## Volumetric Efficiency

To determine the actual inlet capacity of a cylinder, the calculated displacement must be modified. There are two reasons why modification is needed. The first is because of the clearance at the end of the piston travel.

Earlier in the chapter, when the compression cycle was described, a portion of the indicator, Path 3-4, was referred to as the expansion portion of the cycle. The gas trapped in the clearance area expands and partly refills the cylinder taking away some of the capacity. The following equation reflects the expansion effect on capacity and is referred to as the theoretical volumetric efficiency Evt.

where f = ratio of discharge compressibility to inlet compressibility as calculated by Equation 3.6 rp = pressure ratio c = percent clearance k = isentropic exponent

The limit of the theoretical value can be demonstrated by substituting zero for the clearance c, which results in a volumetric efficiency multiplier of 1.0.

The second reason for modification of the displaced volume is that in real world application, the cylinder will not achieve the volumetric performance predicted by Equation 3.4. It is modified, therefore, to include empirical data. The equation used here is the one recommended by the Compressed Air and Gas Institute [1], but it is somewhat arbitrary as there is no universal equation. Practically speaking, however, there is enough flexibility in guidelines for the equation to produce reasonable results. The 1.00 in the theoretical equation is replaced with .97 to reflect that even with zero clearance the cylinder will not fill perfectly. Term L is added at the end to allow for gas slippage past the piston rings in the various types of construction. If, in the course of making an estimate, a specific value is desired, use .03 for lubricated compressors and .07 for nonlubricated machines. These are approximations, and the exact value may vary by as much as an additional .02 to .03.

The inlet capacity of the cylinder is calculated by Q,=EvxPd Piston Speed

Another value to be determined is piston speed, PS. The average pis ton speed may be calculated by

The basis for evaluation of piston speed varies throughout industry. This indicates that the subject is spiced with as much emotion as technical basics. An attempt to sort out the fundamentals will be made. First, because there are so many configurations and forms of the reciprocating compressor, it would appear logical that there is no one piston speed limit that will apply across the board to all machines. The manufacturer is at odds with the user because he would like to keep the speed up to keep the size of the compressor down, while the user would like to keep the speed down for reliability purposes. As is true for so many other cases, the referee is the economics. An obvious reason to limit the speed is maintenance expense. The lower the piston speed, the lower the maintenance and the higher the reliability. The relationship given by Equation 3.1 defines the size of the cylinder. Therefore, if the speed is reduced to lower the piston speed, then the diameter of the cylinder must increase to compensate for the lost displacement to maintain the desired capacity. As cylinder size goes up, so does the cost of the cylinder. It is not difficult to see why the user and manufacturer are at somewhat of a cross purpose. If the user's service requires a high degree of reliability and he wants to keep cylinder and ring wear down, he must be aware of the increase in cost.

To complicate the subject of piston speed, look at Equations 3.1 and 3.8. Note the term St (stroke). The piston speed can be controlled by a shorter stroke, but because of loss of displacement, the diameter and/or the speed must be increased. If only speed is increased, the whole exercise is academic as the piston speed will be back up to the original value. If, however, diameter alone or both diameter and speed are increased, the net result can be a lower piston speed. Another factor comes to bear at this point concerning valve life, that decreases with the increase in the number of strokes and can negate the apparent gain in maintenance cost if not adequate. It would appear that the engineer trying to evaluate a compressor bid just can't win. The various points are not tendered just to frustrate the user but rather are given to help show that this is another area that must have a complete evaluation. All facets of a problem must be considered before an intelligent evaluation can be made.

After all the previous statements, it would seem very difficult to select a piston speed. For someone without direct experience, the following guidelines can be used as a starting point. Actual gas compressing experience should be solicited when a new compressor for the same gas is being considered. These values will apply to the industrial process type of compressor with a double-acting cylinder construction. For horizontal compressors with lubricated cylinders, use 700 feet per minute (fpm) and for nonlubricated cylinders use 600 fprn. For vertical compressors with lubricated cylinders, use 800 fpm and for nonlubricated cylinders use 700 fpm.

Another factor to consider is the compressor rotative speed relative to valve wear. The lower the speed, the fewer the valve cycles, which contribute to longer valve life. A desirable speed range is 300 to 600 rpm

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