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Friday, 11 October 2019

MACH NUMBER FOR CENTRIFUGAL COMPRESSOR

We were discussing the basic principle of operations, functions of various parts and performance characteristics of different types of fluid machines such as hydraulic turbinescentrifugal pumps and reciprocating pumps in our previous posts. We have seen there that working fluid for above mentioned fluid machines was liquid such as water. 

Now it’s time to discuss few other types of fluid machines such as centrifugal compressors, axial flow compressors, fans and blowers where working fluid will be steam, air or gases. 

We have already seen the working principle of centrifugal compressorvelocity diagram of centrifugal compressor and slip phenomenon and slip factor for centrifugal compressor in our last 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 a very important criteria i.e. Mach number for centrifugal compressor with the help of this post. 

Mach number for centrifugal compressor 

Mach number is basically a dimensionless number which is used to specify the flow in all types of machines that handles the compressible fluid. 

Mach number is basically defined as the ratio of flow velocity to the velocity of sound related to the fluid flow at the state of the fluid. It is indicated by Ma. 

Mach number is very much dependent over the state of fluid. State of fluid indicates the density and temperature of the fluid.   
Mach number = Flow velocity /velocity of sound

Ma = V/a 
Where,
Ma = Mach number

V = Flow velocity

a= Velocity of sound 

Now we will classify the types of flow on the basis of Mach number 

When flow velocity is equal to the velocity of sound, Mach number will be one and such flow will be termed as sonic flow. 

When flow velocity is less than the velocity of sound, Mach number will be less than one and such flow will be subsonic flow. 

When flow velocity is more than the velocity of sound, Mach number will be greater than one and such flow will be supersonic flow.  

Things to remember – 

Sonic flow, V = a or Ma = 1 
Subsonic flow, V < a or Ma < 1 
Supersonic flow, V > a or Ma > 1 
Incompressible flow, Ma < 0.3 

We have mentioned above incompressible flow. Incompressible fluid flow indicates that density will not be changing with respect to pressure. In case, if density is changing with respect to pressure then it will be negligible and could be neglected and considered that density of fluid is constant with respect to pressure.  

If flow is supersonic i.e. Mach number is greater than one, there will be some losses in the static pressure of the centrifugal compressor and these losses will not be desirable and therefore a compressor designer has to be very careful to avoid the unnecessary increment in Mach number.  

Important Notes:  

In above equation of mach number i.e. Ma = V/a, V is the velocity of flow. Velocity of flow here is the velocity related to the solid surface. In a turbo machine, solid surface is also moving and therefore relative velocity of the fluid will be considered to determine the Mach number in turbo machine i.e. centrifugal compressor. 

Mach number = Relative velocity of fluid flow /velocity of sound 

Ma = Vr/a  

Mach number must be less than 1 to secure the subsonic flow in order to avoid the losses in the static pressure of the centrifugal compressor. A centrifugal compressor designer will determine the Mach number for each and every section of the compressor.  

Fluid flowing through centrifugal compressor will gain the kinetic energy from the impeller and therefore velocity of fluid flow will be high at the outlet of the impeller. Hence, Mach number will be maximum at the outlet of the impeller tip. 

In order to restrict the Mach number at the outlet of impeller tip where it will be maximum, we need to check the mach number at the inlet of the impeller tip. Therefore inlet design of centrifugal compressor will be carried out in such a way that mach number at the inlet of the impeller tip will be relatively low.   

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Further we will find out, in our next post, function of diffuser in centrifugal compressor.   

Reference:  

Fluid mechanics, By Prof S.K. Som 
Image courtesy: Google  

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