JNTU B.Tech IV Year TURBO MACHINERY Previous Question Paper (July/August - 2022 - R18)

The preheat factor in a multistage compressor is defined as the ratio of the sum of the isentropic enthalpy rises of individual stages to the isentropic enthalpy rise of the overall compression process from the initial pressure to the final pressure. It accounts for the fact that the increase in enthalpy due to stage inefficiency (irreversibility) in one stage increases the inlet temperature of the subsequent stage, thereby increasing the work required for the same pressure ratio.

Mathematically, if Δh_s is the isentropic enthalpy rise of a single stage and ΔH_s is the isentropic enthalpy rise of the total process, the preheat factor (F) is given by:

To prove F > 1 (note: the preheat factor is typically greater than unity for compressors, while the reheat factor is less than unity for turbines):

1. In a compressor, the constant entropy lines on an h-s diagram diverge as pressure increases.
2. The isentropic enthalpy change for a given pressure ratio increases as the initial temperature increases.
3. Because stage inefficiencies cause the actual temperature at the exit of a stage to be higher than the isentropic exit temperature, the subsequent stages operate at higher temperature levels.
4. Consequently, the sum of the individual isentropic enthalpy rises (ΣΔh_s) is greater than the isentropic enthalpy rise of the overall process (ΔH_s) between the same total pressure limits, resulting in a preheat factor greater than unity.

Infinitesimal stage efficiency, also known as polytropic efficiency, is the efficiency of an infinitesimally small stage in a turbine where the change in pressure and temperature is negligible. It represents the efficiency of the expansion process at any point along the expansion line, independent of the total pressure ratio.

It is determined by considering the ratio of the actual work done to the isentropic work done for an infinitesimal pressure change:

For an ideal gas undergoing an expansion process, this is expressed in terms of temperature and pressure changes:

By integrating this relationship between the initial and final states, the polytropic efficiency can be related to the overall isentropic efficiency of the turbine. It is a useful design parameter because it remains nearly constant throughout the expansion process, allowing designers to predict the performance of turbines across varying pressure ratios without the influence of the reheat effect.