Control of Energy Transfer in Visual Studio .NET

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Control of Energy Transfer
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process whose flow coefficient is kS is given by F2
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Substituting for F2 in Eq. (9.23) yields the response of discharge pressure to speed: (9.26) Or, solving for flow,
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Alanipulating speed is very much like positioning a linear valve. Note that HHP varies with speed cubed. This is favorable for variable speed couplings, in that the load placed on them is quite low when speed is gradually increased from zero.
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Compressor Control
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Reciprocating compressors are considered in the same light as pumps, with the exception that their outflow can be measured easily. Their higher speed and the compressibility of the fluid help to reduce pulsations. Control methods previously described for gear and vane pumps (Fig. 9.12) can also be used for reciprocating compressors. Alulticylinder compressors cm have their flow reduced by L unloading some of the cylinders sequentially. This consists of holding the suction valve open during the entire stroke, effectively disabling the cylinder. Most multicylinder compressors are equipped with solenoid or pneumatic unloaders which may be operated from the output of a controller. There is a discrete number of flow conditions for such a compressor, so limit cycling cannot be avoided. Again, manipulation of speed where practicable has the advantage of being both continuous and efficient . Centrifugal or turbocompressors are analogous to centrifugal pumps in principle. But the compressibility of the fluid being transported affects their characteristics considerably. While discharge head was plotted against flow for a pump, compression ratio is typically t he ordinate used to display compressor characteristics. But the most, significant propert y Cerof a centrifugal compressor is the presence of an area of instability. tain combinations of low flow and high pressure fall into what is known as the lsurge region. Figure 9.14 shows where this region lies. In bhe surge region, a compressor exhibits positive feedback: decreasing flow causes pressure to fall until it is less than that in t he discharge line.
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Then a momentary reversal of flow occurs until the line pressure falls below what is being developed. These flow reversals can develop into pulsations violent enough to cause severe damage. It is obviously essential to stay clear of the surge region, yet the greatest power efficiency is ordinarily realized directly adjacent to it. So it is important to outline this region carefully. The ordinate for both plots in Fig. 9.14 is discharge-suction pressure ratio p,Jp,, starting from 1.0, or pd/p, - 1.0; the abscissa F is the volumet,ric flow at suct,ion conditions. The locus of the surge line varies with su&on temperakrre T, and can be represent.ed by the equation (9.28) Interestingly, a simple transposition allows a remarkably easy calculation of surge condit ions. Multiplying both sides of Eq. (9.28) by p, gives
pd - p, = k4F2 $ s
If a conventional orifice meter is inserted in the suction line, a differential, h, is developed relative to the volumetric flow:
Combining the last t wo expressions yields a relation between compressor differential and flow differential which describes the surge line: h = K(pd - PA (9.29)
Constant-speed compressors operate on one of the curves shown in Fig. 9.14. To control pressure, a valve in the suction or discharge may
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FIG 9.14. Plotting pressure ratio against flow squared allows easier identification of the surge region.
Control of Energy Transfer
FIG 9.15. The bypass valve only opens when the flow drawn from the compressor approaches the minimum calculated for surge protection.
Motor Compressor
be thrott led, but only to a point. If the load should call for flow falling within the surge region, part of the output of the compressor must be bypassed t)o the suction to maintain stable conditions. A control system5 which calculates the minimum flow tolerable for current values of suction and discharge pressure is illustrated in Fig. 9.15. A differential pressure transmitter senses pd - p,, and its output is multiplied by coefficient K in a ratio station, whose output in turn sets the flow controller. As long as the flow measurement exceeds the minimum value calculated above, the flow controller will leave the bypass valve closed. The ratio K should be set to allow some margin of safety, and the flow controller should be protected from overshoot with an antiwindup switch. As t he surge line is approached, the flow controller will begin to open the bypass, which increases flow, reduces discharge pressure, and increases suction pressure all at t,he same time, positively preventing surge. Rather than closing a valve in the suction line, many large compressors have an arrangement of inlet guide vanes, which may be manipulated for more efficient throttling by reducing entrance losses. In addition, the guide vanes shift the surge line to the left as they are closed, which increases the working range of the compressor. If upon a reduction in load, the speed of a compressor is reduced, pd - p, mill also decrease, and with it, the minimum flow requirement for surge protection. Thus with speed as the manipulated variable, the bypass valve usually does not need to be opened. Together with the reasons mentioned under centrifugal pumps, this makes manipulation of speed economically attractive. Control may be exercised over suction as well as discharge pressure or volumetric or weight flow. Or selection may be made between two variables as was illustrated in Fig. 6.15. These variables are all similar in nature, particularly if flow is in the differential form. As with a centrifugal pump, flow varies linearly with speed, pressure wit h speed squared.
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