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.

A main goal o f noncontacting mechanical seals is to provide minimal leakage during oper ation. 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 o f the fluid through a tortuous path, so the sealing performance depends on the geometric characteristics o f the leakage path. This study focuses on annular hole-pattern seals, which are noncontacting mechanical seals commonly used in high pressure compressors. A design o f experiments (DOE) approach is used to investigate the effects o f various geometric variables on the leakage rate o f a hole-pattern seal during normal operating conditions. The design space, defined by the ranges o f hole diameter, hole depth, axial space between holes and number o f 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 o f the hole-pattern seal leakage rate with respect to design variables selected, response surfa ces 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 o f this study will assist in improving the design o f annular hole-pattern seals.

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.

Annular seals serve an important role in the dynamics of turbomachinery by reducing leakage of a process fluid while also contributing potentially destabilizing forces to the rotor system. Hole-pattern seals have been the focus of many investigations, but recent experimental studies have shown that there are still many phenomena that require exploration. One such phenomenon is the influence of hole depth on the static and dynamic characteristics of the seal. In this paper, a hybrid computational fluid dynamics (CFD)/bulk-flow method is employed to investigate the nonmonotonic relationship between hole depth and leakage shown in experimental measurements of a hole-pattern seal by Childs et al. (2014, “The Impact of Hole Depth on the Rotordynamic and Leakage Characteristics of Hole-Pattern-Stator Gas Annular Seals,” ASME J. Eng. Gas Turbines Power, 136(4), p. 042501). Three hole depths (1.905 mm, 3.302 mm, and 6.604 mm) and three running speeds (10,200 rpm, 15,350 rpm, and 20,200 rpm) are considered. For the steady-state flow, the 3D Reynolds-Averaged-Navier-Stokes (RANS) equations are solved with the k-ϵ turbulence model for a circumferentially periodic sector of the full seal geometry. The steady-state results are input into the first-order equations of a bulk-flow model to predict rotordynamic coefficients. Results of the hybrid method are compared to experimental data. CFD predicted leakage showed good agreement (within 5%) for the 3.302 mm and 6.604 mm hole depth configurations. For the 1.905 mm hole depth seal, agreement was within 17%. An additional set of calculations performed with the shear stress transport (SST) turbulence model produced worse agreement. Examination of streamlines along the seal show that the hole depth controls the shape of the vortex that forms in the hole, driving the resistance experienced by the jet flow in the clearance region. For the rotordynamic coefficients, good agreement is shown between predictions and experiment for most excitation frequencies.

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 multistage centrifugal pump was chosen as a starting point. A design of experiments (DOEs) study was performed to investigate the influence of groove scale on leakage rate across the seal for a fixed pressure differential. The computational fluid dynamics (CFD) model of the selected labyrinth seal has an upstream region lead ing to 20 evenly spaced semicircular grooves along a 267 mm seal length, with a clear ance 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 5 deg sector of the full 3D seal. A noncentral composite designed experiment was performed to investigate the effects o f five parameters on leakage rate in the system. This study demonstrates a practi cal approach for investigating the effects of various geometric factors on leakage rate for balance drum seals. The empirical ten-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.