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Authors: Rohini Das, Subhasish Das, Smruti Rekha Sahoo, Shagupta Yesmin

Abstract:

The Paleoproterozoic Kolhan Group (Purana) ensemble constitutes the youngest lithostratigraphic 'outlier' in the Singhbhum Archaean craton. The Kolhan unconformably overlies both the Singhbhum granite and the Iron Ore Group (IOG). Representing a typical sandstone-shale ( +/- carbonates) sequence, the Kolhan is characterized by the development of thin and discontinuous patches of basal conglomerates draped by sandstone beds. The IOG-fault limits the western 'distal' margin of the Kolhan basin showing evidence of passive subsidence subsequent to the initial rifting stage. The basin evolved as a half-graben under the influence of an extensional stress regime. The assumption of a tectonic setting for the NE-SW trending Kolhan basin possibly relates to the basin opening to the E-W extensional stress system that prevailed during the development of the Newer Dolerite dyke. The Paleoproterozoic age of the Kolhan basin is based on the consideration of the conformable stress pattern responsible both for the basin opening and the development of the conjugate fracture system along which the Newer Dolerite dykes intruded the Singhbhum Archaean craton. The Kolhan sandstones show progressive change towards greater textural and mineralogical maturity in its upbuilding. The trend of variations in different mineralogical and textural attributes, however, exhibits inflections at different lithological levels. Petrological studies collectively indicate that the sandstones were dominantly derived from a weathered granitic crust under a humid climatic condition. Provenance-derived variations in sandstone compositions are therefore a key in unraveling regional tectonic histories. The basin axis controlled the progradation direction which was likely driven by climatically induced sediment influx, a eustatic fall, or both. In the case of the incongruent shift, increased sediment supply permitted the rivers to cross the basinal deep. Temporal association of the Kolhan with tectonic structures in the belt indicates that syn-tectonic thrust uplift, not isostatic uplift or climate, caused the influx of quartz. The sedimentation pattern in the Kolhan reflects a change from braided fluvial-ephemeral pattern to a fan-delta-lacustrine type. The channel geometries and the climate exerted a major control on the processes of sediment transfer. Repeated fault controlled uplift of the source followed by subsidence and forced regression, generated multiple sediment cyclicity that led to the fluvial-fan delta sedimentation pattern. Intermittent uplift of the faulted blocks exposed fresh bedrock to mechanical weathering that generated a large amount of detritus and resulted to forced regressions, repeatedly disrupting the cycles which may reflect a stratigraphic response of connected rift basins at the early stage of extension. The marked variations in the thickness of the fan delta succession and the stacking pattern in different measured profiles reflect the overriding tectonic controls on fan delta evolution. The accumulated fault displacement created higher accommodation and thicker delta sequences. Intermittent uplift of fault blocks exposed fresh bedrock to mechanical weathering, generated a large amount of detritus, and resulted in forced closure of the land-locked basin, repeatedly disrupting the fining upward pattern. The control of source rock lithology or climate was of secondary importance to tectonic effects. Such a retrograding fan delta could be a stratigraphic response of connected rift basins at the early stage of extension.

Keywords: Kolhan basin, petrology, sandstone, tectonics

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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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