Publications

The modeling and control of a recently developed utility-scale, shaftless, hubless, high strength steel energy storage flywheel system (SHFES) are presented. The novel flywheel is designed with an energy/power capability of 100 kWh/100 kW and has the potential of a doubled energy density when compared to conventional technologies. In addition, it includes a unique combination magnetic bearing (CAMB) capable of providing five-degrees-of-freedom (5DOF) magnetic levitation. Initial test results show that the CAMB, which weighs 544 kg, can provide a stable lift-up and levitation control for the 5543 kg flywheel. The object of this paper is to formulate and synthesize a detailed model as well as to design and simulate a closed-loop control system for the proposed flywheel system. To this end, the CAMB supporting structures are considered flexible and modeled by finite element modeling. The magnetic bearing is characterized experimentally by static and frequency-dependent coefficients, the latter of which are caused by eddy current effects and presents a challenge to the levitation control. Sensor-runout disturbances are also measured and included. System nonlinearities in power amplifiers and the controller are considered as well. Even though the flywheel has a large ratio of the primary-to-transversal moment of inertias, multi-input–multi-output (MIMO) feedback control demonstrates its effectiveness in canceling gyroscopic toques at the designed operational spinning speed. Various stages of proportional and derivative (PD) controllers, lead/lag compensators, and notch filters are implemented to suppress the high-frequency sensor disturbances, structural vibrations, and rotor imbalance effects.

 

Multi-Input-Multi-Output Control of a Utility-Scale, Shaftless Energy Storage Flywheel with a 5-DOF Combination Magnetic Bearing

This paper proposes a framework for the design of a coreless permanent magnet (PM) machine for a 100 kWh shaft-less high strength steel flywheel energy storage system (SHFES). The PM motor/generator is designed to meet the required specs in terms of torque-speed and power-speed characteristics given by the application. The design challenges of a motor/generator for this architecture include: the poor flux paths due to a large scale solid carbon steel rotor and zero-thermal convection of the airgap due to operation of the machine in vacuum. In order to tackle these challenges, several other parameters such as a proper number of magnets and slots combination, wire thickness, number of turns in each coil, magnets with high saturated flux density and magnets size are carefully considered in the proposed design framework. Magnetic levitation allows the use of a coreless stator that is placed on a supporting structure. The motor/generator is designed and simulated using a finite element analysis (FEA) package. The torque, power, and speed determined by the FEA electromagnetic analysis are met by the application design requirements and constraints for both the charging and discharging modes. Finally, the design and analysis of the coil holding structures are also discussed.

 

A Coreless Permanent-Magnet Machine for Magnetically Levitated Shaft-Less Flywheel

The American Petroleum Institute (API) level II vibration stability analysis for impellers requires higher fidelity models to predict the dynamic forces of the whirling impeller. These forces are in turn required to predict the vibration stability, critical speeds, and steady-state vibration response of the shaft-bearing-seal-impeller system. A transient computational fluid dynamics (CFD)-based approach is proposed which is applicable to nonaxisymmetric turbomachinery components, such as the volute and/or diffuser vanes, unlike its predecessor models like the bulk-flow or the quasi-steady model. The key element of this approach is the recent advancements in mesh deformation techniques which permit less restrictive motion boundary conditions to be imposed on the whirling impeller. The results quantify the contributions of the volute and/or the diffuser to the total forces which guides the analyst on whether to include these components in the model. The numerical results obtained by this approach are shown to agree well with experimental measurements and to be superior to the earlier quasi-steady alternative in terms of accuracy. Furthermore, several volute shapes were designed and analyzed for the sensitivity of the solution to the geometrical properties of the volute. The design flow rotordynamic forces show a significant dependence on the presence of the volutes in the model, with the specific shape of the volute having a lesser influence. The dimensionless forces are shown to be almost independent of the spin speed.

 

Rotordynamic Force Coefficients of Volutes and Diffusers for Improved Prediction of Turbomachinery Vibration

The Morton effect ME is a thermally induced, rotordynamic instability, which is frequently reported in overhung machines supported with oil-lubricated bearings. Synchronous journal whirling results in an uneven viscous shearing of the lubricant film and temperature variation around the journal circumference. This bends the shaft and under certain conditions causes increasing synchonous vibration. Previous research focused solely on oil-lubricated bearings. A transient, high-fidelity ME methodology is presented to expand the scope to tilting pad gas bearing (TPGB) systems. Three dimensional finite element models are established to predict the rotor and bearing temperature and dynamic responses in the time domain. Simulations indicate that the ME can occur in the TPGB systems and may be sensitive to imbalance and overhung mass.

 

Tilting Pad Gas Bearing Induced Thermal Bow – Rotor Instability (Morton Effect)

The catcher bearing (CB) is a crucial part of the magnetic bearing system. It can support the rotor when the magnetic bearing is shut down or malfunctioning and limit the rotor’s position when large vibration occurs. The sleeve bearing has the advantages of a relatively large contact surface area, simple structure, and an easily replaced surface. There are already many applications of the sleeve type CBs in the industrial machinery supported by the magnetic bearings. Few papers though provide thorough investigations into the dynamic and thermal responses of the sleeve bearing in the role of a CB. This paper develops a coupled two-dimensional (2D) elastic deformation—heat transfer finite element model of the sleeve bearing acting as a CB. A coulomb friction model is used to model the friction force between the rotor and the sleeve bearing. The contact force and 2D temperature distribution of the sleeve bearing are obtained by numerical integration. To validate the finite element method (FEM) code developed by the author, first, the mechanical and thermal static analysis results of the sleeve bearing model are compared with the results calculated by the commercial software solidworks simulation. Second, the transient analysis numerical results are compared with the rotor drop test results in reference. Additionally, this paper explores the influences of different surface lubrication conditions, different materials on rotor-sleeve bearing’s dynamic and thermal behavior. This paper lays the foundation of the fatigue life calculation of the sleeve bearing and provides the guideline for the sleeve type CB design.

 

Dynamic and Thermal Analysis of Rotor Drop on Sleeve Type Catcher Bearings in Magnetic Bearing Systems

The performance of a vibration enhanced reverse osmosis membrane module for desalination of artificial seawater was investigated with computational fluid dynamics (CFD) simulations and experiments. The computational model couples fluid dynamics with solutes transport inside the full length domain containing ‘zigzag’ spacers using a two dimensional, transient Large Eddy Simulation turbulence model. Both the local concentration dependent solute properties and variation of permeate flux over the membrane surface were predicted with the model. Membrane local permeate flux, concentration polarization, shear rate, and mass transfer were also calculated. The results suggest concentration polarization in the seawater desalination process could be reduced by imposing vibration on the reverse osmosis membrane. It was determined that the higher the vibration frequency the higher the membrane permeate flux while keeping the vibration amplitude constant. The CFD simulation predictions are validated against experimental data of permeate fluxes with good agreement.

 

Concentration Polarization and Permeate Flux Variation in a Vibration Enhanced Reverse Osmosis Membrane Module

This paper presents analytical bifurcations analysis of a “Jeffcott” type rigid rotor supported by five-pad tilting pad journal bearings (TPJBs). Numerical techniques such as nonautonomous shooting/arc-length continuation, Floquet theory, and Lyapunov exponents are employed along with direct numerical integration (NI) to analyze nonlinear characteristics of the TPJB-rotor system. A rocker pivot type five-pad TPJB is modeled with finite elements to evaluate the fluid pressure distribution on the pads, and the integrated fluid reaction force and moment are utilized to determine coexistent periodic solutions and bifurcations scenarios. The numerical shooting/continuation algorithms demand significant computational workload when applied to a rotor supported by a finite element bearing model. This bearing model may be significantly more accurate than the simplified infinitely short-/long-bearing approximations. Consequently, the use of efficient computation techniques such as deflation and parallel computing methods is applied to reduce the execution time. Loci of bifurcations of the TPJB-rigid rotor are determined with extensive numerical simulations with respect to both rotor spin speed and unbalance force magnitude. The results show that heavily loaded bearings and/or high unbalance force may induce consecutive transference of response in forms of synchronous to subsynchronous, quasi-periodic responses, and chaotic motions. It is revealed that the coexistent responses and their solution manifolds are obtainable and stretch out with selections of pad preload, pivot offset, and lubricant viscosity so that the periodic doubling bifurcations, saddle node bifurcations, and corresponding local stability are reliably determined by searching parameter sets. In case the system undergoes an aperiodic state, the rate of divergence/convergence of the attractor is examined quantitatively by using the maximum Lyapunov exponent (MLE).

 

Bifurcation Analysis of a Rotor Supported by Five-Pad Tilting Pad Journal Bearings Using Numerical Continuation

Energy storage is crucial for both smart grids and renewable energy sources such as wind or solar, which are intermittent in nature. Compared to electrochemical batteries, flywheel energy storage systems (ESSs) offer many unique benefits such as low environmental impact, high power quality, and larger life cycles. This paper presents a novel utility-scale flywheel ESS that features a shaftless, hubless flywheel. The unique shaftless design gives it the potential of doubled energy density and a compact form factor. Its energy and power capacities are 100 kWh and 100 kW, respectively. The flywheel is made of high-strength steel, which makes it much easier to manufacture, assemble, and recycle. Steels also cost much less than composite materials. Design and analysis of the shaftless flywheel are presented first. In addition, the system incorporates a new combination active magnetic bearing. Its working principle and levitation control for the flywheel are discussed. The design of an integrated coreless permanent-magnet (PM) motor/generator for the flywheel is given as well. Initial test results show that the magnetic bearing provides stable levitation for the 5443-kg flywheel with small current consumption.

 

A Utility Scale Flywheel Energy Storage System with a Shaft-Less, High Strength Steel Rotor

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.

The journal is the part of a shaft that is inside a fluid film bearing and is usually assumed to be circumferentially isothermal. Recent work has shown that under certain vibration conditions, a significant temperature difference (⁠ΔT⁠) can develop around the journal circumference. The ΔT may cause the shaft to bend leading to a synchronous vibration instability problem, termed the “Morton effect” (ME). A test rig was developed to verify the asymmetric journal temperature of the ME and its prediction using a five-pad tilting pad journal bearing (TPJB) operating with an eccentric shaft to replicate a circular vibration orbit. The bearing is tested at various conditions including: supply oil temperature at 28 °C and 41 °C, bearing operating eccentricities of zero and 32%Cb⁠, and rotor speed up to 5500 rpm. The journal temperature distribution is recorded with 20 sensors located around the journal circumference, and the measurements provide a benchmark for predictions from a time transient model with the three-dimensional (3D) fluid and solid finite element method (FEM), and with a simplified ME prediction approach using only steady-state results. The test results follow the predictions exhibiting a sinusoidal-like temperature profile around the circumference with an angular lag of the hot spot location behind the high spot location (angular position on the rotor that arrives at the minimum film thickness condition each rotation) by a speed-dependent angle. Increasing the supply oil temperature reduced the journal ΔT⁠, while increasing the bearing operating eccentricity increased the journal ΔT. The agreement between the test and predicted results is significantly better for the 3D FEM transient model than for the steady-state-based model in terms of journal ΔT and hot spot position. An improved version of the latter approach is proposed and yields significantly better correlation with the test measurements.

 

Measurement and Prediction of the Journal Circumferential Temperature Distribution for the Rotordynamic Morton Effect