## Curve Shape

Figure 1-3 presented a general form performance curve for each of the compressors. The centrifugal compressor exhibited a relatively flat curve compared to the other machines. Flat is defined as a relatively low head rise for a volume change. Translated to pressure terms, it means a relatively low pressure change for a given volume change. It is important to understand some of the basics that contribute to the curve shape.

Figure 5-24 shows that if the flow is reduced for the radial wheel, a reduction occurs in the vector, Vr2, but there is no influence on the tangential component of the absolute velocity, Vu2. In fact, the ratio of Vu2/u2 = 1. In this case, the ideal curve would be flat, something that really does not happen due to the effect of slip and efficiency. Looking at the 60° curve, the Vu2 vector will increase with a decrease in flow. This is shown as decrease in the length of the Vr2 vector, raising the work input coefficient and putting a slope into the curve. Then, if the 45° vector triangle is examined, the same thing will happen; Vu2 will increase for a decrease in the flow. Because the angle (32 is less, the Vu2 increases faster for 45° than for 60°, making for a steeper curve. This is consistent with the earlier statement about the higher reaction wheel having a steeper curve.

Flow passing through an impeller is constantly changing in volume because of the compressible nature of the gas. If an impeller is operated first with a light molecular weight gas and then a heavy gas, the curve will be steeper with the light gas because the volume ratio is higher for the heavy gas. An examination of Equation 5.12 shows that head for a given geometry is fixed, within reasonable limits. Therefore, substituting different molecular weights in the head equation will indicate a higher pressure ratio directly proportional to the molecular weight. The volume ratio, then, is directly proportional to the pressure ratio making it also directly proportional to the molecular weight. Since the geometry was not modified to match the different volume ratio, the vectors, Vr2, arc shorter for the lower outlet volume. As such, the change to the vector Vu3 is not as great and the curve is not as steep.

The compressibility of the gas going through the impeller causes some problems. The assumption in the use of the fan law, when speeding up an impeller, is that the inlet volume follows the speed in a proportional manner. At the same time, the head is increased as a function of the speed squared. Just as the head increases with a given gas, so does the pressure ratio and therefore the volume ratio. It wasn't pointed out, but the alert reader may have noticed that the outlet triangle, not the inlet triangle, was used to discuss the curve shape. The problem is that the outlet volume is not exactly proportional to the inlet volume. For a 10% speed change, the compressor does not truly respond with a 21% head change. For small speed changes the problem is not serious; however, the basics should be remembered if a compressor is being rerated.

One last item should be noted regarding the shape of the curve. As stages are put together, the overall flow range of the combined stages is never larger and, in most cases, is less than the smallest flow range of the individual stages. Because of the compounding effect, as the volume is changed, the combined curve is always steeper.

Surge

Notice that the left end of a centrifugal compressor pressure volume curve does not reach zero flow. The minimum flow point is labeled as the surge limit and is the lowest flow at which stable operation can be achieved. Attempted operation to the left of that point moves the compressor into surge. In full surge the compressor exhibits an extreme instability; it backflows to a point and then temporarily exhibits forward flow. This oscillating flow is accompanied by a large variety of noises, depending on the geometry and nature of the installation. Sometimes it is a deep low frequency booming sound and for other machines it is a squeal. The pres sure is highly unsteady and the temperature at the inlet rises relatively fast. The latter is caused by the same gas backing up in the machine and then recompressing until the next backflow. Each pass through the compressor adds additional heat of compression. Mechanically, the thrust bearing takes the brunt of the action and, if not left in surge indefinitely, most compressors do survive. In fact, most compressors that have operated for any period have experienced surge at one time or another. If left unchecked, and assuming the thrust bearing is well-designed, the compressor will more than likely destroy itself from the temperature rise.

Surge is due to a stalling of the gas somewhere in the flow path, although opinions seem to differ as to exactly where. For the process plant type low head compressor, it would appear to start in the diffuser. It can also take place at one of several points in an impeller depending on the geometry. For compressors designed for higher heads, the primary stall point appears to move into the impeller. Compressors exhibit a phenomenon referred to as incipient surge or stall. This is where one element stalls but not severely enough to take the stage into a complete stall. An experienced listener can readily hear and identify the stall. If the flow is not further reduced, it can remain in this condition without further stalling. It is very close to the limit, however, and only a minor flow disturbance can trigger a full-stage surge, which may then spread through the whole compressor. Stall is a flow separation. It may be compared to an airplane wing that produces lift until the angle of attack exceeds a limiting value at which point separation becomes great and the ability to continue producing lift is lost.

Choke

The right side of the curve tends to slope in an orderly manner and then fails off quite rapidly. If taken far enough, the compressor begins to choke or experience the effect of "stonewall." If the internal Mach numbers are near 1 and/or the incidence angle on the inlet vane becomes high enough to reduce the entrance flow area and force the Mach number high enough, the compressor will choke. At this point, no more flow will pass through the compressor. The effect is much greater on high molecular weight gas, particularly at a low temperature and with the k value on the low side. The problem is that the compressor reaches the "stonewall" limit in flow before the designer had intended. If compressors are rerated, this effect must be kept in mind, particularly when the new conditions are for a lower molecular weight gas. It is possible to choke the front-end stages and starve the downstream stages, causing these stages to be in surge.

Normally, operation of a compressor in choke flow is relatively benign, particularly for compressors operating at nominal pressures of less than 2,000 psig. As the application pressurs are raised, with the higher resulting density, there is the possibility that the off-design differential pressures could become high enough to increase the stresses to a level of concern, ft would be wise if in the application of very high density compressor, due to the nature of the operation, the supplier be advised if prolonged operation in choke flow is anticipated. The supplier should review past experience with similar installations and critique the design to avoid potential problems.

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