Labyrinth seals are widely used in rotating machinery and have been shown to experience aeroelastic instabilities. The rapid development of computational fluid dynamics now provides a high fidelity approach for predicting the aeroelastic behavior of labyrinth seals in three dimension and exhibits great potential within industrial application, especially during the detailed design stages. In the current publication a time-marching unsteady Reynolds- averaged Navier-Stokes solver was employed to study the various historically identified parameters that have essential influence on the stability of labyrinth seals. Advances in understanding of the related aeroelastic (flutter) phenomenon were achieved based on extensive yet economical numerical analysis of a simplified seal model. Further, application of the same methodology to several realistic gas turbine labyrinth seal designs confirmed the perceived knowledge and received agreements from experimental indications. Abbott’s criteria in describing the labyrinth seal aeroelastic behaviors were reaffirmed and further developed.

The growing popularity of additive manufacturing in commercial applications has al- lowed for new ideas and new ways of thinking when designing components. Further optimization at the component level is possible, though powder metallurgy is in its infancy. This study explores the possibility of using additive manufacturing to develop better labyrinth seals in turbomachinery. Labyrinth seals have a torturous fluid path with high losses, thus limiting the amount of fluid leakage. These types of seals can be non-rotating, allowing them to better take advantage of the additive manufacturing process due to the absence of rotating stresses. Labyrinth seal performance is defined by its ability to limit leakage through a seal. Investigations on the ability to reduce this leakage using the inherent roughness from the additive manufacturing process and the addition of complex geometry only capable of being produced by additive manufacturing are explored. Incompressible and compressible fluid models are utilized in the study. Perfectly smooth seals with tooth counts of four, six, and eight are first simulated using ANSYS FLUENT and compared to theoretical models to determine accuracy. Roughness is then applied to the seals and leakage decreases of 0.5% to 1.5% are experienced for the incompressible model. Decreases of 1.0% to 3.5% are experienced for the compressible model. Flow visualization and line analysis are conducted for all seals tested to understand how fluid flow is behaving within the clearance region of the seal and seal chambers. Several additive manufacturing geometries are simulated against a control seal to determine geometries with the largest effect on leakage rates. These geometries are then adapted to a six tooth seal and simulated with roughness. This additively manufactured seal is then compared to the smooth and rough six tooth seal for both incompressible and compressible fluids. Leakage was decreased by 5% to 8% for the incompressible model and 5% to 7% reductions for the compressible model when compared to the smooth seal. Flow visualization and line analysis were also conducted for the additively manufactured six tooth seal. A basic outline for an experiment and test stand were developed for future work.

The labyrinth seal is widely used in turbo machines to reduce leakage flow. The stability of the rotor is influenced by the labyrinth seal because of the driving forces generated in the seal. The working fluid usually has a circumferential velocity component before entering the seal; the ratio of circumferential velocity and shaft synchronous surface velocity is defined as pre-swirl rate. It has been observed that pre-swirl rate is an important factor affecting driving forces in the labyrinth seal thus affecting the stability of the rotor. Besides the pre-swirl, the eccentricity, the clearance, and the configuration of tooth locations are all factors affecting the rotordynamic properties of the labyrinth seal. So it is of interest to investigate the exact relationships between those factors and the seal's rotordynamic properties. In this research, three types of labyrinth seals have been modeled: the straight eye seal, the stepped eye seal, and the balance drum seal. For the straight eye seal, a series of models were built to study the influence of eccentricity and clearance. The other two seals each have only one model. All models were built with Solid Works and meshed with ANSYS-ICEM. Flows in those models were simulated by numerically solving the Reynolds-Averaged Navier-Stokes (RANS) equations in the ANSYS-CFX and then rotordynamic coefficients for each seal were calculated based on the numerical results. It had previously been very difficult to generate a pre-swirl rate higher than 60% in a numerical simulation. So three ways to create pre-swirl in ANSYS-CFX were studied and finally the method by specifying the inlet velocity ratio was employed. Numerical methods used in this research were introduced including the frame transfer, the k-ε turbulence model with curvature correction, and the scalable wall function. To obtain the optimal mesh and minimize the discretization error, a systematical grid study was conducted including grid independence studies and discretization error estimations. Some of the results were compared with previous bulk-flow or experimental results to validate the numerical model and method. The fluid field in the labyrinth seal must be analyzed before conducting rotordynamic analysis. The predicted pressure distributions and leakages were compared with bulk-flow results. A second small vortex at the downstream edge of each tooth was found in the straight eye seal. This has never been reported before and the discovery of this small vortex will help to improve seal designs in the future. The detailed flows in discharged region and in chambers were also discussed. Radial and tangential forces on the rotor were solved based on the fluid field results. It is shown that the traditional first-order rotordynamic model works well for low pre-swirl cases but does not accurately reflect the characteristics for high pre-swirl cases. For example compressor eye seals usually have pre-swirl rates bigger than 70% and the second order model is required. Thus a second-order model including inertia terms was built and applied to the rotordynamic analysis in this research. The influence of pre-swirl, eccentricity and clearance were studied using the straight eye seal model. The rotordynamic characteristics of the stepped eye seal and the balance drum seal were studied considering high pre-swirl rates. Some relationships between influencing factors and the four rotordynamic coefficients were concluded. The results also showed that for all the three seals higher pre-swirl leads to higher cross-coupled stiffness which is one of the main factors causing rotor instability. The rotor stability analysis was conducted to study the influence of drum balance seal on the stability. The rotor was designed with typical dimensions and natural frequencies for a centrifugal compressor rotor. The parameters for bearing and aerodynamic force were also set according to general case in compressors to minimize the effects from them. The result shows that the high pre-swirl rate in balance drum seal leads to rotor instability, which confirmed the significant effect of pre-swirl on the seal and the rotor system. / Ph. D.

Labyrinth seal force estimates are important to the prediction of the stability of turbomachinery. The force prediction methods fall into several categories: experiments, bulk flow analysis, and finite volume analysis. Finite volume analysis can be split into two subcategories: self-developed and commercial. In this research, a commercial computational fluid dynamics (CFD) program called ANSYS-CFX was used to predict the forces generated in a labyrinth seal whirling at specified speeds. The results were compared to data from VT-FAST, a bulk flow code, and TASCflow, another commercial CFD program. It was shown that there were discrepancies among the results, and several hypotheses were made as to the reason for these discrepancies. Additionally, ANSYS-CFX was used to study the effect of labyrinth seal eccentricity ratio on the resultant force generated. It was shown that the radial force component within the seal behaved linearly with respect to eccentricity ratio. However, the tangential force component had no distinguishable relationship with the eccentricity ratio. It was hypothesized that the lack of a relationship was caused by the small fluctuations in the inlet swirl. Although the inlet swirl varied very little at each eccentricity ratio, it was shown there was a relationship between the tangential force and inlet swirl. / Master of Science

Vibrations caused due to aerodynamic excitation may cause severe limitation to the performance of turbomachines. The force resulting from the non-uniform pressure distribution within the labyrinth cavity is identified as a major source of this excitation. In order to perform rotor dynamic evaluation of rotor-bearing-seal system, accurate prediction of this force is essential. A visual basic based front-end, for a labyrinth seal analysis program, has been designed herein. In order to accurately predict the excitation force, proper modeling of labyrinth leak path is important. Thus, the front-end developed herein incorporates a leak-path geometric diagram for visual analysis of labyrinth leak path and tooth location. Furthermore, to investigate influence of various operating conditions and gas properties on excitation force (effective cross-coupling stiffness), a parametric study is performed on both the eye seal and the balance piston labyrinth seal. / Master of Science

A seal is a component used in a turbomachine to reduce internal leakage of the working fluid and to increase the machine's efficiency. The stability of a turbomachine partially depends upon the rotodynamic coefficients of the seal. The integral control volume based rotodynamic coefficient prediction programs are no more accurate than the accuracy of the leakage mass flow rate estimation. Thus an accurate prediction of the mass flow rate through seals is extremely important, especially for rotodynamic analysis of turbomachinery. For labyrinth seals, which are widely used, the energy dissipation is achieved by a series of constrictions and cavities. When the fluid flows through the constriction (under each tooth), a part of the pressure head is converted into kinetic energy, which is dissipated through small scale turbulence-viscosity interaction in the cavity that follows. Therefore, a leakage flow rate prediction equation can be developed by comparing the seal to a series of orifices and cavities. Using this analogy, the mass flow rate is modeled as a function of the flow coefficient under each tooth and the carry over coefficient, which accounts for the turbulent dissipation of kinetic energy in a cavity. This work, based upon FLUENT CFD simulations, initially studies the influence of flow parameters, in addition to geometry, on the carry over coefficient of a cavity, developing a better model for the same. It is found that the Reynolds number and clearance to pitch ratios have a major influence and tooth width has a secondary influence on the carry over coefficient and models for the same were developed for a generic rectangular tooth on stator labyrinth seal. The discharge coefficient of the labyrinth seal tooth (with the preceding cavity) was found to be a function of the discharge coefficient of a single tooth (with no preceding cavity) and the carry over coefficient. The discharge coefficient of a single tooth is established as a function of the Reynolds number and width to clearance ratio of the tooth and a model for the same is developed. It is also verified that this model describes the discharge coefficient of the first tooth in the labyrinth seal. By comparing the coefficients of discharge of compressible flow to that of incompressible flow at the same Reynolds number, the expansion factor was found to depend only upon the pressure ratio and ratio of specific heats. A model for the same was developed. Thus using the developed models, it is possible to compute the leakage mass flow rate as well as the axial distribution of cavity pressure across the seal for known inlet and exit pressures. The model is validated against prior experimental data.

This research compares the leakage and rotordynamic characteristics of a slanted-tooth labyrinth seal to a conventional straight-tooth labyrinth. Detailed results comparing the rotordynamic coefficients and leakage parameters of a slanted-tooth see-through labyrinth seal and a straight-tooth see-through labyrinth seal are presented. The straight-tooth labyrinth seal used in this research was originally tested by Arthur Picardo. The slanted-tooth labyrinth seal was designed and fabricated to be identical to the straight-tooth labyrinth seal in terms of pitch, depth, and the number of teeth. The angle of inclination of the teeth in the slanted-tooth labyrinth seal was chosen to be 65° from the normal axis. The seals were tested at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10,200, 15,350, and 20,200 rpm, and a radial clearance of 0.2 mm (8 mils). The experiments were carried out at zero, medium, and high inlet preswirl ratios. The experimental results show only minute differences in the rotordynamic coefficients between the two seals. But, the slanted-tooth labyrinth seal leaked approximately 10% less than the straight-tooth labyrinth seal. A study of prediction versus experimental data was done. XLlaby was used for prediction. XLlaby was developed for a straight-tooth labyrinth seal design and did not do a good job in predicting the rotordynamic coefficients and the leakage rate.

Seals are considered one of the important flow elements of a turbomachinery device. Traditional labyrinth seals have proven their performance functionality by reducing leakage rates. Significant improvements on labyrinth seal functionality were obtained through altering the design geometry of labyrinth seals to prevent contamination across a seal and maintaining small leakage flowrates. This results in a windback seal that has only one tooth which continuously winds around the shaft like a screw thread. These seals are used in gas compressors to isolate the gas face seal from bearing oil. A purge gas is passed through the seal into the bearing housing. The helical design allows the seal to clear itself of any oil contamination. Windback seal performance is controlled through changing the seal geometry. A 2D graphical design tool for calculating the total and cavity leakage flowrates for windback seals is introduced. The effectiveness of the Fluent CFD (Computational Fluid Dynamics) commercial code to accurately predict the leakage rate for windback seals was evaluated. The objective is to determine if CFD simulations can be used along with a few experimental tests to study windback seals of this design with air as the working fluid. Comparison of measurement and predictions for a windback seal using the κ-ε turbulence model with enhanced wall treatment functions show predictions and measurements comparing very well with a maximum difference of 5% for leakage rate. Similarly, the leakage rate of the tested smooth seal compares favorably with two dimensional CFD predictions, with a difference of 2%-11% and 8%-15% using laminar and κ-ε turbulent flow models, respectively. The variation of leakage with shaft speed and pressure ratio across the seals is accurately predicted by the CFD simulations. Increasing the rotor speed to 15000 rpm increases the measured leakage flowrate for the windback seal by 2% at high differential pressure and 4.5% at low differential pressure, and decreases it by 10 % for the smooth seal. The effects of seal clearance, tooth pitch, cavity depth and the tooth number of starts on leakage flowrate, velocity and pressure distributions were studied numerically for three differential pressures and four rotor speeds.

This work deals with the determination of the heat transfer coefficient in small channels with a rotating wall. The research part of the thesis is focused on specific geometry, namely labyrinth seals used in rotary machines. Existing criteria equations determining heat transfer coefficients and other parameters in these specific geometries are described. The central part describes the built experimental device for the determination of values of heat flows and heat transfer coefficients on both stator and rotor for given airflow and rotor speed. The following section is devoted to presenting the results of the performed experiments with the corresponding criteria equations. The next part describes the basic mathematical models of inverse heat conduction problems. Calculations of heat flux using these inverse methods are performed and compared with reference heat flux sensors.

This thesis in introductory part aims to analyze the available literature on the heat transfer coefficient in labyrinth seals and rotating discs of steam turbines. The available experiment studies were processed to summarize heat transfer coefficients on the rotating parts of the turbine. Then, this thesis specifies a design calculation to determine the heat transfer coefficient in selected parts of the turbine, exercisable for specific geometric and operating parameters. The outcome of this work is simulation of rotor dilation of operating steam turbine in the program Ansys during cold start of turbine.