Search results for: nonlinear elasticity

Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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Authors: Ali Kadir, S. R. Mishra, M. Shamshuddin, O. Anwar Beg

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Motivation- Rotating disk bio-reactors are fundamental to numerous medical/biochemical engineering processes including oxygen transfer, chromatography, purification and swirl-assisted pumping. The modern upsurge in biologically-enhanced engineering devices has embraced new phenomena including bioconvection of micro-organisms (photo-tactic, oxy-tactic, gyrotactic etc). The proven thermal performance superiority of nanofluids i.e. base fluids doped with engineered nanoparticles has also stimulated immense implementation in biomedical designs. Motivated by these emerging applications, we present a numerical thermofluid dynamic simulation of the transport phenomena in bioconvection nanofluid rotating disk bioreactor flow. Methodology- We study analytically and computationally the time-dependent three-dimensional viscous gyrotactic bioconvection in swirling nanofluid flow from a rotating disk configuration. The disk is also deformable i.e. able to extend (stretch) in the radial direction. Stefan blowing is included. The Buongiorno dilute nanofluid model is adopted wherein Brownian motion and thermophoresis are the dominant nanoscale effects. The primitive conservation equations for mass, radial, tangential and axial momentum, heat (energy), nanoparticle concentration and micro-organism density function are formulated in a cylindrical polar coordinate system with appropriate wall and free stream boundary conditions. A mass convective condition is also incorporated at the disk surface. Forced convection is considered i.e. buoyancy forces are neglected. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Karman and other transformations to render the boundary value problem (BVP) into an ordinary differential system which is solved with the efficient Adomian decomposition method (ADM). Validation with earlier Runge-Kutta shooting computations in the literature is also conducted. Extensive computations are presented (with the aid of MATLAB symbolic software) for radial and circumferential velocity components, temperature, nanoparticle concentration, micro-organism density number and gradients of these functions at the disk surface (radial local skin friction, local circumferential skin friction, Local Nusselt number, Local Sherwood number, motile microorganism mass transfer rate). Main Findings- Increasing radial stretching parameter decreases radial velocity and radial skin friction, reduces azimuthal velocity and skin friction, decreases local Nusselt number and motile micro-organism mass wall flux whereas it increases nano-particle local Sherwood number. Disk deceleration accelerates the radial flow, damps the azimuthal flow, decreases temperatures and thermal boundary layer thickness, depletes the nano-particle concentration magnitudes (and associated nano-particle species boundary layer thickness) and furthermore decreases the micro-organism density number and gyrotactic micro-organism species boundary layer thickness. Increasing Stefan blowing accelerates the radial flow and azimuthal (circumferential flow), elevates temperatures of the nanofluid, boosts nano-particle concentration (volume fraction) and gyrotactic micro-organism density number magnitudes whereas suction generates the reverse effects. Increasing suction effect reduces radial skin friction and azimuthal skin friction, local Nusselt number, and motile micro-organism wall mass flux whereas it enhances the nano-particle species local Sherwood number. Conclusions - Important transport characteristics are identified of relevance to real bioreactor nanotechnological systems not discussed in previous works. ADM is shown to achieve very rapid convergence and highly accurate solutions and shows excellent promise in simulating swirling multi-physical nano-bioconvection fluid dynamics problems. Furthermore, it provides an excellent complement to more general commercial computational fluid dynamics simulations.

Keywords: bio-nanofluids, rotating disk bioreactors, Von Karman swirling flow, numerical solutions

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Authors: Mina Naeini, Thomas A. Adams II

Abstract:

Solid Oxide Fuel Cells (SOFCs) feature high electrical efficiency and generate substantial amounts of waste heat that make them suitable for integrated community energy systems (ICEs). By harvesting and distributing the waste heat through hot water pipelines, SOFCs can meet thermal demand of the communities. Therefore, they can replace traditional gas boilers and reduce greenhouse gas (GHG) emissions. Despite these advantages of SOFCs over competing power generation units, this technology has not been successfully commercialized in large-scale to replace traditional generators in ICEs. One reason is that SOFC performance deteriorates over long-term operation, which makes it difficult to find the proper sizing of the cells for a particular ICE system. In order to find the optimal sizing and operating conditions of SOFCs in a community, a proper knowledge of degradation mechanisms and effects of operating conditions on SOFCs long-time performance is required. The simplified SOFC models that exist in the current literature usually do not provide realistic results since they usually underestimate rate of performance drop by making too many assumptions or generalizations. In addition, some of these models have been obtained from experimental data by curve-fitting methods. Although these models are valid for the range of operating conditions in which experiments were conducted, they cannot be generalized to other conditions and so have limited use for most ICEs. In the present study, a general, detailed degradation-based model is proposed that predicts the performance of conventional SOFCs over a long period of time at different operating conditions. Conventional SOFCs are composed of Yttria Stabilized Zirconia (YSZ) as electrolyte, Ni-cermet anodes, and LaSr₁₋ₓMnₓO₃ (LSM) cathodes. The following degradation processes are considered in this model: oxidation and coarsening of nickel particles in the Ni-cermet anodes, changes in the pore radius in anode, electrolyte, and anode electrical conductivity degradation, and sulfur poisoning of the anode compartment. This model helps decision makers discover the optimal sizing and operation of the cells for a stable, efficient performance with the fewest assumptions. It is suitable for a wide variety of applications. Sulfur contamination of the anode compartment is an important cause of performance drop in cells supplied with hydrocarbon-based fuel sources. H₂S, which is often added to hydrocarbon fuels as an odorant, can diminish catalytic behavior of Ni-based anodes by lowering their electrochemical activity and hydrocarbon conversion properties. Therefore, the existing models in the literature for H₂-supplied SOFCs cannot be applied to hydrocarbon-fueled SOFCs as they only account for the electrochemical activity reduction. A regression model is developed in the current work for sulfur contamination of the SOFCs fed with hydrocarbon fuel sources. The model is developed as a function of current density and H₂S concentration in the fuel. To the best of authors' knowledge, it is the first model that accounts for impact of current density on sulfur poisoning of cells supplied with hydrocarbon-based fuels. Proposed model has wide validity over a range of parameters and is consistent across multiple studies by different independent groups. Simulations using the degradation-based model illustrated that SOFCs voltage drops significantly in the first 1500 hours of operation. After that, cells exhibit a slower degradation rate. The present analysis allowed us to discover the reason for various degradation rate values reported in literature for conventional SOFCs. In fact, the reason why literature reports very different degradation rates, is that literature is inconsistent in definition of how degradation rate is calculated. In the literature, the degradation rate has been calculated as the slope of voltage versus time plot with the unit of voltage drop percentage per 1000 hours operation. Due to the nonlinear profile of voltage over time, degradation rate magnitude depends on the magnitude of time steps selected to calculate the curve's slope. To avoid this issue, instantaneous rate of performance drop is used in the present work. According to a sensitivity analysis, the current density has the highest impact on degradation rate compared to other operating factors, while temperature and hydrogen partial pressure affect SOFCs performance less. The findings demonstrated that a cell running at lower current density performs better in long-term in terms of total average energy delivered per year, even though initially it generates less power than if it had a higher current density. This is because of the dominant and devastating impact of large current densities on the long-term performance of SOFCs, as explained by the model.

Keywords: degradation rate, long-term performance, optimal operation, solid oxide fuel cells, SOFCs

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