Search results for: Navier-Stokes equation

Authors: Joyjit Dey, Souvik Sen

Abstract:

Middle Permian Barakar formation is the major economic coal bearing unit of vast east-west trending Damodar Valley basin of Gondwana coalfield. Primary sedimentary structures were studied from the core holes, which represent majorly four facies groups: sandstone dominated facies, sandstone-shale heterolith facies, shale facies and coal facies. Total eight major coal seams have been identified with the bottom most seam being the thickest. Laterally, continuous coal seams were deposited in the calm and quiet environment of extensive floodplain swamps. Channel sinuosity and lateral channel migration/avulsion results in lateral facies heterogeneity and coal splitting. Geophysical well logs (Gamma-Resistivity-Density logs) have been used to establish the vertical and lateral correlation of various litho units field-wide, which reveals the predominance of repetitive fining upwards cycles. Well log data being a permanent record, offers a strong foundation for generating log based property evaluation and helps in characterization of depositional units in terms of lateral and vertical heterogeneity. Low gamma, high resistivity, low density is the typical coal seam signatures in geophysical logs. Here, we have used a density cutoff of 1.6 g/cc as a primary discriminator of coal and the same has been employed to compute various coal assay parameters, which are ash, fixed carbon, moisture, volatile content, cleat porosity, vitrinite reflectance (VRo%), which were calibrated with the laboratory based measurements. The study shows ash content and VRo% increase from west to east (towards basin margin), while fixed carbon, moisture and volatile content increase towards west, depicting increased coal quality westwards. Seam wise cleat porosity decreases from east to west, this would be an effect of overburden, as overburden pressure increases westward with the deepening of basin causing more sediment packet deposited on the western side of the study area. Coal is a porous, viscoelastic material in which velocity and strain both change nonlinearly with stress, especially for stress applied perpendicular to the bedding plane. Usually, the coal seam has a high velocity contrast relative to its neighboring layers. Despite extensive discussion of the maceral and chemical properties of coal, its elastic characteristics have received comparatively little attention. The measurement of the elastic constants of coal presents many difficulties: sample-to-sample inhomogeneity and fragility and velocity dependence on stress, orientation, humidity, and chemical content. In this study, a conclusive empirical equation VS= 0.80VP-0.86 has been used to model shear velocity from compression velocity. Also the same has been used to compute various geomechanical moduli. Geomech analyses yield a Poisson ratio of 0.348 against coals. Average bulk modulus value is 3.97 GPA, while average shear modulus and Young’s modulus values are coming out as 1.34 and 3.59 GPA respectively. These middle Permian Barakar coals show an average 23.84 MPA uniaxial compressive strength (UCS) with 4.97 MPA cohesive strength and 0.46 as friction coefficient. The output values of log based proximate parameters and geomechanical moduli suggest a medium volatile Bituminous grade for the studied coal seams, which is found in the laboratory based core study as well.

Keywords: core analysis, coal characterization, geophysical log, geo-mechanical moduli

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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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Authors: Katerina Zaharieva, Katya Milenova, Zara Cherkezova-Zheleva, Alexander Eliyas, Boris Kunev, Ivan Mitov

Abstract:

The synthesized nanosized manganese ferrite-type of samples have been tested as photocatalysts in the reaction of oxidative degradation of model contaminant Reactive Black 5 (RB5) dye in aqueous solutions under UV irradiation. As it is known this azo dye is applied in the textile-coloring industry and it is discharged into the waterways causing pollution. The co-precipitation procedure has been used for the synthesis of manganese ferrite-type of materials: Sample 1 - Mn0.25Fe2.75O4, Sample 2 - Mn0.5Fe2.5O4 and Sample 3 - MnFe2O4 from 0.03M aqueous solutions of MnCl2•4H2O, FeCl2•4H2O and/or FeCl3•6H2O and 0.3M NaOH in appropriate amounts. The mechanochemical activation of co-precipitated ferrite-type of samples has been performed in argon (Samples 1 and 2) or in air atmosphere (Sample 3) for 2 hours at a milling speed of 500 rpm. The mechano-chemical treatment has been carried out in a high energy planetary ball mill type PM 100, Retsch, Germany. The mass ratio between balls and powder was 30:1. As a result mechanochemically activated Sample 4 - Mn0.25Fe2.75O4, Sample 5 - Mn0.5Fe2.5O4 and Sample 6 - MnFe2O4 have been obtained. The synthesized manganese ferrite-type photocatalysts have been characterized by X-ray diffraction method and Moessbauer spectroscopy. The registered X-ray diffraction patterns and Moessbauer spectra of co-precipitated ferrite-type of materials show the presence of manganese ferrite and additional akaganeite phase. The presence of manganese ferrite and small amounts of iron phases is established in the mechanochemically treated samples. The calculated average crystallite size of manganese ferrites varies within the range 7 – 13 nm. This result is confirmed by Moessbauer study. The registered spectra show superparamagnetic behavior of the prepared materials at room temperature. The photocatalytic investigations have been made using polychromatic UV-A light lamp (Sylvania BLB, 18 W) illumination with wavelength maximum at 365 nm. The intensity of light irradiation upon the manganese ferrite-type photocatalysts was 0.66 mW.cm-2. The photocatalytic reaction of oxidative degradation of RB5 dye was carried out in a semi-batch slurry photocatalytic reactor with 0.15 g of ferrite-type powder, 150 ml of 20 ppm dye aqueous solution under magnetic stirring at rate 400 rpm and continuously feeding air flow. The samples achieved adsorption-desorption equilibrium in the dark period for 30 min and then the UV-light was turned on. After regular time intervals aliquot parts from the suspension were taken out and centrifuged to separate the powder from solution. The residual concentrations of dye were established by a UV-Vis absorbance single beam spectrophotometer CamSpec M501 (UK) measuring in the wavelength region from 190 to 800 nm. The photocatalytic measurements determined that the apparent pseudo-first-order rate constants calculated by linear slopes approximating to first order kinetic equation, increase in following order: Sample 3 (1.1х10-3 min-1) < Sample 1 (2.2х10-3 min-1) < Sample 2 (3.3 х10-3 min-1) < Sample 4 (3.8х10-3 min-1) < Sample 6 (11х10-3 min-1) < Sample 5 (15.2х10-3 min-1). The mechanochemically activated manganese ferrite-type of photocatalyst samples show significantly higher degree of oxidative degradation of RB5 dye after 120 minutes of UV light illumination in comparison with co-precipitated ferrite-type samples: Sample 5 (92%) > Sample 6 (91%) > Sample 4 (63%) > Sample 2 (53%) > Sample 1 (42%) > Sample 3 (15%). Summarizing the obtained results we conclude that the mechanochemical activation leads to a significant enhancement of the degree of oxidative degradation of the RB5 dye and photocatalytic activity of tested manganese ferrite-type of catalyst samples under our experimental conditions. The mechanochemically activated Mn0.5Fe2.5O4 ferrite-type of material displays the highest photocatalytic activity (15.2х10-3 min-1) and degree of oxidative degradation of the RB5 dye (92%) compared to the other synthesized samples. Especially a significant improvement in the degree of oxidative degradation of RB5 dye (91%) has been determined for mechanochemically treated MnFe2O4 ferrite-type of sample with the highest extent of substitution of iron ions by manganese ions than in the case of the co-precipitated MnFe2O4 sample (15%). The mechanochemically activated manganese ferrite-type of samples show good photocatalytic properties in the reaction of oxidative degradation of RB5 azo dye in aqueous solutions and it could find potential application for dye removal from wastewaters originating from textile industry.

Keywords: nanostructured manganese ferrite-type materials, photocatalytic activity, Reactive Black 5, water treatment

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