Compressor polytropic head

The computer program PROG61 calculates the polytropic and adiabatic heads of a compressor. Table 6-5 shows the input data and results of the gas mixture. The gas discharge temperature is 310.4°F and the compressor polytropic head is 76874 ft with a total break horsepower = 960 hp. 

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. 

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. 

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... 

The centrifugal compressor, unless it is dirty or mechanically defective, has to operate on its curve. As the compressor discharge pressure increases, then Hp, the feet of polytropic head required, must also increase. Also, as can be seen from the compressor curve, the volume of gas compressed (ACFM) must decrease. When the volume of gas drops below a critical flow, the compressor will be backed up to its surge point. 

We can increase AP by either of the following options raise the density of the vapor or raise the feet of polytropic head, developed by the compressor. 

Jane concludes that the lower-density gas will require more feet of polytropic head to develop the required AP. To avoid the possibility of surge, she decides to increase the number of wheels on the compressor from five to six. While Jane has used good engineering judgment, she has made a serious error. It turns out that John should not have been trusted. The actual molecular weight of the gas turns out not to be 24 or 30, but 36. The gas is 50 percent more dense than Jane s design specifications. 

Wouldn t it be more simple to just slow down the compressor as the molecular weight increases After all, it seems as if we need less feet of head when the gas density increases. As we slow the compressor by 10 percent, the feet of polytropic head would drop by 20 percent. Fine. But 99 percent of motor-driven compressors are fixed-speed machines. 

According to the compressor curve shown in Fig. 28.3, the feet of polytropic head Hp increases as the ACFM decreases. 

The most cost-effective way to produce a high polytropic head is to increase the number of wheels on the rotor. But the longer the rotating assembly, the more difficult it is to properly balance the rotor. Especially for high-speed machines, rotors which become unbalanced are subject to destructive vibration. Therefore, for low-molecular-weight gas services (less than 10), it is not uncommon to use reciprocating compressors. 

While it is possible to use isentropic head as a characterizing variable for a compressor, most manufacturers who appeal to the concept of head prefer to use a numerically similar parameter, the polytropic head . The poly tropic efficiency and polytropic head will be discussed in the next section. 

The power absorbed by the compressor section is given by equation (17.68). We may use equation (17.80) to express the power in terms of polytropic specific work/ polytropic head and polytropic efficiency ... 

It should be emphasized that the polytropic head is an idealization in the same way that the isentropic head was an idealization. Taken together with the polytropic efficiency, however, it provides a way of analysing compressor performance, as will be shown in the next section. 

Since the polytropic head has the same units as the pump head times the acceleration due to gravity, it follows that we may apply the dimensional analysis of Section 17.2 to the compressor as well as the pump, with H p replacing gH. This reveals the same independence of the specific volume of the fluid being passed, and the same dependence on volume flow rate at suction, Q, and speed, N. 

Instead of considering polytropic head, it is possible to carry out an alternative dimensional analysis based on inlet and outlet pressures of a compressor section. We will begin by assuming that the compression process may be represented using the parameter set ... 

Dimensionless parameters are also used to characterize compressor performance. The impeller work eoeffieient r is defined as the total enthalpy change across the impeller (per unit mass) divided by the tip speed squared. The polytropic efficiency tjp is defined as shown in Eq. (3) below. The polytropic head coefficient fx is calculated by multiplying the polytropic efficiency with the impeller work coefficient... 

Let s look at Figure 25-2. The discharge pressure of the compressor is fixed by the absorber fuel gas pressure control (PC). If we start to raise the absorber pressure by closing this PC, the compressor will have to develop more differential pressure. That means it will have to produce more feet of polytropic head (Hp). As shown in Figure 25-1 the compressor will be backed up on its curve. The volume of gas compressed will be reduced. The pressure in the wet gas drum will then rise. The other PC on the spill-back line will then start to close in order to reduce the volume of gas flowing back to the compressor s suction. 

A surging compressor is really attempting to over-produce polytropic head. As the operator, you are asking it to produce more polytropic head than it is really capable of developing. Each surge is a distress call for help "Reduce your demand for polytropic head or I will die "... 

To save the compressor we can reduce our demand for polytropic head by ... 

Compressor performance is quoted in terms of polytropic head. This is the work done on the gas and its definition is developed from basic gas laws. Firstly Boyle s Law states that the volume (V) occupied by a gas is inversely proportional to its absolute pressure (JP). 

Compressor performance curves should strictly be plots of polytropic head H against suction flow measured in actual volumetric units (F ). However, it is common for discharge pressure, or the ratio of discharge to suction pressure, to replace polytropic head. In order to simplify the description of how possible flow controls operate, we will use the curves in this form. These approximations assume suction conditions and molecular weight remain constant. Should either change then the performance curve, drawn on this basis, will move. 

Dy = density of the vapor at the suction of the compressor = polytropic feet of head... 

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