 what we're going to do now is we're going to take a look at both the process schematic as well as the process diagram for the Brayton and we'll call this the simple cycle later in this lecture what we'll do is we will look at adding more complexity to the cycle itself but we'll begin with the schematic of the Brayton cycle and so what we start with is a compression process and we will call that state 1 so we compress atmospheric air when we leave the compression process we're at state 2 and it's at that point that we enter into the combustion chamber and in order to have combustion we have to mix in fuel the mass flow rate of fuel will be much lower than that of air coming in we have combustion there is heat release going on and as a result the temperature goes up that takes us to state 3 when we enter then into a turbine and finally we exit out at state 4 and that would be our exhaust gas stream now the turbine and the compressor within the gas turbine engine are going to be mechanically coupled and consequently there will be a shaft that is rotating and connecting the two together and whatever power being generated by the turbine that is not used to drive the compressor becomes the work net out of our engine and so we could use that for electricity production you could use it in the case of a turbo fan to power the fan itself or a turbo prop that could be used for empowering the turbo propeller many different uses that you could have depending upon the particular application so that is our process schematic what we'll do now is take a look at process diagrams and we're going to look at two different types one on a TS and the other a PV diagram so we'll start with the TS and this is the one that I tend to work with whenever I'm dealing with the Brayton I'm more comfortable with it but you start here at state 1 you go through an isentropic compression process so the entropy is not changing and that takes us to state 2 you then go into your combustor and that is a heat addition process so here we have Q in so that takes us to state 3 we then go through isentropic expansion taking us to state 4 and finally we have the heat rejection process which is in reality our exhaust cycle however we will model that as being a heat rejection process so from 2 to 3 that's where we have heat addition Q in and then from 4 to 1 that is where we have heat rejection or exhaust and that is Q out so that is the Brayton cycle or the simple Brayton cycle on a TS diagram next what we'll do let's take a look at it on a PV diagram we'll start down here at state 1 we then go into isentropic compression which takes us up to state 2 so during isentropic compression entropy is constant we then go into what we will consider to be a constant pressure heat addition process taking us to 3 in reality what happens is we do have a little bit of a pressure drop in our combustion chamber however for a simple analysis we will assume that to be zero pressure drop and then we go through isentropic expansion taking us out to state 4 and then finally the heat rejection or the exhaust cycle bringing us back and 3 to 4 as well as constant entropy so putting our heat addition and heat rejection on here this is where we have Q in and then down here is where we have Q out so labeling the different steps of our process what we have is 1 to 2 is isentropic compression 2 to 3 is constant pressure heat addition that's in our combustion chamber then 3 to 4 we have isentropic expansion and then finally 4 through 1 that's where we are doing heat rejection and we will consider that to be constant pressure heat rejection so that is the simple Brayton cycle now what we're going to do just like we did with the auto and the diesel and the sterling let's take a look at the thermal efficiency of this cycle okay so that is the thermal efficiency now we have a new term in this equation and that is rp and little r subscript p refers to the pressure ratio in our compression stage so that would be p2 divided by p1 and again k is the ratio of specific heat sometimes it is gamma although we're not using it in this version of the course usually in gas dynamics they use gamma and so rp is the pressure ratio so that is the thermal efficiency for the break the other thing is the amount of work that you get out of the Brayton cycle as I mentioned sometimes you may have an industrial process or electricity power generation and you want work out so here we can write the network is the work that we get out of the turbine minus the work that we have to put into the compressor so that kind of makes sense those are the two aspects that are doing the work and there's another definition called the back work ratio and that is just the work of the compressor divided by the work of the turbine now typically in a gas turbine engine it's going to vary dependent upon the design but typically about two thirds of the turbine power goes into powering the compressor so that's an introduction to the simple Brayton cycle what we're going to do next is we're going to take a walk through the engine and we'll look at a turbojet and we'll be looking at the different components that is the compression stage the combustion and then the turbine stage so that'll be what we'll cover in the next segment