A QUANTIFIED STUDY OF ROTHALPY CONSERVATION IN TURBOMACHINES

Previous studies are generally confined to establishing the fundamenta l validity of the assumption of rothalpy conservation and usually comm ent on its significance without providing any quantitative assessments to support their stated conclusion. This study attempts to quantify i n terms of the order of error of temperature and velocity that may typ ically occur in practical turbomachine calculations involving a real f luid (one supporting both viscous stress and heat conduction) as a res ult of assuming that rothalpy is conserved. To this end, (constant) tr ansport coefficients for molecular/turbulent momentum and heat conduct ion are included in the analysis, which derives a complete general exp ression for the transport of rothalpy in flow through generalised roto r blades. Flow norms are taken from a typical centrifugal compressor ( being regarded as a more;extreme geometry) to assess orders of error a rising from each term in the rothalpy transport equation for a particl e. In assessing the error significance, account is taken of how rothal py conservation might be employed in a practical calculation scheme an d to what use the error variable might subsequently be put. The genera l conclusion is that errors arising from the assumption of rothalpy co nservation are, in practice, negligible. in particular, the effect of rotating blades, as compared to stationary ones is completely negligib le, and one of the greatest errors arises from the term involving Pran dtl number. Ii the Prandtl number is assumed to be unity, as has been the case in some classical boundary layer studies, then this very sign ificant term vanishes from consideration.