Performance Characteristics:

The principal performance curve of any centrifugal machine is the head-flow characteristic.

With       ?₂ = radius of impeller

             β₂ = angle of exit at impeller tip

            C = velocity having suffix r for radial, u for tangential & 2 for exit

            ω = angular speed of impeller in rad/s

            u = velocity of impeller tip

We can write for the tangential velocity at the exit

C _u2 =u₂ -C_r2cot β₂                              ... 3.14

We already know that head developed having no pre-whirl is given by,

w = C_{u 2} u₂                                         ... 3.15

form the above two equations we get,

w = u₂ (u₂  - C_{r 2} cot β ₂ )                       ... 3.16

Therefore we find that for a given compressor, for which ?₂ & β2 are fixed, & a rotating having definite speed, the head developed is a straight line function of the radial velocity C_r2. In turn, the flow rate a is proportional to C_r2, The limiting head is u₂ that is developed at, C_r2=0, that means, at zero flow rate. This take place when the impeller is merely rotating in a mass of the fluid having the delivery valve closed.

This is seen that the nature of the characteristic based on the outlet blade angle β₂ as follows:

Three kinds of blades are identified. They are backward-curved, radial & forward curved.

(a) For backward-curved blades, β₂ < 90° head reduced with flow and therefore with                      Q

 (b) For radial blades, β₂ = 90° head = u ₂ = const.

 (c) For forward-curved blades, β₂ > 90°, head enhance with flow

Mollier Diagram of Centrifugal Stage

From the point of view of the optimal design, an outlet blade of angle of 32° is generally preferred. However, A simple design will have radial blades.

Given fig indicate the theoretical head-flow characteristic for the three cases of angle β₂. For the particular case of backward-curved blades, this is a drooping characteristic.

Though, the actual characteristic may be obtained by considering the following losses as shown in given fig.

 (a) Leakage loss L₁ proportional to the head.

 (b) Friction loss L₂ proportional to and so Q₂

 (c) Entrance loss L₃ because of turning of the fluid to enter the impeller, being zero at the designing point, that also corresponds to highest efficiency.

 Performance Characteristic and Losses of a Centrifugal Compressor