A Differential Turbomachinery Equation with Viscous Correction
Abstract
A differential turbomachinery equation describing the energy transfer between a fluid and any body moving in that fluid was derived. The derivation is based upon the Coriolis form of the Navier-Stokes Equations. A differential equation for the total relative rothalpy was also obtained. The equalities contain a rigorous viscous correction for the total enthalpy and rothalpy. The differential equation defines the substantial derivative of the total enthalpy at any point in a fluid. This substantial derivative represents the energy transfer rate into or out of the fluid at the point. In order to obtain the total enthalpy transfer between the fluid and the body, it is necessary to integrate over the entire domain. For ideal flow regimes, the integration domain may be restricted entirely within the rotor. For real fluids, viscous coupling requires that regions outside the blade area be considered. One integration of the differential equations, a form of the Euler Turbomachinery Equation with viscous correction is derived. The resultant form contains two distinct work rate terms for the axial and radial components of the flow. The fact that integration yields a result which approximates the classic Euler Turbomachinery Equation constitutes confirmation of the derivation. An application of the equation to an ideal infinite linear cylinder with bound vorticity was developed. The cylinder was made to act like a turbine blade performing work by lifting an ideal airframe against gravity. The integration yielded the expected known result. (jhd)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 30, 1990
- Accession Number
- ADA226183
Entities
People
- Herman B. Urbach