Straight Labyrinth Seal Research Articles

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.

Higher Order Conceptual Model for Labyrinth Seal Flutter

Abstract A simple nondimensional model to describe the flutter onset of two-fin straight labyrinth seals (Corral, R., and Vega, A., 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) is extended to account for nonisentropic flow perturbations. The isentropic relationship is replaced by the more general integral energy equation of the inter-fin cavity. A new expression for the Corral and Vega stability criterion is derived, which is very consistent with the previous model in the whole design space of the seal but for torsion centers located in the high-pressure side close to the seal. The new model formally depends on more dimensionless parameters since the existing parameter grouping of the previous model does not hold anymore, but this dependency is weak in relative terms. The model blends the limit where the discharge time of the inter-fin cavity is much longer than the vibration period, and the flow is nearly isentropic, and the opposite limit, where the perturbations are isothermic, gracefully. A few numerical examples obtained using a three-dimensional linearized frequency domain solver are included to support the model and show that the trends are correct, but the body of the numerical work will be presented in a separated article. The matching between the work-per-cycle obtained with the model and frequency domain solver is good. It is shown that some weird trends obtained using linearized unsteady simulations are qualitatively consistent with the current model but not with the previous one (Corral, R., and Vega, A., 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006). The largest differences between the new and the previous model are seen when the seal is supported at the high-pressure side.

Shape Optimization of Labyrinth Seals to Improve Sealing Performance

To reduce gas leakage, shape optimization of a straight labyrinth seal was carried out. The six design parameters included seal clearance, fin width, fin height, fin pitch, fin backward, and forward expansion angle. The CFD (Computational Fluid Dynamics) model was solved to generate the training and testing samples for the surrogate model, which was established by the least square support vector machine. A kind of chaotic optimization algorithm was used to determine the optimal design parameters of the labyrinth seal. As seal clearance, fin width, fin height, fin pitch, fin backward and forward expansion angles are 0.2 mm, 0.1 mm, 7 mm, 9 mm, 0°, and 15°, the discharge coefficient can reach its minimum value in the design space. The chaotic optimization algorithm coupled with least square support vector machine is a promising scheme for labyrinth seal optimization.

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.

Leakage Degradation of Straight Labyrinth Seal Due to Wear of Round Tooth Tip and Acute Trapezoidal Rub-Groove

In this paper, labyrinth seal leakage is numerically quantified for an acute trapezoidal rub-groove accompanied with a rounded tooth, as a function of rub-groove sizes and tooth-groove axial positions. Analyses parameters include clearance, pressure ratio, number of teeth, and rotor speed. Labyrinth seals wear during engine transients. Radial incursion and axial movement of the rotor–stator pair cause the labyrinth teeth to rub against the unworn stator surface. The labyrinth teeth and/or stator wear depending on their material hardness. Wear damage in the form of material loss or deformation permanently increases seal clearance, and thus, leakage. This leakage is known to be dependent on the shape and geometry of the worn tooth and the stator rub groove. There are two types of reported tooth tip wear. These can be approximated as a mushroom shape and a round shape. The stator rub-groove shapes can be approximately simulated in five forms: rectangle, trapezoid (isosceles and acute), triangle, and ellipse. In this paper, the acute trapezoidal rub-groove shape is specifically chosen, since it is the most similar to the most commonly observed rub-groove form. The tooth tip is considered to be rounded, because the tooth tip wears smoothly and a round shape forms during rub-groove formation. To compare the unworn tooth, the flat stator is also analyzed as a reference case. All analyzed parameters for geometric dimensions (groove width, depth, wall angle, and tooth-groove axial position) and operating conditions (flow direction, clearance, pressure ratio, number of teeth, and rotor speed) are analyzed in their practical ranges. Computational fluid dynamics (CFD) analyses are carried out by employing a compressible turbulent flow solver in a 2D axisymmetrical coordinate system. CFD analyses show that the rounded tooth leaks more than an unworn sharp-edged tooth, due to the formation of a smooth and streamlined flow around the rounded geometry. This smooth flow yields less flow separation, flow disturbance, and less of vena contracta effect. The geometric dimensions of the acute trapezoidal rub-groove (width, depth, wall angle) significantly affect leakage. The effects of clearance, pressure ratio, number of teeth, and rotor speed on the leakage are also quantified. Analyses results are separately evaluated for each parameter.

Mechanical Growth of Labyrinth Seal

A preliminary numerical study has been conducted to study the effect of rotational speed on centrifugal growth in a six-tooth straight labyrinth seal. The distribution of the radial deformation along the seal axis for the rotational speed ranging from 100 rpm to 1500 rpm is reported in this paper. The radial deformation which decreases the clearance between the rotating and stationary parts of sealing surface is an indication that centrifugal growth occurs. The results of the simulation indicate that centrifugal growth increases as rotational speed increases. This finding is in qualitative agreement with other numerical and experimental work reported in the literature.

CFD Study on Stepped and Drum Balance Labyrinth Seal

The stability of rotors in turbomachines is affected by the labyrinth seal where driving forces are generated. Recent research results have shown that the preswirl has a significant influence on the rotordynamic characteristics of the straight labyrinth seal including both tooth-on-stator and tooth-on-rotor configurations. However, modern turbomachines require higher and higher pressure drop for the seal so that the eye seal is usually designed as stepped labyrinth, whereas the balance drum usually employs a tooth-interlocking labyrinth and a larger number of teeth. Both designs could generate greater forces on the rotor than the straight labyrinth seal. Therefore, it is necessary to further study the influence of preswirl on stepped and tooth-interlocking labyrinth seals. This article employed 3D calculational fluid dynamics (CFD) to solve the flow in those seals. Then the rotordynamic coefficients of the two seals at different preswirl rates were calculated based on the CFD results. The results were compared with test data and bulk flow results. A rotor stability analysis was conducted considering the balance drum seal with the coefficients predicted by the numerical method.

Numerical Analysis of Compressible Flow in Labyrinth Seal

Numerical simulation code for compressible flow based on OpenFOAM-1.6 was developed to compute a high Mach number flow. Total enthalpy transport equation was solved to calculate temperature and a flow around a rotor was solved in whirling rotating frame to predict a hydraulic force on an eccentric whirling rotor. Straight and high-low labyrinth seals were simulated by the developed code and numerical results regarding hydraulic force were compared with experimental ones to validate the prediction accuracy. The non-diagonal component of spring constant was predicted well, but the diagonal component of damping constant was largely under-predicted. The maximum and minimum pressures were observed at the circumferential positions of 270° and 90° respectively in inlet region of the straight labyrinth seal. Therefore large hydraulic force in the whirling direction was generated. On the other hand, the maximum and minimum pressures were observed at 180° and 0° respectively in the high-low labyrinth seal. Therefore the hydraulic force in the whirling direction was lower than that of the straight labyrinth seal. Pressure distribution in the circumferential direction was uniform in a large clearance region surrounded by two fins in the straight labyrinth seal, where the hydraulic force in whirling direction was largely decreased.

Experimental and Theoretical Study on Swirl Braked Labyrrinth Seal

The objects of this study are to present new gas seals, which have several control fins at a groove part of straight labyrinth seal, and to evaluate the dynamic characteristics of the seals experimentally and theoretically. The new seals are expected to reduce the tangential velocity and to control the instability of the rotor system. The experimental test results are presented for eight multiple-pocket grooved gas seals with different number of control fins and stages to put control fins. In the theoretical study, seal chamber is divided into two control volumes. Then, the equations are formulated for each control volumes. The fluid forces acting on the rotor are obtained. For the circumferential velocity, the groove part is divided into three control volumes then the decrease in circumferential velocity by the effect of the control fins is evaluated at each control volume. Then, the circumferential velocity and dynamic fluid force were measured for 8 types of seals which were changed the number of fins and location of the fins in the experiment. In the theoretical analysis the flow equation which suppress the circumferential velocity was taken into account in the conventional labyrinth seal equation and solved numerically. From the above experimental and theoretical investigations, the followings are concluded that control fin installed in the grooves is effective to suppress the circumferential velocity. The effect of the fins is large at the first and second stage from the inlet of a seal. The effect of fins on the stabilization of rotor was large for 8 and 4 fins in the first stage.

A General Method for Correlating Labyrinth-Seal Leak-Rate Data

The proper selection of an optimum labyrinth seal for a given application depends upon an accurate estimate of the seal leak rate. Suitable accuracy, particularly for straight labyrinth seals, can only be obtained from actual seal tests. Testing a complete series of seals is time-consuming and expensive. A method for correlating test data is presented which allows calculation of the leak rates for an entire family of labyrinth seals on the basis of tests of only two characteristic seals. Leak rates predicted by the method are within 3 per cent of the basic test data.