# Solving the equations of a gas turbine (elementary level)

1. Nov 25, 2012

### LaxeyT

This question is about solving the elementary thermodynamic equations of a gas turbine using an iterative solver - below I give background explanation - and can anyone say I'm on the right path here?

Undergraduate questions on gas turbines (i.e. the basic single-compressor Brayton cycle) usually, if not always, specify the parameters in such a way that the energy equations may be applied directly to find pressures and temperatures in the cycle, and hence the resultant thrust or power and fuel flow. For real engineering applications, the known input is usually inconvenient (e.g. fuel flow), and nothing else is known other than atmospheric conditions - therefore, iteration is required. I want to apply the multi-variate Newton-Raphson method in a spreadsheet and then solve for flow, pressures and temperatures, and am having trouble. (As I understand it, most commercial gas turbine solvers use compressor and turbine maps, but I want to avoid this level of detail, and simply keep it at the undergrad level that is quite commonly understood.)

So far I have tried this by specifying fuel flow (as the single fixed input), and then solving for 3 independent variables: air flow, compressor pressure ratio, and nozzle throat Mach number. There are 3 constraints: compressor work = turbine work, enthalpy rise = fuel energy released, and exit static pressure = atmospheric.

Has anyone done this for a gas turbine or similar problem, and can say I'm on the right path here?

Thanks a lot!

Last edited: Nov 25, 2012