Normal Velocity Research Articles

Characteristic boundary layer evolution in globulitic solidification of alloys with interface curvature and attachment kinetics

The characteristic boundary layer evolution in globulitic solidification of alloys was investigated by using the Landau transformation method that takes into account attachment kinetics and interface curvature. The accuracy of the numerical solution was verified by comparing numerical results with an analytical solution without curvature and kinetic effects. Numerical results show that the increase of the kinetic coefficient results in the decrease of the value of the equilibrium interface liquid concentration, and the normal velocity of the interface was negatively correlated with the kinetic coefficient. We found that the thickness of the quasi-steady characteristic boundary layer is close to that of the unsteady one during globulitic solidification when the supersaturation is small. With the supersaturation increasing, it deviates from the unsteady one. This indicates that the kinetic effect cannot be ignored in the numerical simulations of rapid solidification. It is of practical significance to study the rapid solidification process and predict the microstructure.

Transient Characteristics of Three-Dimensional Flow in a Centrifugal Impeller Perturbed by Simple Pre-Swirl Inflow

The pre-swirl inflow generated by guide vanes could improve the hydrodynamic performances of centrifugal pumps as long as the inflow matches the patterns of internal flow of the impeller. In this work, we present a numerical investigation on the internal flow in a centrifugal impeller subjected to inflow artificially constructed with simple pre-swirling; unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are performed at the designed flow rate with five values of rotating velocity of the inflow, i.e., Urot/Uref = −0.5, −0.3, 0.0, 0.3 and 0.5, where Urot and Uref denote the rotating and normal velocity component at the entrance of the inflow tube, respectively. The primary objective of this work is to reveal the three-dimensional characteristics of internal flow of the impeller as influenced by the superimposed pre-swirl inflow, and to identify the propagation of inflow within the impeller. The numerical data are presented and analyzed in terms of the streamline fields, the distributions of various velocity components along the circumferential and axial directions, the pressure distribution and limiting streamlines on the surfaces of a blade. Numerical results reveal that separation occurs around the leading edge of the blades and occasionally at the trailing edge, and the internal flow is more uniform in the central region of the channels. A noticeable fluctuation of both radial and circumferential velocities is observed at the outlet of the impeller as it is subjected to counter-rotating inflow, and the greatest fluctuation is close to the hub instead of the middle channel and shroud as for the co-rotating inflow. The boundary layer flow of suction surface is more sensitive to the inflow; occasional small-scale separation bubble occurs on the suction surface around the leading edge for some blades, and reattachment of separated flow is reduced for the counter-rotating inflow.

Numerical and Experimental Research on Rectification Measures for a Contraction Diversion Pier in a Pumping Station

In order to improve the flow state of a forebay, a contraction diversion pier is discovered, the geometric parameters of which affect the improvement of the flow state. In this paper, the standard k-ε model in the computational fluid dynamics (CFD) numerical simulation method is used to research the flow state improvement of the forebay with a contraction diversion pier. In our research, the single factor method is used to analyze the influence of different geometric parameters. Then, the optimal geometric parameters of the contraction diversion pier are given. Results show that the contraction diversion pier can be used to concentrate the water flow. In the area where reflux is formed, the contraction diversion guides water flow along the diversion pier wall. In particular, when the retractable diversion pier is located in the middle of a reflux zone, the water backflow is effectively reduced, the flow state is improved, and the inlet condition of the pump is optimized. By comparing the cross-sectional streamlines, the velocity contour, the normal velocity uniformity of the longitudinal section, and the normal weighted mean angle, the optimal geometric parameters of the contraction diversion pier are obtained as follows: the distance from the contraction pier to the inlet sump is 0.1 L, the contraction angle is 20°, and the length of pier is 0.3 L.

Isogeometric Level Set-Based Topology Optimization for Geometrically Nonlinear Plane Stress Problems

This paper addresses geometrically nonlinear topology optimization using IsoGeometric Analysis (IGA) and Level Set Method (LSM) under plane stress assumptions. The IGA is employed to solve governing equations and accurately describe geometric modeling. The pointwise gradient-based sensitivity analysis is applied to derive the normal velocity of the Reaction–Diffusion Equation (RDE) to update the control net of the Level Set Function (LSF). The Generalized Displacement Control Method (GDCM) is used to obtain the equilibrium path based on the Total Lagrange (TL) formulation. A pointwise energy interpolation strategy is employed to avoid low-density instabilities. The exact Heaviside function is also applied to obtain a 0/1 manufacturable design. The objective is to maximize the total strain energy of structure, which is defined as the total external work within a specified displacement, while a certain volume of the design domain is considered. To demonstrate the ability and efficiency of the proposed method, several numerical examples are presented. By making comparisons, the results of both optimization algorithm and nonlinear analysis are shown to be in good agreement with the literature. Also, it is shown that obtained layouts are different from those in the linear behavior modeling due to considering buckling effects. In addition, linear and nonlinear final layouts are analyzed under large deformation assumption and the load–displacement curves are compared to illustrate the improvement of the objective function and final load. • Optimized topologies are parameterized using NURBS. • A pointwise energy interpolation strategy is employed to avoid low-density instabilities. • The control net of the design domain is updated by the reaction–diffusion equation. • Pointwise sensitivity analysis of the optimization problem is analytically derived. • 0/1 manufacturable design was performed using an exact (binary) Heaviside step function.

Analytic investigation of the compatibility condition and the initial evolution of a smooth velocity field for the Navier–Stokes equation in a channel configuration

A partial differential equation has usually a regular solution at the initial time if the initial condition is smooth in space, fulfills the governing equations and is compatible with the boundary condition. In the case of the Navier–Stokes equation, the initial velocity field must also be divergence–free. It is common belief that the initial condition is compatible with the boundary condition if the initial condition fulfills the boundary condition but this is not sufficient. Such a field does not necessarily fulfill the full compatibility condition of the Navier–Stokes equation. If the condition is violated, the solution is not regular at the initial time (). This issue has been known for a while but not in the full breadth of the engineering fluid dynamics community. In this paper, a practical calculation method is presented for checking the compatibility condition. Furthermore, a smooth initial condition is presented in a periodic channel flow that violates the compatibility condition and has therefore no smooth solution at the initial instant. The calculations were performed in an analytical framework. The results for a channel configuration show that in the absence of wall–normal velocity the condition is always fulfilled and the problem has a regular solution. If the wall–normal velocity component is non-zero, the condition is usually not fulfilled but exceptional cases, fulfilling the compatibility condition can be generated with optimization methods. The generation procedure of such a field is useful to provide correct initial conditions for such time-dependent numerical flow simulations, where the very first instances are important from an engineering point of view. The presented methods can provide insight about the applicability of the chosen initial conditions.

Free convection of temperature-dependent thermal conductivity based ethylene glycol-Al2O3 nanofluid in an open cavity with wall heat flux

The natural or free convection flow in an open cavity filled with ethylene glycol-Al2O3 nanofluid has been integrated numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) with the Graphics Process Unit (GPU) acceleration. The applications of this type of problem frequently appear in open-door ovens and refrigerators and in the cavities of central solar receptors. The ceiling and bottom walls of the cavity are thermally adiabatic. The right side of the cavity is fully opened while heat flux condition is imposed on its opposite wall. The thermal conductivity of the nanofluid varies with fluid temperature. Numerical simulations have been conducted for a fixed Prandtl number, Pr=16.6, with varying other controlling parameters, i.e., the Rayleigh number from Ra=105 to 107, and nanoparticle volume fraction from 0 to 5%. The streamlines, isotherms, mid-line temperature and velocity distributions, and the rate of heat transfer regarding the Nusselt number have been presented in this article. The isolines and tabular form give the local and total entropy generation due to the fluid friction and temperature gradients. The tangential and normal velocity components grow dramatically as Ra increases; however, the temperature diminishes with Ra. Also, the locally distributed Nusselt number increases in magnitude with nanofluids’ volume fraction and Rayleigh number. The total entropy enhances significantly for the augmentation of the nanoparticles volume fraction, and the entropy due to fluid friction dominates over the entropy generated by the temperature gradients.

Third-harmonic-assisted four-wave mixing in a chip-based microresonator frequency comb generation.

Microcombs generated in photonic integrated circuits can provide broadband and coherent optical frequency combs with a high repetition rate from microwave to terahertz. Coherent microcombs formed in normal group velocity dispersion microresonators usually have a flat-top temporal profile, called platicon. Here, we propose a novel scheme to generate platicon in Si3N4 microresonator with the assistance of third-harmonic generation. The nonlinear coupling between the fundamental and the third-harmonic waves that draws support from third-order sum/difference frequency generation provides a new mechanism to achieve the phase matching of four-wave mixing in normal dispersion microresonators. We show that single or multiple platicons can be obtained by changing the third-harmonic nonlinear coupling strength and phase matching condition for third-order sum/difference frequency generation. Our work provides a promising solution to facilitate coherent and visible microcomb generation in a pure χ(3) microresonator, which is potential for self-referencing combs and optical clock stabilization.

Vorticity amplification in wavy viscoelastic channel flow

Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. In Newtonian fluids, the vorticity induced by small surface undulations on the lower wall is advected by the background flow and diffuses into the fluid. When the fluid is viscoelastic, we identify new mechanisms by which significant vorticity perturbations can be generated in both inertialess and elasto-inertial channel flows. We focus on the case where the lengthscale of the surface distortion is much longer than the channel depth, where we find significant departure from plane shear (Page & Zaki, J. Fluid Mech., vol. 901, 2016, pp. 392–429) due to the non-monotonic base-flow streamwise-normal elastic stress. In inertialess flows, a purely elastic response results in streamlines deforming to match the bottom topography in the lower half the channel. However, the vanishing stress at the centreline introduces a blocking effect, and the associated $O(1)$ jump in normal velocity is balanced by a large-amplitude streamwise-oscillating ‘jet’ in a boundary layer, resulting in a localised, chevron-shaped vorticity perturbation field. In elasto-inertial flows, resonance between the frequency of elasto-inertial ‘Alfvén’ waves and the frequency apparent to an observer moving with the fluid results in vorticity amplification in a pair of critical layers on either side of the channel. The vorticity in both layers is equal in magnitude, to leading order in Weissenberg number, and as such the perturbation vorticity field penetrates the full channel depth even when inertia is dominant. The results demonstrate that long-wave distortions, which are relatively innocuous in Newtonian fluids, can drive a significant flow distortion in viscoelastic fluids for a wide range of parameter values.

Accuracy of clinical versus oculographic detection of pathological saccadic slowing

Saccadic slowing as a component of supranuclear saccadic gaze palsy is an important diagnostic sign in multiple neurologic conditions, including degenerative, inflammatory, genetic, or ischemic lesions affecting brainstem structures responsible for saccadic generation. Little attention has been given to the accuracy with which clinicians correctly identify saccadic slowing. We compared clinician (n = 19) judgements of horizontal and vertical saccade speed on video recordings of saccades (from 9 patients with slow saccades, 3 healthy controls) to objective saccade peak velocity measurements from infrared oculographic recordings. Clinician groups included neurology residents, general neurologists, and fellowship-trained neuro-ophthalmologists. Saccades with normal peak velocities on infrared recordings were correctly identified as normal in 57% (91/171; 171 = 9 videos × 19 clinicians) of clinician decisions; saccades determined to be slow on infrared recordings were correctly identified as slow in 84% (224/266; 266 = 14 videos × 19 clinicians) of clinician decisions. Vertical saccades were correctly identified as slow more often than horizontal saccades (94% versus 74% of decisions). No significant differences were identified between clinician training levels. Reliable differentiation between normal and slow saccades is clinically challenging; clinical performance is most accurate for detection of vertical saccade slowing. Quantitative analysis of saccade peak velocities enhances accurate detection and is likely to be especially useful for detection of mild saccadic slowing.

3-D pre-stack diffraction separation by extending the PWD method with parametrized local slope

SUMMARY Diffractions comprise the seismic response of subsurface geological discontinuities and thus can provide detailed geological information during 3-D seismic exploration. The separation of weak diffractions from specular reflections is challenging, especially when the diffractions and reflections have similar kinematical characteristics in the 3-D pre-stack case. Conventional separation methods often estimate the local slope based on optimization or the Hilbert transform, which directly depends on the distribution behaviour of seismic events and may lead to the aliasing effects of the hyperbolic reflected and diffracted slopes in the shot domain. In this study, a different method is employed: local slopes are parametrized and constrained to the normal moveout velocity and ray parameter, which can distinguish reflections and diffractions in the shot domain and enhance the stability and accuracy of local slopes. Interestingly, when the receiver line and the geological edge are coplanar, the corresponding edge diffractions and reflections exhibit extremely similar behaviour, rendering them indistinguishable. Considering this phenomenon, a 3-D pre-stack diffraction separation strategy is proposed based on the estimation of the local slopes in two orthogonal directions. Thus, the accurate local slope can be used for plane-wave destruction when separating diffractions in the 3-D pre-stack domain. Synthetic and field data applications demonstrate that the proposed separation strategy is effective and can obtain high-quality diffraction wavefields for detecting the subsurface discontinuous structure.

Uniqueness of Yudovich’s solutions to the 2D incompressible Euler equation despite the presence of sources and sinks

In 1962, Yudovich proved the existence and uniqueness of classical solutions to the 2D incompressible Euler equations in the case where the fluid occupies a bounded domain with entering and exiting flows on some parts of the boundary. The normal velocity is prescribed on the whole boundary, as well as the entering vorticity. The uniqueness part of Yudovich’s result holds for Hölder vorticity, by contrast with his 1961 result on the case of an impermeable boundary, for which the normal velocity is prescribed as zero on the boundary, and for which the assumption that the initial vorticity is bounded was shown to be sufficient to guarantee uniqueness. Whether or not uniqueness holds as well for bounded vorticities in the case of entering and exiting flows has been left open until 2014, when Weigant and Papin succeeded to tackle the case where the domain is a rectangle. In this paper we adapt Weigant and Papin’s result to the case of a smooth domain with several internal sources and sinks.

Acoustic radiation from random waves on plates

Controlling and simulating the sound radiating from complex structures is of importance in many engineering applications. We calculate the radiated acoustic power from plates with diffuse bending vibrations. We characterise the diffuse field by a two-point correlation function (CF) of normal velocities. Given the relation between field–field CFs and ray-dynamical phase space densities, the approach taken here offers a basis for coupling structure borne ray-tracing techniques with acoustic radiation. At the same time, it caters for stochastic, noisy driving of such systems. The results for the radiation efficiency of a plate are presented in an asymptotic form analogous to the Weyl formula for the density of states. Leading contributions from the plate interior and its boundary are derived, with corner corrections also being given for particular boundary conditions and right-angled corners. A notable feature of this analysis is that the bulk contribution vanishes below a critical frequency, and the asymptotic estimate of radiated power then leads with a boundary contribution. This is shown to agree well with a more traditional calculation based on modal analysis in the special case of a rectangular plate.

A Robin-Type Domain Decomposition Method for a Novel Mixed-Type DG Method for the Coupled Stokes--Darcy Problem

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes-Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the stress-velocity formulation is employed for the Stokes equations, where the symmetry of stress is strongly imposed. The staggered DG method is exploited to discretize the Darcy equations. As such, the discrete formulation can be easily adapted to account for the Beavers-Joseph-Saffman interface conditions without introducing additional variables. Importantly, the continuity of normal velocity is satisfied exactly at the discrete level. A rigorous convergence analysis is performed for all the variables. Then we devise and analyze a domain decomposition method via the use of Robin-type interface boundary conditions, which allows us to solve the Stokes subproblem and the Darcy subproblem sequentially with low computational costs. The convergence of the proposed iterative method is analyzed rigorously. In particular, the proposed iterative method also works for very small viscosity coefficient. Finally, several numerical experiments are carried out to demonstrate the capabilities and accuracy of the novel mixed-type scheme, and the convergence of the domain decomposition method.

Water wave interaction with dual unequal horizontal flexible porous barriers using integral equations

ABSTRACT Under the assumption of linear wave theory, this work investigates the interaction of surface gravity waves with two asymmetric horizontal flexible porous barriers. Three types of barriers are considered, namely, (i) step barriers, (ii) partially overlapped barriers and (iii) fully overlapped barriers. Green's integral theorem and the boundary condition on the barriers are utilised to produce four integral equations for functions related to potential difference and normal velocity of fluid across the barriers which are solved numerically by an expansion-collocation method. As a result, the role of asymmetric flexible porous barriers with an additional comparison between dual and single horizontal flexible porous barriers is studied by analysing numerical solutions of different hydrodynamic quantities. This study shows that the upper barrier plays a major role compared to the lower one in the propagation of surface waves. The current analysis is validated by reviving previous results and utilising energy balance relationship.

Experimental Validations of Reconstructed Excitation Forces Acting Inside a Solid Enclosure. Part I: Exterior Region

This paper presents the experimental validations of reconstructing the characteristics of the excitation forces that act inside a vibrating structure, which includes the location, type, amplitude, and spectrum, based on a single set of measurements of the normal surface velocity on the exterior surface by using the modified Helmholtz Equation Least Squares (HELS) method, as if one could see through this solid structure. Phase I of this paper shows the reconstruction of the vibroacoustic responses in the exterior region of the structure, including the field acoustic pressure, the surface acoustic pressure, the normal surface velocity or Operational Deflection Shape (ODS), the normal component of the time-averaged acoustic intensity, and the time-averaged acoustic power. Phase II of this paper illustrates the reconstruction of the excitation forces with the fluid-loading effects taken into consideration, based on the vibroacoustic responses reconstructed in the exterior region. The significance of the study, namely, the interrelationships among the excitation force, structural vibration, and acoustic radiation is discussed. The knowledge thus acquired may be important for engineers to analyze various complex noise and vibration issues in practice and to come up with the most cost-effective noise and vibration mitigation strategies.

Detecting Quench in HTS Magnets With LTS Wires—A Theoretical and Numerical Analysis

Protecting a high temperature superconducting (HTS) magnet from a quench event is a challenging task. Because of the slow normal zone propagation velocity, the long reliable quench detection method by directly monitoring coil voltage may not be timely for HTS anymore, leaving HTS magnets under danger of overheating. Using a NbTi low temperature superconducting (LTS) wire to detect quench in coils wound with ReBCO HTS tapes have recently been experimentally proved, yet a theoretical study is still needed to further develop this technique and make it prepared to be applied more generally in high field magnets. In this manuscript, we have demonstrated that it is the significant difference in the temperature dependence of critical current between LTS and HTS but not the normal zone propagation velocity (NZPV), that makes LTSs good quench detectors. Simulations show that LTS quench detectors should have low matrix fraction or high matrix resistivity. At last, at field up to 15 T or 20 T, Nb3Sn is proven to be a good quench detector.

A CFD-DEM investigation of powder transport and aerosolization in ELLIPTA® dry powder inhaler.

We have performed Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations of air and particles in a commercial ELLIPTA® inhaler. We simulated the fluidization, deagglomeration and transport of carrier and API particles, with two realistic inhalation profiles that are representative of moderate asthma and very severe COPD patients, and three different mouthpiece designs. In each of the ten cases simulated, we determined the fine particle fraction (FPF) in the stream leaving the mouthpiece, the temporal evolution of the spatial distribution of the particles, the mean air (slip) velocity seen by the carrier particles, and the average numbers and normal impact velocities of carrier-carrier and carrier-wall collisions inside the inhaler. In the cases examined, the air-carrier and carrier-carrier interactions affected the FPF, while the carrier-wall interactions were too infrequent to have a substantial effect. The simulations revealed the benefit of loading both blisters even when only a single medication needs to be delivered.

Experimental Validations of Reconstructed Excitation Forces Acting Inside a Solid Enclosure. Part II: Interior Region

Part II of this paper discusses experimental validations of the reconstructed excitation forces acting inside a vibrating structure with the fluid-loading effect taken into consideration. Specifically, the characteristics of the excitation forces such as their locations, types, amplitudes, and spectra are reconstructed by using the modified Helmholtz Equation Least Squares (HELS) method, based on a single set of measurements of the normal surface velocity on the exterior surfaces, as if one could see through such a solid structure. Since the fluid-loading effect has a direct impact on the vibration responses of a structure, it is not possible to derive analytic solutions to vibration responses of the structure. Therefore, numerical solutions are sought by using the boundary element method (BEM). The fluid-loading effect, a.k.a., the reverberation sound field inside the structure is calculated based on the absorption coefficients and surface areas of the interior objects. The reconstructed excitation forces are then compared to the benchmark values and satisfactory agreements are obtained.

Quench Protection Study of a Large Scale REBCO Magnet With Additional Copper Tapes

REBCO coated conductors (CCs) are expected to be applied to high field magnets due to their high longitudinal tensile strength and excellent critical current characteristics in high fields. For large scale magnets with large stored energy, quench protection is a key issue. Although various quench protection methods have been proposed for REBCO magnets, the most traditional and straight forward approach is to increase the copper stabilizer and reduce the current density. This approach leads to a significant increase in conductor length to generate a required magnetic field in case a small bore diameter magnet, while the conductor increase would not be serious in case a large bore diameter one. Based on this approach, we have successfully fabricated a practical cryogen-free superconducting magnet (CSM) with a large bore of 200 mm-diameter and a central field of 5 T using REBCO CCs laminated with 0.3 mm-thick copper tapes. For further study, we designed a MJ-class 10 T-CSM with the same inner-diameter as the 5 T-CSM and investigated the feasibility of the magnet through quench tests in this study. We conducted quench tests on short samples of copper-plated REBCO CCs with copper tape soldered on different surfaces, and quench tests on a small coil assuming an energy recovery method with external resistance. In the short sample tests, it was found that the temperature rise was suppressed regardless of the position of the copper tape lamination, and the normal zone propagation velocity was improved when the copper tape was laminated to the substrate side. In the small coil tests, the decay time constant after shutdown was varied to find the conditions that can protect the magnet with high stored energy. We confirmed that quench protection of 10 T-CSM was feasible under practical conditions.

Numerical and Experimental Study on Thermal Stability of BSCCO/REBCO Hybrid Tapes

This paper studies the thermal stability of BSCCO (Bi-2223) /REBCO hybrid tapes with different stacking methods under various operating currents in liquid nitrogen (LN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) bath. The thermal stability of single REBCO tape and BSCCO tape are also studied as the comparison. A 3D numerical model considering the anisotropic thermal conductivity is established to calculate the normal zone propagation velocity (NZPV) and minimum quench energy (MQE) of different hybrid tapes, and the temperature distributions of the tapes are obtained as well. The experiments of thermal stability of single tape and RB hybrid tape are also carried out. Results show the hybrid tape has better thermal stability than the REBCO tape and faster NZPV than the BSCCO tape.