Chord Length Distribution Research Articles

Optimal design of hydrokinetic turbine for low-speed water flow in Golden Gate Strait

Marine current power has been utilized in recent years as one of the most foreseeable renewable energy sources. In this study, the optimal design of hydrofoil is carried out for hydrokinetic turbines to improve their hydrodynamic performance in Golden Gate Strait with the low-speed current. In order to design optimal hydrofoils for different sections of a blade, Particle Swarm Optimization (PSO) and XFoil are coupled. For hydrofoil’s shape parameterization, the B-spline curve is used. The coordinate’s values of the control points are designated to act as optimization parameters. Five hydrofoils from root to tip are designed for a turbine at low current speed with three blades. Hydrofoils are optimized from hub to tip in distances 0.4, 1.2, 2.4, 3.4, and 4.4 m. Optimum chord length and twist angle distribution along the blade are obtained using Harp_Opt, which is based on Blade Element Momentum theory. Finally, the power coefficient, rotational speed, cavitation criteria, and power are calculated for an optimized turbine and compared to the first turbine and Betz criterion. It is assured that cavitation will not occur at the tip of the blade which the linear velocity is maximum. The summation of cavitation number and minimum pressure coefficient (σ+CpMin) is estimated to be 1.8. The power coefficient is computed using Harp_opt for both initial turbines with hydrofoil NACA 4415 and turbine with optimized cross sections from hub to tip. The power coefficient is improved 26% for speeds of 0.5–2 m/s and 50% for speeds of 2–3 m/s. An optimal marine current turbine which is useable for relatively lower currents is designed in this study by applying and combining different tools for different stages of research.

Propeller-wing coupled aerodynamic design based on desired propeller slipstream

Considering the multi-propeller characteristics of DEP configuration, the lift-to-drag ratio of the wing is improved by optimizing the slipstream of the propeller, rather than changing the chord length and twist distribution along the span of the wing. First, a propeller design method is proposed to obtain the target induced velocity distribution, and then, a calculation model Prop−wing of propeller-wing integration is established based on the designed induced velocity distribution and panel method. Finally, an efficient optimization algorithm based on genetic algorithm (GA) and Kriging surrogate modeling is used to optimize the induced velocity distribution of the slipstream for higher lift-to-drag ratios. The optimization results show that when the thrust is constant, the larger the axial induced velocity close to the hub, the better the drag characteristics of the wing. When the chord length of propeller is not limited, the drag decreases by 30.48% and the lift-to-drag ratio increases by 51.93%. A 13.68% drag reduction and 18.80% lift-to-drag ratio improvement can be obtained.

Blade design and optimization of a horizontal axis tidal turbine

Tidal turbine is a device which converts the kinetic energy of water into electric energy. The blade element momentum theory (BEM) is used to design the blade in this paper. Although tidal power resources are abundant, the actual operation of hydraulic turbines is not very good due to the limitations of turbine conversion efficiency and production cost. Therefore, this paper establishes a neural network model for variables and objective functions, and then applies multi-objective optimization algorithm to genetic optimization of the power coefficient, the main index of hydraulic performance of tidal turbines. The optimized results are verified by model test and sea trial. The results show that after optimizing the blade chord length distribution and pitch Angle distribution, the power coefficient of the turbine increases by 2%, and the optimal tip speed ratio range is also expanded, which is more conducive to the actual tidal turbine power generation, and has certain engineering significance.

Number-sensitive particle size measurements for monitoring flocculation responses to different grinding conditions

In gravity thickening, higher levels of fine particles within the feed slurry typically lead to reduced flocculation performance relative to that achieved at the optimal solids concentration and flocculant dosage. Grinding is applied prior to separation processes (e.g. flotation, leaching) to liberate valuable material, and the higher grinding required for finely disseminated minerals substantially increases the fines fraction. To quantify the potential impact on flocculation efficiency of excessive fines formation within feeds to gravity thickeners, slurries of one ore type with seven different particle size distributions (PSDs) were produced by a combination of grinding and blending different size fractions. Sizings by volume- or mass-sensitive methods for these broad PSDs are dominated by coarser particles, despite their contribution to particle numbers being very low. Chord length distributions acquired in situ by focused beam reflectance measurement (FBRM) give real-time indications of size at high solids concentrations, and the raw (unweighted) counts are sensitive to particle number. The results of experiments with the different feed PSDs showed flocculation was strongly affected by fines and thereby particle number. FBRM therefore offers considerable scope for monitoring feed properties in terms of potential flocculation performance.Many flocculation studies focus on a single solids concentration, but useful comparisons for different PSD feed slurries can only be made by testing across multiple concentrations and flocculant dosages, with settling data then converted to solids settling flux. Flux values varied by an order of magnitude at a fixed dosage across the PSD extremes. While tripling the dosage significantly increased fluxes for slurries containing high levels of fines at their optimum solids concentration (~100 kg m−3), much higher fluxes were attained with coarser PSDs at both higher concentrations and lower dosages. When flocculating slurries of the seven PSDs at a fixed dosage, the solids settling flux increased as FBRM counts <20 µm prior to flocculation declined; scope for using FBRM in feed-forward control is discussed.

The unsteady hydrodynamic response of lightly loaded tidal turbines

An investigation on the unsteady hydrodynamic behaviour of a new scale model tidal turbine at the University of Auckland has been conducted, using FAST software from National Renewable Energy Laboratory. The turbine blades are designed to achieve the optimal angle of attack based on maximizing lift-to-drag ratio, and then the distribution of chord lengths and pitch angles is determined. In this way, a highly efficient but a lightly loaded tidal turbine model design utilizing the S814 profile, is achieved. Oscillatory motions of flows with single frequency over a range of current numbers and reduced frequencies have been considered. The investigation shows that the unsteadiness of the hydrodynamics on the blades is governed by the dynamic inflow phenomenon. The mean angle of attack along the blade is maintained at or very near the initial optimal value. The effects of the oscillatory frequency and velocity amplitude on the unsteady hydrodynamic loading are explored. A quasi-steady analysis is used to clarify the hydrodynamic response of the model as a lightly loaded rotor. A mathematical model is added to the investigation to analyse the role of the forcing components relative to oscillatory velocity and acceleration on the phase of the unsteady loading.

Assessment of self- and cross-absorbed SAF values for HDRK-man using Geant4 code: internal photon and electron emitters

The ultimate need to account for the partial amount of energy deposited in target tissue/organ resulting from internal inhalation, ingestion, and injection intakes of radionuclides, defined by the Medical Internal Radiation Dosimetry committee as the specific absorbed fraction (SAF), has become obvious. In this study, we assessed the SAF values for self- and cross-absorption, which were calculated for a uniform distribution of monoenergetic photon and electron emitters with energies ranging from 15 keV to 3 MeV. The voxelized human phantom “High-Definition Reference Korean-man” (HDRK-man), which was implemented using the Monte Carlo simulation code Geant4 (version 10.1), was used for several combinations of target–source organs. The results were compared to those of the International Commission on Radiological Protection Reference (ICRP133) and Zubal phantoms. It was found that the SAF values of the three models have a similar trend. However, the SAF values for the HDRK-man phantom were higher than those of the other two models, with a relatively good agreement with those for the ICRP133 phantom (differences of 13.9 ± 2.8 and 12.1 ± 3.2 for photon and electron emitters, respectively). To analyze the differences in SAF values, we calculated the chord length distributions (CLDs) for selected target–source combinations. The parameters of organ mass (or volume) and CLDs, in addition to the adopted computational procedures, mainly cause such discrepancies. For realistic radionuclide emission spectra, an overall overestimation was observed when computing the S values for three radiopharmaceuticals studied (I-131, In-111, and Lu-177) and for liver–spleen intra- and inter-organ absorption when compared with published data. The new arrangement of S and SAF values is expected to add value for multidisciplinary research and clinical communities.

COVARIOGRAM OF A RIGHT PARALLELEPIPED

In this paper we obtain explicit expressions for the covariogram and the orientation-dependent chord length distribution of a right parallelepiped with square base.

Rotor blade aerodynamic shape optimization based on high-efficient optimization method

In order to design a high-performance rotor, a high-efficient optimization method is established by coupling Kriging model and sequential quadratic programming with high-accuracy computational fluid dynamics method. In order to obtain the global optimal design point, the initial blade shape is optimized by using the Kriging model coupled with genetic algorithm based on the baseline rotor blade (Helishape 7A rotor). After that, the modified sequential quadratic programming method is employed to search the final blade shape based on the initial blade shape deeply. In the optimal process, the regions of design variables are restricted considering rotor dynamic characteristics. As a result, a new shape of rotor blade with characters of nonlinear twist, variational chord length, complex swept, and anhedral distributions is obtained. Compared with the baseline rotor, blade-tip vortex of the final optimized rotor is significantly weakened, the figure of merit of the final optimized rotor increases about 3.42%, and the peak of sound pressure decreases about 16.9%. At the same time, it is demonstrated that the final optimized rotor has better forward flight characteristics.

Optimization Study on the Blade Profiles of A Horizontal Axis Tidal Turbine Based on BEM-CFD Model

In order to increase the performance of horizontal tidal turbines, a multi-objective optimization model was proposed in this study. Firstly, the prediction model for horizontal tidal turbines was built, which coupled the blade element momentum (BEM) theory and the CFD calculation. Secondly, a multi-objective optimization method coupled the response surface method (RSM) with the multi-objective genetic algorithm NSGA-II was applied to obtain the optimal blade profiles. The pitch angle and the chord length distribution were chosen as the design variables, while the mean power coefficient and the variance of power coefficient were chosen as the objective functions. With the mean power coefficient improved by 4.1% and the variance of power coefficient decreased by 46.7%, results showed that both objective functions could be improved.

The aerodynamic coupling design and wind tunnel test of contra-rotating wind turbines

The performance of contra-rotating wind turbines (CRWTs) is highly dependent on aerodynamic design. However, flow interaction between two rotors hasn't been fully understood. In this paper, flow interaction was considered in theoretical model based on actuator disc theory with wake rotation. As a consequence, a coupling design method was formulated. Simultaneous blade design of both rotors was originally expressed by a global optimization problem. The input variables include axial and tangential velocity induction factors of both rotors. The output is energy efficiency of CRWT at the annular disc. As a result, chord length and blade section pitch distribution were determined synchronously. This method was applied on the 500W cases of a CRWT and a single rotor wind turbine (SRWT) with identical radius. Wind tunnel test were carried out on the prototypes, with rotating speed and pitch of both rotors controlled independently under various wind velocity. Result validated the effectiveness of design method. At rated wind velocity, the maximum power coefficients of CRWT and SRWT were 0.426 and 0.373. Despite a slightly high start-up wind speed, CRWT demonstrated a higher power coefficient than single turbine at wind velocity 8–14 m/s, with power coefficient relative increment 5.3–28.9%.

Acid precipitation of kraft lignin from aqueous solutions: the influence of anionic specificity and concentration level of the salt

Abstract In this study, the formation of particles and evolution of the particle size distribution in the micron range were monitored in situ during acid precipitation of kraft lignin. The objective of this work was to study the influence of anionic specificity and the ion concentration level. The concentrations of ions in the solution were altered both in terms of the concentration of Na+ and the type of anion in the salt added ( SO 4 2 − ${\rm{SO}}_4^{2 - }$ and Cl−). The results indicate that a salting-out phenomenon occurred as NaCl was added (Na+ ≥2 mol kg−1 water) to the kraft lignin solution at high pH, but not when Na2SO4 was added. However, the onset pH of the formation of particles (≥1 μm), triggered by acidification, showed to be virtually non-specific to the anion but strongly dependent on the Na+ concentration. As the pH decreased further to below the onset pH of the formation of particles ≥1 μm, the chord length distributions (particle-size related) indicated that most of the volume of the precipitated kraft lignin (and thus possibly also the mass) may be found among the micron-sized particles, despite the fact that a relatively large number of submicron particles may also be present. The volume-based distributions tended to be wide at relatively low pH and high Na+ concentrations (e.g. pH 9.4 and 2.0 mol kg−1 water).

Experimental and numerical investigation on mixing of dilute oil in water dispersions in a stirred tank

Stirred tanks are commonly employed for liquid–liquid dispersion processes in many industries. This study investigated the effects of agitation speed, and oil type and volume fraction on the hydrodynamic characteristics and chord length distribution (CLD) of dilute oil in water dispersions in a stirred tank. Electrical resistance tomography (ERT) and a focused beam reflectance measurement (FBRM) instrument were used to assess the liquid–liquid flow and to measure droplet size inside the tank, respectively. We also simulated flow field via computational fluid dynamic and modeled droplet size distribution in a stirred tank by population balance modeling. An increase in agitation speed was found to decrease the mean and Sauter mean diameter while improving the homogeneity of the system. Wider distributions were observed at higher oil volume fractions, without a significant change in droplet size. Increasing the viscosity of the oil phase resulted in poor mixing, with a gradual shift towards smaller droplets. The effect of the dispersion process on droplet shape and deformation rate were also investigated using CLD results. Further shape analysis was performed using Python coding. Our results show that the shape of the droplets changed from sphere to spheroid with an increase in agitation speed. An increase in droplet deformation rate was also observed with an increase in the oil phase viscosity and a decrease in the interfacial tension between the two immiscible liquids.

Experimental study of slug and churn flows in a vertical pipe using plug-in optical fiber and conductance sensors

It is of great significance to explore the flow structures in gas-liquid slug and churn flows. Aiming at this purpose, a novel plug-in optical probe combined with conductance sensors are designed. Furthermore, we perform experimental study of gas-liquid flows in vertical upward pipe with 20 mm inner diameter. Simultaneously, the local time average of void fraction in axial direction, cross-correlation velocity and instantaneous bubble chord distribution in slug and churn flows at seven radial positions are obtained. The research results show that big deformed bubbles in churn flow spiral up in test pipe, but sometimes they rise along pipe center just as gas slugs in slug flow. Besides, bubble chord length distributions in liquid slug of slug and churn flows are analyzed in this study.

Using focused beam reflectance measurement (FBRM) to monitor aggregate structures formed in flocculated clay suspensions

The shear sensitivity of fragile, low-density aggregates formed in particle suspensions by polymer-bridging flocculation makes characterisation methods needing sampling or dilution problematic. Focused beam reflectance measurement (FBRM) probes can readily monitor such structures in real-time, but interpretation of resulting chord length data can be superficial, often missing detail within the distributions. However, the potential for deeper insights can’t be realised if flocculating with poor control of applied shear conditions (intensity and duration). In this study, continuous flocculation was achieved in a Couette mixing device with a vertical flow-through arrangement, acquiring operator-independent settling rate and FBRM chord data. The performance of a series of anionic flocculants (same charge density but different molecular weights) was investigated when applied to kaolin suspensions, with the introduction of 10 or 20% bentonite used to induce ‘bad’ flocculation responses. Size-density relationships in selected samples were determined separately by image analysis of free-settling aggregates.Following well controlled flocculation, distinct relationships between settling rate and mean volume-weighted chord length were attributed to variations in both substrate mineralogy and applied mixing intensity impacting on aggregate density. No such distinctions could be drawn from variations in flocculant molecular weight. Unweighted chord length distributions offered sensitivity to inefficiencies in fines capture and aggregate breakage under higher shear, which were both impacted by flocculant molecular weight. The unweighted chord counts <10 µm for the unflocculated clay slurries better anticipated dosage demand than conventional (volume-based) particle sizing, showing the potential of FBRM feed monitoring for flocculation control.

Identification of Mesoscale Flow in a Bubbling and Turbulent Gas–Solid Fluidized Bed

Based on the moment consistency principle, the bubble threshold was determined by using the traversing method. A novel approach was proposed to identify bubbles and agglomerates from transient signals registered in a cold mode fluidized bed dealing with different particles. Bubble and agglomerate hydrodynamics including volume fraction, solid holdup, immigration velocity, and frequency were investigated. Adding fine powder promotes the formation of particle agglomerates at low superficial gas velocity and leads to a great bubble volume fraction at high superficial gas velocity. Bubble frequency increases significantly during the flow pattern transition from bubbling to turbulence bed. Compared with FCC particles, the mixed particles have a narrow bubble chord length distribution. The net velocity of agglomerates is positive in the center and close to zero or even negative in the vicinity of the wall. The agglomerate frequency in the mixed particle bed is significantly lower than that in the FCC particle bed.

Relationship between bed heterogeneity, chord length distribution, and longitudinal dispersion in particulate beds

We analyse a relationship between the bulk microstructure of randomly packed beds, which we quantify through chord length distribution (CLD) analysis of the interparticle void space, and the associated flow heterogeneity, as expressed by the longitudinal dispersion coefficient at a Péclet number of Pe = 10. A random collection of physically reconstructed packings is complemented with a systematic set of computer-generated packings of monosized spheres, for which the packing-generation algorithm has been carefully adjusted to realize a monotonic variation of the bed porosity and microstructural heterogeneity. The most relevant difference in the morphology between these computer-generated and the physically reconstructed packings are structural defects present in the real packings, such as particle oligomers and larger voids as well as contaminations and particle debris. These defects influence the pore space morphology and introduce additional structural heterogeneity. Hydrodynamic dispersion coefficients for all packings are derived by implementing the lattice-Boltzmann method to simulate fluid flow and a random-walk particle tracking technique to record the transport of passive, point-like tracers in the flow fields. We propose a morphological descriptor, σ/μ, based on statistical parameters of a CLD (standard deviation σ and mean chord length μ) that can be used to predict the dispersion coefficient in packed beds, independent from the underlying particle size distribution, packing-generation protocol, bed porosity, and the occurrence of structural defects.

Characterization of the 3D microstructure of Ibuprofen tablets by means of synchrotron tomography.

A new methodology to segment the three-dimensional (3D) internal structure of Ibuprofen tablets from synchrotron tomography is presented, introducing a physically coherent trinarization for greyscale images of Ibuprofen tablets consisting of three phases: microcrystalline cellulose, Ibuprofen and pores. For this purpose, a hybrid approach is developed combining a trinarization by means of statistical learning with a trinarization based on a watershed algorithm. This hybrid approach allows us to compute microstructure characteristics of tablets using methods of statistical image analysis. A comparison with experimental results shows that there is a significant amount of pores which is below the resolution limit. At the same time, results from image analysis let us conjecture that these pores constitute the great majority of the surface between pores and solid. Furthermore, we compute microstructure characteristics, which are experimentally not accessible such as local percolation probabilities and chord length distribution functions. Both characteristics are meaningful in order to quantify the influence of tablet compaction on its microstructure. The presented approach can be used to get better insight into the relationship between production parameters and microstructure characteristics based on 3D image data of Ibuprofen tablets manufactured under different conditions and elucidate key effects on the strength and solubility kinetics of the final formulation. LAY DESCRIPTION: A typical formulation of uniaxial compacted Ibuprofen tablets consist of a mixture of an excipient (microcrystalline cellulose) with an active ingredient (a ground fraction of Ibuprofen). The final mechanical strength of the tablet as well as the release kinetics are strongly influenced by the underlying microstructure, i.e. the spatial arrangement of the microcrystalline cellulose and Ibuprofen within the tablet. In order to optimize the performance of the tablet, it is important to investigate the relationship between its microstructure and the corresponding production parameters. For this purpose, 3D imaging is a powerful tool as it allows computing microstructural properties such as the internal arrangement, interconnectivity and pore location and distribution, characteristics that cannot be computed by experimental characterization techniques. In the present study, a new algorithm for an accurate trinarization of 3D image data obtained by synchrotron tomography is presented. Trinarization means that we reconstruct microcrystalline cellulose, Ibuprofen and pores on the basis of the 3D images, where one can only observe different greyscale values, but not the different constituents themselves. For this purpose, a hybrid approach combining a trinarization by means of artificial intelligence with a trinarization based on a geometrically motivated algorithm is developed. This hybrid approach allows to compute microstructure characteristics of tablets using image analysis. A comparison with experimental results shows that there is a significant amount of pores below the resolution limit. At the same time results from image analysis lead to the conjecture that these pores constitute the major part of the surface between pores and solid. Moreover, characteristics are computed by image analysis, which are meaningful in order to quantify the influence of tablet compaction parameters on its microstructure. The presented novel approach can be used to elucidate the relationship between production parameters and microstructure characteristics based on 3D image data of Ibuprofen tablets manufactured under different mixing, loading and processingconditions.

Determining particle‐size distributions from chord length measurements for different particle morphologies

AbstractA recently proposed model to determine particle‐size distributions (PSDs) from chord length measurements has been applied to different particle morphologies, namely compact, platelet‐ and rod‐shaped particles. To study these systems, chord length distributions (CLDs) were measured at varying particle size and solids concentration for each compound and were subsequently utilized to determine the system‐specific parameters. Each model was successfully applied to its respective compound such that the experimental PSDs and model predictions were in good agreement. Moreover, the effect of other variables such as agitation rate and solvent composition was investigated and found to be negligible for the specific systems tested. Finally, potential model optimizations of the general model construct have been studied. Two variants of the CLD compression step, namely principal component analysis and a geometric model have been considered as surrogate models. However, neither of these approaches yielded superior results than the previously proposed approach.

Hairy cationic nanocrystalline cellulose as a novel flocculant of clay

HypothesisThe present paper investigates, for the first time, the potential of cationic hairy cellulose nanocrystals (CNCC) to induce the flocculation of a model suspension of kaolinite. CNCC belong to a brand new family of nanocelluloses characterized for presenting a crystalline rod-like body and functionalized amorphous chains at both ends. Given that these chains can be easily tuned, these nanocelluloses present a high potential as fit-to-purpose flocculants. ExperimentsCNCC were produced through periodate oxidation, cationization and thermal treatment of cellulose. Flocculation was monitored by both photometric dispersion analysis and laser reflectance. Flocs were characterized by the determination of zeta potential, supernatant turbidity removal and optical microscopy. A recently developed machine learning random forest regression model was used to estimate fractal dimension (Df) from chord length distribution data. FindingsAlthough a high efficiency was achieved for CNCC dosages between 7.5 and 75 mg/g, the maximum floc size and the fastest flocculation were found near the isoelectric point (10–30 mg/g). Thus, CNCC acted through charge neutralization mechanism. The model used to estimate flocs Df was found very successful to describe the flocculation process. The clay/CNCC flocs Df values suggest a relation between floc conformation and CNCC dosage, presenting an opener structure when closer to the isoelectric point.

Effective sapphire repellency treatment to reduce fouling of a focused beam reflectance measurement (FBRM) probe in bituminous systems

AbstractThe use of a focused beam reflectance measurement (FBRM) probe to track the chord length distribution dynamics in a bituminous system can be very challenging. Material coats the sapphire window of the probe and the quality of the data is compromised. The fouling index is a parameter used to assess the quality of the FBRM data. It is provided by the software and is the percentage similarity between two consecutive scans of the instrument, indicating how much of the reading has not changed due to material that is stuck to the optical window. When the FBRM was used in bitumen froth, the fouling index was higher than 90 %. In this work the significant reduction in fouling achieved with a sapphire repellency treatment is presented. The reduction in fouling was sufficient to detect broad trends in the FBRM data that will be used in future studies but was not sufficient to ensure quantitative measurement of the chord length distribution.