Gas Turbines - Introduction — Page 206, Lesson 274

Let's start with the temperature limit of the engine, because that's the single most important constraint on how a turbojet performs. The turbojet is a heat engine. That means it takes heat energy from burning fuel and converts it into thrust. The fundamental rule here is simple: the higher the temperature you achieve in combustion, the greater the expansion of the gases, and therefore the greater the efficiency of the engine. More heat in means more expansion, means more thrust for the same fuel. So, on the face of it, you'd want to run the engine as hot as physically possible. But there is a hard limit to how much heat can be released into the turbine from combustion. And that limit is imposed by the materials from which we manufacture two specific components: the nozzle guide vanes and the turbine blades. These are the parts that sit directly in the hot gas stream coming out of the combustion chamber, and they have to survive that temperature without melting or deforming. Now, here's the engineering story. In the latest engines, we've been able to use much higher gas temperatures than their predecessors. How? Through two things: the use of modern materials, and extremely efficient cooling methods in those nozzle guide vanes and turbine blades. Because we can cool them internally, we can push the combustion temperature higher without destroying the metal. The consequence is that these modern engines have a higher thermal efficiency than older ones. So the temperature limit isn't a fixed number — it's a moving target that improves as materials and cooling technology improve. Now let's move to the physics that governs what happens to the air inside the engine. The air is the working fluid of the gas turbine engine. During the working cycle, it receives and gives up heat, and as a result its pressure, temperature, and volume all change. These changes aren't random — they conform to principles that come from a combination of two classic gas laws: Boyle's Law and Charles's Law. Let me give you Boyle's Law first. It states that if a given mass of gas is compressed at a constant temperature, the absolute pressure is inversely proportional to its volume. In other words, if you squeeze a fixed amount of gas while keeping its temperature constant, the pressure goes up as the volume goes down. Mathematically, we write it as P × V = K, where P is absolute pressure, V is volume, and K is a constant for that mass of gas at that temperature. Now, in isolation, this law is not much use to us. Why? Because in practice we cannot compress a gas at a constant temperature. Compression always heats the gas up. So Boyle's Law alone doesn't describe what really happens in the engine. But if we use it in conjunction with Charles's Law, it becomes much more useful. Charles's Law states that if a gas is heated at a constant pressure, the change in volume will vary directly with the change in the absolute temperature — and this change is the same for all perfect gases. So, the volume of a given mass of gas that remains at a constant pressure is directly proportional to the absolute temperature of that gas. The mathematical form is V/T = K, where V is volume, T is absolute temperature, and K is a constant. Now, this law on its own is a little better for us. At least in theory, we have combustion occurring at a constant pressure in the gas turbine engine. That's the ideal — the burning happens at roughly constant pressure. But as we've seen, it does not happen perfectly in practice. There are pressure losses in the combustion chamber, so even this law is an approximation. That brings us to the Combined Gas Law, which is the one that actually ties everything together. It states that the product of the pressure and the volume of a quantity of gas, divided by its absolute temperature, is a constant. In other words, P × V / T = K. This single equation combines Boyle's Law and Charles's Law into one relationship that accounts for changes in all three variables — pressure, volume, and temperature — at once. That's the law that really governs the behaviour of the air as it moves through the compressor, the combustion chamber, and the turbine. So, to pull it all together: the engine's efficiency is driven by combustion temperature, but that temperature is capped by the materials and cooling of the nozzle guide vanes and turbine blades. And the behaviour of the air — the working fluid — as it changes pressure, volume, and temperature through the cycle, is described by the Combined Gas Law, which is just Boyle's and Charles's Laws working together.