David L. Rhode

Labyrinth seal rotordynamic forces using a three-dimensional Navier-Stokes code

A finite difference method for determining rotor dynamic forces on an eccentric whirling labyrinth cavity has been developed. A coordinate-transformation was applied to the Reynolds time-averaged Navier-Stokes equations in order to use the modified bipolar coordinate system. The SIMPLER algorithm with QUICK differencing and the high Reynolds number k-e turbulence model are used to compute the complex turbulent flow field. A circular whirl orbit about the geometric center of the housing was specified for simplicity. The new model was tested against the rotordynamic force measurements, and close agreement was found

Three-dimensional computations of rotordynamic force distributions in a labyrinth seal

A numerical method employing a finite volume approach for calculating the rotordynamic force on eccentric, whirling labyrinth seals has been presented. The SIMPLER algorithm is used to calculate the three-dimensional flowfield within a seal. The modified bipolar coordinate system used accurately describes the geometry of an eccentric seal. The turbulent flow form of the fully elliptic Navier-Stokes equations was solved. A three-percent eccentric, single labyrinth cavity rotating at 7000 cpm was investigated for three different inlet swirl conditions, each with and without a whirl orbit frequency of 3500 cpm. It was found that the circumferential pressure variation around the downstream tooth periphery is by far the most important contribution to both rotordynamic force components. Thus the flowfield details near each tooth throttling should be carefully considered. Further, a substantial increase of shaft whirl frequency was found to decrease and increase the effect of cavity inlet swirl on Ft and Fr , re...

A New CFD-Perturbation Model for the Rotordynamics of Incompressible Flow Seals

A new, quasi-three-dimensional perturbation model is developed for the computation of rotordynamic forces for all incompressible flow seals with an axisymmetric geometry. The model assumes a small circular whirl motion of the rotor around the stator center. By avoiding the complicated perturbation coordinate transformation, the perturbation solution directly accounts for the disturbance of the wall shear stresses that are caused by the whirl motion of the rotor. The primary advantage of the present model is that it can immediately be applied to any radial-clearance seal of axisymmetric geometry without ad hoc adjustments. It was found from computations that include the upstream chamber that the magnitude of the first-order variables at the seal inlet are much larger and abruptly changing than was previously assumed.Copyright

Flow Visualization and Leakage Measurements of Stepped Labyrinth Seals: Part 1—Annular Groove

An improved understanding of a new category of stepped labyrinth seals, which feature a new annular groove, was obtained. A water leakage and flow visualization test facility of very large scale (relative to a typical seal) was utilized. Flow visualization experiments using a new method and digital facilities for capturing and editing digital images from an 8 mm video were conducted. The presence of an annular groove machined into the stator land increases the leakage resistance by up to 26 percent for the cases considered here. Tracer particles show the degree of throughflow path penetration into the annular groove (i.e., serpentining), which gives the largest and the smallest leakage resistance improvement over that of the corresponding conventional stepped seal.

NEW. STRONGLY CONSERVATIVE FINITE-VOLUME FORMULATION FOR FLUID FLOWS IN IRREGULAR GEOMETRIES USING CONTRAVARIANT VELOCITY COMPONENTS: PART 1. THEORY

Abstract A strongly conservative finite-volume procedure is presented for flows in complex geometries. The technique is based on a complete transformation of the governing equations, and physical velocity components, rather than the traditionally used Cartesian velocity components, are used as primitive variables. It was found that projecting the discretized vector transport equation in the direction of the covariant base vectors eliminated two substantial difficulties associated with flows in complex geometries. These difficulties stem from the presence of cross-pressure gradient terms and the need for a transformation between the different types of curvilinear velocity components in the mass conservation equation. It is shown that the present formulation ensures that the computational scheme is diagonally dominant. It was found that partially implicit treatment of nonorthogonal diffusion terms improved the convergence rate primarily for high-cell-Reynolds-number values. For nonstaggered grids, a new sol...

Leakage Optimization of Labyrinth Seals Using a Navier-Stokes Code

It has been demonstrated that design optimization of labyrinth seals using the present numerical model is quite beneficial. The results shown include important, but previously unknown effects on the leakage rate, especially that of step height. Further, complete details are given of a very effective seal designed using this technique. Measurements using turbine flow meters revealed that the optimized configuration gives a 60 and 79 percent leakage reduction over the baseline design at laboratory and higher (extrapolated) seal pressure drops, respectively.

A STUDY ON CONVERGENCE CRITERIA FOR A SIMPLE-BASED FINITE-VOLUME ALGORITHM

Two commonly used quantities for deciding numerical iteration convergence of elliptic and parabolic flow fields are assessed. Three 2-D test case problems, which are representative of many problems of momentum and/or heat transport, are used. The numerical model employed is the pressure-based finite-volume algorithm SIMPLE to solve the steady, incompressible-flow Navier-Stokes equations in full elliptic form. Considerable insight is gained by comparing the variation of the two quantities with the true mean relative error for the velocity components, the local mass imbalance, and the temperature. It is concluded that, except when using low underrelaxation factors, use of the maximum local value of the relative change, over two consecutive iterations, of the dependent variable is somewhat more appealing than the nondimensionalized sum of the local residual magnitudes.

Predicted Effects of Shunt Injection on the Rotordynamics of Gas Labyrinth Seals

A recent CFD perturbation model for turbomachinery seal rotordynamics was extended for labyrinth shunt injection with an arbitrarily high pressure gas. A large number of measured cases with labyrinth injection pressure at approximately 13.8 bars (200 psi) were computed and compared with measurements. The drastically reduced (negative) cross-coupled stiffness, which is the primary advantage from the use of shunt injection in gas labyrinth seal applications, was well predicted. The agreement with measurements for k, C, and C eff was within about 40%, 60% and 10%, respectively. In addition, it was found that moving the injection toward the high pressure end of the seal gives k, C, and C eff values that are rotordynamically only slightly more stabilizing. Further, the radial distributions of the flow perturbation quantities give support to the two-control volume approach for developing bulk-flow models for labyrinth seal rotordynamics.

Visualization and Measurements of Rub-Groove Leakage Effects on Straight-Through Labyrinth Seals

For the first time flow visualization images and leakage measurements were obtained and analyzed for an enhanced understanding of the effect of rub-grooves on straight-through labyrinth seal leakage. It was found that leakage resistance decreases sharply with increasing rub-groove axial width. Further, for small tooth clearances with medium- or large-width rub-grooves, the groove gives an approximate 50 percent drop in leakage resistance. At the medium clearance, the presence of medium- or large-width rub-grooves increases and decreases the resistance at low Re and high Re, respectively. At the large clearance, the presence of grooves increases the resistance by some 200 percent and 40 percent for low Re and high Re, respectively. However, large clearance applications generally give very high Re where the 40 percent increase occurs.In addition, a vena contracta effect from the throughflow jet penetration into the rub-grooves was found on the flow pattern and on the leakage resistance. When penetration occurs, the trajectory angle of the jet entering the subsequent labyrinth cavity is sometimes dramatically altered, giving less kinetic energy carry-over to the subsequent tooth clearance.Copyright

Rub-groove width and depth effects on flow predictions for straight-through labyrinth seals

A fully compressible, two-dimensional axisymmetric, turbulent Navier-Stokes code using the finite-volume discretization approach was utilized to obtain an enhanced understanding of the effects of rub-grooves in straight-through, abradable labyrinth seals. The high-Re form of the k-e turbulence model was used. The code was first validated against measurements of straight-through honeycomb labyrinths, and accurate results were obtained. It was found that in most of the cases considered (tooth tip outside of its rub groove), the presence of rub-grooves increases the leakage, except for the case of the large pre-rub clearance and narrow rub-groove width. The presence of the large- or the intermediate-width rub-grooves allows the rub-groove depth to exert a fairly large effect on the leakage, especially for the smallest pre-rub radial clearance. Further, the presence of a narrow rub-groove with the smallest pre-rub radial clearance gives a dramatic effect on the streamwise (i.e., cavity-to-cavity) variation in overall flow patten.