2 Choice of blade profile, pitch and chord Annulus areaRotor blade stresses:centrifugal stress:gas bending stresses reduce as cube of chord:centrifugal bending stressSource for fatigue failureCombination steady/ fluctuatingA 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 bladeforged
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 methodsexternal coolingFilm coolingTranspiration coolinginternal coolingTechniques to coolrotor blade
6 The cooled turbine - methods Stator coolingJet impingement cools the hot leading edge surface of the blade.Spent air leave through slots in the blade surface or in the trailing edgeTechniques to coolstator blade
7 3D axi-symmetric flow (inviscid) Allow radial velocity components.Derive relation in radial directionBalance inertia, FI, and pressure forces (viscous forces are neglected)Derived results can be used to interpret results from CFD and measurements2D 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 flowFor 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 flowThe stagnation enthalpy at any radius is (neglecting radial components):The radial variation is therefore:We have the thermodynamic relation: which produces:
11 3D flowWe 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 radiimaintain Ca constant across the annulusThus Cwr must be kept constant to fulfill our design assumption.This condition is called the free vortex conditionDesigns 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 rootFree 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 assumeconstant specific work at all radii, i.e. h0 constant over annulus (dh0/dr=0)maintain Ca constant across the annulus (dCa/dr=0)We getCwr must then be kept constant to satisfy the radial equilibrium equationThus 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 flowsEngines 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 10MWAxial compressor cross section area may only be one half or a third of the radial machineBetter 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 trendsPressure 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 guessedCr => C => T => M, MrPerform check on area (stagnation propertiesconstant):
19 The diffuserBoundary layer growth and risk of separation makes stagnation process difficultDiffuser 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 massUnacceptable 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 parametersFour primary variablesmass, length, time and temperature9 - 4 = 5 independent non-dimensional parametersAccording 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 mapsData is usually collected in diagrams called compressor mapsWhat is meant by surgeWhat happens at right-hand extremities of rotational speed lines
27 Surge What will happen in point D if mass flow drops infinitesimally Delivery pressure dropsIf pressure of air downstream of compressor does not drop quickly enough flow may reverse its directionThus, onset of surge depends on characteristics of compressor and components downstreamSurge can lead to mechanical failure
28 Choke What happens for increasing mass flow? Increasing mass flow Decreasing densityEventually M = 1 in some section in impeller (frequently throat of diffuser
29 Overall turbine performance Typical turbine mapDesigned to choke in statorMass flow capacity becomes independent of rotational speed in choking conditionVariation in mass flow capacity below choking pressure ratio decreases with number of stagesRelatively large tolerance to incidence angle variation on profile and secondary losses give rise to limited variation in efficiency with rotational speed
30 Learning goalsHave a basic understanding of how cooling is introduced in gas turbinesBe familiar with the underlying theory and know what assumptions the radial equilibrium design principle is based onHave some knowledge aboutthe use and development of radial compressorthe physics governing the diffuser and vaneless spaceUnderstand what are the basis for compressor and turbine maps.Know about limitations inherent to the maps