Question

An industrial gas turbine operates at an 8.8:1 pressure ratio and a mass flow of 77 kg/s. The
exhaust temperature is at 437?C and the inlet temperature to the machine is around 1000?C.
The machine is to be designed for a constant axial velocity of 200 m/s. (This data is based on
the Rolls-Royce Avon, an engine that dates from the 1950s but is still used as low efficiency
high reliability engine for stationary power such as pipeline pumping.)
For this gas turbine, draw to scale the meridional view with:
(a) a constant mean radius of 0.4 m.
(b) a constant outer diameter (to minimise cross sectional area) of 1.05 m.

Answer 1

This problem requires to apply the continuity equation at the inlet and exit from the turbine,to do this we need to know the density of the fluid at the inlet and exit.Thus obtained from basic fluid dynamics,

where P is the pressure , R the gas constant and T is the temperature.For air R=287J/KgK is a good approximation.The temperature has to be expresed in Kelvin.

At the entry of the turbine :

p1=8.8 bar=8.8*10^5 pa

T1=1000+273=1273K

At the exit from the turbine:

p2=1.0bar=1.0*10^5 pa

T2=473+273=730 K

The corresponding densities are therefore,

Finally we apply continuity eqation to obtain the the required blade heights:

Since mass flow from conservation applies to the turbine .This can be applied to the entry and exit of the turbine.

This is for a constant mean radius although its equally possible to design height through typical gas turbine.This is based on the assumption that the axial velocity remains constant.

THE FIGURE IS BELOW

Here the turbine is split into 3 stages with a stator and rotor.