## Sizing

A short procedure will enable the reader to size an axial compressor. The complete and rigorous sizing of the axial is quite tedious and requires a comprehensive computer program. By making a few simplifying assumptions, a reasonable first approximation can be derived. While axials have been used rather extensively for gas service in their history, the bulk of the applications has been in air service. This is the first limitation to the sizing method, as it is only good for gases in the air molecular weight range eliminating the Mach number considerations. The head is assumed to be reasonably well divided over the various stages, and axial velocity is assumed constant throughout the machine. The numerical values are tabulated as follows:

Hub/tip ratio, dh/dt = 0.7 minimum, 0.9 maximum

Adiabatic efficiency, rja = 0.85

Pressure coefficient, \x = 0.29

Mean blade velocity, um = 720 fps

Because the constants and frame data include units, the relations presented here will depart from the primitive form used elsewhere in the book and will incorporate the necessary units.

Calculate an inlet volume, correct for moisture, if necessary, as outlined in Chapter 2. Select the frame size using Figure 6-9. It's probably a good idea to select the smallest frame that seems to accommodate the volume at the start. The frame size has been made easy as it is the hub diameter in inches. There have been five sizes presented, which should cover most ranges encountered, although the commercially available size range extends over a somewhat broader volume range. Select the number of stages, z.

Calculate the overall required head from the pressure ratio and the inlet temperature using Equation 2.70 from Chapter 2. It is repeated here for convenience.

If the pressure coefficient is now, or was in an earlier step, 5% under the 0.29 value, calculate a new mean blade velocity using the rounded -off number of stages and the original pressure coefficient, 0.29. Use the calculated blade velocity in the subsequent step for compressor speed Calculate the speed.

In order to calculate the speed, a mean blade diameter must be established, and to calculate the mean diameter, a tip diameter is needed. The first step is to calculate the tip diameter.

where d, = tip diameter, inches dit = hub diameter, inches Q ] = inlet flow, cfm utT1 = mean blade velocity, fps then calculate a mean diameter, dm in inches:

Before proceeding, make sure the hub tip ratio is within the minimum limn of 0.67. If satisfactory, continue with the speed calculation. If the value is unsatisfactory, repeat the previous steps with an alternate frame choice:

where

N - shaft speed, rpm

The speed must not exceed the speed given in Figure 6-9 for the selected hub diameter. Calculate the last stage volume using the following:

where

Qis = last stage inlet volume, cfm rp = pressure ratio across the compressor k = isentropic compression exponent

Using Equation 6.16, calculate a stage tip diameter. Then check the hub tip ratio against the maximum value, 0.9. If the value is greater, the last stage blading is getting too short and probably the only solution is to use a smaller frame.

The guidelines presented are simplified and may not be sufficient for all applications. This does not mean that an axial cannot be used, because the vendors can perform a much more complex analysis and change factors that this simplified method chose to hold constant. Undoing some of these values is probably beyond the scope of most of the users. The best way to interpret a potential application is that an extra measure of care might be exercised when going out for bid. This can generate additional questions concerning the vendor's proposal.

To complete the sizing, calculate the discharge temperature using the Equation 4.6 from Chapter 4.

t2 = discharge temperature, °F Tj = inlet absolute temperature, °R tj = inlet temperature, °F T|a — adiabatic efficiency

Calculate the shaft horsepower, using Equation 4.7 from Chapter 4. Read the mechanical losses from Figure 6-9.

where w x H

33.000 r\n

where w = weight flow of the gas in the compressor, lb/min. Ha = total adiabatic head, ft-lb/lb

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