What are the key factors in calculating the thrust of a turbofan engine?

[Nemos]

Hi there.
I am trying to work out a basic turbo fan model for a simulator I am working on and I have got a bit lost. I’m ok with ridged body physics but this is a bit outside of what I know. Here’s what I have so far given that the engine is running:

So, the compressor sucks air in at the front increasing the pressure of the air entering the engine. I am using this to calculate the force of the compressor:
BladeForce = 0.5 * DensityOfAir*(VelOfBlade* VelOfBlade) * AreaOfBlade
CompForce = (BladeForce*LiftCoeff)*NumBlades

I am using what I know from ridged body simulation to do this so it might be nonsense. I thought that having got the overall force applied to the air by the compressor I could then get the acceleration of the air through the engine but I can't work out how to apply the CompForce to the air. I think I need to work out the pressure exerted on the volume of air in the compressor stage. Then I would be able to calculate the volume of air being forced into the combustion chamber (Around 12% of overall intake?).

So then the issue is how hot the combustion chamber is given the amount of fuel. This then expands the air coming in and forces it through the turbine stage. This is a big blind spot in my knowledge. I can’t find any formulas for air expansion under heat so if anyone knows a good online resource that would help a great deal. I read somewhere that air pressure goes down when it expands but I assume the expansion causes acceleration that exerts pressure on the turbines. I think I might be a bit confused about pressure in general.

If I know the pressure coming out of the combustion chamber I think a can calculate the effect on the main turbine and fan turbine.

The overall pressure coming out of the engine will then allow me to calculate the thrust.

Keep in mind that I have no education in physics and just do this for fun. I’m actually a computer programmer. So please keep any answers relatively simple, well as simple as this stuff can be. Sorry for the massive post, I did try to condense it as much as I could. Any info at all will be much appreciated.

 

[Clausius2]

Hi there.

So, the compressor sucks air in at the front increasing the pressure of the air entering the engine. I am using this to calculate the force of the compressor:
BladeForce = 0.5 * DensityOfAir*(VelOfBlade* VelOfBlade) * AreaOfBlade
CompForce = (BladeForce*LiftCoeff)*NumBlades

I am using what I know from ridged body simulation to do this so it might be nonsense. .

Forget all these.

In Turbomachinery, there are two main ways of think of a compressor (turbine) device. The first is to think of it globally, I mean, you are given a compression (expansion) ratio and an isentropic efficiency. The second one, is to think of it particularly, you are given the internal geometry of the machine and then you derive global parameters from it.

For your purposes, the first thing you must do is to specify the compression (expansion) ratio, namely $$\Pi=P_1/P_2$$ as the quotient of pressure just in the front of the compressor and just behind it. Also, an isentropic efficiency is needed to evaluate the thermo-fluid-dynamic efficiency of the mahine.

Anyway, I'll try to resume how a gas turbine works, because it seems you want to simulate a jet engine or so. Pay attention to the words I employ, because I'll describe you the equations with them.

The first stage is the compressor. It sucks air from the ambient and increases it pressure and temperature by adding enthalpy to the flow. The work spent in doing that will be a bit greater than the enthalpy change (remind isentropic efficiency). Once the flow leaves the compressor at a higher pressure and temperature, it enters into the combustion chamber, which usually has a diffuser to slow down the flow and stabilize the flames. There it is injected some quantity of fuel, usually enhancing a lean mixture to don't damage the turbine blades because of the high temperature of the reaction products. The mixture reaches a higher temperature and pressure. The heat injected, which is given approximately by the fuel mass flow multplied by the enthalpy reaction release, will be the same than the change of enthalpy of the mixture across the combustor. Then the flow enters into the turbine, which expands it lowering the pressure and temperature, extracting enthalpy. The fact is that jet turbines in turbofans have a diffusor at the rear, in order to take advantage of all the flow pressure and don't leave any mechanical energy in form of Kinetic Energy. That pressure energy will be communicated to the shaft and eventually to the external fan which is the main responsible of thrust.

I hope it could help you. It is very difficult to explain it without equations. I advice you to consult some book of turbomachinery for principiants.

 

[FredGarvin]

Your best bet is to start looking into the air standard ideal Brayton cycle. It's going to be more complicated than you were hoping, but not too bad. It allows you to think of things with constant specific heats and thus reduces a lot of complexity. That doesn't mean that you don't have a whole lot of work ahead of you.

The overall pressure coming out of the engine will then allow me to calculate the thrust.

As a side note, don't think of the f=ma side of things. You do get a slight P/A addition to the thrust depending on the design of the exhaust nozzle, but it's not your main thrust component. Think more along the lines of $$F=\Delta (m*v)$$ because really you are interested in the change of momentum of the gas stream. I know it's getting nit-picky, but it always helped me in my thinking of the cycle.

 

[Nemos]

Hi there.
Many thanks for all the info chaps. Looks like i have some more revision to do. Will post back when i get it running.
Again, thanks for the help.