Three-Dimensional Thermohydrodynamic Analyses of Rayleigh Step Air Foil Thrust Bearing with Radially Arranged Bump Foils

Abstract

A three-dimensional (3D) thermohydrodynamic (THD) model for air foil thrust bearings (AFTBs) is presented. The nonisothermal Reynolds equation is solved using pressure boundary conditions at the cooling air plenum considering local temperature-dependent viscosity and density. Air film temperature is calculated using the 3D energy equation with thermal boundary conditions at the top foil, thrust runner, and top foil’s leading edge. The cooling air plenum distributes the cooling air to multiple radially arranged cooling channels. The plenum temperature and pressure are found from mass and energy balance equations applied to the plenum. Temperature fields of the top foil, bump foils, thrust disc runner, bearing plate, and cooling air channels are also solved through appropriate energy balance equations with their surroundings. A robust computational algorithm with multiple iteration loops was developed to find all the temperature fields. THD analyses were performed for AFTB with outer radius of 50 mm up to 100,000 rpm. As the cooling air source pressure is increased, the plenum pressure also increases and its temperature decreases due to more cooling capacity. However, cooling effectiveness is not necessarily proportional to the pressure because the flow residence time inside the cooling channels is inversely proportional to the pressure. The analyses show that the thrust disc temperature is a parabolic function with speed, and thermal expansions of the thrust disc and thrust plates contribute to the most significant driving force of thermal instability. Optimum cooling air pressure was found around 12,500 Pa for the proposed AFTB design at the reference simulation condition.

KEY WORDS:

• Thermohydrodynamic
• Air Foil Thrust Bearing
• Rayleigh Step

Acknowledgments

Review led by Luis San Andres

Notes

¹The authors personally observed bump foil arrangements of several commercial foil thrust bearings. Due to the proprietary nature of their designs, the authors cannot disclose details.

²An ideal sharp Rayleigh step found in solid bearing pads (Hamrock and Anderson ( 46 )) cannot be formed on the top foil because typical manufacturing process of the Inconel top foil would be cold-forming followed by heat treatment.

³Between the bump and top foil and also between the bump and thrust plate.

⁴BC at r=R_i is not necessary when conduction of cooling air is not considered.

⁵The Reynolds flow numbers through the channels using hydraulic diameter and channel cross-section area were evaluated for various plenum pressures and they are mostly laminar except the highest cooling air pressure of 20,000 Pa. Therefore, the authors used the laminar flow model for all the simulation cases as a conservative measure.

⁶The cooling channel cross-section area was assumed uniform along the radial direction and the average cross-section area was chosen.

⁷In reality, the cooling air is discharged to another dead volume with non-zero gauge pressure. However, unless the cooling air is redirected for the next adjacent radial foil bearings, the dead volume is connected to a discharge port to the outside the housing, which is at ambient pressure.

⁸Preliminary simulations using a laminar flow model resulted in Reynolds flow much larger than 5,000 for all of the cooling air supply pressures.

⁹If minimum thermal interaction between the housing and thrust plate is desirable, the thrust plate or housing has many undercuts to reduce the actual contact area. If maximum thermal interaction between the housing and plate is required, the plate will be hard-mounted with full surface contact.

¹⁰Circumferential direction: 43 = 4 × 7 (bumps) + 2 × 7 (cooling channels) + 1 (overhung trailing edge); radial direction: 19 = 9 (bumps) + 8 (between bumps) + 2 (overhung portion of top foil without bump supports underneath it at both inner diameter [ID] and outer diameter [OD] regions).

¹¹However, heat flux or fixed temperature boundary conditions can be implemented.

¹²When they were placed facing each other, the rotational direction was the same.