Numerical Analysis of Labyrinth Seal Performance for the Impeller Backface Cavity of a Supercritical CO_(2) Radial Inflow Turbine

For a radial inflow turbine(RIT),leakage flow in impeller backface cavity has critical impacts on aerodynamic performance of the RIT and axial force acting on the RIT impeller.In order to control this leakage flow,different types of labyrinth seals are numerically studied in this paper based on a supercritical carbon dioxide(S-CO_(2))RIT.The effects of seal clearance and cavity outlet pressure are first analyzed,and the impacts of seal design parameters,including height,number and shape of seal teeth,are evaluated.Results indicate that adding labyrinth seal can improve cavity pressure and hence adequately inhibits leakage flow.Decreasing the seal clearance and increasing the height of seal teeth are beneficial to improve sealing performance,and the same effect can be obtained by increasing the number of seal teeth.Meanwhile,employing seals can reduce leakage loss and improve RIT efficiency under a specific range of cavity outlet pressure.Finally,the influences of seal types on the flow field in seal cavity are numerically analyzed,and results demonstrate that isosceles trapezoidal type of seal cavity has better sealing performance than triangular,rectangular and right-angled trapezoidal seal cavities.

Investigation and Improvement of the Staggered Labyrinth Seal

Recent studies on staggered labyrinth seals have focused on the effects of different parameters,such as the pressure ratio and rotational speed on the leakage flow rate.However,few investigations pay sufficient attention to flow details and the sealing mechanism,which would be of practical importance in designing seals having higher performance.This paper establishes a theoretical model to study the seal mechanism,thus revealing that leakage is determined by the pressure ratio and geometric structure.Numerical simulation is implemented to illustrate details of the flow field within the seal structure.Viscous dissipation is used to quantitatively investigate the contribution that each location makes to the seal performance,revealing that orifices and stagnation points are the most important positions in the seal structure,generating the most dissipation.The orifice is carefully studied by using the theoretical model.Experiments for different pressure ratios are conducted and the results match well with those of the theoretical model and numerical simulation,verifying the theoretical model and analysis of the seal mechanism.Three new designs,based on a good understanding of the seal mechanism,are presented,with one reducing leakage by 24.5%.

ANALYSIS OF COUPLING INFLUENCES OF LABYRINTH SEAL PARAMETERS ON CROSS COUPLED STIFFNESS AND DIRECT DAMPING COEFFICIENT

Labyrinth seal can cause steam-exciting, the structural and operating parameters of labyrinth seal have effect on stability of rotor-system. For investigating the coupling influences of the structure and operating parameters of labyrinth seals on dynamic coefficients, a model of calculating dynamic coefficients of labyrinth seals is presented using a two control volume model. The coupling influences of parameters on cross-coupled stiffness and direct damping of labyrinth seal are discussed. In the conclusion, a reference of preventing steam-exciting vibration and optimum determination of design parameters of labyrinth seals are provided.

Labyrinth seal leakage and dynamics characteristics analysis based on Black Model

One of the important problems to be tackled in turbo machines is the leakage dynamics characteristics of labyrinth seals. In this paper we analyzed the effect of labyrinth seal structure and the change in fluid flow pressure on the leakage characteristics of seal. Computational fluid dynamics (CFD) model for 3D labyrinth seal was built which provides a basis for reducing steam flow excitation. The streamline pattern and the pressure drop characteristics for leakage of steam through a labyrinth seal was investigated. Simulations of internal flow and leakage characteristics had been performed by CFD software and Black-Child model. The results showed that the amount of leakage is directly proportional to the tooth gap and inlet pressure and inversely proportional to the cavity depth and outlet pressure. The proposed CFD model provides a feasible method to predict the leakage characteristics of labyrinth seal in response to the structure of seal and the change in inlet-outlet pressures.

Nonlinear dynamic characteristics model of labyrinth seal based on Muszynska model

An accurate seal forces model is the foundation to analyze the rotor-seal systems. In this paper, the Navier-Stokes equation and energy equation are solved to simulate the interior flow field in the labyrinth seal gap. The leakage rate is compared with the experimental results in the literatures. The maximum error is 4%, which proves that the method of employing CFD to simulate the interior flow field of labyrinth seal gap is reliable. Based on this, the interior flow field and fluid exciting force of stage teeth labyrinth seal are studied. By coupling with the Muszynska model, the method of defining the experience loss parameters in Muszynska model is proposed. The results indicate that the experience parameters obtained by the proposed method can depict the nonlinear exciting force of labyrinth seal better.

Labyrinth Seal Design Optimization Based on Quadratic Regression Orthogonal Experiment

The influence of labyrinth seal structure parameters and their interaction on the characteristics of leakage amount are numerically investigated by conducting a quadratic regression orthogonal experiment. To determine the optimal structure parameters of the steam seal for minimizing the leakage amount, a reliable regression equation that does not lack of fit is established. The flow characteristics of the fluid in the labyrinth seal are analyzed in detail. Results show that the leakage amount is greatly influenced by seal cavity depth, convex platform height, seal tooth thickness, and tooth tip clearance, with the tip clearance having the most significant effect. The interaction among the four items exerts a certain impact on the leakage amount. The proposed regression equation exhibits a good significance and does not lack of fit. After optimization, the labyrinth seal demonstrates increased entropy and energy dissipation at the tip of the seal tooth, as well as decreased speed and inertia effect in the cavity, suggesting that the resistance leakage performance of the optimized labyrinth seal is improved.

NUMERICAL ANALYSIS OF LEAKAGE FLOW THROUGH TWO LABYRINTH SEALS

The leakage flow through two labyrinth seals, e.g the interlocking seal and the stepped seal, was numerically investigated. Preliminary calculation of the seal-cavity averaged pressure by using the one-dimensional control volume method showed favorable agreement with the experimental measurements. Subsequently, in-depth understanding of the fluid flow through the labyrinth seals was obtained by employing Computational Fluid Dynamics （CFD） and k -ε turbulence model, which resulted in a potential wealth of information like the streamline pattern, velocity vector field, and distribution of turbulent kinetic energy and static pressure. At the clearance of the seal the turbulent kinetic energy reached the peak value, while in the bulk region of the cavities it decayed fast. The static pressure rapidly dropped as the fluid flow went through the clearance; no distinct difference of the static pressure was inspected in the cavities. Also noted from the numerical results was that the stepped seal showed better sealing performance than the interlocking seal.

Effects of tooth bending damage on the leakage performance and rotordynamic coefficients of labyrinth seals

Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.

Effects of swirl brake axial arrangement on the leakage performance and rotor stability of labyrinth seals

Swirl brakes are usually introduced at the seal entrance in industry to improve the seal stability,especially for labyrinth seals suffering low seal clearance and high inlet preswirl ratio.However,how to arrange swirl brakes at the seal entrance to obtain better seal stability retains unknown,such as the axial distance between the brake trailing edge and the first tooth.To this end,the effects of the distance between brakes and the first tooth on the leakage flow rate and seal rotordynamic coefficients were numerically investigated at typical inlet preswirl ratios of 0.45 and0.8,and the predicted results were in comparison with the results for no-brake configuration.The obtained results disclose that the brake configuration arranged against the first tooth produces lower circumferential velocity in the downstream of the brakes as a result of the larger counterclockwise vortex moving from the brake trailing edge to the brake leading edge when compared to the brake configuration away from the first tooth.Besides,the dropped circumferential velocity in the downstream of brakes will cause larger pressure fluctuation in the circumferential direction and thus generates larger tangential force to restrain the rotor forward whirl.On the other hand,the effective damping is further increased when the distance between brakes and the first tooth decreases to zero,that is,the crossover frequency is even disappeared at the inlet preswirl ratio of 0.45 and successfully drops from 69.9 Hz to 32.7 Hz at the preswirl ratio of 0.8.

Leakage performance of labyrinth seal for oil sealing of aero-engine

Experimental investigation has been done to evaluate the leakage performance of labyrinth seal for oil sealing on high-speed sealing test rig at different working and geometric parameters.Typical values of pressure ratio ranging from 1.0 to 2.0 were used and the rotating speed varied from 0 to 30,000 tpm.Dimensionless Taylor number was invited to response the effect of rotation.Oil was injected at the rate from 1.2 L/min to 2.8 L/min to check the sealing capacity.Leakage was measured at different seal configurations including sealing clearance,tooth tip thickness,pitch,teeth number,front inclined angle and oil-throwing angle.Different from gas sealing,the application of oil-throwing tooth in oil sealing attracted much interest as an obvious alternative to the conventional labyrinth seal.A blocking ring was captured during testing,which establishes understanding of underlying flow mechanisms in the clearance and plays an important role in oil sealing.There is a critical Taylor number at which the leakage coefficient drops drastically.After the critical Taylor number,a parabola rule appears.An optimal composition of tooth tip thickness,teeth number,oil-throwing angle and front inclined angle exists where the leakage performance behaves better.

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 vibration modes has been compared.It's found that the increase of pressure ratio leads to the 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.

Fluid dynamic modeling of a free piston engine with labyrinth seals

Preliminary design and simulation of a free piston engine suitable for small-scale energy production in distributed energy systems is presented in this paper.The properties,particularly the properties of gas seals of the engine are simulated using a simulation program developed for this case,and the results are utilized in preliminary main design parameter selection.The engine simulation program was developed by combining and modifying the source codes of the simulation and calculation programs obtained from Helsinki University of Technology,Tampere University of Technology,and Lappeenranta University of Technology.Because of the contact-free labyrinth seal used in the piston,the efficiency of the motor is lower than the efficiency of a conventional motor with oil lubricated piston rings.On the other hand,the lack of bearing losses,and the lack of losses associated with a crankshaft system and a gearbox,as well as the lack of lubrication oil expenses,compensates this effect.As a net result,this new motor would perform slightly better than the conventional one.Being completely oil-free,it is very environmentally friendly,and its exhaust gases are completely free of oil residuals which are causing problems in normal gas motors.

Dimensional Analysis on Resistance Characteristics of Labyrinth Seals

Experimental investigation of stepped and straight-through labyrinth seals was designed to study the sealing performance of two different typical labyrinth seals.In order to facilitate dimensional analysis on the flow resistance characteristics of labyrinth seals,the variable cross-section of the flow channels are considered as constant cross-section flow.The mechanical energy loss of flow caused by throttle turbulence intensity is considered as caused by friction along the way.The friction coefficient of stepped labyrinth seals is bigger than that of straight-through labyrinth seals by more than 40% for the same Reynolds number and the ratio of equivalent diameter and the seal length.The expression of friction coefficient /and /Re are obtained from experimental data.The verifications indicate that the expressions are highly accurate.The contribution to the total pressure drop of each tooth cavity gradually becomes less along the flow direction.

Effect and sensitivity analysis of the rotational speed on the fluid-induced force characteristics of the straight-through labyrinth gas seal

The effects of the rotational speed on the fluid-induced force characteristics of a straight-through labyrinth gas seal( STLGS) are numerically investigated using the steady computational fluid dynamics( CFD) method based on a three-dimensional model of the STLGS. The fluid-induced force characteristics of the STLGS for five rotational speeds at a pressure drop of △P = 5000 Pa with and without eccentricity are computed. The grid density analysis ensures the accuracy of the present steady-CFD method. The effect and sensitivity analysis show that the changes in rotational speed affect the pressure forces,viscous forces and total pressure distributions on the rotor surface,velocity streamlines,leakage flow rates,and maximum flow velocities. The results indicate that the rotational speed inhibits the pressure forces,leakage flow rates and maximum flow velocities and promotes the viscous forces and total pressure on the rotor surface.

Effects of Four Types of Pre-swirls on the Leakage, Flow Field, and Fluid-Induced Force of the Rotary Straight-through Labyrinth Gas Seal

The labyrinth seal in turbomachinery is a key element that restricts leakage flow among rotor-stator clearances from high-pressure regions to low-pressure regions. The fluid-induced forces on the rotor from seals during machine operation must be accurately quantified to predict their dynamic behavior effectively. To understand the fluid-induced force characteristics of the labyrinth seal more fully, the effects of four types of pre-swirls on the leakage, flow field, and fluid-induced force of a rotary straight-through labyrinth gas seal (RSTLGS) were numerically investigated using the proposed steady computational fluid dynamics (CFD) method based on the three-dimensional models of the RSTLGS. The leakage, flow field, and fluid-induced force of the RSTLGS for six axial pre-swirl velocities, four radial preswirl angles, four circumferential positive pre-swirl angles, and four circumferential negative pre-swirl angles were computed under the same geometrical parameters and operational conditions. Mesh analysis ensures the accuracy of the present steady CFD method. The numerical results show that the four types of pre-swirls influence the leakage, flow field, and fluid-induced force of the RSTLGS. The axial pre-swirl velocity remarkably inhibits the fluid-induced force, and the circumferential positive pre-swirl angle and circumferential negative pre-swirl angle remarkably promote the fluid-induced force. The effects of the radial pre-swirl angle on the fluid-induced force are complicated, and the pressure forces and viscous forces show the maximum or minimum values at a specific radial pre-swirl angle. The pre-swirl has a negligible impact on the leakage. The four types of pre-swirls affect the leakage, flow field, and fluidinduced force of the RSTLGS to varying degrees. The pre-swirl is the influence factor affecting the leakage, flow field, and fluid-induced force of the RSTLGS. The conclusions will help to understand the fluid-induced force of labyrinth seals more fully, by providing helpful suggestions for engineering practices and a theoretical basis to analyze the fluid–structure interaction of the seal-rotor system in future research.

具有前置凸台防旋板的汽轮机交错齿迷宫密封动力学特性研究

为提高汽轮机多级轴端迷宫密封动力学性能,针对汽轮机两级轴端交错齿迷宫密封,开展了具有前置凸台的新型防旋板结构方案设计和止旋抑振性能评估。首先,针对两级轴端交错齿迷宫密封,设计了一级和两级传统防旋板、一级和两级前置凸台新型防旋板等动密封防旋板结构方案,并建立了具有“虚拟旁路边界”的有、无防旋板多级交错齿迷宫密封动力学计算模型,实现了对多级动密封进口压力场和高预旋速度场的精准模拟;然后,采用基于多频椭圆轨迹涡动模型的动密封气流激振动力学特性(CFD)摄动数值预测方法,对比分析了无防旋板、传统防旋板和新型前置凸台防旋板作用下,两级交错齿迷宫密封泄漏特性和气流激振动力学特性;最后,通过分析不同防旋板结构方案下,两级交错齿迷宫密封腔室旋流发展、腔室速度场和动态压力分布、转子面气流激振力,阐明了防旋板的止旋抑振机制。结果表明:无防旋板的迷宫密封具有最低的泄漏量,一级传统防旋板或一级前置凸台防旋板的设置会使密封齿数减少,导致密封泄漏量增加约4.5%;相比于一级防旋板,具有两级防旋板的迷宫密封泄漏量增加约5.5%;相比于传统防旋板,前置凸台防旋板可减小交叉刚度、增大有效阻尼;相比于一级防旋板,两级防旋板可减小高涡动频率下的交叉刚度、增大直接阻尼,进而提高密封的有效阻尼;在传统防旋板的基础上设置前置凸台可提升防旋板的止旋性能,且两级防旋板可有效抑制密封下游区域的旋流发展,能显著提升迷宫密封动力学性能、抑制汽轮机轴系振动失稳。

进口防旋板对汽轮机交错齿迷宫密封泄漏特性和动力学特性影响研究

为提高汽轮机高压缸和中压缸之间过桥汽封的气流激振动力学性能、抑制汽轮机轴系振动失稳,针对交错齿迷宫密封,开展了进口防旋板结构方案设计和动力学性能评估研究。首先,建立了具有“虚拟旁路边界”的交错齿迷宫密封动力学计算模型,实现了对动密封进口压力场和高预旋速度场的精准模拟;然后,采用基于多频椭圆轨迹涡动模型的非定常计算流体动力学(CFD)摄动数值方法,对比分析了进口预旋(预旋比为0、0.3、0.5)对无防旋板结构的迷宫密封的动力特性系数的影响规律;最后,详细评估了不同进口防旋板结构方案的止旋抑振性能,比较分析了防旋板倾角和数量对迷宫密封的泄漏量、动力特性系数和周向旋流比分布的影响规律。研究结果表明:迷宫密封泄漏量对防旋板倾角和数量变化不敏感(泄漏量变化小于0.5%);进口预旋会导致迷宫密封交叉刚度和有效阻尼穿越频率增大、有效阻尼减小,易诱发轴系失稳;进口防旋板能够显著减小迷宫密封的交叉刚度(约为53%)和有效阻尼穿越频率(约为24 Hz)、增大有效阻尼,使密封泄漏量略有增加(约为4.5%);相较于直防旋板,45°倾角斜防旋板使密封交叉刚度进一步降低约14%,有效阻尼穿越频率变化较小;当防旋板数由36增加到72时,密封交叉刚度降低约24%,有效阻尼穿越频率减小约5 Hz;而当防旋板数由72增加到144时,密封的转子动力特性对防旋板数变化不敏感;综合考虑加工成本和止旋抑振性能,具有72个直防旋板的迷宫密封进口防旋板结构方案最优。研究结果可为交错齿迷宫密封防旋板设计提供参考。

基于能量法的篦齿封严环气弹稳定性数值研究

针对航空发动机篦齿封严环气弹稳定性问题,采用基于三维插值及非定常动网格技术的能量法,建立了篦齿封严环气弹稳定性数值求解模型。在验证数值方法准确性的基础上,研究了供气压力、转速和进气畸变对篦齿封严环气弹稳定性的影响,分析了篦齿封严环气动力、气动功分布特性,揭示了进气畸变对篦齿封严环气弹稳定性的影响机理。研究表明:在本文研究中,外篦齿封严环相对于内篦齿封严环更易发生气弹失稳;随供气压力增加,外篦齿封严环气弹稳定性呈现降低趋势,当供气压力为0.55 MPa和0.7 MPa时,外篦齿封严环存在气弹失稳的风险;转速2000 r/min和4000 r/min相对于6000 r/min具有更大的气弹失稳风险。相比于360°圆周进气,90°圆周进气的外篦齿封严环气动力存在相互抵消的耦合作用,所以90°圆周进气的外篦齿封严环具有较高的气弹稳定性。篦齿封严环在发生气弹失稳时,齿腔底部做功占总气动功百分比会显著增加,故在进行结构优化时,可改变齿腔底部的结构参数以对篦齿封严环气弹稳定性进行改善。

周向进气畸变对篦齿封严环气弹稳定性影响研究

针对航空发动机篦齿封严环在周向进气畸变状态下的气弹稳定性问题,采用三维插值和非定常动网格技术,建立了基于能量法的篦齿封严环气弹稳定性求解模型,在验证求解模型准确性的基础上,研究了对称进气与非对称进气、进气畸变程度对篦齿封严环气弹稳定性的影响规律,分析了气动功在齿腔不同区域分布特性,揭示了周向进气畸变对篦齿封严环气弹稳定性影响机理。研究表明,周向进气畸变可改变气动阻尼比,对篦齿封严环气弹稳定性影响较大。非对称进气时,篦齿封严环气弹稳定性随畸变度的增加先降低后增加再降低。对称进气时,篦齿封严环气弹稳定性随畸变度的增加先增加后降低,相对于非对称进气畸变,对称进气方式对气弹稳定状态影响较小。篦齿封严环在发生气弹失稳时,周向进气畸变对气动功影响最大的区域位于首级篦齿迎风区域,是流场周向压力均匀性最差的区域,周向进气畸变的影响随相对距离增加而降低;篦齿封严环所有齿腔底部的总气动功受周向进气畸变影响较大,在进行结构设计时可改变齿腔底部尺寸、形状等,以降低周向进气畸变对篦齿封严环气弹稳定性的影响。

基于瞬态有限元的齿轮箱迷宫密封泄漏研究

针对某高速列车齿轮箱迷宫密封的润滑油泄漏问题,基于ANSA软件建立齿轮箱及迷宫密封结构的有限元模型,并采用FLUENT软件对其进行多相流瞬态仿真分析,研究迷宫密封结构的相对啮合深度、节流齿厚、径向间隙、回油孔直径及个数、齿与台阶距离、齿宽、密封间隙对润滑油泄漏量的影响。结果表明:当相对啮合深度大于0.5时,润滑油泄漏量与相对啮合深度呈负相关;润滑油泄漏量与节流齿厚、回油孔直径、回油孔数量呈负相关;润滑油泄漏量与径向间隙、齿宽、齿与台阶距离、密封间隙呈正相关。根据研究结果对迷宫密封结构进行改进,改进后的迷宫密封结构润滑油泄漏量降低为原始泄漏量的3.6%。