Advanced design methods and non-ideal gas lubrication applied to aerodynamic bearings

Clean and energy-efficient turbomachinery are playing an increasingly important role in the decarbonization of heating systems, waste heat recovery and transportation, as the use of small-scale heat pumping and fuel cells spreads. Such machines typically employ aerodynamic bearings because of their olfreeness and very large lifespan. In particular, grooved bearings enjoy a high stiffness and repeatable performance under similar manufacturing conditions and are particularly well suited for small-scale rotors. However, such gas bearings are usually modeled under the assumption that the lubricant follows the ideal gas law, which may not be valid in conditions met in heat pumping (high pressure condensable gases) and ambient air compression (condensation of moisture). In addition, a strict separation between grooved and compliant bearings exist without justification and optimization methods used for the design of such elements ignore the concept of robustness. This thesis explores these shortcomings. First, the classical modeling theory for grooved bearings, the Narrow-Groove Theory (NGT), is experimentally validated in dynamic conditions. A test rig is built, consisting of a 16mm rotor rotating at 100 krpm on two herringbone grooved journal bearings (HGJBs) driven by an impulse turbine. The bearing bushings are excited in two orthogonal directions using piezo-electric shakers, allowing the deduction of the frequency-dependent force coefficients. The measurements are in good qualitative agreement with the theory, although stiffness and damping coefficients were observed 23 and 29% lower than the predicted values, respectively. The influence of real-gas effects and humid air on the static and dynamic performance of plain bearings and HGJBs is theoretically and numerically investigated on a wide range of operating conditions. Real-gas effects were found to negatively affect the load capacity and either have a positive or negative influence on the stability depending on the operating conditions. Humid air effects have a negligible yet negative influence on the static performance and can decrease the critical mass of HGJBs by 25%. The effects of pure-fluid condensation are assessed theoretically using a 1D slider bearing. Further, an experimental setup consisting of a 20mm three-pad Rayleigh step journal bearing operating at 30 krpm in pressurized R245fa is built to experimentally validate the proposed model by measuring and comparing the pressure in the thin gas film. Theoretically- predicted characteristic features of a condensing gas film are observed experimentally, suggesting sustained operation of a gas lubricated bearing with local condensation. The path toward hybrid foil and grooved bearings is explored, as a tentative to combine the best of the two worlds. A model based on the simple foundation approach is pro- posed and the improvement potential of spiral grooves applied on foil thrust bearings is numerically assessed using multi-objective optimization of the grooved pattern. Results suggest that the load capacity can be improved while reducing the drag torque. However, the ultimate load capacity does not systematically benefit from the presence of spiral grooves. Finally, a novel design procedure maximizing the robustness of aerodynamic bearings against manufacturing deviation is proposed and applied to HGJBs

Multi-Objective Optimization of Grooved Gas Journal Bearings for Robustness in Manufacturing Tolerances

A tolerancing method highlighting trade-offs against key design variables of mechanical systems is proposed and applied to herringbone-grooved gas journal bearings. Gas bearings typically suffer from a subsynchronous instability, demanding a very tight tolerance on the bearing clearance and groove depth. Classical optimization techniques look for the most stable design, which does not necessarily lead to most robust design against manufacturing deviations. The proposed method uses a normalized multidimensional lookup table of stability score (critical mass), covering a large design space of gas bearings. It then dimensionalizes the table for a specific rotor–bearing system, highlighting regions of the hyperspace where the system is stable. The hyperspace is sliced into 2D maps and a Monte Carlo method creates windows within the stable domain along the two most critical design variables regarding manufacturing: the bearing clearance and the groove depth. Width and length of the windows represent the manufacturing tolerance allowed for the two parameters to remain stable. A Pareto front of optimum windows in the entire hyperspace is then compiled. It displays the trade-off between the tolerance against deviation in clearance and groove depth, allowing the designer to select a nominal geometry tailored to the available manufacturing methods. A test rotor is analyzed with this method and the effects of pressure, speed, viscosity, radius, mass, and centrifugal growth on manufacturing tolerances are investigated, highlighting that the radius and viscosity have the greatest impact on the robustness

A Review of Grooved Dynamic Gas Bearings

This paper offers an extensive review of publications dealing with the modeling, the design and the experimental investigation of grooved dynamic gas lubricated bearings. Recent years have witnessed a rise in small-scale and high-speed turbomachinery applications. Besides the well-known gas foil bearings, grooved bearings offer attractive advantages, which unveil their potential in particular at small scale due to the structural simplicity as well as satisfying predictability. This paper starts with a general background of the application of gas lubricated bearings and introduces and compares the different gas bearing topologies. Further, the state-of-the-art modeling of grooved gas lubricated bearings is introduced in a systematic way assessing the advantages and inconveniences of two major approaches, the Narrow Groove Theory (NGT) and direct discretization method. Since NGT method is an elegant and efficient approach to model the complex effects of periodic grooves, a critical section is dedicated to the Narrow Groove Theory. In a second phase different models to include additional physical phenomena such as real gas lubrication, rarefaction or turbulence effects are reviewed. The paper concludes with a critical assessment of the state-of-the-art and indicates potential fields of research that would allow to shed more light into the understanding of these bearings, as well as with some thoughts on the integrated design methodologies of gas bearing supported rotors

Potential of Small-Scale Turbomachinery for Waste Heat Recovery on Automotive Internal Combustion Engines

This paper investigates the waste heat recovery potential of internal combustion engines, using organic Rankine cycles running on small-scale radial turbomachinery. ORC are promising candidates for low-grade thermal sources and the use of dynamic expanders yields very compact systems, which is advantageous for automotive applications. As engine coolant and exhaust gases are the major available heat sources, different cycle configurations and working fluids have been investigated to capture them, in both urban and highway car operation. Pareto fronts showing the compromise between net power output and total heat exchange area have been identified for a set of cycle’s variables including turbine inlet conditions and heat exchanger pinches. A preliminary optimization, including only R-1234yf working fluid, shows that a single-source regenerative cycle harvesting the high temperature exhaust gas stream performs averagely better than coolant-driven and dual-source cycles. A more in-depth optimization including eight working fluids as well as aerodynamic and conceptual limitations related to radial turbomachinery and automotive design constraints, finally shows that an ICE exhaust heat recovery ORC could improve the first law efficiency of the driving system by up to 10% when implemented with fluid R-1233zd