Dara W. Childs

A test apparatus and facility to identify the rotordynamic coefficients of high-speed hydrostatic bearings

A facility and apparatus are described which determine stiffness, damping, and added-mass rotordynamic coefficients plus steady-state operating characteristics of high speed hydrostatic journal bearings. The apparatus has a current top speed of 29,800 rpm with a bearing diameter of 7.62 cm (3 in.). Purified warm water, 55 C (130 F), is used as a test fluid to achieve elevated Reynolds numbers during operation. The test-fluid pump yields a bearing maximum inlet pressure of 6.9 Mpa (1000 psi). Static load on the bearing is independently controlled and measured. Orthogonally mounted external shakers are used to excite the test stator in the direction of, and perpendicular to, the static load. The apparatus can independently calculate all rotordynamic coefficients at a given operating condition.

Experimental Versus Theoretical Characteristics of a High-Speed Hybrid (Combination Hydrostatic and Hydrodynamic) Bearing

The high-speed test facility designed and installed at Texas A&M to study water lubricated journal bearings has been successfully used to test statically an orifice compensated five-recess-hybrid (combination hydrostatic and hydrodynamic) bearing for two radial clearance configurations. Measurements of relative-bearing position, torque, recess pressure, flow rate, and temperature were made at speeds from 10,000 to 25,000 rpm and supply pressures of 6.89 MPa (1,000 psi), 5.52 MPa (800 psi), and 4.14 MPa (600 psi)

Angled Injection—Hydrostatic Bearings Analysis and Comparison to Test Results

Hydrostatic/hydrodynamic (hybrid journal bearings handling process liquids have limited dynamic stability characteristics and their application as support elements to high speed flexible rotating systems is severely restricted. Measurements on water hybrid bearings with angled orifice injection have demonstrated improved rotordynamic performance with virtual elimination of cross-coupled stiffness coefficients and null or negative whirl frequency ratios. A bulk-flow model for prediction of the static performance and force coefficients of hybrid bearings with angled orifice injection is advanced. The analysis reveals that the fluid momentum exchange at the orifice discharge produces a pressure rise in the hydrostatic recess which retards the shear flow induced by journal rotation, and thus, reduces cross-coupling forces. The predictions from the model are compared with experimental measurements for a 45 deg angled orifice injection, 5 recess, water hydrostatic bearing operating at 10.2, 17.4, and 24.6 krpm and with supply pressures of 4, 5.5 and 7 MPa. The correlations include recess pressures, flow rates, and rotordynamic force coefficients at the journal centered position. An application example for a liquid oxygen hybrid bearing also demonstrates the advantages of tangential orifice injection on the rotordynamic coefficients and stability indicator for forward whirl motions, and without performance degradation on direct stiffness and damping coefficients.

Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment

Reliable high-speed data are presented for leakage and rotordynamic coefficients of a plain annular seal at centered and eccentric positions. A seal with L/D = 0.45 was tested, and measured results have good signal-to-noise ratios. The influence on rotordynamic coefficients of pressure drop, running speed, and static eccentricity was investigated. There is an excellent agreement between experimental and theoretical results in the centered position, even for direct inertia terms, which have not shown good agreement with predictions in past studies. However, the rotordynamic coefficients are more sensitive to changes in eccentricity than predicted. These results suggest that, in some cases, annular seals for pumps may need to be treated more like hydrodynamic bearings, with rotordynamic coefficients which are valid for small motion about a static equilibrium position versus the present eccentricity-independent coefficients.

Thermal Effects in Cryogenic Liquid Annular Seals—Part I: Theory and Approximate Solution

A thermohydrodynamic (THD) analysis is introduced for calculation of the performance characteristics of cryogenic liquid annular seals in the turbulent flow regime. A full-inertial bulk-flow model is advanced for momentum conservation and energy transport. The liquid material properties depend on the local absolute pressure and temperature. Heat flow to the rotor and stator is modeled by bulk-flow heat transfer coefficients. An approximate analytical solution is obtained to the governing equations when the seal operates at a steady-state and concentric condition

Rotordynamic-Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals—Measurements Versus Predictions

Selected test results are presented for an annular gas seal using a smooth rotor and a hole-pattern-roughness stator for a supply pressure of 70 bar, three pressure ratios, three speeds up to 20,000 rpm, two clearances, and three preswirl ratios. Dynamic data include frequency-dependent direct and cross-coupled stiffness and damping coefficients. Static data include leakage and upstream and downstream pressures and temperatures. Very good agreements are found between measurements and predictions from a two-control-volume bulk-flow model.

Friction-Factor Data for Flat-Plate Tests of Smooth and Honeycomb Surfaces

Friction factors for honeycomb surfaces were measured with a flat plate tester. The flat plate test apparatus was described and a method was discussed for determining the friction factor experimentally. The friction factor model was developed for the flat plate test based on the Fanno Line Flow. The comparisons of the friction factor were plotted for smooth surfaces and six-honeycomb surfaces with three-clearances, 6.9 bar to 17.9 bar range of inlet pressures, and 5,000 to 100,000 range of the Reynolds number. The optimum geometries for the maximum friction factor were found as a function of cell width to cell depth and cell width to clearance ratios.

Rotordynamic Coefficients for a Tooth-on-Stator Labyrinth Seal at 70 Bar Supply Pressures: Measurements Versus Theory and Comparisons to a Hole-Pattern Stator Seal

Rotor dynamic and leakage coefficients are presented for a labyrinth seal that was tested at a supply pressure of 70 bar-a and speeds up to 20,200 rpm. Tests were conducted at clearances of 0.1 mm and 0.2 mm, pressure ratios of 0.10, 0.31, and 0.52, and three preswirls ratios. Comparisons are made between test data and predictions from one-control-volume and two-control-volume bulk-flow models. Generally, theoretical predictions agree poorly with the test results, with the one-control volume model giving better predictions. The one-control-volume model provides a conservative prediction for effective damping; i.e., this parameter is underestimated. Both models under predict leakage rates. Comparisons are also made between rotordynamic coefficients of labyrinth and hole-pattern seals.

A Study of the Effects of Inlet Preswirl on the Dynamic Coefficients of a Straight-Bore Honeycomb Gas Damper Seal

Honeycomb seals are frequently used as replacements for labyrinth seals in high-pressure centrifugal compressors to enhance rotordynamic stability. A concern exists that this enhanced stability will be lost if the honeycomb cavities become clogged. Static and dynamic tests were conducted on a honeycomb and a smooth seal (representing the honeycomb seal with completely clogged cells) at the same constant clearances using air with a supply pressure of 70 bars. The test matrix included three speeds, three pressure ratios, and three inlet preswirl conditions. The results show increased leakage, decreased synchronous stiffness, and decreased dynamic stability for the smooth seal with pre-swirled flow. The results strongly support the use of swirl brakes at the entrance of a honeycomb seal if clogging is a concern. Comparisons between test results and predictions from a two-control-volume theory by Kleynhans and Childs showed excellent agreement in general.

Frequency Dependency of Measured and Predicted Rotordynamic Coefficients for a Load-On-Pad Flexible-Pivot Tilting-Pad Bearing

Experimental dynamic-stiffness-coefficient results are presented for a high-speed, lightly loaded, load-on-pad, flexible-pivot tilting-pad (FPTP) bearing. Results show that the real parts of the direct dynamic-stiffness are quadratic functions of the excitation frequency. Frequency independent [M], [K], and [C] matrices can be used in place of frequency dependent [K] and [C] matrices to model the FPTP bearing for the conditions tested. The model reduction that results in moving from twelve degrees of freedom (three degrees of freedom for each of four pads) to two degrees of freedom in the bearing reaction model seems to account for most of the observed and predicted frequency dependency. Predictions indicate that pad and fluid inertia have a secondary impact for excitation frequencies out to synchronous frequency. Experimental results are compared to numerical predictions from models based on: (i) The Reynolds equation, and (ii) a Navier-Stokes (NS) equations bulk-flow model that retains the temporal and convective fluid inertia terms. The NS bulk-flow model results correlate better with experimental dynamic stiffness results, including added-mass terms. Both models underestimate the measured added-mass coefficients for the full excitation range; however they do an adequate job for excitation frequencies up to synchronous frequency. The advantage of using a frequency-independent [M]-[K]-[C] model is that rotordynamic stability calculations become non-iterative and much quicker than for a frequency dependent [K]-[C] model. However, these results only apply to this bearing at the conditions tested. Conventional tilting pad and/or FPTP bearings with different geometry and operating conditions (or even this FPTP bearing at higher loads) may require a frequency-dependent [K]-[C] model.