Tangential Flux Research Articles

On the flow structures and hysteresis of laminar swirling jets

In this paper different flow patterns of an annular jet with a stepped-conical nozzle as well as the transition between these patterns are numerically investigated as a function of the swirl number S which is the ratio of tangential momentum flux to axial momentum flux. The Reynolds number of the jet based on the axial velocity and the nozzle hydraulic diameter is 180. The 3D Navier Stokes equations are solved using the direct numerical simulation. Four different flow patterns are identified and their associated flow structures are discussed. Starting from an annular jet at zero swirl, spinning vortices around the central axis originate with increasing swirl. As the swirl is further increased, the onset of vortex breakdown occurs, followed by jet attachment to the nozzle. Decreasing the swirl number back from this flow pattern, the Coanda effect near the nozzle outlet creates a wall jet. This wall jet remains till the decreasing swirl number equals to zero, showing hysteresis in flow patterns between an increase and a subsequent decrease in swirl. The determined flow states are experimentally validated. Potential applications related to these flow patterns and their hysteretic behavior are also briefly discussed.

A Study on Magnetic Decoupling of Compound-Structure Permanent-Magnet Motor for HEVs Application

The compound-structure permanent-magnet (CSPM) motor is used for an electrical continuously-variable transmission (E-CVT) in a hybrid electric vehicle (HEV). It can make the internal combustion engine (ICE) independent of the road loads and run in the high efficiency area to improve the fuel economy and reduce the emissions. This paper studies the magnetic coupling of a new type of CSPM motor used in HEVs. Firstly, through the analysis of the parameter matching with CSPM in the HEV, we receive the same dynamic properties’ design parameters between the CSPM motor and the THS (Toyota Hybrid System) of the Toyota Prius. Next, we establish the equivalent magnetic circuit model of the overall and the secondary model considering the tangential and radial flux distribution in the outer rotor of the CSPM motor. Based on these two models, we explore the internal magnetic coupling rule of the CSPM motor. Finally, finite element method analysis in 2D-ansoft is used to analyze the magnetic field distribution of the CSPM motor in different operation modes. By the result of the finite element method analysis, the internal magnetic decoupling scheme is put forward, laying the theoretical foundation for the further application of the CSPM motor in HEVs.

Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow

The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.

Experimental validation of an enhanced permeance network model for embedded magnet synchronous machines

This paper presents an enhanced permeance network model (PNM) for embedded permanent magnet synchronous machines. PNMs are characterized by very fast and accurate results. This approach overcomes some weaknesses associated to analytical models, such as the difficulty of accurately predicting the embedded magnet machines behavior or taking into account the nonlinear behavior of the magnetic materials. The proposed model is a parameterized, rotor motion accounting, nonlinear PNM capable of computing the radial and the tangential airgap fluxes, the back electromotive force and the electromagnetic torque. A fully sensorized, 75kW PMSM has been designed and manufactured in order to perform an experimental validation. The validation has also been supported by finite-element analysis (FEA) in FLUX2D®. The experimental results confirmed the accuracy of the proposed model and the possibility of avoiding the time-consuming FEA in PMSM designs.

Flamelet characteristics at the leading edge and through the flame brush of statistically steady incompressible turbulent premixed flames

Conditional analysis is performed on statistical behavior of the flamelet characteristics at the leading edge and through the flame brush of incompressible turbulent premixed flames. The effective Lewis number is equal to unity with no stretch effect associated with differential diffusion. It is shown that the flamelet thickness, δf, is a crucial parameter to determine the local displacement speed, Sd, as well as the global turbulent burning velocity, ST. There hold asymptotic relationships for ST and conditional velocities at the leading edge in the statistically steady state. Sd is correlated with finite δf not in terms of stretch, but through independent effects of tangential strain rate and curvature. Sd and δf show strong correlations with curvature due to significant influence of tangential flux, while they show weak correlations dependent on the location in a flamelet with tangential strain rate. Flamelets tend to thicken according to the gradient of Sd due to focusing or defocusing of c transport for both positive and negative curvatures. The range of Sd is scaled by the tangential component, Sdt, with additional contribution of the normal Sdn component due to δf varying with curvature. Variation of Sdt is given in terms of the product of curvature and molecular diffusivity in the reaction–diffusion layer retaining a relatively invariant structure under turbulence. The stretched laminar flamelet model needs to be complemented by the additional effects of tangential flux and variation of finite δf in fully turbulent premixed flames.

Energetic particles, tangential discontinuities, and solar flux tubes

AbstractThis study examines the probable sources of sharp changes in the flux of energetic particles (EPs) in the solar wind. Data acquired by the ACE Low Energy Magnetic Spectrometer sensors during 1999 were used to identify EP boundaries that were not located at interplanetary shocks or caused by intermittent connection to the Earth's bow shock. It was found that at least 68%, and probably 80%, of such boundaries occur at significant changes in the plasma and magnetic field in the solar wind. Those changes are consistent with crossing preexisting tangential discontinuities or flux tube boundaries rather than by local MHD turbulence or time‐dependent bursts of acceleration. Because some of the EP boundaries would not have been detected by Borovsky's (2008) analysis of flux tube boundaries, it is concluded that such boundaries in the solar wind are at least 30% more prevalent than previously suggested. The result can also be used to explain some observations of localized variations in EP flux both ahead of and behind the interplanetary shocks where particle acceleration occurred without requiring local acceleration.

Free surface Neumann boundary condition for the advection–diffusion lattice Boltzmann method

The main objective of this paper is the derivation and validation of a free surface Neumann boundary condition for the advection–diffusion lattice Boltzmann method. Most literature boundary conditions are applied on straight walls and sometimes on curved geometries or fixed free surfaces, but dynamic free surfaces, especially with fluid motion in normal direction, are hardly addressed. A Chapman–Enskog Expansion is the basis for the derivation of the advection–diffusion equation using the advection–diffusion lattice Boltzmann method and the BGK collision operator. For this numerical scheme, a free surface Neumann boundary condition with no flux in normal direction to the free surface is derived. Finally, the boundary condition is validated in different static and dynamic test scenarios, including a detailed view on the conservation of the diffusive scalar, the normal and tangential flux components to the free surface and the accuracy. The validation scenarios reveal the superiority of the new approach to the compared literature schemes, especially for arbitrary fluid motion.

Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion

This work demonstrates that in advection–diffusion Lattice Boltzmann schemes, the local mass-conserving boundary rules, such as bounce-back and local specular reflection, may modify the transport coefficients predicted by the Chapman–Enskog expansion when they enforce to zero not only the normal, but also the tangential boundary flux. In order to accommodate it to the bulk solution, the system develops a Knudsen-layer correction to the non-equilibrium part of the population solution. Two principal secondary effects—(i) decrease in the diffusion coefficient, and (ii) retardation of the average advection velocity, obtained in a closed analytical form, are proportional, respectively, to freely assigned diagonal weights for equilibrium mass and velocity terms. In addition, due to their transverse velocity gradients, the boundary layers affect the longitudinal diffusion coefficient similarly to Taylor dispersion, as they grow as the square of the Péclet number. These numerical artifacts can be eliminated or reduced by a proper space distribution of the free-tunable collision eigenvalue in two-relaxation-time schemes.

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

This paper at first shows the details of finite volume-based lattice Boltz- mann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conser- vation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parame- ter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three mod- els for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test prob- lems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV- LBM simulation of hypersonic flows. AMS subject classifications: 76T10

Tip-splitting instability in directional solidification based on bias field method**Project supported by the National Basic Research Program of China (Grant No. 2011CB610401), the National Natural Science Foundation of China (Grant No. 51371151), and the Free Research Fund of State Key Laboratory of Solidification Processing, China (Grant No. 100-QP-2014).

Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width , which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.

Dewetting films with inclined contact lines.

A partially wetting plate withdrawn from a liquid reservoir causes the deposition of a liquid film that is characterized by inclined contact lines. It has been experimentally indicated that the normal component of the contact-line velocity relative to the plate remains constant and is independent of the inclination angles, a fact that has never theoretically been justified. We demonstrate, in the framework of lubrication theory, that the speed-angle independence is only approximate and the normal velocity actually exhibits a weak decrease with the inclination angle of the contact line. This correlation is attributed to the variation of the effective separation of microscopic and macroscopic length scales. In addition, the inclination of the contact line results in a tangential flux of the liquid, which is confined in the vicinity of the contact line. Simple scaling relations are provided for both the normal velocity and the tangential flux.

Сравнение статических моделей явнополюсных двигателей с реактивным ротором

Two substitution schemes for one pole pitсh of stator of the motor with a reluctance rotor are considered in the report. The schemes are made in consideration of magnetic flux branching at the edges of the stator pole tips either in the radial direction or in the tangential direction, respectively. The comparison of calculated and experimental results of torque determination allows to make a conclusion about the greater reliability of the scheme with the tangential magnetic flux.

Use of Ceramic Membrane for Indigo Separation in Effluent from Textile Industry

The production of fabrics is one important sectors of the national economy, especially in jeans production. During dyeing step, in the production of jeans, it is generate a large amount of wastewater rich in indigo, a strong blue dye that when released directly into the environment is responsible for several environmental impacts. The aim of this work is to study the use of microfiltration ceramic membranes for indigo separation in effluents from textile industry. Initially the ceramic membranes were characterized in relation to the pore size and tangential flux. It was produced an indigo solution whose concentration and composition similar to the effluent of textile industry. The solution was characterized and submitted to a filtration through ceramic membranes by tangential flow, by applying a pressure of 3 Bar. At the end it was verified that 99% of the indigo was retained.

Study of the Influence of Granite Residue in Different Compositions to Prepare Ceramic Membranes

The exploitation and processing of granite is responsible for generating large quantities of residue, mainly in the sawing step where is producing a dark color mud that is generally discharged directly in the environment without any treatment. The use of granite residue in the production of red ceramic has been widely studied and has shown promising results. The aim of this work is to verify the incorporation of granite residue in the preparation of tubular ceramic membrane in substitution of quartz. In this research it was done the characterization of the raw materials, the membrane preparation with different amount of granite residue and characterization of the membranes by scanning electron microscopy, mercury porosimetry and tangential flux measurements. The results showed that the changing in 10% of granite residue amount in the ceramic body was enough to change the morphological characteristics of the membranes.

Temperature and heat flux fast estimation during rolling process

Monitoring and controlling flatness during the rolling process becomes critical for ensuring the product quality. Flatness defects are due to highly three-dimensional phenomena. Indeed, strips with different widths are rolled during the same campaign and cooling systems are heterogeneous along the axial direction to modify the thermal expansion of the roll. Therefore this paper presents a fully three-dimensional inverse analytical method to determine the temperature field and heat fluxes (especially at the surface of the roll) by interpreting measurements of temperature done with several thermocouples fully embedded in the roll body and aligned along the axial direction. Since the method is dedicated to on-line interpretation and designed as a tool for adapting the rolling parameters during the rolling process, iterative methods are not studied to avoid long computation times, which justifies the development of an analytical solution of the problem. The computation time displayed by Scilab 5.3 with a quadcore 2.8 GHz is around 0.5 s by cycle for accurate computation and 0.07 s by cycle for rough computation. This paper improves a previous work (2D and relying on four assumptions designed for the prediction of wear). In the present contribution the 3D unsteady heat equation of the rotating roll is solved analytically with only one assumption in order to deal with the restriction of the measurement system (i.e., measurement according to successive times). Therefore not only radial and tangential heat fluxes are taken into account but also axial heat flux. The solution is validated by comparing the outputs of the method and some prescribed analytical temperature fields. Good agreement is obtained. Noise sensitivity is estimated by adding artificial random numbers to the inputs, and good accuracy is observed. Moreover sensitivity to sensor depth is estimated and demonstrated to be not compromising.

Nonequilibrium gaseous heat transfer in pressure-driven plane Poiseuille flow

Nonequilibrium heat and mass transfer in a pressure-driven plane Poiseuille flow is investigated using the direct simulation Monte Carlo method from the early slip to the free molecular regime. Our investigations reveal several nonintuitive, nonequilibrium thermal flow patterns, including expansion cooling near the walls, a nonconstant pressure profile, and counter-gradient heat transfer along the channel center-line. A bimodal trend in the tangential heat flux is found in the slip and the early transition regime. In the upper transition and free molecular regime, the net heat flow in the entire channel is largely unidirectional and in the opposite direction of mass flow. However, in the slip and the early transition regime, a two-way heat flow is observed in the channel as the normal heat flux profile plays a key role in determining the net gaseous heat flow direction. Moreover, the heat flow rate profile exhibits a maximum value at an intermediate value of Knudsen number. The effects of incomplete surface accommodation on nonequilibrium heat flow are also investigated in this work. It is shown that for very low values of the accommodation coefficient, the gaseous heat flow direction is reversed and is consistently in the direction of mass flow.

Analytical Calculation Model of Air-Gap Magnetic Field for Claw Pole Machine with Outer PM Rotor

In view of the time consuming and sensitive to finite element meshes, the finite element method is not suitable for claw pole machine with outer permanent magnet rotors with complicated and asymmetric 3D structure. A new analytical calculation model based on air-gap magnetic field analysis in polar coordinates is proposed. According to boundary conditions, the radial and tangential flux density is obtained by using the Fourier’s series, and then the cogging torque and no load EMF is calculated. In order to verify the accuracy of the analytical method, the finite element analysis is finished. Moreover, one prototype is manufactured and measured also. The analytical results well agree with those obtained by the FEM and experiments, confirmed the feasibility of this method.

Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction

For highly charged dielectric surfaces, the asymptotic structure underlying electrokinetic phenomena in the thin-double-layer limit reshuffles. The large counterion concentration near the surface, associated with the Boltzmann distribution in the diffuse layer, supports appreciable tangential fluxes appearing as effective surface currents in a macroscale description. Their inevitable nonuniformity gives rise in turn to comparable transverse currents, which, for logarithmically large zeta potentials, modify the electrokinetic transport in the electroneutral bulk. To date, this mechanism has been studied only using a weak-field linearization. We present here a generic thin-double-layer analysis of the electrokinetic transport about highly charged dielectric solids, which is not restricted to weak fields. We identify the counterion concentration amplification with the emergence of an internal boundary layer--within the diffuse part of the double layer--characterized by distinct scaling of ionic concentrations and electric field. In this multiscale description, surface conduction is conveniently localized within the internal layer. Our systematic scheme thus avoids the cumbersome procedure of retaining small asymptotic terms which change their magnitude at large zeta potentials. The electrokinetic transport predicted by the resulting macroscale model is inherently accompanied by bulk concentration polarization, which in turn results in nonlinear bulk transport. A novel fundamental subtlety associated with this intrinsic feature, overlooked in the weak-field approximation, has to do with the ambiguity of the "particle zeta potential" concept: In general, even uniformly charged surfaces are characterized by a nonuniform zeta-potential distribution. This impairs the need for a careful identification of the dimensionless number representing the transition to large zeta potentials.

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

AbstractThis paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.

A Galerkin projection technique for the evaluation of potential derivatives on a smooth boundary in 2D BEM

Abstract A new simple and general technique for potential gradient recovery along the boundary in two-dimensional BEM is introduced and studied numerically. This technique is based on generalized Galerkin projections, and its basic formulation corresponds to a least-squares method. In preliminary numerical tests for Dirichlet and Neumann problems on smooth boundaries, this technique shows excellent accuracy. The normal flux is evaluated more accurately than direct BEM results, and the tangential flux values are calculated more accurately than with a local averaging technique.