rise to limited variation in efficiency with rotational speed

30. Learning goals
Have a basic understanding of how cooling is introduced in gas turbines
Be familiar with the underlying theory and know what assumptions the radial equilibrium design principle is based on
Have some knowledge about
the use and development of radial compressor
the physics governing the diffuser and vaneless space
Understand what are the basis for compressor and turbine maps.
Know about limitations inherent to the maps