## Example

Rerate the compressor considered in Example 4-1 for an alternate set of conditions given below. Use all other conditions from the previous example.

P2 = 50.75 psia new discharge pressure rp = 3.5 new pressure ratio rv = 2,77 new volume ratio

Step 1. Calculate a new inlet volume using the value of displaced volume from the previous example.

Qd = 2,809 cfm displaced volume

Refer to Figure 4-6 and, at a pressure ratio = 3.5, read the volumetric efficiency = 87%. Use Equation 4.4 to develop the inlet volume.

Qi = 2,444 cfm inlet volume

By proportion, obtain a new inlet weight flow.

Step 2. Reuse the rotor tip speed and sonic velocity from Example 4-1 as the conditions used in their development that have not changed.

a = 1220.6 fps sonic velocity u = 286,0 fps rotor tip speed

Refer to Figure 4-4 and, at a pressure ratio = 3.5, read the Mach number, u(./a = 0.27. Calculate the optimum tip speed uQ.

u0 = 329.6 fps optimum tip speed

Now calculate the tip speed ratio.

u/u0 = .868 tip speed ratio

Step 3. Use Figure 4-7 to obtain the adiabatic efficiency for pressure ratio = 3.5 and volume ratio of 2.77. From the curve, adiabatic efficiency = 73%. Next, look up the efficiency ratio on Figure 4-5 for the tip speed ratio just developed and obtain a value of .98. Use this value as a multiplier to derate the adiabatic efficiency for operation at other than the optimum tip speed.

Step 4. Solve for the adiabatic power, making the same conversions used in Step 4 of Example 4-1.

14.5x2444x5.34(3.5

.187

.715x229

Use Equation 4.6 to solve for the discharge temperature.

.715

399°F discharge temperature

Step 5. For the final step, compute the new shaft power value using Equation 4.7.

W =346.4 hp new shaft horsepower

The example demonstrates that operating the compressor off the built-in pressure ratio means operating at a lower efficiency. This could be anticipated from Figure 4-3. The optimum port configuration for the various types of screw compressors was determined from a series of prototype tests. The change in volumetric efficiency is not a result of the built-in volume ratio, but is due to the increased slip (internal leakage) from the higher operating pressure ratio. In the last example, a slight loss of efficiency was shown for operation at other than the optimum tip speed. While, in the example, the penalty was not too severe, it does give a directional indication of the potential problems with off-design operation.

Figure 4-8 shows a comparison of the two currently used rotor profiles. Figure 4-8a shows the circular profile used in the past for both the dry and flooded compressor. The newer asymmetric profile shown in Figure 4-8b is being adopted for use in both dry and flooded service by various vendors because of the improved efficiency due to a lower leakage in the discharge area of the compressor. Because size is a factor, the improvement in efficiency is more dramatic in the smaller compressors.

Figure 4-8. The two rotor profiles of helical screw compressors.

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