Understanding the gas turbine engine…

Gas Turbine Engines! They’re the honeypots of any propulsion course. You’d need a book to cleverly explain the clockworks behind that thing! Because it’s much much more than what you think it is. It’s not just a machine that sucks-air, spits fuel, burns, and farts-gas. Inside that beautiful casing, goes an exotic molecular dance. In order to understand this nightmare, firstly you need thermodynamics. Then, as you get deeper and deeper, aerodynamics comes in.

Now, I’m not gonna explain this in the usual way, dealing with each & every component, speaking technically, and all – Nope! Today, we’re gonna see what’s (more or less) going on inside this engine (turbofan engine, in our case). I’ve come up with a bunch of analogous thermodynamic stuff (pretty basic ones) which can help in visualizing the components of the gas turbine. But, we need to have a look at our key ingredients before we get inside.

Before I begin, you should understand that physical concepts (say, temperature, pressure, or density) mean something “only” if we can define how to measure them operationally. So, measuring is very necessary for our definition!

(You can skip to the end if you don’t wanna visualize temperature and pressure)

Ingredients for the recipe…

We know that air has molecules. There’s a simulation below. What you see there is a bunch of molecules exhibiting pseudo-random motion (in reality, it’s random, defined by the laws of quantum mechanics, especially probability). As you can see, the molecules are always jiggling. They have kinetic energy. It’s this “jiggly-wiggly”ness that brings pressure and temperature into reality. Let’s now see how we can measure temperature and pressure. There’s a difficulty that arises when we try to measure these parameters.

Temperature:

Temperature is a measure of the kinetic energy of molecules. It’s also a measure of the velocity of molecules, heat radiation, etc., but never mind. Kinetic energy is all we need.

Now, how shall we measure temperature? You say, “Well, that’s easy. Stick a thermometer into the thing you wanna measure (air, in this case), and you’ll get it.” Not quite. The thermometer just reaches the thermal equilibrium with the object. That’s how the world works. Heat is transferred from the object to the thermometer to heat up the liquid inside, causing it to expand (rise), and voila!

Basically, you’re slowing down the jiggling of air molecules, and raise the jiggling of the molecules of the liquid inside the thermometer. So, we don’t know what the temperature was before we slowed them down. Right? We have a name for this measure of temperature. It’s called the total temperature (or) stagnation temperature. At any moment, what you feel, what you touch, is the total temperature. We can’t measure the static or dynamic temperature in any way.

Now you say, “Then, we can use an infrared thermometer which can sense its surroundings.” Yes, but it has its limitations, bounded by its operating range. You can’t put that inside a gas turbine where the (total) temperature can exceed 500° C. So, how do we measure it? Let’s see what pressure has got. It may help us in measuring the temperature.

Pressure:

I once talked about temperature when I wrote about fire. Let’s bring it inside for today’s argument. We need to relate temperature and pressure somehow microscopically (at least, classically). Because, that’s how it gets very exciting. I’ll get that HTwins simulation here…

The simulation of these ferocious molecules is based on the ideal gas law. You see the bumping? When you reduce the volume, the chaoticness of the molecules starts increasing (temperature rises). Then, if you continuously click on one of the red or blue buttons, you vary the temperature, thereby the jiggling. Yep, it still swirls around the same point.

What about pressure then? Pressure (unlike Temperature) isn’t based on volume. It’s based on the surface area. But, it still sticks to the jiggling-of-molecules thing. For pressure, we need the molecules to bump on our instrument, just like the classical thermodynamic example – a piston. Well, pressure can also be defined as the kinetic energy density (i.e. kinetic energy per unit volume).

When you heat the air inside a piston cylinder, the piston starts to rise. Because, you’re increasing the jiggling of the molecules, and they start bumping everywhere. When they attain a critical kinetic energy, they can bump very well, and can push the piston. That collective “pushing” behavior is what we call pressure. As you can see, it can only be felt at a surface.

To realize that, let’s make use of a fluid (air or water, anything that suites you) flowing through a tube.

Mind you! This is a rough picture. It just makes my life easier!

The blue arrows indicate fluid flow velocity vector. It’s directed along the pipeline. Note the black arrows. Those are the velocity vectors of individual molecules. The molecules don’t obey your intuition! They’re random and chaotic hocus-pocus. Well, at least they have a forward component. That makes us happy!

So, we can measure the pressure in two ways. Even though the water is flowing horizontally, both the surfaces $\mathcal A$ and $\mathcal B$ can be connected to a manometer to measure the pressure at any moment. What they both mean is what matters here.

On the surface A, we’re measuring the static pressure, whereas the surface B indicates the total (or stagnation) pressure. How? Static pressure is present all the time. It’s uniform throughout the environment – it’s the pressure in an undisturbed fluid, the pressure exerted on surfaces by the “bumping” of molecules in random motion. In layman’s terms, that’s the pressure of still air – no wind or gust or any kind of turbulence that could otherwise disturb the air. Period!

Now, what about surface B? It measures the dynamic pressure along with the static pressure. As you’re measuring the pressure of still air, say a strong wind blows into your instrument. Along with the bumping of still air molecules, you measure the bumping of the wind molecules. This case is different. It’s similar to the difference between a person knocking on a door, and another person throwing himself (smashing) onto the door while the other one was knocking!

Hurray! We’re able to measure the total as well as static components of pressure. So, the difference between both of them indicate the dynamic pressure, from which the velocity of the fluid can be found. At the same time, if we knew the density of air, we can find the different temperatures (static or total) using the relation $P=\rho R T$

And, that’s what we do in our wind tunnels. We place the model with some holes drilled on its surface. Then, we plug small tubes into these holes, and connect them to a multi-tube manometer, which measures the static pressure at these specific holes. We also use a similar tube to measure the total pressure of the flow (directly). Then, we use the parameters to calculate temperature, mass flow rate, and other boring stuff, etc.

An easy realistic example…

I bet you’ve seen hurricanes and tornadoes in TV, pulling off the terraces of the houses. How do you think it happens? Before the strong wind comes in, the air is (relatively) still. Normal day, normal life. As the wind starts blowing, molecules just above the terrace are getting carried away, which means that very few molecules are left to bump over the surface.

As the total pressure remains the same (in this case), static pressure decreases. When this pressure difference between either side of the terrace overcomes the ultimate tensile strength (breaking stress) of the terrace, it breaks. Now, air rushes outward, carrying the terraces away! Whoo!

Anyways, I’ll leave the remaining imagination to you. Now, that puts an end to our discussion on pressure and temperature. Let’s get back to gas turbines. With this understanding, intuition is enough to capture the working of a gas turbine engine. Oh, and I forgot to tell you. We’re talking about a typical turbofan engine operating at subsonic speeds. I guess you don’t want shock waves here & there (But, do believe me – shocks are very interesting! I like high speed aerodynamics compared to the low speed one!)

Inlet sucks air…

The inlet is just a diverging duct (called a diffuser), which means that the area does affect the flow. As the molecules rush inside, they realize that the cross-sectional area starts increasing. So, they slow down and start bunching up together! It’s quite obvious that the static pressure is increased as the molecules come out through the exit of the inlet.

What’s interesting is that the dynamic pressure goes down since the flow is getting decelerated as a result of the area gradient! Intuitively, one could argue that the velocity should decrease as the area increases, which is true. Let’s see how…

In our case (for a flying airplane in steady level flight), you should always remember that the mass flow rate of the incoming air is approximately a constant. Air doesn’t flow as per our own desires. Mathematically, the mass flow rate is given by $\dot m=\rho A v$.

It can be easily seen that as the area increases, the velocity should decrease, if the mass flow rate is constant. Thus, the dynamic pressure decreases while the static pressure increases. It could also be shown in another “not-so-obvious” way. As long as we don’t do any external work on the fluid, the total pressure remains the same. Thus, as static pressure increases, dynamic pressure decreases.

Similarly, the total temperature remains the same, whereas the static temperature increases. Whoo! That’s it! Next stop – compressor… Light speed!

Compressing the air…

Now, the air enters into the compressor (we’re talking about an axial compressor). In a compressor, we do something. We push the molecules forward (In other words, we do some work on the fluid). Think of the fan in your home.

You can see that the blades are tilted at some angle. The purpose is to push the molecules normal to blade (outwards). Sometimes, they’re tilted and curved, to uniformly push the air outward (but, the working is as simple as that!). That’s why you get much of the air sideways (well, depending on the tilt angle). Only due to turbulence, the air gets distributed throughout the entire room. Try experimenting it out…

Inside the compressor, there’s a similar component called the rotor which does exactly this. It pushes the air normal to its blade. In order to make the flow direction along the line, there’s another component called stator. It doesn’t move. Its blades are attached to the engine frame (cantilevers). But, they’re inclined in such a way that they direct the flow in straight line (parallel to the axis).

They don’t just direct the flow. Along with that, they decrease the velocity, thereby increasing the static pressure of the flow (i.e) the stators try to stagnate the molecules, causing them to “bunch up”, increasing the static pressure.

Dynamic rotors & static stators in a convergent duct!

Here’s a nice animation (I robbed from Wikipedia) on axial compressor, showing how exactly the rotors move between the stators.

I could add more facts about their awesome design. In most of the engines today, there are more stages in a compressor (a rotor-stator pair is called a stage – this one has four stages) to increase the fluid velocity further. And, the spacing between a rotor blade and the engine frame is of the order of a millimeter, or even smaller.

This diagram shows how the velocity and pressure varies along the flow field inside a compressor. That’s what we’re gonna investigate now…

Yeah, this is rather disgusting! It didn’t come handy. Think that the first circle is shrunk to second circle…

Let’s get to the thermodynamics. It’s quite simple. We’re doing additional work on the molecules. Like I said, we’re pushing them using the rotors, (increasing the dynamic pressure with constant static pressure, thereby increasing total pressure), and stopping them using stators (increasing the static pressure with constant total pressure, thereby decreasing dynamic pressure). Anyways, the total pressure increases (obviously), due to the result of static pressure increase. Similarly, both the total & static temperatures increase.

Well, if it isn’t quite obvious, here’s an compare-contrast explanation[*]. Let’s compare a closed volume (shown aside) to a compressor. Initially (state 1), the molecules exhibit only static pressure (by which I mean that the dynamic pressure is terribly “low” in a closed volume and so, we don’t need that for our discussion). It’s similar to the cross section of the compressor (except the fact that dynamic pressure is almost a constant in compressor). As the molecules progress along a stage (rotor-stator pair), they get compressed by the molecules coming behind (“push-stop” method in stage!).

So, what happens when we start compressing the molecules in our closed volume? (state 2) Clearly, the molecules start bunching up. So, the static pressure increases (i.e) the number of molecules bumping on a chosen surface parallel to the flow increases. Dynamic pressure is constant as before. In our closed volume, you’re not doing anything to the velocity of molecules. Molecules still remain static (static, in the sense – the random motion). In actual compressor, it’s increased by rotor, and decreased by stator – thus, it’s more or less constant[*]. So, the net result is that the total pressure increases!

[*]: Note that this alternative example is made to understand how the static pressure rises! In a compressor (like I said), the stators stagnate the molecules, thereby decreasing the dynamic pressure, and increasing the static pressure.

That’s it! Moving on to the combustion chamber…

Cooking the stuff up!

Let’s make use of the same closed volume. But instead of compressing, we’re heating it up! Obviously, the static & total temperatures increase (that’s what happens in combustion). If the volume is closed, then it constrains expansion. As a result, the static & total pressures increase.

But, the combustion chamber is open. It allows the gas to freely expand, and get into the turbine, allowed to occupy the volume. So, the static pressure is maintained a constant. The fast expansion increases the velocity of the molecules (actually, it’s a kind of explosion – burning does increase molecule velocity!) , thereby increasing the dynamic component, and hence the total pressure. Wrapping it up, we can see that all the parameters other than the static pressure increases in a combustion chamber.