Polytropic efficiency

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... 

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

To start, convert the flow to values estimated to be the compressor inlet conditions. Initially, the polytropic head equation (Equation 2.73) will be used with n as the polytropic compression exponent. If prior knowledge of the gas indicates a substantial nonlinear tendency, the real gas compression exponent (Equation 2.76) should be substituted. As discussed m Chapter 2, an approximation may be made by using the linear average ut the inlet and outlet k values as the exponent or for the determination of the polytropic exponent. If only the inlet value of k is known, don t be too concerned. The calculations will be repeated several times as knowledge of the process for the compression cycle is developed. After selecting the k value, u,se Equation 2.71 and an estimated stage efficiency of 15 / to de clop the polytropic compression exponent n. 

Step 6. Recalculate the polytropic exponent using Equation 2.71 and the new efficiency. 

Step 5. Calculate the discharge temperature for the total pressure ratio to check against the stated temperature limit, using the assumed efficiency, rjp =. 75 and the polytropic exponent. Apply Equation 5.14. 

Step 14. Use the polytropic exponents calculated in the previous step and recalculate the discharge temperature of each section to correct for the average stage efficiency. 

Pitch line velocity, 330 Polytropic compression exponent, 160 Polytropic efficiency, 34 Polytropic exponent, 34 Polytropic head... 

Fig. 2.9 illustrates this approach of tracing exergy through a plant. The various terms in Eq. (2.49) are shown for an irreversible open gas turbine plant based on the JB cycle. The compressor pressure ratio is 12 1, the ratio of maximum to inlet temperature is 5 1 (T,nax = 1450 K with To = 290 K), the compressor and turbine polytropic efficiencies are... 

The analysis of Hawthorne and Davis [1] for irreversible a/s cycles is developed using the criteria of component irreversibility, firstly for the simple cycle and subsequently for the recuperative cycle. In the main analyses, the isentropic efficiencies are used for the turbomachinery components. Following certain significant relationships, alternative expressions, involving polytropic efficiency and. tc and jcj, are given, without a detailed derivation, in equations with p added to the number. 

In their graphical interpretations, using isentropic rather than polytropic efficiencies, Hawthorne and Davis plotted the following non-dimensional quantities, all against the parameter. v = ... 

Fig. 3.13 shows the overall efficiency for the [CBTJic, plant plotted against the i.sentropic temperature ratio for various maximum temperatures Tj (and 6= Ty/Ti, with T, = 27°C (3(X) K)). The following assumptions are also made polytropic efficiency, rjp = 0.9 for compressor and turbine pressure loss fraction in combustion 0.03 fuel (methane) and air supplied at 1 bar, 27°C (3(X) K). 

If the polytropic efficiency in the absence of cooling is Tjp, then it may be shown [5] that... 

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