On the Conservation of Rothalpy in Turbomachines

Abstract

The conditions under which rothalpy is conserved are investigated by means of the energy and moment-of-momentum equations for unsteady flow of a viscous, compressible fluid. Differential and integral equations are given for the total enthalpy and rothalpy in both stationary and rotating coordinates. From the equations in rotating coordinates it is shown that rothalpy may change due to: (1) pressure fluctuations caused by flow unsteadiness in the rotating frame; (2) angular acceleration of the rotor; (3) work done by viscous stresses on the relative flow in the rotating frame; (4) work done by body forces on the relative flow; (5) changes in entropy due to viscous dissipation and heat transfer. Conclusions of this investigation are compared with those of previous authors, some of whom have stated that rothalpy is conserved even in viscous flows. A modified Euler’s turbomachine equation, which includes viscous effects, is derived and errors in previous derivations noted.

Some Implications of a Differential Turbomachinery Equation With Viscous Correction

“…Therefore, the pseudo-ideal term cannot be ideal unless the system is ideal. Similar conclusions apply to the total relative rothalpy [12], which depends upon the pseudo-ideal term.…”

“…Now Equation (8) may be used to replace the pressure gradient in (12). From the dot product of U with the moving frame equality in (8) the pressure gradient term becomes (see Reference [10] ):…”

“…Wu's totp.1 relative rothalpy relation [7][8][9] (see also [12]) with I defined by h + W 2 /2 -U 2 /2 -h,-UVU is given by:…”

Unsteady Cooled Turbine Simulation Using a PC-Linux Analysis System

“…As presented by Lyman (1992), Rothalpy has properties in a rotor similar to total enthalpy in a nozzle. It is conserved on a steady streamline in inviscid flow.…”

Multi-Fidelity Simulation of a Turbofan Engine With Results Zoomed Into Mini-Maps for a Zero-D Cycle Simulation

“…An entropy equation is applied which accounts for mixing loss and other loss mechanisms. The unshrouded rotor in the HPT has an extra term in the energy equation that is calculated in the high fidelity simulation and described by Lyman [25].…”