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**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

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**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

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**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

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**The cooled turbine Typical cooling distribution for stage:**

Distribution required for operation at 1500 K

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**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

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**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

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**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)

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

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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.

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

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

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**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

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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!

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**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:

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**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

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

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**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.

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**The vaneless space - diffuser**

Use Cw and guessed Cr => C => T => M, Mr Perform check on area (stagnation properties constant):

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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

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**Shrouds Removes losses in clearance. Not used in gas turbines**

Add additional mass Unacceptable for high rotational speed where high stresses are produced

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**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.

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**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.

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**Non-dimensional numbers**

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

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**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!!!

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**Non-dimensional numbers**

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

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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

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**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

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**Choke What happens for increasing mass flow? Increasing mass flow**

Decreasing density Eventually M = 1 in some section in impeller (frequently throat of diffuser

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**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

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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

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