Stepped Labyrinth Research Articles

Labyrinth seal design for space applications

Labyrinth seals, extensively used in space applications, serve to prevent the loss of liquid lubricants and shield satellite subsystems from contamination. These seals are essential for the reliable functioning of bearings and for protecting satellite subsystems from contamination. This study compares analytical predictions of lubricant loss against experimental measurements and computer simulations to optimize labyrinth seal configurations. Analytical models tend to overestimate mass loss by 5–8 times compared to experimental data, indicating limited reliability for complex seal geometries. Simulations using MolFlow+ and COMSOL Multiphysics align closely with experimental results, providing accurate mass loss predictions. Key findings highlight that labyrinth length, width, and surface roughness are critical factors in minimizing evaporative mass loss. Notably, stepped labyrinth seals with relief grooves and optimized step positioning effectively reduce molecular beaming effects and improve sealing performance compared to straight geometries. Effective sealing not only reduces mission failures but also helps to minimize space debris, thereby promoting safer satellite missions.

A study on the rotational effect of a stepped labyrinth seal according to the casing type

A study on the rotational effect of a stepped labyrinth seal according to the casing type

Topology optimization of labyrinth seals using interface identification techniques

Labyrinth seals are mechanical devices that reduce the leakage between moving components of rotating machines. They are crucial for determining the performance of these machines and essential for reducing greenhouse gas emissions. Therefore, mathematical optimization algorithms for labyrinth seals are of high interest. This work concerns the topology optimization of labyrinth seals, which is a challenging task because the optimizer must distribute solids at different velocities to properly model the flow in the cavity of the labyrinth seal. Also, the model must not allow the optimizer to close the fluid channel or to leave free-floating islands of solid elements in the final design. Therefore, the interface identification method based on a series of erosion-dilate projection filters is used to model the fluid channel as the interface between the rotor and stator, allowing the representation of different velocities and avoiding the channel closure. The virtual temperature method is employed as a connectivity constraint to avoid free-floating islands of solid material. Still, thin structural members appear in the optimized designs, so geometric constraints are used to impose the minimum length scale on rotor and stator components. The final topology optimization results are labyrinth seals with contorted channels constricted to the minimum allowed gap size (as expected for low Reynolds flows), showing the success of the proposed formulation. The staggered and stepped labyrinth seal configurations are optimized to show the generality of the method.

Analysis of discharge characteristics of a symmetrical stepped labyrinth side weir based on global sensitivity

Abstract In this paper, the discharge coefficient prediction model for this structure in a subcritical flow regime is first established by extreme learning machine (ELM) and Bayesian network, and the model's performance is analyzed and verified in detail. In addition, the global sensitivity analysis method is introduced to the optimal prediction model to analyze the sensitivity for the dimensionless parameters affecting the discharge coefficient. The results show that the Bayesian extreme learning machine (BELM) can effectively predict the discharge coefficients of the symmetric stepped labyrinth side weir. The range of 95% confidence interval [−0.055,0.040] is also significantly smaller than that of the ELM ([−0.089,0.076]) and the Kernel extreme learning machine (KELM) ([−0.091,0.081]) at the testing stage. The dimensionless parameter ratio of upstream water depth of stepped labyrinth side weir p/y1 has the greatest effect on the discharge coefficient Cd, accounting for 55.57 and 54.17% under single action and other parameter interactions, respectively. Dimensionless step number bs/L has little effect on Cd, which can be ignored. Meanwhile, when the number of steps is less (N = 4) and the internal head angle is smaller (θ = 45°), a larger discharge coefficient value can be obtained.

Numerical study of erosion on labyrinth seals of Francis turbine

Sediment erosion is one of the most challenging problems in hydropower plants in Nepal. The sediments like quartz erode the turbine components like runner blades, labyrinth seals and others. This study has focused on the erosion effects in different labyrinth seals of the Francis turbine. Labyrinth seals are non-contact seals used for minimizing unwanted leaks between stationary and rotating parts. The labyrinth consists of two parts: a static seal connected to the turbine covers and a rotating part connected to the runner. The labyrinth gap is small for a new turbine and so the leakage is low. The leakage grows as the gap widens due to erosion in the seals. This causes a reduction in the efficiency of the turbine. Thus, numerical analysis performed on 2-dimensional straight-through (unilateral and bilateral), stepped, and full-length labyrinth seals of Francis turbine have been covered in this research paper. The numerical models were constructed with a structured grid using ICEM. CFD simulation in OpenFOAM was carried out to understand the flow with sediment particles in different labyrinth seals. The volume eroded was evaluated using the Finnie erosion model. The pressure, velocity profile and volume eroded in labyrinth seals were investigated. The study showed stepped labyrinth seal had a maximum volume eroded on both the stator wall and rotor wall compared to other seals. Similarly, the study revealed that the rotating part of the labyrinth seal is more affected by sediment erosion than the stationary part of the seal. This is due to the high accumulation of sediment particles in the rotor wall of the labyrinth seal.

A three-dimensional study of flow characteristics over different forms of stepped–labyrinth spillways in the skimming flow regime

Abstract To improve the performance of stepped spillways, their combination with labyrinth spillways is an interesting topic. In this study, several labyrinth configurations of stepped spillways were presented. Validation of the numerical model was done using the results of the previous physical models. After that, three configurations including: conventional stepped, trapezoidal-labyrinth, and rectangular-labyrinth were modeled using the OpenFOAM model for the skimming flow regime. For simulation, the InterFOAM solver and RNG k–ε turbulence model were used. The results showed an increase of 34.7 and 21.1% in energy dissipation in the trapezoidal and rectangular stepped–labyrinth spillways compared to the conventional stepped type, for dc/h = 1.45 (the range of dc is between 8 and 14.5 cm). The flow velocity in the end step of the trapezoidal- and rectangular-labyrinth configuration is reduced by 50.5 and 31.1%, respectively. Furthermore, in the trapezoidal configuration, a 14.7% reduction in flow velocity has been achieved compared to the rectangular stepped–labyrinth configuration. The results showed that the minimum pressure on the vertical faces of the steps occurred in their upper half and the rectangular configuration has resulted in the highest amount of negative pressure. The turbulence kinetic energy, especially in trapezoidal configuration, has increased toward the downstream.

Experimental Assessment of Correlative Approaches for the Prediction of Leakage Flow through Labyrinth Seals

Simple analytical models can be employed to estimate the leakage mass flow rate from labyrinth seals, resulting in a quick procedure, well suited for the early design process. Different formulas were proposed by many authors during the past decades and most of them employ a carry-over factor and a flow coefficient to predict the mass flow rate across the clearance area. The present work aims to compare the analytical prediction with the results of an experimental campaign. The experimental results were retrieved from a dedicated test rig for both a straight-through and a stepped labyrinth seal. Hence, for each seal, the effect of the clearance size, the Reynolds number and the pressure ratio has been investigated. Starting from the experimental required inputs, six different correlations are considered, with both direct and indirect methods. The results are shown as a function of pressure ratio and clearance gap. Despite some differences in the comparison, and most of the used correlation underestimate the measured mass flow rate, some general trends and guidelines can be highlighted.

Discharge Coefficient of Symmetrical Stepped and Triangular Labyrinth Side Weirs in a Subcritical Flow Regime

The labyrinth side weir structure is an optimal solution to regulate and divert excess flows across rivers, and irrigation and drainage channels when the opening length of the side weir is limited. Changing the geometry of the side weir is considered one way to improve its efficiency. The present study investigates the hydraulic effects of stepped labyrinth side weirs to increase their discharge capacity. To estimate the outflow over symmetrical stepped labyrinth side weir, the discharge coefficient needs to be determined. Normal triangular labyrinth side weir in one cycle mode has been modified by increasing the crest path using different steps. A total of 417 experiments were conducted on normal and stepped side weirs for various weir opening lengths, weir heights, internal head angles, and hydraulic conditions. The results were analyzed and compared. It was found that efficiency improved, and the discharge coefficient increased as the number of the steps decreased. Furthermore, the water surface profile becomes more uniform with decreasing number of steps. A lower number of steps, smaller head angle, and high weir length produce a higher discharge coefficient by approximately 15%–35% compared to a normal triangular labyrinth side weir; in addition, the Knope length decreases by approximately 40%–70% for the same effective length. Additionally, a reliable equation to estimate the discharge coefficient of the stepped labyrinth side weir was presented. The results of this study can be used to design side weirs with high hydraulic performance when the weir-included angle selected is small or there is a lack of space.

Effect of anti-vortex structures installed on stepped labyrinth side weirs on discharge capacity

Side weirs are essential structural elements commonly used to control water levels in rivers and canals. If the length of the opening is limited, a labyrinth side weir can be used to increase the amount of water diverted out of the channel and the effective length. This research studied the influence of installing an antivortex structure in stepped labyrinth side weirs on discharge capacity. It has four types of antivortex installed in different hydraulic conditions at different Froude numbers, dimensionless crest height, dimensionless weir opening length, step number, and head angle. Using data from 168 experimental runs without antivortex to allow comparison and 672 experimental runs to determine the best performance of antivortex structures that improved discharge capacity, and 528 runs measured velocity to investigate the intensity of secondary currents generated by lateral flow and other hydraulic conditions, including water surface profiles. According to the research results, installing antivortices regulated the flow, significantly improved the efficiency of the single-cycle stepped labyrinth side weir, and lowered secondary flows caused by interaction with the vertical axis. Finally, the discharge coefficient improves to 18% after analyzing the best type of antivortex, considering shape and height.

Numerical study on the leakage characteristics of a stepped labyrinth seal with mixed honeycomb cell diameters

Numerical study on the leakage characteristics of a stepped labyrinth seal with mixed honeycomb cell diameters

Optimizing the Geometric Parameters of a Stepped Labyrinth Seal to Minimize the Discharge Coefficient

A series of numerical simulations were performed to study the discharge coefficient based on the geometric parameters of a stepped labyrinth seal that sealed the secondary flow path of a gas turbine. In contrast with straight-through seals, stepped labyrinth seals introduce additional geometrical parameters related to the steps. In this study, three shape variables were observed: step height (SH), position, and cavity width (CW). The sensitivity to the leakage flow of the shape variable in the stepped labyrinth seal was analyzed. The mechanism for improving the sealing performance of stepped labyrinth seals was investigated. The results indicated that the stepped labyrinth seal exhibited up to 17.9% higher leakage-suppression performance than the straight labyrinth seal. Seals with large discharge coefficients had a large vena contracta upstream of each tooth structure and a rapidly accelerated axial velocity in the radial direction. We could observe that the discharge coefficient changed according to the flow field in the cavity. The wall shear stress was sensitive to the SH but not to the CW or step position.

Turbulence dissipation of leakage flow in supercritical CO2 labyrinth seals

Supercritical CO2 (S-CO2) leakage through seals significantly reduces the efficiency of turbomachinery. Improving the labyrinth seal structure is potentially the key to the reduction of the leakage flow rate, but its application is greatly limited by the uncertainties of supercritical CO2 turbulent flow inside the turbomachines with irregular chambers. In this work, we numerically investigated the S-CO2 flow field and dissipation rate of turbulence kinetic energy in stepped labyrinth seals. The RANS method and hexahedral structural mesh were employed. The look-up table containing the real gas properties of carbon dioxide was created and imported into the flow solver. The developed numerical method was validated by experiment results and proved its applicability. We have discovered that the fully developed rotating vortices inside each chamber of the turbomachine significantly increase the turbulent dissipation rate and decrease the fluid carried energy, thus reducing the leakage flow rate. With the seal clearance increasing form 0.5 mm–1.3 mm at pressure ratio π = 0.7, the vortices development is gradually limited, causing the decrease of turbulent dissipation rate. The leakage rate is found to be heavily dependent on the distance between the seal tip and step. The increase in this distance from 2 mm to 6 mm results in greater space for the continued development of the vortices within the first chamber, thus the enhancement of the turbulent dissipation rate of fluid. Therefore, we defined a geometry coefficient, (δ-b)/s, and analyzed its effects on turbulent dissipation rate and leakage flow rate. With this geometry coefficient increases from 2.8 to 11.2 at π = 0.7, the maximum turbulent dissipation rate increases from 7.09 × 107 to 1.23 × 108 and the leakage flow rate decreases from 3.98 × 10−2 kg/s to 1.62 × 10−2 kg/s. An improved leakage model characterizing seal geometry, gas properties and compressibility effects was proposed.

Study of dynamic characteristics of stepped labyrinth seals

Study of dynamic characteristics of stepped labyrinth seals

Experimental and Numerical Investigation of Free Surface Vortex in Stepped Labyrinth Side Weir

Experimental and Numerical Investigation of Free Surface Vortex in Stepped Labyrinth Side Weir

Large Eddy Simulation of Leakage Flow in a Stepped Labyrinth Seal

Large eddy simulation (LES) and Reynolds averaged Navier-Stokes simulation (RANS) of leakage flow in straight-through and stepped labyrinth seals were performed in order to compare their performances in sealing the secondary flow passage of the gas turbine based on the respective discharge coefficients. The results indicate a 17.8% higher leakage prevention performance for the stepped seal relative to that of the straight seal. Further, while the LES predicts an ~7% reduction in the discharge coefficient due to shaft rotation, this effect is underestimated by the RANS. Moreover, the LES correctly predicts a laminarized flow pattern in the clearance, whereas the RANS overestimates the turbulence kinetic energy. In addition, a turbulence kinetic energy spectrum analysis was performed based on the vorticity at selected points in order to identify the flow structure that has a dominant influence on the oscillation of the discharge coefficient. This analysis also enabled identification of the changes in the flow structure due to shaft rotation.

A Study on the Leakage Characteristics of a Stepped Labyrinth Seal with a Ribbed Casing

A new type of stepped seal with a ribbed casing is proposed to efficiently reduce the leakage at the tips of turbine blades. The leakage characteristics of two different types of labyrinth seals (conventional seal vs. ribbed seal) were compared and analyzed through computational fluid dynamics (CFD) in a wide operating range of pressure ratios and clearances. The analysis showed that the ribbed seal has superior leakage performance to the conventional seal at all clearance sizes. With the same clearance size (S/H = 1.0), the flow function of the ribbed seal was approximately 21.5–42.6% less than that of the conventional seal. Also, different trends of variation in the flow function according to the increase of the clearance were found between the conventional and ribbed seals. The leakage flow inside the labyrinth seal was analyzed to explain the cause of this difference in tendency, and it was confirmed that the added ribs cause collision between the leakage flow and the tooth wall, even with the increase of the clearance. Also, the ribbed seal enables operation at a larger clearance with the same leakage performance when comparing the absolute leakage flow rate of the two seals. In addition, a parametric study on the influence of the rib height and rib inclination angle revealed that the flow function generally decreases as both parameters increase.

Effects of tip clearance, number of teeth, and tooth front angle on the sealing performance of straight and stepped labyrinth seals

In the gas turbine, gaps inevitably exist between the stationary and rotating parts. To improve the performance of gas turbines, tip leakage flow through the gaps must be minimized. The labyrinth seal increases the flow resistance by placing a number of teeth to minimize leakage flow. The labyrinth seal is still adopted in many fields because of its relatively high thermal resistance, simple structure, and wide pressure range. In this paper, the effects of geometric parameters (straight and stepped with solid land, tip clearance, number of teeth, and tooth front angle) on leakage flow were experimentally studied and the seal performance was described using the flow function. Also, flow visualization within the labyrinth seal was conducted using the Schlieren method. The dimensionless tip clearance (C/a) was adjusted from 0.8 to 3.3 (where a is tooth tip width) and the pressure ratio was adjusted from 1.1 to 3.0. The tooth front angle of the stepped seal was 90° and 60°. Results show that the flow function increased as the pressure ratio increased, however it tended to remain constant if the pressure ratio was higher than 2.0. At the same test condition, the flow function of the stepped labyrinth seal was smaller than that of the straight seal for all tested pressure ratios. Also, the seal performance was better for larger number of teeth, smaller tip clearance, and smaller tooth front angle cases. Based on the measured results, a new correlation for the labyrinth seals was suggested.

Study of Dynamic Characteristics of Stepped Labyrinth Seals

Study of Dynamic Characteristics of Stepped Labyrinth Seals

Effect of Clearance and Cavity Geometries on Leakage Performance of a Stepped Labyrinth Seal

This study evaluated the leakage characteristics of a stepped labyrinth seal. Experiments and computational fluid dynamics (CFD) analysis were conducted for a wide range of pressure ratios and clearance sizes, and the effect of the clearance on the leakage characteristics was analyzed by determining the performance of the seal using a dimensionless parameter. It was observed from the analysis that the performance parameter of the seal decreases as the clearance size increases, but it tends to increase when the clearance size exceeds a certain value. In other words, it was revealed that there exists a specific clearance size (Smin) which minimizes the performance parameter of the seal. To identify the cause of this tendency change, a flow analysis was conducted using CFD. It was confirmed that the leakage characteristics of the stepped seal are affected by the size of the cavity, which is the space between the teeth. Therefore, a parametric study was conducted on the design parameters related to the cavity size (tooth height and pitch). The results show that the performance parameter decreases as the tooth height and pitch decreases. Moreover, Smin increases as the tooth height increases and the pitch decreases.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

Abstract A simple nondimensional model to describe the flutter onset of two-fin straight labyrinth seals (Corral and Vega, 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models—Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot's criterion stating that seals supported on the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the nondimensional work-per-cycle is derived and new nondimensional parameters controlling the seal stability identified. It is finally concluded that the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.