Search Results (24)

We investigate the effects of the magnetostatic ($B$) field topology on the plasma behavior in a 2D collisionless simulation setup that represents an axial–azimuthal cross-section of a Hall thruster. The influence of the $B$-field topology is assessed in terms of two principal design properties of the field in a typical Hall thruster, i.e., the field’s peak intensity along the axial direction, and the field’s axial distribution. The effects of the field’s intensity are investigated for three propellants—xenon, krypton, and argon. Whereas, the effects of the axial profile of the magnetic field are studied only for the xenon propellant as an example. We primarily aim to understand how the changes in the $B$-field topology affect the spectra of the resolved instabilities as well as the electrons’ transport characteristics and the contributions of various momentum terms to transport. The numerical observations on the instabilities’ characteristics are compared against the relevant existing theories to determine the extent to which the simulated and the theoretically predicted characteristics are consistent across the studied parameter space. It was, most notably, found that modes related to ion acoustic instability are dominantly present across the simulation cases. The ion transit time instability additionally develops at the highest $B$-field intensities as a long-wavelength structure. The main influence of the axial profile of the $B$ field on the plasma discharge was observed to be in terms of the electrons’ transport characteristics. Where possible, the insights from the simulations are discussed with respect to the relevant experimental observations available in the literature. Full article

The results from a wide-ranging parametric investigation into the behavior of the collisionless partially magnetized plasma discharge of three propellants—xenon, krypton, and argon—are reported in this two-part article. These studies are performed using high-fidelity reduced-order particle-in-cell (PIC) simulations in a 2D configuration that represents an axial–azimuthal cross-section of a Hall thruster. In this part I paper, we discuss the effects of discharge voltage and current density (mass flow rate). Our parametric studies assess the spectra of the resolved instabilities under various plasma conditions. We evaluate the ability of the relevant theories from the literature to explain the variations in the instabilities’ characteristics across the studied plasma parameter space and for various propellants. Moreover, we investigate the changes in the electrons’ cross-magnetic-field transport, as well as the significance of the contribution of different momentum terms to this phenomenon across the analyzed cases. In terms of salient observations, the ion acoustic instability (IAI)-related modes are found to be dominant across the simulation cases, with the ion transit time instability also seen to develop at low current density values. Across the explored parameter space, the instabilities have the main contributions to the electrons’ transport within the plume region. The peak of the electric momentum force term, representing the effect of the instabilities, overall shifts toward the plume as either the current density or the discharge voltage increases. The numerical findings are compared against relevant experimental observations reported in the literature. Full article

This contribution underscores the importance of selecting an appropriate interphase momentum transfer model for accurately predicting the distribution of the solid phase in a full-scale circulating fluidized bed (CFB) riser equipped with a smooth C-type exit. It also explores other critical factors such as domain configuration, grid size, the scope of time averaging, and turbulence modulation. The flow in a cold-CFB riser is simulated using the Eulerian–Eulerian two-fluid model within a commercial CFD package. Particle interactions in the rapid-flow regime are determined utilizing the kinetic theory of granular flow while enduring particle contacts are accounted for by incorporating frictional stresses. The turbulent dynamics of the continuous phase are described using two-equation turbulence models with additional modulation terms. The three-dimensional computational domain replicates an actual CFB riser geometry where experimental measurements are available for particulate phase axial and radial solid concentration. The simulation results reveal that the choice of drag model correlation significantly impacts both axial and radial solid distribution. Notably, the energy-minimization multi-scale drag model accurately depicts the dense solid region at the bottom and core–annular flow structure in the upper part. The solid-phase fluidization is overestimated in the lower riser section when a 2D domain is utilized. Neglecting turbulence modulation terms in the k-$\omega$ SST model results in nearly flat solid volume fraction radial profiles in the analyzed upper sections of the riser, resembling those obtained with the k-$ϵ$ model. Full article

Recent developments in electrical Vertical Take-off and Landing (eVTOL) vehicles show the need for a better understanding of transient aero-mechanical propeller loads for non-axial inflow conditions. The variety of vehicle configurations conceptualized with different propellers in terms of blade geometry, number of blades, and their general integration concept results in aerodynamic loads on the propellers which are different from those on conventional fixed-wing aircraft propellers or helicopter rotors. Such varying aerodynamic loads have to be considered in the vehicle design as a whole and also in the detailed design of their respective electric propulsion systems. Therefore, an experimental approach is conducted on two different propeller blade geometries and a varying number of blades with the objective to explore the characteristics at non-axial inflow conditions. Experimental data are compared with calculated results of a low-fidelity Blade Element Momentum Theory (BEMT) approach. Average thrust and side force coefficients are shown to increase with inflow angle, and this trend is captured by the implemented numerical method. Measured thrust and in-plane forces are shown to oscillate at the blade passing frequency and its harmonics, with higher amplitudes at higher angles of inflow or lower number of blades. Full article

The use of a diffuser in hydrokinetic turbines can improve the power coefficient. However, the risk of cavitation in the rotor blades increases. Studies suggest that backward-curved blades can reduce the axial load on the rotor and therefore prevent cavitation. Therefore, this work develops an optimization procedure applied to backward-curved blades in hydrokinetic turbines with diffusers based on the Blade Element Momentum Theory. The main contribution is to consider both the sweep effect and the presence of a diffuser in the optimization in an innovative way. We use a radial transformation function that adjusts the radial position considering the curvature of the blade during optimization under the effect of the diffuser. The results showed that the increase in blade curvature resulted in greater chord distributions and twist angles, especially at the blade tips. The Prandtl’s loss factor was not sensitive to sweep, but the linked circulation increased at the blade tips, suggesting an increased risk of cavitation. Depending on the sweep angle, the optimized blades were able to mitigate or avoid cavitation. In particular, a sweep angle of 30${}^{\circ }$ eliminated cavitation. This study indicated that the proposed optimization can effectively prevent cavitation, showing satisfactory results. Full article

In this paper, an analytical method for studying the radiation force (RF) of chiral spheres generated by dual laser beams is presented under the framework of generalized Lorenz–Mie theory (GLMT). According to the coordinate transformation relations, the arbitrarily incident laser beam is represented by vector spherical harmonic functions (VSHFs) in the sphere system. The entire induced field expression coefficients of dual laser beams can be obtained by superposition of each illuminated field. Based on the momentum conservation theory, the concrete expression of lateral and axial RF on chiral sphere is derived. The current theories are shown to be valid by comparison with the existing reference. To investigate the stable capture state of chiral sphere, the influences of the corresponding parameters of chiral particles and dual laser beams on the trapping and manipulation are investigated in detail. The analytical study on the RF of dual laser beams on chiral particles is an efficient method for improving optical tweezers technology and can become an encouraging approach to realize the high accuracy operation of chiral particles. Full article

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus. Full article

Blade Element Momentum Theory (BEMT) is the most used method to design horizontal-axis wind turbines worldwide. This is because BEMT has a low computational cost and easy numerical implementation. Additionally, it is demonstrated in the literature that the prediction of output power using BEMT agrees well with experimental data. Another important feature of the BEMT is its applicability to small, medium, and large-sized turbines. However, BEMT models are usually implemented and adjusted for a specific power range turbine, and they are not applied in a more general form. Thus, this article presents an analysis of additional correction methods for tip and root losses, high values of the axial induction factor, and high angle of attack to better represent horizontal-axis turbines in terms of numerical stability. The approach has the intention of combining several complementary correction methods strategically inserted in the BEMT in order to compile an algorithm that is more general, stable, and workable for any turbine size. The main contribution of this work is to propose a stable BEMT numerical algorithm through the assessment of the combination of the correction methods available in the literature, i.e., classical and modern ones. The algorithm ensures applicability for small, medium, and large-sized wind turbines, as well as being fast and easy to implement in any computer and extendable even to turbines with a diffuser. This approach is validated by comparing the results with experimental data from four turbines of different power ranges (1.9 kW to 7.3 MW). The results show the best approximations for performance power curves against the measured values of all turbines. Moreover, it is effective, less complex, and quick in analyzing the performance of those turbines. Furthermore, the need for high-performance computers to analyze the performance of horizontal-axis turbines is avoided. Full article

The conditions for achieving the maximal unquenched orbital angular momentum L = 3 and the highest magnetic anisotropy in mononuclear 3d complexes with axial coordination symmetry are examined in terms of the ligand field theory. It is shown that, apart from the known linear two-coordinate 3d⁷ complex Co^II(C(SiMe₂ONaph)₃)₂ characterized by record magnetic anisotropy and single-molecule magnet (SMM) performance (with the largest known spin-reversal barrier U_eff = 450 cm⁻¹), the maximal orbital angular momentum L = 3 can also be obtained in linear two-coordinate 3d² complexes (V³⁺, Cr⁴⁺) and in trigonal-prismatic 3d³ (Cr³⁺, Mn⁴⁺) and 3d⁸ (Co⁺, Ni²⁺) complexes. A comparative assessment of the SMM performance of the 3d², 3d³ and 3d⁸ complexes indicates that they are unlikely to compete with the record linear complex Co^II(C(SiMe₂ONaph)₃)₂, whose magnetic anisotropy is close to the physical limit for a 3d metal. Full article

The hydrokinetic turbine is used worldwide for electrical generation purposes, as such a technology may strongly reduce environmental impact. Turbines designed using backward swept blades can significantly reduce the axial load, being relevant for hydro turbines. However, few works have been conducted in the literature in this regard. For the case of hydrokinetic rotors, backward swept blades are still a challenge, as the authors are unaware of any optimization procedures available, making this paper relevant for the current state of the art. Thus, the present work develops a new optimization procedure applied to hydrokinetic turbine swept blades, with the main objective being the design of blades with reduced axial load on the rotor and possibly a reduction in the cavitation. The proposed method consists of an extension of the blade element momentum theory (BEMT) to the case of backward swept blades through a radial transformation function. The method has low computational cost and easy implementation. Once it is based on the BEMT, it presents good agreement when compared to experimental data. As a result, the sweep heavily affects the chord and twist angle distributions along the blade, increasing the turbine torque and power coefficient. In the case of the torque, it can be increased by about 18%. Additionally, even though the bound circulation demonstrates a strong change for swept rotors, Prandtl’s tip loss seems to be not sensitive to the sweep effect, and alternative models are needed. Full article

Due to the fact that the noise caused by axial fan blades of vehicles is large, which seriously affects ride comfort, and there is no effective mathematical model to quantitatively study the contribution of the various parameters of the blades to the noise, a new method for calculating the load force of the blades is proposed. This method obtains the constant load force of the blade according to the blade element momentum theory and the characteristics of the blade structure of the axial fan for a vehicle. At the same time, this method obtains the non-constant load force of the blade by combining the non-constant thin-wing theory and experimental data and then vectors the constant load force and the non-constant load force to obtain the total load force of the blade to build a mathematical model of the relationship between the noise of the fan and the parameters of the blade. According to the model, the total sound pressure level of a fan is calculated numerically and further compared with the FLUENT software simulation and experimental results. The results show that the error of the total sound pressure level calculated by the numerical value is within 3 dB(A). This method provides an important basis for the study of a high-accuracy noise mathematical model and the optimization of blade parameters of low Mach-number fans. Full article

Extremely slow recession of the Moon from the Earth has been recently proposed and attributed to conversion of Earth’s axial spin to lunar orbital momentum. This hypothesis is inconsistent with long-standing recognition that the Moon’s orbit involves three-body interactions. This and other short-comings, such as Earth’s spin loss being internal, are summarized here. Considering point-masses is justified by theory and observational data on other moons. We deduce that torque in the Earth-Moon-Sun system increases eccentricity of the lunar orbit but decreases its inclination over time. Consequently, the average lunar orbital radius is decreasing. We also show that lunar drift is too small to be constrained through lunar laser ranging measurements, mainly because atmospheric refraction corrections are comparatively large and variations in lunar cycles are under-sampled. Our findings support co-accretion and explain how orbits evolve in many-body point-mass systems. Full article

This paper considers the effect of wake expansion on the finite blade functions in blade element/momentum theory for horizontal-axis wind turbines. For any velocity component, the function is the ratio of the streamtube average to that at the blade elements. In most cases, the functions are set by the trailing vorticity only and Prandtl’s tip loss factor can be a reasonable approximation to the axial and circumferential functions at sufficiently high tip speed ratio. Nevertheless, important cases like coned or swept rotors or shrouded turbines involve more complex blade functions than provided by the tip loss factor or its recent modifications. Even in the presence of significant wake expansion, the functions derived from the exact solution for the flow due to constant pitch and radius helical vortices provide accurate estimates for the axial and circumferential blade functions. Modifying the vortex pitch in response to the expansion improves the accuracy of the latter. The modified functions are more accurate than the tip loss factor for the test cases at high tip speed ratio that are studied here. The radial velocity is important for expanding flow as it has the magnitude of the induced axial velocity near the edge of the rotor. It is shown that the resulting angle of the flow to the axial direction is small even with significant expansion, as long is the tip speed ratio is high. This means that blade element theory does not have account for the effective blade sweep due to the radial velocity. Further, the circumferential variation of the radial velocity is lower than of the other components. Full article

Currently, the actuator disk theory (ADT) and the rotating annular stream-tube theory (RAST), both of which predicate on the axial momentum and generalized momentum theories, among others, are commonly used in investigating the aerodynamic characteristics of horizontal axis wind turbines (HAWTs). These theories, which are based on a rotor with an infinite number of blades, typically do not properly capture the flow physics of wind blowing past the rotors of HAWTs. A vortex ring theory (VRT) that analyzes HAWTs based solely on the characteristics of fluids flowing past obstructions is proposed. The VRT is not predicated on the assertion that the induced velocity in the wake is twice the induced velocity at the rotor. On the contrary, it splits the axial induction factor in the wake into two components, namely, the induction or interference factor due to the solidity of the rotor and the induction factor due to the wake of the rotor a_w; a_w and its azimuthal counterpart are determined using the Biot–Savart law. The pressure differences across the rotor segments of a HAWT are derived from the Bernoulli equation for all the three theories. Blade segment/local areas based on the blade sectional geometry of the rotor are used in the case of the VRT to estimate the local forces. All the calculations in this study are based on the design parameters of the 5 MW National Renewable Energy Laboratory’s reference offshore wind turbine. Pressure differences are plotted as functions of local radii using the calculated axial and azimuthal induction factors for each theory. The local power coefficient is plotted as a function of the local tip-speed ratio, while the local thrust coefficient is plotted as a function of the local radii for all the three theories. There is piece-wise agreement between the VRT, the ADT, the RAST and numerical and experimental data available in the literature. Full article

This study presents the decays of three components of velocity for a ship twin-propeller jet associated with turbulence intensities using the Acoustic Doppler Velocimetry (ADV) measurement and computational fluid dynamics (CFD) methods. Previous research has shown that a single-propeller jet consists of a zone of flow establishment and a zone of established flow. Twin-propeller jets are more complex than single-propeller jets, and can be divided into zones with four peaks, two peaks, and one peak. The axial velocity distribution is the main contributor and can be predicted using the Gaussian normal distribution. The axial velocity decay is described by linear equations using the maximum axial velocity in the efflux plane. The tangential and radial velocity decays show linear and nonlinear distributions in different zones. The turbulence intensity increases locally in the critical position of the noninterference zone and the interference zone. The current research converts the axial momentum theory of a single propeller into twin-propeller jet theory with a series of equations used to predict the overall twin-propeller jet structure. Full article