Compression polytropic

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. 

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

For polytropic compression, the change may be described by the following equations ... 

For the theoretical cycle work performed in a polytropic compression cycle (nonideal fluid) ... 

Polytropic compression is characterized by being neither adiabatic nor isothermal but is a variable entropy process. Its relation is expressed... 

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. 

The output power of P of a fan is the rate at which useful energy is delivered to the gas stream, based on polytropic 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... 

Equation B.21 assumes the compression to be adiabatic ideal gas (isentropic) compression. In practice, the compression will be neither perfectly adiabatic nor ideal. To allow for this, the gas compression can be assumed to follow a polytropic compression represented by the empirical expression ... 

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. 

Work in polytropic compression of a gas with equation of state PV = zRT is entirely analogous to Eq. (7.26). The hydrodynamic work or the work absorbed by the gas during the compression is... 

For polytropic compression the final temperature is given directly... 

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. 

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. 

Pcp compressor power for a polytropic compression Pe electric motor power Pp fan power Pp pump power Pj turbine power R gas constant s entropy T absolute temperature... 

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