Chalmers University of Technology Lecture 8 Axial turbines

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

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

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 200 -300 K. – blades are either: • cast - conventional, directionally solidified, single crystal blade • forged

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

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

Chalmers University of Technology 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

Chalmers University of Technology 3 D 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

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

Chalmers University of Technology 3 D 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.

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

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

Chalmers University of Technology 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

Chalmers University of Technology 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!

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 Ca constant across the annulus (d. Ca/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:

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 10 MW • 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

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

Chalmers University of Technology Axial centrifugal combination - T 700

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

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

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

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 ηc depends.

Chalmers University of Technology 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.

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

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!!!

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!!!

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

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

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

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

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