Turbine scaling with similarity laws

[ortabe]

Hi,

I'm trying to scale up an existing air expansion turbine using similatiry laws, specifically getting the same non-dimension mass flow parameter for the scaled up turbine. I know various conditions for the existing turbine and the power requirement for the scaled up turbine.

01 = stagnation condition at inlet
03 = stagnation condition at outlet

m = mass flow
rho01 = air density
a01 = speed of sound
r = tip radius

Non-dimensional mass flow:
theta = m/(rho01*a01*r^2)

k = Cp/Cv
R = gas constant

Enthalpy change:
dh = [k*R*T01/(k-1)]*(1-T03/T01)

Work:
W = m*dh

The only way I can work out the new mass flow is to assume T03/T01 is equal for both and then find the new tip radius.

The question is:
Is it valid to assume T03/T01 is equal for both turbines or is there another method?

Thanks

 

[turb1]

The dimensionless parameter for the turbine impeller is specific speed, which has a certain range for optimal efficiency.

Assuming that the process can be scaled exactly (which it usually can since it is based on thermodynamics) then it is safe to assume that the inlet and outletr conditions are the same except for mass flow.

If you match the specific speed of the turbine impeller, then the diameter will be larger with the higher mass flow but the efficiency should be basically the same since it is more a function of U/C (tip speed over isentropic spouting velocity) and specific speed which are all constant.