Straight-through Labyrinth Seal Research Articles

Numerical simulation of flow and heat transfer characteristic in straight-through labyrinth seals of aeroengines under eccentric and rotating conditions

Numerical simulation of flow and heat transfer characteristic in straight-through labyrinth seals of aeroengines under eccentric and rotating conditions

Nonlinear Flutter Analysis of Labyrinth Seals

Abstract A simple nonlinear model to describe labyrinth seal flutter has been developed to assess the aeromechanic stability of straight-through labyrinth seals subjected to large gap variations. The model solves the one-dimensional integral mass, momentum, and energy equations of the seal for a prescribed motion numerically until a periodic state is reached. The model accounts for the effect, previously neglected, of high clearance variations on the stability. The results show that when the vibration amplitudes are small, the work-per-cycle coincides with the prediction of the Corral and Vega model (2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) and Corral et al. (2021, “Higher-Order Conceptual Model for Seal Flutter,” ASME J. Turbomach., 143(7), p. 071006), but for large vibration amplitudes nonlinearities alter the stability limit. In realistic cases, when the discharge time of the seal is much longer than the vibration period, the nonlinear effects are significant and tend to increase the unstable range of operating conditions. Furthermore, seals supported either on the high-pressure or low-pressure sides, stable for small vibration amplitudes, can destabilize when the vibration amplitude increases. The linear stability, though close in many situations to the nonlinear threshold, is not conservative, and attention must be paid to nonlinear effects.

Development of a New Loss Model for Turbomachinery Labyrinth Seals

Abstract The preliminary design of labyrinth seals requires fast and accurate estimate of the leakage flow. While the conventional bulk flow models can quickly predict labyrinth seal discharge characteristics, they lack the accuracy and pragmatism of modern computational fluid dynamics (CFD) techniques and vice-a-versa. This paper presents a new one-dimensional loss model for straight-through gas labyrinth seals that can provide quick seal leakage flow predictions with CFD-equivalent accuracy. The present seal loss model is developed using numerical experimentation technique. Multiple CFD computations are conducted on straight-through labyrinth seal geometries for a range of pressure ratios. A distinct postprocessing methodology is developed to extract the through-flow stream tube in seal. Total pressure losses and flow area variations experienced by the flow in seal stream-tube are systematically accounted for based on the well-known knife-to-knife (K2K) methodology. Regression analyses are conducted on the trends of variations of loss and area coefficients to derive the independent pressure loss and flow area correlations. These novel correlations can predict the bulk leakage flow rate, windage flow rate, and interknife static pressures over a wide range of variations of flow and geometry parameters. Validation study shows that the leakage mass flow rate predicted by this model is accurate within ±8% of measured test data. This fast and accurate model can be employed for various applications such as in seal design-analysis workflows, for secondary air system (SAS) performance analysis, and for the rotor-dynamic and aeroelastic assessments of seals.

THE SEALING CAPACITY AND HEAT TRANSFER CHARACTERISTICS OF A STRAIGHT-THROUGH LABYRINTH SEAL WITH DIFFERENT GEOMETRIC PARAMETERS

The sealing capacity and heat transfer characteristics of the straight-through labyrinth seal with different geometric parameters are analyzed in this paper through numerical investigation. The geometric parameters studied include the gap width varying from 2 mm to 6 mm, the tooth tip thickness varying from 1 mm to 3 mm, and the front inclination angle varying from 75° to 100°. For each case, the Reynolds number is varied from 10,000 to 40,000. According to the results, the sealing performance is mainly influenced by the gap width, and less affected by the tooth tip thickness and the front inclination angle. As the gap width is increased, the discharge coefficient is increased by about 40%. With the tip thickness or the front inclination angle increased, the discharge coefficient is increased by less than 5%. For the heat transfer of the end wall, the gap width has significant effects, while the effects of the other two parameters are mainly in the first tooth cavity. For the stator, the increased flow rate at the tooth tip results in enhanced local heat transfer. For the rotor, the heat transfer is determined by the vortex intensity in the tooth cavity. The presence of small secondary vortices weakens the local heat transfer.

Nonuniform Clearance Effects on Pressure Distribution and Leakage Flow in the Straight-through Labyrinth Seals

Straight-through labyrinth seal is a simple and reliable noncontact seal structure widely used in aeroengines. During the actual operation of aeroengines, the labyrinth seal clearance might experience a nonuniform variation in the flow direction due to asymmetric structure and uneven temperature. In order to characterize the degree of nonuniformity, the nonuniformity coefficient is defined in current paper. The effect of nonuniform causes (rotor deformation or stator deformation), nonuniform type (convergent clearance or divergent clearance), and nonuniformity coefficient (nonuniformity degree) is carefully studied by numerical simulation. Comparative analysis has shown that there is no obvious difference in flow coefficient (less than 0.8% in current studies) between two nonuniform causes. As for nonuniform type, the nonuniformity impact of divergent type on the flow coefficient is more significant than that of convergent type, as a result of stronger axial inertia. Pressure distributions of teeth cavities indicate that the total pressure drop of the divergent type is more obvious than that of the convergent type when the pressure ratio is the same. With the same dimensionless minimum tip clearance, clearance nonuniformity would result in the increase of leakage flow of the straight-through labyrinth, particularly for the condition with small pressure ratio, large circumferential Mach number, and small dimensionless minimum tip clearance. When the nonuniformity coefficient is within the range of -0.1 to 0.1, the variation curves of nonuniformity impact factor versus the nonuniformity coefficient almost coincide (the maximum deviation is no more than 1.2%) under different operation conditions (Reynolds number, pressure ratio, circumferential Mach number, and dimensionless minimum tip clearance). Current work proves it that the effect of seal clearance nonuniformity on the leakage flow requires special attention for the refined design of aeroengines.

Nonuniform Clearance Effects on Windage Heating and Swirl Development in Straight-Through Labyrinth Seals

Straight-through labyrinth seals are reliable noncontact seal structures widely used in aeroengines. Windage heating and swirl development of labyrinth seals are of great significance to the design of secondary air systems. In the operation process of an aeroengine, a labyrinth seal is supposed to experience uneven temperature distribution, which may cause deformation and resulting nonuniformity along the flow direction. The nonuniformity coefficient was defined to characterize the degree of nonuniformity so that the influence of nonuniform clearance on windage heating and swirl development can be analyzed quantitatively. Windage heating and swirl development were analyzed from the perspectives of different Reynolds numbers, pressure ratios, circumferential Mach numbers, and dimensionless minimum tip clearances. Simulation results showed that when other dimensionless parameters are the same, both windage heating number and exit swirl ratio decrease with the increase of the nonuniformity degree. With the same nonuniform degree, the decrease rate of divergent clearance is larger than that of convergent clearance. The changing trends of the decrease rate of both windage heating number and exit swirl ratio were analyzed in detail. It can be concluded that the decrease rate of the exit swirl ratio reaches the peak when the dimensionless minimum tip clearance is about 0.067. This result makes it clear that the effect of nonuniform clearance is indispensable for the safety assessment of aeroengines.

Effective Clearance and Differential Gapping Impact on Seal Flutter Modeling and Validation

Abstract This paper presents an update of the model derived by Corral and Vega (2018, “Conceptual Flutter Analysis of Labyrinth Seal Using Analytical Models. Part I—Theoretical Support,” ASME J. Turbomach., 140(12), p. 121006) for labyrinth seal flutter stability, providing a method of accounting for the effect of dissimilar gaps. The original Corral and Vega (CV) model was intended as a conceptual model for understanding the effect of different geometric parameters on the seal stability comprehensively, providing qualitative trends for seal flutter stability. However, the quantitative evaluation of seal flutter and the comparison of the CV model with detailed unsteady numerical simulations or experimental data require including additional physics. The kinetic energy generated in the inlet gap is not dissipated entirely in the inter-fin cavity of straight-through labyrinth seals, and part is recovered in the downstream knife. This mechanism needs to be retained in the seal flutter model. It is concluded that when the theoretical gaps are identical, the impact of the recovery factor on the seal stability can be high. The sensitivity of the seal stability to large changes in the outlet to inlet gap ratio is high as well. It is concluded that fin variations due to rubbing or wearing inducing inlet gaps more open than the exit gaps lead to an additional loss of stability concerning the case of identical gaps. The agreement between the updated model and 3D linearized Navier–Stokes simulations is excellent when the model is informed with data coming from steady Reynolds-averaged Navier–Stokes simulations of the seal.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based on the Applicability Analysis of Leakage Models Using Bulk-Flow Method

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial to the analysis of the fluid excitation rotordynamics of labyrinth seals. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of seventy-two leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Numerical validation of an analytical seal flutter model

An analytical model to describe the flutter onset of straight-through labyrinth seals has been numerically validated using a frequency domain linearized Navier-Stokes solver. A comprehensive set of simulations has been conducted to assess the stability criterion of the analytical model originally derived by Corral and Vega (2018), “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models - Part I: Theoretical Support,” ASME J. Turbomach., 140 (12), pp. 121006. The accuracy of the model has been assessed by using a simplified geometry consisting of a two-fin straight-through labyrinth seal with identical gaps. The effective gaps and the kinetic energy carried over are retained and their effects on stability are evaluated. It turns out that is important to inform the model with the correct values of both parameters to allow a proper comparison with the numerical simulations. Moreover, the non-isentropic perturbations included in the formulations are observed in the simulations at relatively low frequencies whose characteristic time is of the same order as the discharge time of the seal. This effect is responsible for the bending of the stability limit in the <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mn>0</mml:mn><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> ND stability map obtained both in the model and the simulations. It turns out that the analytical model can predict accurately the stability of the seal in a wide range of pressure ratios, vibration mode-shapes, and frequencies provided that this is informed with the fluid dynamic gaps and the energy carried over to the downstream fin from a steady RANS simulation. The numerical calculations show for the first time that the model can be used to predict accurately not only the trends of the work-per-cycle of the seal but also quantitative results.

Theoretical Leakage Equations Towards Liquid-Phase Flow in the Straight-Through Labyrinth Seal

AbstractLabyrinth seals are widely applied in turbomachinery for gas and liquid sealing. A series of labyrinth seal leakage equations so far have been proposed for compressible gas and few equations for incompressible liquid. Based on the flow conserving governing equations, this paper originally presents semi-empirical analytic equations of the leakage flow rate and tooth-clearance pressure for liquid-phase flow in the straight-through labyrinth seal. The equations indicate that the leakage and pressure are closely related to the inlet pressure, outlet pressure, seal geometrical parameters, and four empirical coefficients, while no relation to the temperature and compressibility effects compared to the common gas equations. The empirical coefficients include the velocity compensation coefficient, friction coefficient, jet contraction coefficient, and resistance coefficient. Particularly, the velocity compensation coefficient is determined through an optimization by the genetic algorithm, while others are referred from previous research. Ultimately, taking the sealing of deeply subcooled liquid nitrogen within the spindle of the cryogenic cooling machine tool as a case, the accuracy of proposed equations is evaluated under various pressure ratios and geometry conditions using the numerical approach, whose numerical model has been validated by the experimental data in the literature. The results show that errors between calculation and simulation are generally within the limit of ±5%, except for the pressure values at the first two teeth. This work provides a theoretical basis for further studies on the liquid leakage equations in other labyrinth seal types.

Influence of flow patterns on the performance of straight-through labyrinth seals. Numerical study and validation against experimental data

When numerically simulating the performance of a complete Francis turbine, it is common practice to omit the seals to save computing power. Volumetric and friction losses are usually taken into account using empirical values. There is abundant literature on the topic, but all analytic formulations rely on widely variable empirical coefficients. To overcome the uncertainty in determining volumetric losses, a detailed analysis of the sealing is necessary. Focusing on straight seals and configurations with cavities, in-house experimental data and numerical simulations have been used to show that few geometric parameters play a fundamental role in defining the flow patterns inside the clearance and even more so inside and between cavities. As is to be expected, the seals effectiveness is heavily influenced by these flow structures. It is also shown that certain methods of dealing with near-wall flow structures are better suited than others for the estimation of the discharge behaviour when compared to experimental results. Even though in the framework of the RANS equations CFD has proven to be a reliable tool for a wide range of geometries, further investigations are necessary on deep cavities. For aspect ratios above 0.75, the flow patterns inside the cavity change drastically, leading to bad convergence rates of the solver and, more important, to a considerable misalignment between numerical and experimental results. Lid-driven cavity flow is known to be a complex problem in 2D domain, and in this case, the flow becomes three-dimensional due to the tangential velocity induced by rotation. However, the reasons behind the problems in CFD analysis are not entirely clear. Given the observed variations of the flow structures inside sealings with different geometric parameters, it becomes clear why a simplified, generic formulation is very difficult to obtain, if not by adopting empirically defined coefficients which are needed to tune the analytical model.

Optimizing the Geometric Parameters of a Straight-Through Labyrinth Seal to Minimize the Leakage Flow Rate and the Discharge Coefficient

A straight-through labyrinth seal is one of the most popular non-contacting annular seals through which energy dissipation by turbulence viscosity interaction is achieved with a series of teeth and cavities. The geometric parameters of the straight-through labyrinth seal, such as clearance, tooth width, tooth height, cavity width, and tooth inclination angle, affect its performance. The space for installing a labyrinth seal in turbomachinery is limited, and so it is important to optimize its geometry for a fixed axial length in order to minimize the leakage flow rate and the discharge coefficient. The objective of the current study is to understand the effects of changing the geometric parameters of the seal on the leakage flow rate and the discharge coefficient, and to determine the optimized geometry for a fixed axial length. When the whole axial length is fixed, the most effective way to decrease the discharge coefficient is to reduce the cavity width by increasing the number of cavities. However, if the number of cavities is too high, the beneficial effect of more cavities can be reversed. The results of this study will help turbomachinery manufacturers to design a more efficient labyrinth seal. Numerical simulations of leakage flow for the straight-through labyrinth seal were carried out using Reynolds-Averaged Navier–Stokes (RANS) models, and the results for their discharge coefficients and pressure distributions were compared to previously published experimental data.

Experimental validation of optimised straight-through labyrinth seals with various land structures

Seals in turbomachinery have a huge impact on efficiency. The labyrinth seal a with honeycomb land is one of the most popular solutions applied in gas turbines to control secondary flows. The presented paper shows experimental validation of labyrinth seal optimisation, working with various innovative honeycomb-type lands. The analysis focuses on the straight-through seal configuration with two fins. Such a configuration is expected in regions with limited space, common in modern jet engines. Four configurations of the straight-through labyrinth seal are presented: with a smooth land, a honeycomb land, a squeezed honeycomb and a rhomboid land. The labyrinth reference geometry and the optimised ones are investigated experimentally. The CFD-based optimisation results presented in the previous work revealed a significant reduction in leakage, up to 24%. The study described in this paper validates the numerical computations and confirms the potential for improvement of labyrinth seals. The tests were performed on an air-fed test stand, with the pressure ratio loading range of 1.05-1.8, which is representative of the aero-engine interstage seals. The leakage amount, the total inlet parameters and the pressure distribution in the sealing specimen were all monitored using high-frequency transducers in real time. The schlieren technique was applied for flow visualisation. Satisfactory agreement is found between the results of the CFD simulations and the experimental data. All the trends and tendencies observed in the CFD study are confirmed proving the robustness of the proposed optimisation methodology. However, in some cases, certain discrepancies between the CFD-optimisation results and the test data can be noticed. The experimental and the numerical schlieren images are presented, which enables a comparison of flow patterns in particular seal configurations. The study indicates that it is possible to design the sealing in a manner that makes it possible to keep leakage relatively stable in a wide range of operating parameters – different clearances and pressure ratios.

直通型迷宫密封动力学特性研究

直通型迷宫密封动力学特性研究

Establishment and solution of governing equation for plana-grooved liquid seals based on three-control-volume theory

PurposeThis paper aims to study the dynamic characteristics of the straight-through labyrinth seals, which is applied on an oil sealing belt of hydrostatic support system (HSS) oil pocket, the establishment and solution process of seal governing equation is deduced.Design/methodology/approachThe three-control-volume model theory is an efficient approach that is applied well. This paper starts with three relative governing equations for the flow characteristics of straight-through labyrinth seals in the plane direction. Referring to the establishment process of governing equations for circumferentially-grooved liquid seals, the governing equation based on space rectangular coordinate system is established, which are transformed into dimensionless equations through a nondimensionalized process and solved by a perturbation method. It contains a zeroth-order equation, through which a steady fluid distribution is determined, and a first-order equation, through which the seal’s dynamic coefficients can be acquired.FindingsThe governing equation for plane-grooved straight-through labyrinth seals can be established and solved by the three-control-volume theory.Practical implicationsThis study have important guiding significance for further theoretical research and structural design of the straight-through labyrinth seals on the oil sealing belt of HSS oil pocket.Originality/valueIn this paper, a straight-through labyrinth seal is installed in an oil sealing belt. The three-control-volume governing equations is established in space rectangular coordinate system, and the shear force of the fluid Y-direction is different from the previous model.

Analysis and simulation of straight-through labyrinth seal in hydrostatic support system

PurposeThe purpose of this paper is to improve the bearing capacity and mechanical properties of the oil pocket.Design/methodology/approachIn this paper, a straight-through labyrinth seal is installed in an oil sealing belt. The main structure of hydrostatic support system (HSS) is introduced, and the factors affecting the leakage loss are analyzed. The governing equations involving the momentum equation and the continuity equation for the land section and groove section are established separately based on the three-control-volume theory. To explain the flow capability of the straight-through labyrinth seal, the labyrinth seal with different clearance widths, groove numbers, groove depths and pressure difference is calculated. The results of the simulation are compared and analyzed.FindingsThe groove dimensions and groove numbers have important impact on the leakage and flow pattern of the seal.Research limitations/implicationsThe fluid flow was simulated by commercial tools executed in the ANSYS Fluent, the computational fluid dynamics (CFD) solver and a steady state scheme with the realizable k-ε turbulence model was applied. The cavity structure of the straight-through labyrinth seal, forming turbulence eddy flows in the groove, which is a valid approach to convert turbulence kinetic energy into thermal energy, reduce leakage mass flow.Practical implicationsThis research can provide the theoretical basis and technical support which is conducive to the practical application of the straight-through labyrinth seal in HSS.Social implicationsA new design structure is proposed to improve the bearing capacity and economic benefit of HSSs.Originality/valueA straight-through labyrinth seal is applied to the oil sealing belt and the three-control-volume governing equation is established.

Analysis of the Gas Flow in a Labyrinth Seal of Variable Pitch

The paper discusses the results of investigations performed for the segments of straight-through labyrinth seals of constant length. Increasing the number of teeth of a segment resulted in a reduction of the pitch length to obtain the slot seals. The phenomena occurring during gas flow in labyrinth and slot seals differ significantly. They are described with different calculation models. The analysis presented in this paper is related to the change of the tightness and the nature of the flow from a straight-through labyrinth seal to a slot seal. The paper includes the results of experimental research and CFD calculations. Models applied for the Neumann and Scharer labyrinth seals as well as the model of the Salzman and Fravi slot seals were discussed. For the Neumann and Scharer models, correction coefficients for the tested geometry were proposed. Based on the assumptions for the said models and the obtained results, the phenomena responsible for the minimization of the leakage were discussed. The leakage rate in segments of different gap heights depending on the number of teeth and the pressure ratio upstream and downstream of the segment has been analyzed. Based on the experimental data, an optimum number of teeth in the segment for minimum leakage was determined. CFD calculations allowed determining the minimum leakage geometry. The experimental data contained in this paper confirm that the determined optimum pitch range is independent of the pressure drop.

Influence of structure parameters on aeroelastic stability for labyrinth seal based on energy method

Numerical analysis of turbomachinery based on energy method is used to predict the aeroelastic stability of the straight-through labyrinth seal by solving aerodynamic work and damping. The aeroelastic stability of the labyrinth seal under different working conditions and vibration modes has been compared. It׳s found that the increase of pressure ratio leads to the greater possibility of aeroelastic instability. The periodic distribution of the aerodynamic work in the circumferential direction of the labyrinth seal corresponds to the number of vibrating nodal diameters. In order to investigate the influence of structure parameters, the effect of relative thickness of the tooth tip, the width of the seal cavity and the eccentricity of the rotor on the aeroelastic stability of the labyrinth seal has been studied. The result of numerical calculation shows that the change of the structural parameters can affect the aeroelastic stability of the labyrinth seal to a certain extent, and can be applied in the structural optimization.

Effect of teeth bending and mushrooming damages on leakage performance of a labyrinth seal

To achieve higher aerodynamic performance, turbine usually works at tight clearance, which results in inevitable rub between the rotor and stator parts of labyrinth seal due to vibrations, misalignment, mechanical force, thermal stress, etc. In the rubbing events, contact between labyrinth fin and rotor part will commonly induce the teeth bending and mushrooming damages, which significantly affect the discharge performance of a labyrinth seal. To account for the influence of teeth bending and mushrooming on leakage performance of a straight-through labyrinth seal, the leakage rates and flow fields in the worn labyrinth seal are measured and also compared with the original design cases. With numerical methods, the discharge behaviors of the labyrinth seal with different degrees of bending and mushroom damages are analyzed. It shows that the predicted leakage performance and flow fields in the labyrinth seals match well with the experimental tests. For the bending cases, the leakage rates and flow patterns in labyrinth seals are dependent on the effective clearance and bending angle. The leakage ratio of forward bending case is smaller than that of backward bending case with the same geometrical dimensions. However, for the mushroomed labyrinth seals, the leakage rates and flow patterns are much dependent on the effective clearance but slightly dependent on the mushroom radius.

Optimization of the Straight-Through Labyrinth Seal With a Smooth Land

This paper presents the methodology and results of the optimization of a straight-through labyrinth seal with two inclined fins against smooth-land. The optimization was performed using commercial tools implemented in the ANSYS environment, such as goal-driven optimization. The response surfaces were created based on Latin hypercube samples found from computational fluid dynamics (CFD) calculations. The CFD solver, using a steady-state scheme with the k–ω shear stress transport (SST) turbulence model, was applied. A screening algorithm was used to find the best candidates on the response surfaces. The objective function adopted in the labyrinth seal optimization was the minimization of the discharge coefficient value. A wide range of parameters of the fins position and shape were taken into account, with physically justified degrees-of-freedom. The optimization results were supported by the results of an in-house experiment performed on a stationary, linear test rig. The test rig was fed by a high-capacity vacuum air blower with high-precision hot-wire anemometry mass flow evaluation. The reductions in the leakage significantly exceed the uncertainties of the CFD model and the test rig accuracy. The factors that had the most substantial impact on the leakage reduction were the location, inclination, and thickness of the fins. The experimental results were compared with the calculations and the optimization effects, highlighting some tendencies in the labyrinth seal flow behavior. Good agreement was obtained between the optimization results and the experimental data, proving that the presented methodology is sufficient for the labyrinth seal optimization.