We were discussing the working principle of centrifugal compressorvelocity diagram of centrifugal compressorslip phenomenon and slip factor for centrifugal compressorMach number for centrifugal compressorfunction of diffuser in centrifugal compressor and losses in centrifugal compressor in our recent posts, where we were also discussing the various important parts of centrifugal compressor and their functions and we have also secured there the work done on air in centrifugal compressor.

Today we will be interested here to discuss another very important topic i.e. performance characteristics of centrifugal compressor with the help of this post i.e. performance characteristics of centrifugal compressor.

### Performance characteristics of centrifugal compressor

Let us first understand here the meaning of performance characteristic curve of a centrifugal compressor and what benefit we will get after studying the performance characteristic curve of a centrifugal compressor.

Performance characteristics curve of a centrifugal compressor will be normally described with the help of curves of delivery pressure and temperature with respect to mass flow rate for various fixed values of rotational speed at given value of inlet pressure and temperature.

If we make an experiment and draw the points to form the curve between the pressure ratio and mass flow rate, we will get a performance characteristic curve as displayed here in following figure.

There are three very important points in the curve i.e. A, B and C. We will find out here the meaning and importance of each point mentioned in the performance characteristic curve.

As we can see here in the performance characteristics curve, it will be increasing with positive slope up to a point B which will be at maximum value of pressure ratio and further it will be decreasing with negative slope and finally it will touch with abscissa at point C when mass flow rate will be huge and at this point the pressure ratio will be unity.

Now we must understand the term used here pressure ratio. What does it mean? Pressure ratio mentioned in the curve is basically the ratio of pressure at outlet of compressor and at inlet of compressor.

Now we will first understand the importance and meaning of point A. What will point A indicate in the following characteristics curve of a centrifugal compressor?

When mass flow rate will be zero, there will be a pressure ratio and point A indicates this pressure ratio when mass flow rate will be zero. Now, we will have one question in our mind that why there will be a pressure ratio even if mass flow rate is zero.

So, let us understand it.

When mass flow rate will be zero i.e. we have closed the delivery valve, impeller will be rotating and energy will be imparted on the working fluid and hence a pressure rise will take place because of the centrifugal action. Hence, fluid may not enter in to the diffuser and there will be a static pressure field which will be due to the churning action of the fluid in the impeller and it will establish a static pressure rise because of the centrifugal action which will be termed as centrifugal head.

Therefore, the centrifugal head because of the impeller rotation will be imposed on the fluid and hence a pressure ratio will be generated even if the delivery valve will be closed. This pressure ratio is displayed here in the characteristic curve by point A.

When we will slowly open the delivery valve, flow of working fluid i.e. air will be started and fluid will pass through the vaneless space and diffuser and hence there will be the diffusion process which will result the increase in the pressure.

Therefore, with increase in the mass flow rate of the fluid, pressure ratio will be increasing and will reach to the point B where pressure ratio will be maximum. It is displayed here in characteristic curve by the line AB. Beyond point B, there will not be any rise in pressure or pressure ratio with increase in mass flow rate due to the losses in the centrifugal compressor.

Therefore, point B will indicate the maximum pressure ratio point and the efficiency of the centrifugal compressor will be maximum at the point B. Beyond point B, the efficiency of the compressor will fall rapidly as there will be decrease in the pressure ratio with increase in the mass flow rate of the fluid.

If we are continuously increasing the mass flow rate of the fluid for a fixed rotational speed, there might be one point where mas flow rate will be huge and pressure ratio will be unity i.e.1 and this point is indicated by point C in the characteristic curve.

Therefore, there will not be any pressure rise and the complete energy which is giving to the compressor will be utilised to overcome the losses (losses in the centrifugal compressor) during handling the huge mass flow rate of the fluid.

Let us see now the characteristic curve, we will see here two parts i.e. AB and BC. Part AB will have positive slope, as displayed in characteristic curve, and will be usually unstable and it will be very difficult to have this part of characteristic curve in practice. While part BC, which will have negative slope, will be stable.

Let us consider that compressor is operating at point D on the part AB of the characteristic curve which is having with positive slope as displayed in the curve. Let us consider that the delivery valve is open partial and compressor is discharging the fluid with steady state.

Let us think that there is reduction in the mass flow rate due to any disturbance or by any chance there is some reduction in the mass flow rate. Due to reduction in the mass flow rate, there will be reduction in the pressure ratio too and it could be understood by observing the point D on the part of AB of the characteristic curve having a positive slop and therefore, delivery pressure of compressor will fall down rapidly.

If the pressure of fluid at downstream side of the compressor, where compressor is discharging the fluid, does not fall quickly then there will be generated a pressure gradient where pressure of the fluid at the downstream side will be higher than the delivery pressure of the compressor.

Therefore, fluid will start to flow back to the compressor from the downstream side of the compressor. Hence, net flow from the compressor will be reduced due to opposing flow and hence there will be further drop in pressure and finally point A will be secured where there will not be any flow but there will be a pressure ratio as discussed above.

Due to reduction in mass flow rate, pressure at the downstream side of the compressor will be reduced sufficiently and therefore again there will be a pressure gradient and flow will start to flow from delivery end of compressor to the downstream side of the compressor i.e. positive flow will be developed again.  Therefore, there will be flow reversal again.

Hence, A small disturbance or reduction in the mass flow rate has been resulted to have the repeating  cycles or where flow reversal will be there.

We must note it here that this type of flow reversal will take place when the compressor is on stiffer side of the part AB of the characteristic curve and that will be termed as surging of the compressor.
Therefore, this part of the characteristic curve AB will be unstable and other part i.e. BC will be stable.

As we can see from the curve that part AB of the characteristics curve is stiffer initially but becomes flat near point B. Therefore there might be one point, over the part AB which is having positive slope, just left to the point B where surging of compressor will not take place.

Surging of compressor will take place if the operating point of compressor is some distance away from point B. Point B indicates the maximum pressure ratio point where the efficiency of the compressor will be maximum.

Now we will consider the part BC of characteristics curve which is having with negative slope. We will find out here the importance and meaning of point E which has been displayed in characteristics curve.

When mass flow rate will be increased, the pressure ratio will be decreased and hence the delivery pressure will be decreased. Density of fluid will be decreased due to decrease in the delivery pressure.

Velocity of flow will be directly proportional to the mass flow rate and inverse proportional to the density of the fluid. Hence there will be huge increase in the flow velocity due to increase in mass flow rate and decrease in the density of the fluid.

Therefore for a fixed value of rotational speed, there will be a point where sonic velocity will be achieved and compressor sonic condition will be there. At this point, there will not be any further increase in the mass flow rate of the fluid even if we keep opening the delivery valve.

This particular point will be termed as a point of maximum delivery obtainable at the particular rotational speed for which the characteristics curve is drawn. Point E indicates this point of maximum delivery obtainable. We must note it here that at point E, there will not be any possibility of increase in the mass flow rate of the fluid and then it will not matter that how much wider delivery valve is opened.

Therefore, we have seen here the characteristic curve of a centrifugal compressor and we have also  seen here the various important features associated with the characteristic curve of a centrifugal compressor.

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Further we will find out, in our next post, axial flow compressor construction and working principle

### Reference:

Fluid Machines, By Prof S.K. Som