The turbine is at the heart of any jet engine with its primary task being to drive the compressor. As described previously  without the compressor no mechanical work would be done on the fluid prior combustion and the thrust produced would only be a function of the chemical energy stored within the fuel. The hot combustion gases that enter the turbine directly after the combustion chamber are expanded across a series of vanes and stators, known as a stage, similar to the compressor. In the case of a turbine the fluid is expanded to extract useful work and therefore the pressure of the fluid falls across each turbine stage. Since the fluid is not working against an adverse (rising) pressure gradient boundary layer separation over the aerofoils of the turbine blades is not as critical such that  turbine blades can have much more agressive angles of attack with respect to the flow. Consequently, the pressure ratio across a turbine stage can be much higher than across a compressor stage and it quite common for a single turbine stage to drive six or seven compressor stages. The amount of power that can be extracted from a turbine stage is tremendous and a single turbine blade (not the full rotor of blades) may contribute up to 250 bhp [1]. The biggest driver behind the progress in turbine technology since Whittle’s first engine in the 1930’s has been the development of advanced cooling methods and the use of high-temperature alloys.

Similar to compressors axial turbines seen on most modern jet airliners are more efficient than their radial counterparts at higher flow rates. However, radial turbines are still being used on modern aircraft for auxiliary power units. Figure 1 below shows a single-shaft three-stage axial turbine i.e. the three turbine stages drive all of the compressor stages through a single shaft.

Fig. 1. Triple Stage Turbine [2]

The hot gases that exist the combustion chamber and impinge on the first row of nozzle guide vanes that turn the flow into the rotating turbine blades at the optimal angle to extract the most amount of work. Each stage of vanes and blades expands the flow thereby resulting in a drop in enthalpy (total amount of energy in the combustion gases) and a transfer of work from the fluid to the turbine. For simple jet engines the overall performance of the engine is more effectively enhanced by developing the compressor stages. However for large by-pass turbofan engines turbine aerodynamic design is crucial. Figure 2 shows the velocity triangles for the flow passing through a single turbine stage. Separate turbine rows are typically placed very close together, around 20% of a blade chord [1], and the tangential velocity of the rotor blades w*r (w is the rotational speed and r the radius of the blades) is close to the local speed of sound.

Fig. 2. Velocity triangles for turbine stage [2]

The main function of the stator is not to do work but to add swirl to the flow into order to convert some of its internal heat into kinetic energy. The turbine rotor then extracts work from the flow by removing the kinetic energy associated with the swirl velocity. In the global reference frame of the engine the flow into the stator and rotor is highly unsteady and of great complexity. However, in a frame of reference fixed to a rotating blade it can be assumed to be fairly steady with sufficient accuracy. For the first row of stators (or nozzle guide vanes) the flow impinges parallel to the axial flow direction and is consequently turned through angle βb with respect to the axial direction by the stator. Thus the flow leaves the stator at with a velocity Vb with respect to the stator which is equivalent to a velocity V’b at an angle β’b with respect to the rotating blade. At optimum design condition β’b is equal to the angle of rotor blade.  V’c and β’c are the relative exit speed and blade angle respectively, such that the turning angle is equal to β’b – β’c. An important design parameter for turbine performance is the blade coefficient φ, which is the ratio of the total temperature drop  (which is proportional to the work done) across a stage divided by the kinetic energy of the rotor.

$\psi=\frac{c_p(T_a - T_c)}{0.5 (\omega r)^2}=\frac{2 w_a}{\omega r}\left(\tan \beta_b + \tan \beta_c\right)$

High efficiency are achieved with lower temperature drops per stage and therefore smaller values of φ and lower turning angles β’b – β’c. However large values of φ are required to reduce the number of stages and keep the weight of the engine down. Consequently a compromise has to be struck between optimising thermodynamic efficiency and weight.

If the high pressure of the fluid exiting the combustion chamber were expanded in a single stage a very high velocity close to 1500 m/s [1] would be produced, which due to losses associated with supersonic shock waves, would be impossible to use efficiently. Therefore the turbine stages make a series of incremental expansions resulting in flows just over the local speed of sound, which, as shown by the velocity triangles, is apparently reduced on entry to the next stage as a result of the change in reference frame. Thus the velocity triangles show that the velocity leaving the stator V is high in the frame of reference appropriate to the stator but much lower when seen at the rotor entry V’. Similarly the velocity leaving the rotor is high in its relative frame of reference V’c. but lower in the absolute frame appropriate to the stator Vc. Thus each of the turbine rows takes in a flow which is almost axial down the engine and turns it towards the tangential thereby reducing the effective cross-sectional flow area, which, by conservation of momentum, must result in an increase in fluid velocity.

Turbine Stresses

The turbine inlet blades of the first stage are the most likely to determine the life of the engine since they are exerted to the highest fluid temperatures, highest rotational speeds and highest aerodynamic loads. Stresses in the rotor blades also place restrictions on the allowable blade heights and annulus flow area. The gross of the mechanical stresses arise from the centrifugal stresses of the rotating turbine and bending moments exerted by the flowing gases, which unfortunately are both maximum at the blade root. The problem of centrifugal root stress was previously discussed for compressor blades. The turbine blades are of course tuned such that none of its natural frequencies coincide with any rotational or fluid  excitation frequencies so as to prevent resonant behaviour. The gas turbine produces higher specific power and thus efficiency as the turbine entry temperature (TET) of the gas exiting the combustion chamber is increased. Of course the TET is bounded by the metallurgy of the turbine blade materials. The TET has increased from around 800°C in 1940 to 1500°C in the 1994 Rolls-Royce Trent engine. This development has in part been due to better materials but more importantly through channelling  of cold compressor air to cool the turbine blades.

In this high temperature environment the life of the turbine blades is limited by creep, which is the continual and gradual extension of a material under constant load over time. Apart from distorting the physical dimensions and thereby reducing performance of the engine, the induced creep stresses exacerbate the centrifugal operating stresses and will therefore lead to premature failure of the material. Under ambient temperature creep is often only a factor for elastomers and other plastics, but at higher temperatures the effects become increasingly more pronounced for metals as well. A rule of thumb is that the blade life is halved (for a specific blade material and cooling technology) for each 10°C rise in temperature of the metal [1]. In the early days of turbine technology blades were forged but later cast for better high temperature performance. It was then found that by elongating the metal crystals along the direction of the span, creating so called directionally solidified blades, resulted in further improvements in creep performance. The standard technique for high-performance blades is to cast the blade out of a single crystal as shown in Figure 3 below. Metals may deform by separate crystals slipping along grain boundaries, such that removing the grain boundaries all together results in great improvements in resisting creep deformation.

Fig. 3. The microstructure of the three different turbine blades [4].

A typical alloy used for turbine blades today is Inconel, a nickel-based alloying containing 13% chromium, 6% iron, with small amounts of manganese, silicon and copper. These metallurgical advances account for some of the improvements in driving up TET and turbine efficiency. The other very interesting and complicated technology are blade-cooling techniques. But that is a topic for another article all together.

References

[1] Rolls-Royce (1996). The Jet Engine. Rolls Royce Technical Publications; 5th ed. edition

[2] http://aeromodelbasic.blogspot.co.uk/2012/01/turbines.html

[3] http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/fig9VelTrianglesTurbine_web.jpg

[4] http://www.doitpoms.ac.uk/tlplib/creep/images/img014.jpg

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1. […] I described in a previous post, the efficiency of the gas turbine cycle increases as the turbine entry temperature (TET) is increase…. Therefore the hotter the combustion gases that enter the first turbine stage the more specific […]