IMPORTANCE OF HEAT-TRANSFER FROM FLUID FILM TO STATOR IN TURBULENT-FLOW ANNULAR SEALS
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abstract
An approximate analytical method is presented to examine the importance of heat transfer from the fluid film to the stator in turbulent flow annular seals. The seal is assumed to operate at a steady state and centered condition. An adiabatic shaft surface and a radial heat flow to the stator are considered. A global energy balance in the fluid film and the seal stator renders two one-dimensional problems which are solved simultaneously to obtain closed-form solutions. The analysis shows that the effects of heat transfer from the fluid film to the stator are controlled by the adiabatic number. A high value of the adiabatic number (greater than 10) means that the thermal energy flow through the stator is negligible. A numerical example shows that for cryogenic liquid turbulent flow annular seals typical of cryogenic turbopump applications, the heat generated in the fluid is carried away mainly by fluid advection while heat conduction through the stator is relatively small. Therefore, the fluid temperature-rise along the seal can be approximated by an adiabatic flow process assumption. The approximate analytical solution is compared with a full thermohydrodynamic analysis, where the three-dimensional heat conduction problem in the stator is solved by the boundary element method. The difference in results between the two methods is less than 3%. 1993.
