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Chalmers University of Technology Lecture 8 – Axial turbines 2 + radial compressors 2 Axial turbines –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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Chalmers University of Technology Choice of blade profile, pitch and chord Rotor blade stresses : 1centrifugal stress: 2gas bending stresses reduce as cube of chord: 3centrifugal bending stress Annulus area Steady stress/Creep Combination steady/ fluctuating

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Chalmers University of Technology 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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Chalmers University of Technology The cooled turbine Typical cooling distribution for stage: Distribution required for operation at 1500 K

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Chalmers University of Technology 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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Chalmers University of Technology The cooled turbine - methods Techniques to cool stator blade 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

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Chalmers University of Technology 3D axi-symmetric flow (inviscid) Allow radial velocity components. –Derive relation in radial direction –Balance inertia, F I, and pressure forces (viscous forces are neglected) Derived results can be used to interpret results from CFD and measurements

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Chalmers University of Technology 3D flow (inviscid) Pressure forces F P balancing the inertia forces in the radial direction are: Equating pressure forces and inertia forces yields:

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Chalmers University of Technology 3D flow The above equation will be used to derive an energy relation. For many design situations r s can be assumed to be large and thus α s small. These approximations give the radial equilibrium equation:

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

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

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Chalmers University of Technology Theory 8.1 – The free vortex design method Use: and design for: –constant specific work at all radii –maintain C a constant across the annulus Thus C w r 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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Chalmers University of Technology Design methods (Λ m = 0.50) Free vortex blading (n = - 1) gives the lowest degree of reaction in the root region! For low root tip ratios a high degree of reaction is required in the mid to ensure positive reaction in the root

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Chalmers University of Technology Free vortex design - turbines We have shown that if we assume –constant specific work at all radii, i.e. h 0 constant over annulus (dh 0 /dr=0) –maintain C a constant across the annulus (dC a /dr=0) We get –C w r must then be kept constant to satisfy the radial equilibrium equation Thus we have C w r = C a tanα r r = constant. But C a constant => tanα r r = constant, which leads to the radial variations:

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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology Axial centrifugal combination - T700

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Chalmers University of Technology The vaneless space - diffuser Use C w and guessed C r => C => T => M, M r Perform check on area (stagnation properties constant):

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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology Non-dimensional numbers - maps We state that: based on the observation that we can not think of any more variables on which P 02 and η c depends.

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Chalmers University of Technology Non-dimensional parameters Nine independent parameters Four primary variables –mass, length, time and temperature = 5 independent non-dimensional parameters –According to pi teorem.

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

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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology 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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Chalmers University of Technology 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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