Zero-staging is demonstrated by the following relationship:
w_2 = (w_2 \frac{\sqrt{T_3}}{P_3}) \times (\frac{P_3}{P_2}) \times (\sqrt{\frac{T_2}{T_3}}) \times (\frac{P_2}{\sqrt{T_2}}) \, where: core mass flow =
w_2 \, core size =
(w_2 \frac{\sqrt{T_3}}{P_3}) \, core total head pressure ratio =
(\frac{P_3}{P_2}) \, inverse of core total head temperature ratio =
\frac{T_2}{T_3} \, i.e. (
\frac{P_3}{P_2} \,) core entry total pressure =
P_2 \, core entry total temperature =
T_2 \, So basically, increasing
\frac{P_3}{P_2} \, increases
w_2 \,. On the other hand, adding a stage to the rear of the compressor increases overall pressure ratio, and decreases core size, but has no effect on core flow. This option also needs a
Turbine with a significantly smaller flow capacity to drive the compressor. Zero-staging a compressor also implies an increase in shaft speed:
N_2 = (N_2 \sqrt{T_3}) \times \sqrt{T_3} \, where: HP shaft speed =
N_2 \, HP compressor "non-dimensional" speed (based on exit total temperature) =
(N_2 \sqrt{T_3}) \, HP compressor exit total temperature =
T_3 \, So if the "non-dimensional" Speed of the original compressor is to be maintained, increasing
T_3 \, increases
N_2 \,. This implies an increase in both the blade and disc stress levels. If the original shaft speed is maintained, then the increase in pressure ratio and mass flow from adding the zero stage will be severely reduced. Although the above equations are written with zero-staging an HP compressor in mind, the same approach would apply to an LP or intermediate-pressure (IP) compressor. ==References==