Читать книгу Fundamentals of Heat Engines - Jamil Ghojel - Страница 55

It was shown in Section 1.2 that dimensional analysis and similitude can be used to derive functional representations of complex flow systems, such as compressors, using a reduced number of nondimensional groups of properties. Among the groups discussed were the velocity parameter and mass flow parameter (Eq. 1.39a). To find a physical interpretation of these seemingly arbitrary combinations of physical properties, consider first the ratio :

Combining this equation with Eq. (1.67) we obtain

(1.69)

Now, for a given compressor blade design and impeller tip speed U, C = f(U) and U = f(ND); hence, from Eq. (1.69) for the compressor inlet conditions

The compressor speed parameter is a function of the flow Mach number at the inlet (flight Mach number for a turbojet engine) and thermodynamic properties of the fluid. For a given gas with known thermodynamic properties and a compressor of fixed size,

(1.70)

Hence, the nondimensional speed parameter is directly proportional to the Mach number.