Polytropic compression and

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 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. 

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 ... 

Relationship between adiabatic compression and polytropic compression ... 

For a compression operation handling some condensable vapors, the temperature rise will be approximately 13°F. These values are considerably lower than for conventional polytropic compression. They are almost isothermal and demonstrate the contact cooling that takes place during compression. 

For centrifugal and axial compressors, the compression path is usually based on polytropic compression. The power required for a polytropic compression can be expressed as... 

Thus, for a specified intercooler outlet temperature T2 for the gas and fixed inlet and outlet pressures Pi and P3, Equation B.53 predicts the intermediate pressure for minimum shaft work for compression of an ideal gas. The corresponding expression for a polytropic compression is given by replacing y by n in Equation B.53. Although Equation B.53 changes the intermediate pressure for an intercooler temperature different from the inlet temperature, the effect on the overall shaft work for compression is often insensitive to modest deviations of the intercooler temperature from the inlet temperature. 

For reciprocating positive pumps and compressors the fluid displacement per stroke depends on the geometry, the fluid compressibility, the polytropic coefficient, and the internal leakages and volumetric losses, but basically not on the speed of machine. 

Caution The equations presented in this chapter for polytropic head and compression work have been simplified for clarity. They cannot be used for rigorous engineering calculations.)... 

Polytropic process. Compression and expansion are important processes in chemical industry. The changes in enthalpy and... 

Example 3.2 Total entropy change in a polytropic compressing of methane We compress methane from an initial state at 100 kPa, 300 K, and 20 m3 to 250 kPa and 400 K. The compression process is polytropic (PVa = constant). The average heat capacity of methane is Cpw = 40.57 J/(mol K). Estimate the supplied work and the total entropy change if the surroundings are at 290 K. 

Assume one stage of compression, and calculate the polytropic work of compression given by Equation 5.7.1. Because the discharge temperature is un-... 

Compressors are rated in feet of compression head developed. This is the energy conveyed to a gas stream by a compressor. It is observed by the increase in gas pressure as the gas passes through the compressor. Centrifugal compressors more nearly follow polytropic operation and are widely used to handle large volumes of gas at pressure ranges of 0.5 to several hundred psi. 

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... 

Polytropic compression. In large compressors the path of the fluid is neither isothermal nor adiabatic. The process may still be assumed to be frictionless, however. It is customary to assume that the relation between pressure and density is given by the equation... 

Compressibility must be taken into account along with the adiabatic coefficient, k, (or, if known, the polytropic coefficient, n) and other losses, which will be presented in the following paragraphs. 

Polytropic system. Figures 12-37D and 12-37E, gets nearer to the conditions of a practical system, with polytropic process having n = 1.2. The gray area Wi compresses air from 1 to 2 while the air rejects heat to atmosphere through compressor cylinder walls. equals area 1-2-y-z in 4e. In the aftercooler-receiver, the air rejects heat Q i equal to gray area 2-3-w-y. 

Adiabatic expansion of the air in the engine causes a maximum temperature drop of the exhaust. Adiabatic compression causes a maximum temperature rise of the compressed air. These effects combine to cause the greatest work loss of any compressed-air system, when pressurized air must be cooled back to atmospheric temperature. The energy analysis parallels the one just made for the polytropic system. This shows that net areas on both PV and TS graphs measure the work lost. 

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