Compressors polytropic

Input Data and Computer Output of Polytropic Compressor Calculations... 

FORMAT (///,26X, POLYTROPIC COMPRESSOR CALCULATION, /, 78(1H )) CALL POLYTR... 

The rotor fouling causes a loss in the polytropic compressor efficiency. To measure the relative polytropic efficiency at two points in time, calculate ... 

Polysulfide wash, 93 Polythionic acid cracking, 425-426 Polytropic compressor efficiency,... 

Since most compressors operate along a polytropic path approaching the adiabatic, compressor calculations are generally based on the adiabatic cui ve. 

The work in a compressor under ideal conditions as previously shown occurs at constant entropy. The actual process is a polytropic process as shown in Fig. 10-65 and given by the equation of state Pv = constant. 

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. 

From this relationship, it is obvious that polytropic efficiency is the limiting value of the isentropic efficiency as the pressure increase approaches zero, and the value of the polytropic efficiency is higher than the corresponding adiabatic efficiency. Figure 3-6 shows the relationship between adiabatic and polytropic efficiency as the pressure ratio across the compressor increases. Figure 3-7 shows the relationship across the turbine. 

Figure 1, Approximate polytropic efficiencies for centrifugal and axial flow compressors.

Figure 2. Uncooled compressor relationship between adiabatic efficiency and polytropic efficiency.

Ludwig states that the usual centrifugal compressor is uncooled internally and thus follows a polytropic path. 

One significant practical difference in use of polytropic head is that the temperature rise in the equation is the actual temperature rise when there is no jacket cooling. The other practical uses of the equation will be covered as they apply to each compressor in the later chapters. 

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. 

Scltultz, J. M., The Polytropic Analysis of Centrifugal Compressors, Journal of Engineering for Power, January 1962, pp. 69-82. 

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... 

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). 

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 approximate number of stages for a centrifugal compressor, column (I), is a function of the adiabatic (and actually the polytropic) head and varies with the efficiency and physical properties of the gas. 

For a polytropic process the change of state does not take place at constant entropy, hut for an adiabatic process, it does. Heat may he added to or rejected from a gas in a polytropic process. For a polytropic process, the correlating exponent for the PiVi" component is the exponent n, which becomes an important part of the compressor design, n values are determined from performance testing. 

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. 

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 usual centrifugal compressor is uncooled internally, and hence, operates with polytropic characteristics having n greater than k however, if the unit is internally cooled, then n will be greater than 1.0 but may be less than k. The inefficiencies caused by internal losses (friction, etc.) keep the operation from being truly adiabatic however, some compressions are close to this condition and may be used for approximations. 

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... 

Polytropic Efficiency. This is the ratio of theoretical polytropic horsepower to actual brake horsepower at the compressor shaft. The polytropic efficiency does not include packing, bearing, or other losses. This efficiency is a measure of the hydraulic perfection of the compressor, and the value remains the same for any gas and for any speed (within reasonable limits). For an uncooled compressor, the polytropic, hydraulic, and temperature rise efficiencies are the same. ... 

Figures 12-65 and 12-65A give the relationship between polytropic and adiabatic efficiencies. The adiabatic efficiency can be calculated from operating data, and the polytropic efficiency can be read from the curves. For other cases, ep may be calculated from the preceding relation and the adiabatic efficiency may be determined from the curves. Figure 12-66 illustrates the relationships that may exist while evaluating a particular compressor design.

Figure 12-66. Comparative efficiencies of a 1,550 bhp centrifugal compressor based on 80% polytropic efficiency. (Used by permission Woodhouse, H. Petroleum Engineer, Oct. 1953. Hart Publications, Inc. All rights reserved.)...

Polytropic Head. The polytropic head more closely approaches the conditions of an actual compressor and is the actual height of a gas column that can be maintained at... 

This is approximately correct because the mechanical losses in the compressor are only about 1-3%. The head determined from Figure 12-67 can be used for the polytropic gas horsepower relation given previously. 

Select a compressor frame as in Table 12-9B and note the average polytropic efficiency listed, speed, and head/stage. 

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. 

The values for polytropic conditions represent an uncooled compressor, that is, no internal diaphragm cooling, no liquid injection, and no external coolers for the pressure range being considered. 

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