Efficiency, compression polytropic

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

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. 

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... 

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. 

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 ... 

Calculate the compression ratio, Pd/Ps = P2/P1 = Pc-From Table 12-9B for the compressor frame selected, select polytropic efficiency, Cp, and using Figure 12-65A, determine adiabatic efficiency, e d. 

Equation B.28 is useful to estimate the polytropic coefficient n if the inlet and outlet pressures are known, along with an estimate of the isentropic efficiency. Knowing the polytropic coefficient allows the outlet temperature for a real gas compression to be estimated from Equation B.26. 

Equation B.27 relates the isen tropic compression efficiency, heat capacity ratio y and polytropic coefficient n to the inlet and outlet pressures and can be rearranged to give ... 

Whereas reciprocating compressors are normally designed on the basis of adiabatic work (together with an isentropic efficiency), centrifugal compressors are usually designed on the basis of polytropic work. By analogy with Equation B.15, the work required for a poly tropic compression is given by ... 

Figure 7.27. Efficiencies of centrifugal and reciprocating compressors, (a) Polytropic efficiencies of centrifugal compressors as a function of suction volume and compression ratio (Clark Brothers Co.), (b) Relation between isentropic and polytropic efficiencies, Eqs. (7.22) (7.23). (c) Isentropic efficiencies of reciprocating compressors (De Laval Handbook, McGraw-Hill, New York, 1970). Multiply by 0.95 for motor drive. Gas engines require 7000-8000 Btu/HP.

Polytropic efficiencies are obtained from measurements of power consumption of test equipment. They are essentially independent of the nature of the gas. As the data of Figure 7.27 indicate, however, they are somewhat dependent on the suction volumetric rate, particularly at low values, and on the compression ratio. Polytropic efficiencies of some large centrifugal compressors are listed in Table 7.6. These data are used in Example 7.9 in the selection of a machine for a specified duty. 

To size a conq)ressor requires calculating the power needed for compression. This can be done by assuming an isentropic compression and then correcting the result by dividing by an isentropic efficiency. The power can also be calculated by assuming a polytropic compression, and then correcting the result by dividing by a polytropic efficiency. Both methods will be considered. The isentropic method is also used for blowers and vacuum pumps, but the polytropic method could also be used if data were available. First, we need to derive relationships to calculate the compressor power. 

To obtain the actual work of compression, divide the polytropic work of conpression by the polytropic efficiency. 

Compression Work with Variable Heat Capacity 157 Polytropic and Isentropic Efficiencies 158 Finding Work of Compression with a Thermodynamic Chart 160... 

The accuracy of the developed polytropic head and efficiency curve may be reduced due to volume ratio effects. These effects are the influences that the performance of one impeller has on those of the impellers downstream. Lapina [ 1 ] stated these effects are greater as the number of impellers within a compression section increases. He proposed some guidelines to assess the volume-ratio effects for differences in the inlet conditions. An equation to calculate the value of 0 for both the old or reference inlet conditions and the proposed new inlet conditions is given by... 

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