The discharge process on a screw compressor will continue until the male rotor lobe has completely rolled into the female flute, displacing all of the gas and lube oil remaining in the threads. Unlike the reciprocating machine, there are no trapped pockets of gas remaining in the machine. As a result, the volumetric efficiency of a screw compressor remains very high as pressure differentials across the machine increase.
Figure 7 provides a comparison of the reciprocating and screw machines at the completion of the discharge process. In View (B) we are still looking at the bottom of the rotors, but we are now looking from the opposite end. All of the previous rotor pictures have been from the suction end of the machine. We are now looking from the bottom at the discharge end of the rotors.
Screw compressors have two discharge ports, referred to as the radial and the axial port. The radial port is the “V” shaped cut in the slide valve and the axial port is the butterfly shaped port machined in the end casing of the compressor between the bearing bores. The discharge process will start when the leading tip of the rotor opens to the radial cut out area in the slide valve as shown in Figure 6 above. The axial port will relieve the last bit of trapped gas and lube oil from the rotors as the male lobe completely fills the female flute, closing the threads as shown in Figure 7 above.
In Figure 8 we can see the radial discharge port machined in the slide valve. The view is from the discharge end of the compressor with the rotors removed from the casing. The two bore holes will normally form the casing around the rotors. In Figure 9 we can see the rotor housing of the machine with the discharge end casing attached. The top half of the rotor housing has been cut away to show the internals. As you can see, the ports are common to the discharge flange of the compressor. They are defined differently because they each serve different purposes.
Volume Ratio
In the previous section we saw how the suction volume of the machine was based on the volume of trapped gas within a flute as it closes off from the suction port. We also showed that the discharge volume is the trapped volume in the same flute just before discharge. The ratio of suction volume divided by discharge volume is referred to as the volume ratio, or Vi, of a compressor.
The position of the radial discharge port along the axis of the rotors will determine the volume of gas in the trapped pocket at the point of discharge. Moving the radial discharge port along the axis will change the effective stroke length of the rotors, changing the volume ratio. A low Vi compressor will provide a shorter effective stroke length than a high Vi machine and vice versa. A low volume ratio machine has a higher volume of gas at the point of discharge than a high Vi machine. The suction volume is the same in both cases. Dividing the suction volume by the discharge volume will result in a lower volume ratio in this case.
The volume ratio, or Vi, on a screw compressor directly affects the internal compression ratio, or Pi, of the machine. A low Vi compressor corresponds to a low compression ratio machine. High Vi compressors are used on higher compression ratio systems.
The relationship between volume ratio and compression ratio is as follows:
Pi = Vik or Vi = Pi1/k , where k = ratio of specific heats, typically 1.26 - 1.3
Volume ratio and compression ratio are calculated using the following formula:
Vi = Vs/Vd, where Pi = Pd/Ps, where Vi = Internal volume ratio; Pi = Internal compression ratio; Vs = Internal suction volume; Pd = Internal discharge pressure,(psia); Vd = Internal discharge volume. Ps = Internal suction pressure,(psia).
Figure 10 shows two different slide valve lengths to give a comparison of a low volume ratio machine to one with a high volume ratio. Looking at the illustrations, the suction gas will enter the rotors as they unmesh in the upper left corner of the diagram. As the rotors continue to unmesh, they will close off from the suction port and establish the input volume. As the rotors turn, the trapped gas is forced towards the discharge end of the machine. The volume of the trapped pocket of gas will reduce until the leading tip of the rotor passes by the radial discharge port. This is when the discharge process begins. View (A) shows a low Vi compressor with a short slide valve. As you can see, the stroke length is short resulting in a higher volume in the flute as it passes the radial discharge port. View (B) shows a high volume ratio machine with a longer stroke length. The volume in the flute at the point of discharge is lower than the machine in View (A), resulting in a higher Vi.
Different manufacturers offer different volume ratio machines. The most common Vi range on a screw compressor is from 2.2 to 5.0. There are some machines offered outside this range for special applications, but this is the most common. Table I provides a comparison of compression ratios and their corresponding ideal volume ratios based on the formulas provided above.
The volume ratio of a compressor is very important. We know the compression process will continue until the flute is opened to the discharge port. If we operate a high Vi compressor on a low compression ratio application, we will encounter over compression. This means the discharge pressure within the machine is higher than the system discharge pressure. If we apply a machine with a Vi of 5.0 to a system with a compression ratio of 3.0 we will see extreme over compression. From Table I above, we see a compressor with a 5.0 Vi corresponds to an internal compression ratio of roughly 8:1.
Looking at a specific example, let’s use a system suction pressure of 25 psia and a discharge pressure of 75 psia. The compression ratio of the system is 3:1. The ratio within the machine is 8:1, which equates to an internal discharge pressure of eight times the suction pressure, or 200 psi, when the leading tip of the flute reaches the radial discharge port and allows the gas to escape. In this application, we would see an approximate power penalty of 40% due to over compression. Although the power penalty resulting from under compression is not quite as extreme, it is still significant. From this we can see the importance of maintaining a volume ratio in the compressor that provides an internal compression ratio as close as possible to the system
requirements.
