Polytrope

The plot of pressure versus volume for each value of exponent n is known as the polytropic curve. Since the work W performed in proceeding from Pi to po along any polytropic cui ve (Fig. 10-65) is... 

Since most compressors operate along a polytropic path approaching the adiabatic, compressor calculations are generally based on the adiabatic cui ve. 

The work in a compressor under ideal conditions as previously shown occurs at constant entropy. The actual process is a polytropic process as shown in Fig. 10-65 and given by the equation of state Pv = constant. 

Likewise for polytropic efficiency which is often considered as the small stage efficiency or the hydraulic efficiency ... 

Polytropic efficiency is the hmited value of the isentropic efficiency as the pressure ratio approaches 1.0, and the value of the polytropic efficiency is higher than the corresponding adiabatic efficiency as seen in Fig. 10-66. 

A characteristic of polytropic efficiency is that the polytropic efficiency of a mnltistage unit is equal to the stage efficiency if each stage has the same efficiency. 

Efficiency for a turboexpander is calculated on the basis of isentropic rather than polytropic expansion even though its efficiency is not 100 percent. This is done because the losses are largely introduced at the discharge of the machine in the form of seal leakages and disk friction which heats the gas leaking past the seals and in exducer losses. (The exducer acts to convert the axial-velocity energy from the rotor to pressure energy.)... 

Above a minimum intake flowrate of about 50,000 m /hr and depending on the required discharge pressure, axial compressors (Figure 4-15) offer certain advantages. Their polytropic efficiencies. 

Figure 3-6. Relationship between adiabatic and polytropic efficiency.

Figure 8-8. Relationship between polytropic and isentropic efficiency during expansion.

The polytropic efficiency in a turbine can be related to the isentropic efficiency and obtained by combining the previous two equations... 

First, the required head is calculated. Either the polytropic or adiabatic head can be used to calculate horsepower so long as the polytropic or adiabatic efficiency is used with the companion head. 

Figure 2 gives the relationship between polytropic and adiabatic efficiencies. 

Figure 1, Approximate polytropic efficiencies for centrifugal and axial flow compressors.

Figure 2. Uncooled compressor relationship between adiabatic efficiency and polytropic efficiency.

K = Adiabatic exponent, Cp/Cv N = Polytropic exponent, (N - 1)/N - (K Pi, P- = Suction, discharge pressures, psia Ti, = Suction, discharge temperatures, °R Ep = Polytropic efficiency, fraction... 

Ludwig states that the usual centrifugal compressor is uncooled internally and thus follows a polytropic path. 

HP = Gas horsepower W = Flow, Ib/min Hpoiy = Polytropic head Had = Adiabatic head Ep = Polytropic efficiency Ea = Adiabatic efficiency... 

For a polytropic (reversible) process, the following definitions need to be considered ... 

---