Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic features of the model were determined through numerical simulations. The equation of heat transfer in this model was analyzed as a function of time. The phenomena observed in the seal include the conduction of heat from the fluid film in the gap to the rotor and the stator, followed by convection to the fluid surrounding them. In the calculations, it is assumed that the working medium is water. The major objective of the study was to compare the results of the classical equation of heat transfer with the results of the equations involving the use of the fractional-order derivative. The order of the derivative was assumed to be a function of time. The mathematical analysis based on the fractional differential equation is suitable to develop more detailed mathematical models describing physical phenomena.

Thrust Force Measurements in an Axial Steam Turbine Test Rig: Effect of Disk Balance Holes

A full-size, full-speed, axial flow steam turbine test rig capable of measuring turbine thrust, and static pressures in the rotor-stator disk cavity was built and commissioned. The test rig was operated in a single-stage configuration for the test results first reported in Stasenko et al. [1], and now in this paper. The stage has stationary axial face seals radially inward of the airfoils, near the rotor disk rim. The face seals divide the rotor-stator cavity into inner and outer circumferential cavities, both of which were instrumented with static pressure probes on the stator radial wall. Axial thrust was measured with load cells in every thrust bearing pad. The test rig was operated over a range of three nominal stage pressure ratios (designated as LPR, MPR, and HPR), five nominal stage velocity ratios (0.25–0.6), and five admission fractions (0.38–0.88). This latest group of tests was conducted without rotor disk balance holes, which were mechanically plugged, and will be compared to the original block of tests with disk balance holes opened. In the upstream disk cavity, the two disk balance hole configurations shared many similar pressure characteristics: nearly uniform pressures in the inner cavity, circumferential pressure distributions in the outer cavity that corresponded with the direction of axial thrust, and radial pressure distributions in the outer cavity that were a direct function of rotor speed. General trends of thrust coefficients with the disk holes plugged were correlated to stage pressure ratio, stage velocity ratio, admission fraction, and leakage mass flow rate. Those trends were consistent with the first block of tests with open disk balance holes, although there was an offset toward more operating conditions with negative aggregate thrust coefficients. This suggests that the rotating disk induces a low-pressure gradient in the inner (upstream) cavity, and the opened disk balance holes tend to equalize the inner cavity static pressure toward the higher static pressure on the exit side of the disk. Additionally, thrust coefficients tended to become less negative (or more positive) with stage pressure ratio and with velocity ratio, but tended to become more negative with admission fraction. Significant thrust coefficient reductions were realized with the open disk balance hole configuration, and were determined to be consistently speed-dependent.

Thermoelastohydrodynamic Characteristics of Low-Temperature Helium Gas T-Groove Face Seals

Thermoelastohydrodynamic lubrication behaviors of helium gas T-groove face seals are numerically simulated under conditions of low temperature and high pressure, with the consideration of real-gas properties including compressibility coefficient, viscosity, and heat capacity. It is found that helium gas T-groove face seal presents a sharp divergent deformation at low temperature and high pressure, which makes the opening performance weaken and the leakage rate increase. This result is obviously different from the case of high-temperature gas face seals. As the sealing temperature drops from 300 K to 150 K, the leakage rate increases about 17% and the opening force decreases about 15%. Moreover, with the growth of rotational speed, both the outlet film pressure and the sealing performance present a non-monotonic trend. Specifically, while the rotating speed of moving ring raises from 3000 to 30,000 r·min−1, the leakage rate changes more than 30%, and the opening force is reduced about 10%.

Physical Model and Calculation of Face Packing Seals

Increasing the reliability and service life of dynamic-pump shaft seals is the most important requirement for their creation. The most common type of seals is still traditional stuffing box seals, which are controlled leakage assemblies that are periodically restored during operation. A radical change in the design of standard stuffing box seals is the transition to face packing seals with a constant pressure against the packing. It is shown that face packing seals can successfully combine the advantages of mechanical face seals and the simplicity and relatively low cost of traditional stuffing box seals. Mechanical face seals, in which one of the packing rings is replaced by a stuffing box packing, have advantages that significantly expand the application of traditional stuffing box seals. A scheme and a physical model of the face packing seal operation are described. During the operation of the seal, the packing is pushed away from the mating metal surface by the pressure of the medium. In this case, a confusor gap is formed, the length of which is proportional to the ratio of the sealed pressure to the pre-compression pressure of the packing. The calculation of the distribution of the hydrostatic pressure and gap along the radius of the face joint of the seal is presented. The irregularity of the contact pressure along the radius, caused by the pressing out of the packing by the sealed inlet pressure, causes premature wear of the overloaded areas of contact surfaces. Expressions are proposed for estimating friction power losses in face packing seals. It is shown that these losses are significantly lower in comparison with the power losses in traditional stuffing box seals. Assessment of the thermal state of face packing seals has been carried out. An expression has been obtained for determining the flow rate that provides the average contact-surface temperature not exceeding the permissible value. Our studies have shown that the load factor of face packing seals, in contrast to mechanical face seals, must be close to unity. The obtained dependencies make it possible to calculate face packing seals at their design stage.

Influence of Thermoelastic Phenomena on the Energy Conservation in Non-Contacting Face Seals

The purpose of this study was to develop a mathematical model for non-contacting face seals to analyze how their performance is affected by thermoelastic phenomena. The model was used to solve thermal conductivity and thermoelasticity problems. The primary goal was to calculate the values of thermal deformations of the sealing rings in a non-contacting face seal with a flexibly mounted rotor (FMR) for a turbomachine. The model assumes the conversion of mechanical energy into heat in the fluid film. The heat flux generated in the fluid film is transferred first to the sealing rings and then to the fluid surrounding them. Asymmetric distribution of temperature within the sealing rings leads to the occurrence of thermal stresses and, consequently, a change in the geometry of the rings. The model is solved analytically. The distributions of temperature fields for the sealing rings in the cross-sections are calculated using the Fourier-Bessel series as a superficial function of two variables (r,z). The thermoelasticity problems described by the Navier equations are solved by applying the Boussinesq harmonic functions and Goodier’s thermoelastic displacement potential function. The proposed method involves solving various theoretical and practical problems of thermoelasticity in FMR-type non-contacting face seals. The solution of the mathematical model was made use of analytical methods, and the most important obtained results are presented in graphical form, such as the temperature distributions and axial thermal distortions in cross-sections of the rings. The calculated thermal deformations of the sealing rings are used to determine the most important seal performance parameters such as the leakage rate and power loss. The article also presents a multi-criteria analysis of seal rings materials and geometry, which makes it easier to choose the type of materials used for the sliding rings.

Influence of Thermoelastic Phenomena on the Energy Conservation in Non-contacting Face Seals

The purpose of this study was to develop a mathematical model for non-contacting face seals to analyze how their performance is affected by thermoelastic phenomena. The model was used to solve thermal conductivity and thermoelasticity problems. The primary goal was to calculate the values of thermal deformations of the sealing rings in a non-contacting face seal with a flexibly mounted rotor (FMR) for a turbomachine. The model assumes conversion of mechanical energy into heat in the fluid film. The heat flux generated in the fluid film is transferred first to the sealing rings and then to the fluid surrounding them. An asymmetric distribution of temperature within the sealing rings leads to the occurrence of thermal stresses and, consequently, a change in the rings geometry. The model is solved analytically. The distributions of temperature fields for the sealing rings in the cross-sections are calculated using the Fourier-Bessel series as a superficial function of two variables (r,z). The thermoelasticity problems described by the Navier equations are solved by applying the Boussinesq harmonic functions and Goodier’s thermoelastic displacement potential function. The proposed method involves solving various theoretical and practical problems of thermoelasticity in FMR-type non-contacting face seals. The calculated thermal deformations of the sealing rings are used to determine the most important seal performance parameters such as the leakage rate and power loss.