 In this module, we shall discuss thermal turbo-machines and this is the last module in this series of lectures. As we already mentioned, thermal turbo-machines are those machines that handle compressible fluid as the working substance. Axial compressors, fans and blowers all handle air, centrifugal turbines as we saw in the case of an automotive turbocharger typically are usually handled a mixture of combustion gases. Axial compressors again typically handle air, axial turbines of the sort that is used in gas turbines or aircraft engines all handle typically a mixture of combustion gases. C-turbines which are also axial although that is not stated here explicitly handle steam as the name implies. In this lecture, we will not or at least in this module, we will not discuss the two centrifugal machines that are indicated in red color here for two reasons. Number one, this is intended to be an introductory course on turbo-machines. Number one, number two, we have already discussed centrifugal machines at length in the module on hydro turbo-machines. So for because of these two reasons, we will not discuss the centrifugal compressors or centrifugal turbines in this module, we will focus our discussion on axial compressors, axial turbines and steam turbines. Gas turbines use both axial compressors and axial turbines and you should be familiar with the gas turbines from your applied thermodynamics course. And the gas turbines typically operate in a Brayton cycle. This is the basic Brayton cycle, many variations of this Brayton cycle are possible as you will be familiar. So basically the air under ambient condition enters the compressor, it's a steady flow device, air enters under ambient conditions into the compressor where it is compressed to high pressure. Hydrocarbon fuel is then mixed with the air and burned and this increases the temperature of the gases and the high temperature gases then enter a turbine where they are expanded. Now the turbine produces sufficient power to run the compressor and the leftover power is actually used to run an electric generator in the case of a land-based gas turbine power generation unit. Now in the case of an air car engine, the leftover power is actually not leftover power, the leftover enthalpy of the gases is actually converted into kinetic energy in a propulsion nozzle for propulsion application. What we are going to do next is to actually take a look at the compressor that is used in a gas turbine which is an axial compressor and the turbine that is used in the gas turbine which is also an axial turbine. What is that? Most modern gas turbine engines operate at pressures as high as 40 bar and temperatures as high as 1700 Kelvin, so these are the kinds of figures that we would be working with. Most modern land-based gas turbine power units like the one that is shown in this picture run at a speed of 3000 rpm in case the supply frequency is 50 hertz or at a speed of 3600 rpm in case the supply frequency is 60 hertz. So here we see the rotor of a land-based gas turbine power generation unit, notice that the casing has been removed so only the rotor blades are shown here. So we see a multi-stage axial compressor here, many rotor blades followed by a combustor and this is followed by an axial turbine. The axial turbine as may be noticed has far fewer stages than the compressor. Now if I take an R equal to constant section of any rotor here and lay out the blade elements horizontally, this is what we would get, we have already seen this picture also before. So if we lay out the blade elements like this, this is what we see and this is what we get if we lay out the blade elements of an axial turbine. We can see that this is, in case it's a reaction machine, we can see that the enthalpy changes across the rotor because by definition it's a reaction machine. So consequently since h plus c square over 2 is a constant, the relative velocity also changes in the rotor. Now in the case of a compressor, the enthalpy increases as a result of the input power, so the relative velocity decreases in the rotor blade passage and in the case of a turbine because work is produced, the enthalpy of the fluid decreases and consequently the relative velocity increases. Now it can be seen that the change in relative velocity is not very high in the case of an axial compressor and this is because the deceleration of the fluid results in an increase in its pressure because basically it's a diffusion process and since the flow faces an adverse pressure gradient, there is a danger that if the pressure gradient is too high, the boundary layer which forms on the surface of the blade can actually separate as a result of the adverse pressure gradient. This usually results in compressor stalling and the erratic performance of the compressor and must be avoided at all costs. So because of this danger, we cannot increase the pressure ratio to very high values. Now in the case of a turbine in contrast, the pressure gradient is favorable in the direction of flow because the pressure decreases and we can actually have as high a pressure drop as we would like in the case of a turbine blade passage. Now since the pressure drop can be as high as possible, consequently the work transfer in a turbine blade passage is also, our turbine rotor is also very high and that is the reason why the turbine blades are thicker when compared to the compressor blades. And the flow turning is also much higher in the case of turbine blade when compared to the compressor blade because the pressure ratio is limited by the danger of boundary layer separation, the pressure rise and consequently the work transfer and flow turning or minimal in the case of a compressor rotor whereas they can be quite high in the case of a turbine rotor. So let us summarize these observations here. The cross sectional area of the blade passage decreases in the case of a turbine and increases in the case of a compressor. Because of this the magnitude of the relative velocity increases in the case of a turbine and decreases in the case of a compressor which suggests that the flow undergoes an expansion due to flow acceleration in the case of the turbine and it undergoes a compression due to the flow deceleration or diffusion in the case of a compressor. So the blade passage of a turbine resembles a nozzle and that of a compressor resembles a diffuser. And as we already mentioned the flow turning and hence the work transfer is high in the case of a turbine on account of the favorable pressure gradient and consequently the blades are thicker and the flow turning is also and as we said is quite high. In the case of a compressor the flow turning and work transfer is limited or quite small going to the danger of flow separation and the blades are consequently slender. So here we show what happens when the flow separates the boundary layer separates from the blade surface. So again separate either on the upper surface or on the lower surface of the blade and when this happens the flow becomes unsteady and the compressor performance also becomes highly unstable and this unsteady mechanical stresses can be catastrophic on the compressor blade. So and this must be avoided at all costs during operation of the axial flow compressor. Now an axial flow impulse turbine looks like this. The rotor of an axial flow impulse turbine looks like this. All the enthalpy drop in this case occurs in the nozzle which is located upstream of the rotor and the fluid which comes out at high velocity impinges on the blades. And it simply changes direction in the rotor blade passage as shown here. Notice that the magnitude of the relative velocity remains constant because it is an impulse machine. There is no change in enthalpy and hence there is no change in relative velocity in the blade passage there is only a change in direction. Because the absolute velocity at inlet to the rotor is very high in the case of an axial turbine the blade rpm usually tends to be quite high in the case of an impulse turbine. For a given amount of work transfer the change in absolute velocity is higher for an impulse machine when compared to a reaction machine which is quite obvious from what we have said so far. So this usually results in higher blade speeds for the impulse machine. Now reaction machines achieve work transfer to a combination of change in relative and absolute velocity as we mentioned earlier and so they tend to be much more compact and can run at lower blade speeds which is desirable because the centrifugal stress from the blades is lessened to that extent. Now one important aspect that we must keep in mind is that because of the limitations that exist in the kind of pressure rise that we can have in a compressor blade passage if we want to operate at pressure ratios around 41 then we cannot achieve that using a single rotor that fact is obvious. So we need to use multiple rotors to accomplish this although the work transfer and the pressure drop can be higher in the case of reaction turbine or even an impulse turbine it is still probably desirable to actually have the work transfer the complete work transfer take place across a few stages of turbine instead of just one stage. So the way forward in the practical design or realization of these machines is to have quite a large number of stages for a compressor because the pressure rise is limited and here because the pressure rise is not limited we can have a fewer number of stages in the case of the turbine and this is obvious from the gas turbine picture that is shown here. So what is that the number of rotors on the compressor side is about 12 to 15 whereas we have only four rotors on the turbine side okay it's further important to note that probably only one or two of the turbine stages drive the entire 12 to 15 compressor stages and the remaining turbine stages convert the enthalpy of the combustion gases to work which is used to run the generator. So the basic idea is we are going to need far more stages in the case of the compressor because of the limit on the pressure rise that we can achieve in each rotor whereas the number of stages on the turbine side can be number of rotors on the turbine side can be lesser. So that is what is actually done okay so in real life application by having multiple rotor blade you can reduce the work transfer in each rotor blade and consequently the rotation speed of the rotor blade can also be brought down okay. So this actually reduces the mechanical stresses on the rotor and that is what is done in practical installation. Now when we say that we need to have multiple rotors as we saw here multiple rotors on the compressor side or turbine side notice that we simply cannot place one rotor after next in these axial machines because the flow angles at the flow angles at the entry and exit of a rotor are not the same so which means that we need to have guide weights or stationary weights in between the rotor blades in order to direct the flow smoothly from one set of rotor blade to the next. Now each stator rotor pair is called the stage and this is the design strategy of having multiple rotor blades with stator blades in between each one of them is called multi-stage okay. The moving blades are obviously attached to the rotor and the hub which in turn is connected to the shaft as we can see here notice that the moving blades are attached to the hub which is connected to the shaft and stationary blades go in between these rotor blades as I said before only the rotor blades are shown in this figure the the guide vanes or stationary blades go in between these rotor blades and they are fixed to the casing and they are fixed to the fixed to the casing. Now it is also possible to actually fix the stator blades to the casing in such a manner that they are goable in which case they are called variable guide vanes and this is something that we will discuss later okay. What is that the inlet exit stator blade angle is the same as the exit inlet rotor fluid angle okay let us see how this comes about. So here we have illustrations of a multi-stage compressor and a multi-stage turbine so we can see that you know this is a rotor so fluid enters the rotor and this rotor and this is the next set of rotor so before the fluid enters the next set of rotor these guide vanes redirect the fluid in a proper manner so that the flow enters these rotor in such a way that the relative velocity is tangential to the blade profile at inlet okay. What is that the flow angle at the inlet of the stator is the same as the flow angle at the exit of the rotor and the flow angle at the exit of the stator is the same as the flow angle at the inlet of the rotor that is what we have said here okay. The inlet exit stator blade angle is the same as the exit inlet rotor fluid angle or flow angle. So here also we see the same thing but again we notice that these blades are slender and the flow turning is not very high whereas here the blades are much thicker and the flow turning is also very high and consequently the stator vanes also are thicker and highly curved when compared to the stator vanes here okay. Now we can actually try to do more with the stator blades than just redirect the flow okay as we said the primary purpose of the stator blade is to achieve the change in direction of the fluid velocity if it is going to do just this then the blade passage area is constant however we can also have a change in static enthalpy or pressure in the stator blade passage in which case we are actually making the stator do more work than just redirecting the fluid so we can actually in the case of a compressor we can have a diverging passage between the stator blades which will cause a certain amount of pressure increase here and so the pressure increase in the rotor stage can be that much lesser or in the case of a turbine we can actually cause the stator blade passage to be like a nozzle causing a pressure drop which will then help in the rotor realizing more expansion okay so we can actually make the stator vanes to much more than just simply redirecting the flow so we can have a pressure drop I'm sorry pressure increase in the case of a compressor or stator blade passage or a pressure drop in the case of turbine blade passage as shown here so in both cases there can be change in the static enthalpy of the fluid in the stator blade passage but not a change in stagnation enthalpy because there is no work interaction in this case but the the static the stator blade passages in this case do more than just redirect the flow that is a very desirable aspect so what happens as a result is that you know in the case of an axial compressor we can achieve pressure ratios as high as 40 through this multi-staging and by designing the status not only to redirect the flow but also to accomplish the desired pressure increase or decrease the number of stages required may reduce a little bit and the the entire compressor assembly stator plus rotor is much more compact so multi-staging is very easy to do in the case of axial compressors and high pressures can be realized while keeping the rpm at reasonably lower values okay so all these features have made axial compressors very attractive and consequently they are extensively used in practical application despite the fundamental problem that in a fluid dynamic perspective from a fluid dynamic perspective increase of pressure through diffusion of the flow is not at all desirable okay so despite the fact that it's a fundamentally not a desirable way of accomplishing pressure rise the axial flow compressors are still extensively used because there are so many other advantages in a practical realization okay so typical pressure ratio across stage of an axial compressor is about 1.152 maybe 1.2 today in the most modern gas turbine engines so if we want a pressure ratio of 40 across the entire compressor then we need to have 27 stages okay because the increase in pressure goes in a geometric progression and typically the axial compressors are designed so that the axial velocity remains constant as much as possible from the first to the last stage so consequently the height of the blade decreases as the density increases from the first to the last stage