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Effect of Mach No. and Shock losses in Compressors
For any kind of Compressor operation at very high ranges of speed, it is mandatory to bear substantial compressibility effects. High compressibilty effects lead to high variation in density of the flow medium. Although high Mach number signifies high mass flow per unit area as well as high pressure ratios across the stage, but excessive increase can result in shock wave generation which decreases the efficiency of the Turbo-machine owing to entropy generation. As we are dealing with compressors and turbines which majorly concerns with pressure variation across the stage, so for that analysis, the empirical formulation to be used is

P2/ P1 = 1+ Cp*γM2/2

For high subsonic flows, Critical Mach number(M1cr) is a characteristic value of considerable importance.It is the Mach No. for which sonic conditions are reached locally in flow field i.e. there will be no shocks. So for minimizing the shock losses and profile losses, the turbo-machine should be operated below M1cr. The mach no. range can be extended beyond M1cr by carefully designing blade shapes as well.

Even with increase in relative Mach number, the value of Cp also increases leading to an even greater rise in static pressure in compressors. Hence the boundary-layer thickness as well as losses increase. So for a given incidence, off-design losses will increase with increasing mach number and there will be an drastic increase close to a Critical Mach Number (resulting in shock waves inside passage)

Estimation of Shock losses
For consideration of two-dimensional shock losses for a compressor, three major contributing factors have been considered:-


 * 1) Bluntness of the leading edge with Supersonic upstream Mach Number.
 * 2) Location and strength of passage shock.
 * 3) Losses from boundary growth and shock-boundary-layer interaction. (Very small for weak shocks)

Koch and Smith in 1976 were the first to develop some correlation for estimation of Shock Loss Coefficient (ζsh). The models used for estimation were empirical correlations for Leading-edge losses and passage shock loss model. They assumed that the passage shock loss is equivalent to entropy rise of oblique shock that reduces passage inlet mach no. to unity.The results shown by their experiments is shown in the following figure.