Efficiencies 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. 

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.

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

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... 

Step 3. Calculate the overall poltropic exponent using Equation 2.71 and an assumed polytropic efficiency of tip =. 75. 

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... 

In the simple approach, the change po due to Q (the first term in Eiq. (4.42)) is usually ignored for both streams. The change of po due to frictional effects in the mainstream flow is usually included in the basic polytropic efficiency (rjp) of the uncooled flow, so that... 

Consider next a similar recuperative cycle, but one in which the compression process approximates to isothermal rather than isentropic, with the work input equal to the heat rejected (this may be achieved in a series of small compressions of polytropic efficiency Tjp, followed by a series of constant pressure heat rejections). It may then be shown that the thermal efficiency of this cycle is given by... 

Fig. 3.16 showed carpet plots of efficiency and specific work for several dry cycles, including the recuperative [CBTX] cycle, the intercooled [CICBTX] cycle, the reheated [CBTBTX] cycle and the intercooled reheated [CICBTBTX] cycle. These are replotted in Fig. 6.17. The ratio of maximum to minimum temperature is 5 1 (i.e. T nx 1500 K) the polytropic efficiencies are 0.90 (compressor), 0.88 (turbine) the recuperator effectiveness is 0.75. The fuel assumed was methane and real gas effects were included, but no allowance was made for turbine cooling.

The assumptions made by the various authors (viz. polytropic efficiencies, combustion pressure loss and temperature ratio, etc.) are all roughly similar to those used in the calculations of uncooled dry cycles. Some modest amounts of turbine cooling were allowed in certain cases [9] but the effect of these on the efficiency should not be large at max 250°C (see later for discussion of more detailed parametric calculations by some of these authors). 

We also give calculations of the performance of some of these various gas turbine plants. Comparison between such calculations is often difficult, even spot calculations at a single condition with state points specified in the cycle, because of the thermodynamic assumptions that have to be made (e.g. how closely conditions in a chemical reformer approach equilibrium). Performance calculations by different inventors/authors are also dependent upon assumed levels of component performance such as turbomachinery polytropic efficiency, required turbine cooling air flows and heat exchanger effectiveness if these are not identical in the cases compared then such comparisons of overall performance become invalid. However, we attempt to provide some performance calculations where appropriate in the rest of the chapter. 

The gas compression in practically all commercial machines is polytropic. That is, it is not adiabatic or isothermal, but some form peculiar to the gas properties and the hydraulic design of the compressor. Actual machines may be rated on adiabatic performance and then related to polytropic conditions by the polytropic efficiency. Other performance rating procedures handle the calculations as polytropic. For reference, both methods are presented. 

Frame Nominal Flow Range (cfm) Nominal Max No. of Casing Stages Max Casing Pressure (psig) Nominal Speed (r/min) Nominal Polytropic Efficiency Nominal H/N (per stage) Maximmn Q/N... 

The polytropic process is mathematically easier to handle than the adiabatic approach for the following (1) determination of the discharge temperature (see later discussion under Temperature Rise During Compression ) and (2) advantage of the polytropic efficiency ... 

This applies with good accuracy for single wheels and for the overall multistage compressor. This is extremely useful in determining polytropic efficiency Values of n may be read from Figure 12-63 for approximate actual inlet flow capacity cfm, to the suction of the... 

---