Dry Compressors

The nonflooded compressor rotor leakage can be related to the rotor tip Much number. The rotor tip velocity can be calculated by u = nxdxN (4.5)

The optimum tip speed is .25 Mach at a pressure ratio of 3. The value shifts slightly for other built-in pressure ratios, as shown in Figure 4-4.

Figure 4-4. Optimum tip speed vs. pressure ratio.

Besides affecting the volumetric efficiency, the leakage also has an effect on the adiabatic efficiency. Figure 4-5 is a plot of the tip speed ratio, u/u0, (operating to optimum) against the efficiency ratio, off-peak-to-peak effi-

Efftciency Ratio

Tip Speed Ratio U/Uo

Tip Speed Ratio U/Uo

Figure 4-5. Tip speed ratio vs. efficiency ratio.

ciency. Figures 4-6 and 4-7 show a set of typical volumetric and adiabatic efficiency curves for three built-in ratios.

The adiabatic efficiency should be corrected for molecular weight. Generally the efficiency decreases with lower molecular weight and increases with increased molecular weight. As an arbitrary rule of thumb, a straight line relationship can be assumed. The correction is a -3 percentage points at a molecular weight of 2, 0 at 29, and +3 at the molecular weight of 56. For example, a compressor with an air efficiency of 78% would have an adiabatic optimum tip speed efficiency of 75% when operating on hydrogen.

The screw compressor can be evaluated using the adiabatic work equation. Discharge temperature can be calculated by taking the adiabatic temperature rise and dividing by the adiabatic efficiency then multiplying by the

Pressure Ratio

Figure 4-6. Pressure ratio vs. volumetric efficiency for an SRM compressor.

Figure 4-7. Pressure ratio vs. adiabatic efficiency for an SRM compressor. (Modified from [41.)

temperature rise efficiency to account for cooling. To obtain the discharge temperature, add the inlet temperature to the temperature rise. The work equation was developed in Chapter 3 and repeated here for convenience

where

Wa = adiabatic work input Pi = inlet pressure Ch = inlet volume n,a = adiabatic efficiency

For the discharge temperature, t2,

Ti(rplT-l)

"Ha

where tt = inlet temperature Tj = absolute inlet temperature rja = adiabatic efficiency r)t = temperature rise efficiency

A typical value for the temperature rise efficiency is .9. For shaft power, Ws,

where mech loss = .07 x Wa for estimating purposes.

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