Patrick J. Migliorini

A Computational Fluid Dynamics/Bulk-Flow Hybrid Method for Determining Rotordynamic Coefficients of Annular Gas Seals

This paper presents a new computational fluid dynamics (CFD)/bulk-flow hybrid method to determine the rotordynamic characteristics of annular gas seals. The method utilizes CFD analysis to evaluate the unperturbed base state flow, an averaging method to determine the base state bulk-flow variables, and a bulk-flow perturbation method to solve for the fluid forces acting on an eccentric, whirling rotor. In this study the hybrid method is applied to a hole-pattern seal geometry and compared with experimental data and numerical and analytical methods. The results of this study show that the dynamic coefficients predicted by the hybrid method agree well with the experimental data, producing results that are comparable with a full, three-dimensional, transient, whirling rotor CFD method. Additionally, the leakage rate predicted by the hybrid method is more agreeable with experiment than the other methods. The benefit of the present method is the ability to calculate accurate rotordynamic characteristics of annular seals that are comparable to results produced by full, transient CFD analyses with a simulation time on the order of bulk-flow analyses.

Hole-Pattern Seals: A Three Dimensional CFD Approach for Computing Rotordynamic Coefficient and Leakage Characteristics

Labyrinth and other annular seals are commonly used in the turbomachinery industry to limit the leakage between different pressure regions. The pressure driven flow these seals experience can produce significant forces on the rotor. These fluid-induced excitation forces can exert a strong influence on the dynamic characteristics of the machine. Such seal forces can cause the rotor to become unstable, or when properly designed, stabilize a troublesome machine. Thus, it is important to accurately quantify the fluid-induced forces exerted on the rotor to effectively predict the dynamic behavior. Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient, due to the assumptions made to simplify the flow equations, seal bulk flow models lack accuracy when dealing with more complex geometry seals, such as hole-pattern seals. Unlike the bulk flow model, computational fluid dynamics (CFD) makes no simplifying assumption on the seal geometry, shear stress at the wall, relationship between wall shear stress and mean fluid velocity, or characterization of interfaces between control volumes. This paper presents a method to calculate the linearized rotordynamic coefficients for a hole-pattern seal by means of a three dimensional CFD approach to estimate the fluid-induced forces acting on the rotor. The system is modeled as a rigid rotor, with rotational speed, ω, and whirl frequency, Ω, describing non-synchronous whirl orbits around a static operating point. The Reynolds-averaged Navier-Stokes equations for fluid flow are solved by dividing the volume of fluid into a discrete number of points at which unknown variables (velocity, pressure, etc.) are computed. As a result, all the details of the flow field, including the fluid forces with potential destabilizing effects, are calculated. A 2nd order regression method is then utilized to express the fluid induced forces in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients.Copyright

A Study of Multicomponent Streams in Off-Design Centrifuge Cascades

International Atomic Energy Agency inspectors employ several safeguards measures to ensure only declared operations are occurring at a gas centrifuge plant. One safeguards tool, environmental sampling, can help quantify the materials present in a cascade and gas centrifuge plant. The sampling results can be compared with expected values to determine if the concentrations found are reasonable. In this paper, a methodology is presented for determining the operating envelope of isotope enrichment and material throughput that can be achieved in a reduced throughput cascade. The effects of feed material and centrifuge performance and optimization are studied.

Semi-Empirical Method for Developing a Centrifuge Performance Map

Centrifuge performance maps are useful for characterizing the separation parameters of a particular centrifuge over a range of operating parameters such as feed rate and cut. Typically, to develop a performance map, the internal hydrodynamics and isotope diffusion must be modeled, requiring knowledge of the centrifuge geometry and operating conditions. Due to the sensitive nature of centrifuge information, these parameters are usually not available. In some cases, some information about the performance of the centrifuge may be inferred from publicly available information. In these cases, a method for estimating the centrifuge performance over a range of operating conditions can be useful. In this paper, a semi-empirical method for developing a centrifuge performance map from known performance data is presented. The method is based on analyzing the centrifuge as a square cascade with three characterizing parameters. To verify the model, centrifuge separative power and separation factor are compared with results from the Pancake code over a range of feed rates and cuts. A cascade level comparison is used to further compare the two models. The comparison shows that the semi-empirical model is in good agreement with the Pancake code for most cases.

A Numerical Study on the Influence of Hole Aspect Ratio on the Performance Characteristics of a Hole-Pattern Seal

In turbomachinery, annular seals are used to reduce leakage between regions of high and low pressure. Many configurations of annular seals have been developed and studied in the literature including plain, labyrinth, pocket-damper, honeycomb, and hole-pattern. In machines experiencing stability issues, honeycomb and hole-pattern type seals have been used to replace labyrinth seals. Bulk-flow models are typically used to predict the leakage and dynamic coefficients of hole-pattern seals, relying on empirically derived friction factor coefficients. Previous experimental studies have shown that, for hole-pattern seals, the leakage and stator friction factor are strongly influenced by hole-depth. However, this behavior is not a monotonic function of hole-depth, a fact that might reduce confidence in future bulk-flow model predictions if not properly accounted for. A recent numerical study has highlighted the role of vortex formation in the holes which has a strong influence on the flow in the clearance region. Depending on the shape of the vortex, the flow in the hole can act much like a pinch valve, reducing the effective clearance of the jet flow.In this paper, computational fluid dynamics simulations of several hole-pattern seal configurations have been performed to study the effect of hole-aspect ratio (depth versus diameter) on the leakage and friction factors. The Reynolds Averaged Navier Stokes (RANS) equations with k-e turbulence model were solved using ANSYS CFX. It was found that the shape of the hole influences the vortex formation within the hole, effecting the jet flow in the clearance region and the seal leakage. The results show that the leakage is heavily dependent on the hole diameter in addition to the hole depth. The relationship between the friction factors and the geometry of the seal was found to be non-monotonic. It is therefore difficult to develop a friction factor model that will accurately encompass all configurations and it is recommended that friction factor data be interpolated from experimental or numerical results.© 2014 ASME

Design of Experiments to Investigate Geometric Effects on Fluid Leakage Rate in a Balance Drum Seal

Annular labyrinth seals are designed as tortuous paths that force a working fluid to expand and contract repeatedly through small clearances between high and low pressure stages of turbomachinery. The resulting expansion and recirculation reduces kinetic energy of the flow and minimizes leakage rate between regions of high and low pressure through the seal. Most current seal geometries are selected based on what has worked in the past, or by incremental improvements on existing designs. In the present research, a balance drum used in a multi-stage centrifugal pump was chosen as a starting point. A design of experiments study was performed to investigate the influence of groove scale on leakage rate across the seal for a fixed pressure differential.The CFD model of the selected labyrinth seal has an upstream region leading to 20 evenly spaced semicircular grooves along a 267 mm seal length, with a clearance region of 0.305 mm. The seal geometry was specified by a set of five variables. The variables allow for variation in scale of the semicircular grooves within a pattern of five independently scaled grooves repeated four times along the seal length.The seal was constructed with a parameterized CFD model in ANSYS CFX as a five degree sector of the full 3D seal. A non-central composite designed experiment was performed to investigate the effects of five parameters on leakage rate in the system. This study demonstrates a practical approach for investigating the effects of various geometric factors on leakage rate for balance drum seals. The empirical 10-parameter linear regression model fitted to the results of the experimental design yields suggested groove radii that could be applied to improve performance of future seals.Copyright

Hybrid Analysis of Gas Annular Seals With Energy Equation

Annular seals are used in turbomachinery to reduce secondary flow between regions of high and low pressure. In a vibrating rotor system, the non-axisymmetric pressure field developed in the small clearance between the rotor and the seal generate reactionary forces that can affect the stability of the entire rotor system.Traditionally, two analyses have been used to study the fluid flow in seals, bulk-flow analysis and computational fluid dynamics (CFD). Bulk-flow methods are computational inexpensive, but solve simplified equations that rely on empirically derived coefficients and are moderately accurate. CFD analyses generally provide more accurate results than bulk-flow codes, but solution time can vary between days and weeks. For gas damper seals, these analyses have been developed with the assumption that the flow can be treated as isothermal. Some experimental studies show that the difference between the inlet and outlet temperature temperatures is less than 5% but initial CFD studies show that there can be a significant temperature change which can have an effect on the density field. Thus, a comprehensive analysis requires the solution of an energy equation.Recently, a new hybrid method that employs a CFD analysis for the base state, unperturbed flow and a bulk-flow analysis for the first order, perturbed flow has been developed. This method has shown to compare well with full CFD analysis and experimental data while being computationally efficient. In this study, the previously developed hybrid method is extended to include the effects of non-isothermal flow. The hybrid method with energy equation is then compared with the isothermal hybrid method and experimental data for several test cases of hole-pattern seals and the importance of the use of energy equation is studied.Copyright

Hole-Pattern Seals Performance Optimization Using Computational Fluid Dynamics and Design of Experiment Techniques

A main goal of non-contacting mechanical seals is to provide minimal leakage during operation. This may be achieved by specifying a small clearance between the mating faces that is just enough to avoid rubbing contact while allowing some tolerable leakage. The amount of leakage flow is reduced through the acceleration and deceleration of the fluid through a tortuous path, so the sealing performance depends on the geometric characteristics of the leakage path.This study focuses on annular hole-pattern seals, which are non-contacting mechanical seals commonly used in high pressure compressors. A Design of Experiments (DOE) approach is used to investigate the effects of various geometric variables on the leakage rate of a hole-pattern seal during normal operating conditions. The design space, defined by the ranges of hole diameter, hole depth, axial space between holes and number of holes in circumferential direction, is discretized using the simple random sampling method. Then, steady-state Computational Fluid Dynamics (CFD) simulations are performed at each design point to evaluate seal performance. To better understand the sensitivity of the hole-pattern seal leakage rate with respect to design variables selected, response surfaces are built through its values at design points using quadratic polynomial fitting. The results show that the optimal solution had a better leakage control ability over the base model design. It is believed that the results of this study will assist in improving the design of annular hole-pattern seals.© 2013 ASME