Numerical and experimental analyses of the static and dynamic characteristics of the liquid annular seals with axially partial helical grooves were conducted to investigate the effects of the axial length g al of a helically grooved section in a seal stator. The numerical solution and experimental procedures were applied in the same manner as in previous studies on through-helically grooved seals, wherein the grooves extend across the seal length. The numerical results qualitatively agreed with the experimental results, demonstrating the validity of the numerical analysis. The leakage flow rate Q was lower in the partially helically grooved seals than that of conventional through-helically grooved seals across a small range of rotor spinning velocities. In contrast, the reduction in Q due to the pumping effect caused by the spin of the rotor diminished with the decrease in g al . For a small concentric whirling motion of the rotor, the radial dynamic reaction force F r and magnitude of variation in the tangential dynamic reaction force F t with the whirling angular velocity increased with the decrease in g al , and their values approached the corresponding values for the smooth-surface seal. Under the same rotor whirling velocity, the F t for the partially helically grooved seals became lower than that for the smooth-surface seal (similar to the case for the through-helically grooved seal), although decreasing g al tended to increase F t . These results suggest that partially helically grooved seals can improve the efficiency and stability margin of the pumps because of the reduction in leakage flow rate and suppression of the rotor forward whirling motion (with large radial and tangential dynamic reaction forces) as compared to conventional through-helically grooved seals.

The paper presents the experimental results obtained for brush seals of 38 mm diameter operating with air at pressure differences up to 7 bars and rotation frequencies up to 500 Hz. The seals had bristles of 70 μ m diameter, made of Haynes 25. Seals with two radial interferences (0 and 100 μ m) between the brush and the rotor were tested. The presented running in procedure underlines the influence of the initial wear on the brush temperatures. The test results consisted of leakage mass flow rates. The temperatures of a limited number of points on the brush and on the rotor were also recorded. The results confirmed the important impact of the radial interference on the leakage. The test data were further confronted with theoretical predictions obtained with an original model. The model considers the brush as a deformable porous medium. Its local porosity and permeability are obtained from a fluid–structure interaction between the bristle pack and the leakage flow. The comparisons showed nearly close values of the mass flow rates. The differences between experimental and theoretical predictions are considered to be due to an underestimation of the porosity because the model neglects the friction forces between bristles and between the bristles and the rotor.

A thermohydrodynamic lubrication model of turbulent cavitating flow for high-speed spiral groove thrust bearing was developed considering the effects of cavitation, turbulence, inertia, breakage, and coalescence of bubbles. Comparing with the classical thermohydrodynamic model, this model can predict not only the distributions of pressure and temperature rise but also the distribution of bubble volume and bubble number density. Static characteristics of the water-lubricated spiral groove thrust bearing in the state of turbulent cavitating flow were analyzed, and the influences of multiple effects on the static characteristics of the bearing were researched. The numerical calculation result shows that the bubbles are mainly distributed in inlet and outlet of the spiral groove, the distribution of bubble volume is skewed under the equilibrium state, and small bubbles account for a large proportion of the cavitating flow under high-speed condition. Furthermore, the load carrying capacity and the leakage flow of the bearing decrease due to the effect of cavitation under high-speed. The maximum temperature rise of the bearing decreases due to the effect of cavitation effect.

Numerical and experimental analyses were carried out to investigate the static characteristics of liquid annular seals with helical grooves in a seal stator. In the numerical analysis, the momentum equations with turbulent coefficients and the continuity equation, which were averaged across the film thickness, were numerically solved to obtain the leakage flow rate and the pressure distributions in the seal clearance. To accurately define the location of the step between the groove and the land regions in the calculation domain, these governing equations were expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. The numerical analysis included the effects of both fluid inertia and energy loss due to expansion during the passage of fluid from the land region to the helical groove region and that due to contraction from the groove region to the land region. In the experimental analysis, the leakage flow rate and the fluid-film pressure distributions in the seal clearance were measured for the helically grooved seals with different helix angles of the helical groove. The numerical results of leakage flow rate and pressure distributions agree reasonably with the experimental results, which demonstrates the validity of the numerical analysis. The leakage flow rate of the helically grooved seals was influenced by two factors: fluid energy loss during passage through the step between the groove and the land, and the pumping effect by which the spinning motion of the rotor pushes the flow back upstream along the helical grooves. Under a low range of rotor spinning velocity, the leakage flow rate decreased with helix angle because the effect of fluid energy loss in the steps was significant. By contrast, under a high range of spinning velocity, the quantitative difference in the leakage flow rate due to the helix angle decreased compared to that under a low range because the reduction in the leakage flow rate due to the pumping effect was pronounced for a larger helix angle. The effects of helix angle and rotor spinning velocity on the leakage flow rate are explained qualitatively using a simplified model.

To clarify the sealing characteristics of metal gasket seals, leakage rates of gas and the real contact area of the seal surfaces were measured under several closing loads. The static seal consisted of a ring-shaped copper gasket and the two steel flanges that held the gasket in place. Gasket widths in the radial direction were 2 mm, 3 mm, and 5 mm. The contact surfaces of the flanges were finished by lathe turning. To determine the leakage flow paths between the gasket and the flanges, the real contact situation between them was observed using a thin polymer film 1 μ m in thickness. The results indicated the leakage flow paths on the gasket surface were the radial direction perpendicular to the lathe-turned groove and the circumferential direction along the groove. As the closing loads increased, the leakage flow in the radial direction ceased and only that in the circumferential direction remained. Therefore, the cross-section of the aperture for the leakage flow in the circumferential direction was evaluated from the measured real contact area, and the leakage rates were estimated by assumption of laminar flow. The results agreed well with the measured leakage rates.

Journal misalignment exists generally in journal bearings. When severe journal misalignment takes place, the minimum film thickness of journal bearings reduces greatly. In this condition, the surface roughness, the oil viscosity-pressure relationship (VPR), and the thermal effect have obvious effects on hydrodynamic lubrication performance of misaligned bearings. In this paper, the oil film pressure, oil film temperature, load-carrying capacity, end leakage flow rate, frictional coefficient, and misalignment moment of a journal bearing with different angles of journal misalignment and surface roughness, and considering oil VPR and thermal effect, were calculated based on the generalized Reynolds equation, energy equation, and solid heat conduction equation. The results show that the oil VPR and surface roughness have a significant effect on the lubrication of misaligned journal bearings under large eccentricity ratio. The thermal effect will affect obviously the lubrication of misaligned journal bearings when eccentricity ratio and angle of journal misalignment are all large. In the present design, the size of the journal bearing is compact more and more, and the eccentricity ratio and angle of journal misalignment are usually large in operating conditions. Therefore, it is necessary to take the effects of journal misalignment, surface roughness, oil VPR, and thermal effect into account in the design and analyses of journal bearings.

A numerical analysis is conducted to investigate the elastohydrodynamic effect of deterministic microasperities on the shaft of a lip seal. Various geometries of microasperities (triangular, square, hexagonal, and circular) are put into a 100 × 100 μ m 2 unit cell and are investigated using Reynolds equation. For each shape, the area fraction of the microasperity is varied between 0.2 and 0.8, and the asperity height is varied between 0.3 μ m and 5 μ m . The calculation for load capacity and friction coefficient indicates that there are values for asperity height, where the load capacity and friction coefficient are optimized. These optimum heights were reached at 1 – 3 μ m . Although the lip seal surface is considered to be smooth, reverse pumping can still be obtained using an oriented triangular design. The Couette flow rate for this asperity showed lubricant is reverted back toward the seal side 2.6 times more than using a conventional lip seal. The addition of microasperities to the shaft surface shows significant improvement in lubrication characteristics for the lip seal in the form of a simultaneous reduction in friction coefficient and increase in the reverse pumping rate.

Honeycomb damper seals with convergent-tapered clearance have been proposed to improve static and dynamic characteristics of liquid annular seals employed in pumps. Their characteristics are experimentally investigated and compared to those for a conventional straight (no taper) annular seal with smooth surface and a straight damper seal with identical honeycomb pattern in seal stator. Three convergent-tapered honeycomb damper seals are used in the test, and have different inlet clearance (maximum clearance) and almost the same outlet clearance (minimum clearance). Their outlet clearance is almost the same as the clearance of the straight smooth seal and is slightly smaller than the clearance of the straight damper seal. Experimental results show that the convergent-tapered damper seals as well as the straight damper seal have lower leakage flow rate and cross-coupled stiffness coefficients, and larger main damping coefficients than the straight smooth seal, resulting in larger effective damping coefficients. These results are mainly due to surface roughness in the seal stator such as a honeycomb pattern used in the present analysis. The convergent-tapered damper seals also have larger main stiffness coefficients than the straight smooth and damper seals, which is mainly due to the convergent-tapered clearance and yields larger radial reaction force for a small concentric whirling motion. Consequently, the convergent-tapered damper seals have better seal characteristics than the conventional straight smooth seal and the straight damper seal with the same roughness pattern from the viewpoints of decreasing the leakage and improving the rotor stability capacity.

Hybrid bearings represent an attractive alternative to ball bearings for use in highspeed cryogenic turbopumps. However, the internally-developed cross-coupled forces can generate instabilities responsible for a speed limitation of the machine. To reduce these forces and raise the onset speed of instability, the use of deliberately-roughened stators, already successfully tested for liquid “damper” seals, is investigated. Rotor-dynamic results are presented for a five-pocket orifice-compensated hole-pattern-land hybrid bearing tested with water at high speed and high pressure. Experimental data show a good prediction of leakage flow rate and direct damping but a significant improvement in stability compared to a conventional smooth-land hybrid bearing, resulting in an elevation of the onset speed of instability. Comparisons between measurements and predictions from a code developed by San Andres (1994) shows good predictions for flowrate and direct damping but an over prediction for the direct and cross-coupled stiffness coefficients by about 30 and 50 percent, respectively. The use of the Moody friction-factor model is thought to be mainly responsible for the poorer predictions of stiffness coefficients.

Static and dynamic characteristics are experimentally investigated for annular plain seals with porous materials applied to the seal surface by insertion into the middle of the seal. Experimental results show that annular plain seals with porous materials have a higher leakage flow rate, larger main stiffness coefficients, and smaller cross-coupled stiffness coefficients and main damping coefficients than conventional annular plain seals with solid surfaces. In the porous seals, an increase of approximately 30 percent in the leakage flow rate and reduction of the same amount in the main damping coefficients are obtained, whereas the main stiffness coefficients for the porous seals are four to six times as much as those for the solid seals due to the increase in the hydrostatic force induced by a function of the hydrostatic porous bearing. This suggests that the quantitative effects of the porous materials on the main stiffness coefficients are much more significant than the effects on the leakage flow rate and the other dynamic coefficients. The larger main stiffness coefficients for the porous seals yield larger radial reaction force for a small concentric whirling motion, which would contribute to rotor stability from the viewpoint of increasing speed limits due to a stiffer rotor support.

A new model for predicting leakage flows through the bristle pack of brush seals is developed. In the model, the bristle pack is treated as a porous medium. Good agreement is demonstrated between predictions from a one-dimensional form of the model and a wide range of experimental data available from the literature, for seals with a bristle pack to rotor interference fit. The results demonstrate that both viscous and inviscid effects contribute significantly to the drag on the bristles within the pack. The model uses a linear superposition of viscous and inertial losses, with a resistance coefficient assigned to each contribution. Formulas that have been deduced for flow in packed beds, are adapted for use in assigning values to the resistance coefficients in the one-dimensional model. Finally, extension of the method to multiple dimensions is discussed, with a view to incorporating the model into a CFD code to form a general predictive capability for brush seal flows.

This paper presents a simple numerical method for modeling the dynamic tracking modes of a grooved face seal. The stability is verified using a method derived from that developed for smooth face seals. The method, enabling the calculation of the kinematic parameters which describe the steady-state response of the grooved seal, is of interest in designing this type of seal. A parametric study is presented for the case of a rotor face with eight semicircular grooves. The principal effect of the grooves is to increase the hydrostatic component of the load. In turn, this makes the seal less sensitive to fluctuations of the hydrodynamic phenomena. Sinusoidal waviness is used to simulate the periodic distortions induced by the grooves and affects the dynamic behavior only in the presence of cavitation. This occurs for very small values of the film thickness and, consequently, for very small leakage flow. In this case, the dynamic response of the seal is then strongly dependent upon the hydrodynamic effects.

Circumferentially-grooved seals are used in centrifugal pumps to reduce leakage flow. They can also have a significant impact on pump rotordynamic characteristics. Florjancic (1990) developed an analysis for leakage and rotordynamic coefficients, using a partition of the seal into three control volumes. This paper presents a new theory, based on an extension of Florjancic’s work (1990) for circumferentially-grooved liquid seals. The current theory differs from Florjancic’s analysis in the retention of transfer momentum terms and the introduction of diverging flow in the through-flow section within a seal groove. Validation of the new analysis is achieved through a comparison with existing experimental data taken from Kilgore (1988), and Florjancic (1990). Theoretical results are reasonable and consistent; i.e., a modification in the seal parameters induces a correct evolution of the rotordynamic coefficients. Direct and cross-coupled stiffness coefficients are slightly underpredicted, whereas the direct damping coefficient is underpredicted within 40 percent. Leakage flow predictions are very good.

Mixed lubrication characteristics of hydrostatic thrust bearings are examined experimentally. The effects of the surface roughness, supply pressure, loads, speed of rotation and size of restrictors on the frictional force, leakage-flow rate and power losses are clarified. Introducing the concept of mean pressure based on load-carrying capacity due to asperities, and the ratios of hydrostatic balance and leakage-flow rate, the experimental data can be normalized. Also good agreement is found between theoretical results based on a mixed lubrication model presented in a previous paper and the experiment.

The existing narrow-groove theory is used for evaluating leakage flow for various configurations which might be of interest in seal design, including variable angle, film thickness and groove/ridge length ratio.

The compressible flow in a seal can be described by the Navier-Stokes equations in connection with a turbulence model (k–ε model) and an energy equation. By introducing a perturbation analysis in these differential equations we obtain zeroth order equations for the centered position and first order equations for small motions of the shaft about the centered position. These equations are solved by a finite difference technique. The zeroth order equations describe the leakage flow. Integrating the pressure solution of the first order equations yields the fluid forces and the rotordynamic coefficients, respectively.

This paper deals with the problem of calculating oil film thicknesses, oil leakage, and friction forces in seal situations like those occurring in hydraulic cylinders. A general scheme for the analysis is presented, covering both piston seals and piston rod seals. The theoretical model considers influence both from the seal itself and from surrounding parallel clearances. It also takes cavitation into account when this occurs. The validity of the model is limited to cases with well lubricated seal contacts, i.e., unbroken oil films. The analysis follows the inverse hydrodynamic theory and requires a known pressure distribution for each seal element. The pressure distributions are calculated with a method presented earlier by the author (at the 5th Leeds-Lyon Symposium on Tribology, September 1978). Calculated values of oil film thicknesses, leakage flows and friction forces are presented for different sealed pressures and different sliding velocities.

It is shown analytically that face seal eccentricity combined with surface waviness can contribute an inward or outward leakage component to the total leakage flow depending on the phase angle between the eccentricity and the waviness.

The “short bearing” equation of lubrication theory, modified to include inertial effects, is used to study the influence of geometric deviations from the ideal. It is found that the centrifugal force could be responsible for hydrodynamic features of the leakage flow which are theoretically unexplainable in the absence of this inertial effect. There is good evidence that the theory and the results are applicable over the entire laminar range of operation, provided the nominal clearance is small compared to the nominal radius.