Inlet velocity limitations at the compressor eye
The inlet eye is an important and critical region in both centrifugal pumps and compressors and requires careful consideration at the design stage. If the relative velocity of the inlet flow is too large in pumps, cavitation (details in next section) may result with consequent blade erosion or even reduced performance. In compressors, large relative velocities can cause an increase in the impeller total pressure losses. In high-speed centrifugal compressors Mach number effects may become important with high relative velocities in the inlet. By suitable sizing of the eye, the maximum relative velocity, or some related parameter (e.g., maximum relative Mach number), can be minimized to give the optimum inlet flow conditions. As an illustration, the following analysis shows a simple optimization procedure for a low-speed compressor based upon incompressible flow theory.
For the inlet geometry shown in Figure 7.4, the absolute eye velocity is assumed to be uniform and axial. The inlet relative velocity is w1 5 ðc2 1U2Þ , which, of course, is a maximum at the inducer’s tip. The volume flow rate is
It is worth noticing that with both Q and rh1 are fixed:
i. if rs1 is made large then, from continuity, the axial velocity is low but the blade speed is high;
ii. if rs1 is made small, the blade speed is small but the axial velocity is high.
Both extremes produce large relative velocities and there must exist some optimum radius rs1 for which the relative velocity is a minimum.
For maximum volume flow, differentiating Eq. (7.5) with respect to rs1 (keeping ws1 constant) and equating to zero,
Equation (7.7) specifies the optimum conditions for the inlet velocity triangles in terms of the hub-tip radius ratio. For typical values of this ratio (i.e., 0.3 # rh1/rs1 # 0.6), the optimum relative flow angle at the inducer tip βs1 lies between 56o and 60o.