Abstract
A steady-state one-dimensional axisymmetric numerical model of a mechanical seal in two-phase flow is presented. In this work a non-linear thermal model is implemented using a coupled (monolithic) approach, linking the fluid film and sealing rings. It is solved for the temperature fields of the fluid and solids, heat fluxes between fluids and solids, enthalpy of the fluid, and the vapor mass fraction, using Newtons method. The novelty of this approach lies in 1) the thermal coupling between fluid and solids, and 2) the implementation of saturation curves to couple temperature, enthalpy, and vapor mass fraction. The temperature across the seal gap is described by an analytical parabolic temperature profile by assuming a plane Couette flow in the radial direction. From this assumption, an equation for the wall heat fluxes is derived, which couples the temperature fields of the fluid and solids. The IAPWS-IF97 standard for the thermodynamic properties of water is used to obtain non-linear equations that couples the fluid temperature, enthalpy and the vapor mass fraction. The model and its implementation is described in detail. Several cases of seal behavior and two-phase flow are studied and show good agreement with other results from literature, validating the coupled approach for modelling phase-change in mechanical seals.
Highlights
Mechanical seals consist of two concentric rings, one rotating and one stationary
In this work a non-linear thermal model is implemented using a coupled approach, linking the fluid film and sealing rings. It is solved for the temperature fields of the fluid and solids, heat fluxes between fluids and solids, enthalpy of the fluid, and the vapor mass fraction, using Newtons method
The IAPWS-IF97 standard for the thermodynamic properties of water is used to obtain non-linear equa tions that couples the fluid temperature, enthalpy and the vapor mass fraction
Summary
Mechanical seals consist of two concentric rings, one rotating and one stationary. During operation the two rings are pressed together, creating a thin interface between them for the sealed fluid to pass through. Hughes et al [5] proposed a discrete boiling model (DBM) where boiling occurs at a discrete interface within the seal, which works well for low-leakage scenarios Using this approach Lebeck [6] studied the effects of seal design parameters on two-phase flow operation, showing that it can in some cases be beneficial and proposed an explanation for the ’puffing’ phenomena. In the present model the solid and fluid domains are instead coupled by assuming a parabolic temperature profile across the film This system is appended with a set of non-linear equations for the saturation conditions of water, resulting in a coupled non-linear system of equations for the thermal equilibrium of the seal. This approach is validated by testing it against well understood theoretical results and used to simulate different behaviors of the seal
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