Top-hat Distribution Research Articles

Effect of concentric intensity distributions on spatter formation in full penetration welding of high-alloy steels

Welding of high-alloy steels results in spatter formation addressing high welding speeds above 8 m/min, i.e., the seam quality is significantly reduced due to material losses and adhering spatter. A reduction of spatter can be addressed by using concentric intensity distributions consisting of core and ring, by affecting melt and metal vapor flow. In this paper, the understanding of spatter formation on sheet top and bottom side is significantly enhanced for full penetration welds of AISI 304. Therefore, different concentric intensities and tophat distributions were systematically studied and compared. Fundamental interactions between concentric intensity distributions and spatter formation during full penetration welding were determined and summarized in model concepts. In particular, spatter formation can be reduced on both sheet sides using a concentric intensity distribution due to a smaller keyhole geometry with a smaller angle of inclination of the keyhole front.

Simultaneous occurrence of four magnetospheric wave modes and the resultant combined scattering effect on radiation belt electrons

We report a representative concurrent event of four wave modes at <italic>L</italic> ≈ 5.0, including electrostatic electron cyclotron harmonic (ECH) waves, exohiss, magnetosonic (MS) waves, and electromagnetic ion cyclotron (EMIC) waves, based on the observations from Van Allen Probe A on October 15, 2015. The diffusion coefficients induced by these waves are calculated by using both the Full Diffusion Code and test particle simulations. Moreover, the scattering effects of these waves on energetic electrons are simulated by using a two-dimensional Fokker–Planck diffusion model. The results show that ECH waves mainly scatter low-pitch-angle (&lt; 20°) electrons at 0.1–10 keV; exohiss can significantly scatter hundreds of kiloelectron volt electrons to form a reversed energy spectrum; MS waves mainly affect high-pitch-angle electrons (&gt; 60°); and EMIC waves scatter only &gt; 5 MeV electrons. The combined scattering effects of exohiss and MS waves are stronger than those of exohiss alone. The top-hat pitch angle distributions produced by exohiss are relaxed after adding the effect of MS waves. Because the energies of electrons scattered by ECH waves and EMIC waves are much lower and higher than those scattered by exohiss and MS waves, respectively, the combined scattering effects with the addition of ECH and EMIC waves show little difference from the results for the combination of MS waves and exohiss. These results suggest that distinct wave modes can occur simultaneously and scatter electrons in combination or individually, which requires careful consideration in future global simulations of the complex dynamics of radiation belt energetic electrons.

Simulation of laser-induced retinal thermal injuries for non-uniform irradiance profiles and the applicability of the laser safety standard

Significance: A validated biophysical computer model simulating retinal thermal damage thresholds is used to investigate elongated retinal images. The International Commission on Non-Ionizing Radiation Protection Guideline and the laser safety standard IEC 60825-1:2014 include a method for averaging non-uniform extended sources, however, there are no studies that have examined the applicability in detail. Our study represents a method that can also support future research in the field of eye safety. Aim: As there is currently no experimental data available for non-uniform irradiance profiles, the calculation procedure given in the laser safety standard is derived from symmetric retinal images. We aim to verify this calculation procedure for such profiles on the retina in the thermal hazard regime. Approach: A three-dimensional computer model, which solves the heat transfer equation and the Arrhenius equation describing the denaturation of the proteins in the retina, is used to simulate the threshold values for the retinal thermal injury. Three different non-uniform irradiance profiles, elliptical Gaussian, elliptical top-hat, and rectangular top-hat distributions, are investigated for a wavelength of 530 nm. The profiles are varied in their sizes and simulated for different single-pulse durations. By applying the laser safety standard, the maximum allowed energies are calculated and divided by the corresponding threshold values to obtain the reduction factor (RF) which is a crucial parameter. Results: Due to the thermal behavior in the retinal tissues, the Gaussian irradiance profiles yield larger threshold values than both top-hat profiles. Furthermore, the ratio between the threshold values and the maximum allowed energies are found to be the lowest for the Gaussian profiles. Conclusion: The simulated retinal thermal injury thresholds for the three investigated non-uniform irradiance profiles show larger RFs than the minimum RF found for symmetric profiles. This supports the applicability of the evaluation scheme of the laser safety standard for non-uniform retinal images.

Universal dynamics in the expansion of vortex clusters in a dissipative two-dimensional superfluid

A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters with thermal friction, and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is an expanding Rankine vortex (i.e.~top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics, and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as $N\sim 11$ vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.

A Wake Modeling Paradigm for Wind Farm Design and Control

Wake models play an integral role in wind farm layout optimization and operations where associated design and control decisions are only as good as the underlying wake model upon which they are based. However, the desired model fidelity must be counterbalanced by the need for simplicity and computational efficiency. As a result, efficient engineering models that accurately capture the relevant physics—such as wake expansion and wake interactions for design problems and wake advection and turbulent fluctuations for control problems—are needed to advance the field of wind farm optimization. In this paper, we discuss a computationally-efficient continuous-time one-dimensional dynamic wake model that includes several features derived from fundamental physics, making it less ad-hoc than prevailing approaches. We first apply the steady-state solution of the model to predict the wake expansion coefficients commonly used in design problems. We demonstrate that more realistic results can be attained by linking the wake expansion rate to a top-down model of the atmospheric boundary layer, using a super-Gaussian wake profile that smoothly transitions between a top-hat and Gaussian distribution as well as linearly-superposing wake interactions. We then apply the dynamic model to predict trajectories of wind farm power output during start-up and highlight the improved accuracy of non-linear advection over linear advection. Finally, we apply the dynamic model to the control-oriented application of predicting power output of an irregularly-arranged farm during continuous operation. In this application, model fidelity is improved through state and parameter estimation accounting for spanwise inflow inhomogeneities and turbulent fluctuations. The proposed approach thus provides a modeling paradigm with the flexibility to enable designers to trade-off between accuracy and computational speed for a wide range of wind farm design and control applications.

Evaluation of fluences and surface characteristics in laser polishing SKD 11 tool steel

The work applied a continuous-wave laser beam from a multimode fiber laser to study the polishing effect. Three kinds of surface morphologies were acquired by fast-speed (FS) & lower-speed (LS) wire electrical discharge machining (EDM), and milling processing methods on SKD11 tool steel. Then influence of laser fluence on the polished surface characteristics was analyzed. The results showed that surface roughness parameters (Ra, Rz, Rt, and Sa) were significantly affected by this effect. With the increasing laser fluence, the polished surface underwent a comprehensive topographical evolution from superficial surface melting to surface over-melting. The improvements by FS-EDM, LS-EDM, and milling in roughness were 86.83, 90.70 and 86.07%, respectively. The corresponding laser fluences were 14.26 , 12.73 and 13.55 J/mm2, indicating that LS-EDM tool steel surface has the optimal polishing effect. The comparative statistical results of the bearing area curve, bidirectional reflectance distribution function, and power spectral density from the LS-EDM surfaces showed the optimal polishing results. In addition, all the pre-prepared surfaces could be polished to Ra < 0.5 μm using high polishing velocities. These findings signified that laser beam with top-hat distribution has a great potential for high-efficiency polishing of tool steel surfaces.

Theoretical Modeling of Vertical-Axis Wind Turbine Wakes

In this work, two different theoretical models for predicting the wind velocity downwind of an H-rotor vertical-axis wind turbine are presented. The first model uses mass conservation together with the momentum theory and assumes a top-hat distribution for the wind velocity deficit. The second model considers a two-dimensional Gaussian shape for the velocity defect and satisfies mass continuity and the momentum balance. Both approaches are consistent with the existing and widely-used theoretical wake models for horizontal-axis wind turbines and, thus, can be implemented in the current numerical codes utilized for optimization and real-time applications. To assess and compare the two proposed models, we use large eddy simulation as well as field measurement data of vertical-axis wind turbine wakes. The results show that, although both models are generally capable of predicting the velocity defect, the prediction from the Gaussian-based wake model is more accurate compared to the top-hat counterpart. This is mainly related to the consistency of the assumptions used in the Gaussian-based wake model with the physics of the turbulent wake development downwind of the turbine.

Diffusion Combustion of a Hydrogen Microjet at Variations of its Velocity Profile and Orientation of the Nozzle in the Field of Gravitation

ABSTRACTExperimental data on diffusion combustion of round hydrogen microjets with a parabolic and a “top-hat” mean velocity profiles at the nozzle exit at different spatial orientation of the microjets are reported. Most of all, we are interested in the behavior of the so-called «bottleneck flame region» of the jet and its contribution to the diffusion combustion. As is found, in the cases of the jet velocity opposite and orthogonal to the direction of the gravitational force, the main features of combustion are practically the same. Otherwise, at the velocity vector matching the direction of the gravitational force, the combustion characteristics become much different. Combustion in the «bottleneck flame region» is found to be more stable at the parabolic profile while the stability of combustion is reduced at the top-hat velocity distribution at the nozzle exit. Then, the flame detachment occurs in the absence of the «bottleneck flame region» and the microjet combustion is terminated at a much higher velocity. An inversion of the dependence l/d = f(U0) is observed at the transition from the parabolic to the top-hat velocity profile of the jet. The ratio of the «bottleneck flame region» size (l) to the nozzle exit diameter (d) is l/d. The nozzle heating is shown to have a profound effect on the microjet combustion.

Microstructure evolution of 316L produced by HP-SLM (high power selective laser melting)

New generation of selective Laser Melting (SLM) machines are evolving towards higher power lasers as well as multi laser systems in order to increase the productivity. The increase in laser power and the modification of the laser power distribution leads to microstructural and mechanical property variations that are still not well understood.This work aims at better understanding the interaction of a 1 kW top-hat power distribution laser on a well know material, 316 L stainless steel. The influence of texture and microstructure on relative density and crack density, when varying scan rotation, was evaluated. The high power (HP) laser and low power (LP) laser were compared with respect to microstructure and mechanical properties. HP leads to an increase in morphological and crystallographic texture together with a coarsening of the cell structure in contrast to the more random and finer cells found in LP processed material. Hot isostatic pressing was applied as a post-process treatment in order to close remaining pores and cracks. This helped in achieving higher elongations for LP and HP processed materials, while competitive mechanical properties to the 316 L material specifications were obtained in both cases.

A High-Energy, 100 Hz, Picosecond Laser for OPCPA Pumping

A high-energy diode-pumped picosecond laser system centered at 1064 nm for optical parametric chirped pulse amplifier (OPCPA) pumping was demonstrated. The laser system was based on a master oscillator power amplifier configuration, which contained an Nd:YVO4 mode-locked seed laser, an LD-pumped Nd:YAG regenerative amplifier, and two double-pass amplifiers. A reflecting volume Bragg grating with a 0.1 nm reflective bandwidth was used in the regenerative amplifier for spectrum narrowing and pulse broadening to suit the pulse duration of the optical parametric amplifier (OPA) process. Laser pulses with an energy of 316.5 mJ and a pulse duration of 50 ps were obtained at a 100 Hz repetition rate. A top-hat beam distribution and a 0.53% energy stability (RMS) were achieved in this system.

Modeling of thermal lensing in a [1 1 1]-cut Nd:YAG rod with temperature-dependent parameters and different pumping profiles

Temperature dependences of the thermo-optical coefficients of YAG crystals are often neglected when thermal lensing in laser rods is investigated, though their influence is very significant. It is especially significant for transversally non-uniform thermal loading. An analytical solution of the heat transfer equation with only the radial heat flow is found in the integral form, which is very convenient for numerical simulations. Uniform, top-hat, parabolic, Gaussian, super-Gaussian and annular heat source distributions are used in the calculations. The generalization of the thermally-induced refractive index change for long enough [1 1 1]-cut YAG rods to the case of temperature-dependent YAG parameters is developed and applied to the calculation of the corresponding optical path differences. Different definitions of the optical power of the aberrated thermal lens (TL) are discussed in detail. It is shown that for each of the heat source distributions, the temperature dependences of the YAG parameters significantly increase (1.5–1.8 times) the paraxial optical power of the induced TL.

Moment method for unsteady flows with heterogeneous condensation

Abstract The classic moment method for homogeneous condensation is extended to unsteady flows with heterogeneous condensation. The moments are defined on the size distribution function of the droplet including the particle core and the liquid layer. The simple instantaneous-wetting model is used for the heterogeneous nucleation and the Gyarmathy model is employed to evaluate the droplet growth. Combining the first three lowest moments with the two-dimensional Euler equations, the governing equations of unsteady flows with heterogeneous condensation are obtained. As a demonstration, the heterogeneous condensation in a closed shock tube problem is simulated with a top-hat radius distribution of insolvable particles for different mean particle radius and particle concentration. It is shown that the extended moment method can not only give the flow details including pressure, density and wave pattern caused by condensation, but also provide the important physical properties of the aerosol.

Ceiling-jet thickness and vertical distribution along flat-ceilinged horizontal tunnel with natural ventilation

A series of fire tests was conducted in a 10.0m (L)×0.75m (W)×0.45m (H) model tunnel with a rectangular cross section, and detailed measurements were taken of the temperature and velocity within a quasi-steady state fire-driven ceiling-jet running along the centre of a ceiling.The ceiling-jet thickness was defined as the distance from the tunnel ceiling to the point where the temperature and/or velocity dropped to half of their maximums. Correlations to represent the variation in the ceiling-jet thickness along the tunnel axis were developed with the aid of a theoretical approach. The coefficients included in these correlations were determined based on the experimental results obtained. It was found that the ceiling-jet thickness derived from the temperature was 1.17 times greater than that from the velocity in the tranquil flow region.In the tranquil region, both the velocity and temperature showed top-hat distributions, with a bulging shape from the apex of the distribution towards the tunnel floor. A cubic function and coordinate transformation were applied to develop empirical formulae for the temperature and velocity distributions, which were represented by the dimensionless distance from the tunnel ceiling and dimensionless temperature rise and/or velocity at a given distance from the fire source. The correlation developed for the temperature distribution was compared with the results of large- and full-scale tunnel experiments, which verified its applicability.

Single-pulse Conduction Limited Laser Welding Using A Diffractive Optical Element

Conduction limited laser welding is commonly used in electronic and battery applications, where a high width-to-depth ratio weld is desirable. A laser beam with Gaussian or top-hat distributions is often used to produce conduction limited spot welds. Both these energy distributions result in a higher proportion of the laser beam energy being introduced towards the centre of the welded spot and consequently, a reduced penetration weld towards the circumference of the beam spot. The use of diffractive optical elements to tailor the energy distribution of the laser beam has been evaluated. An incident laser beam with an energy distribution in the shape of a ring or C-shape was projected onto the material, which results in heat propagating towards the centre, producing a shallow weld with a consistent depth of penetration across the entire overlapped joint. The results confirmed a corresponding thermal model which predicted an even distribution of heat at the joint interface.

On polydispersity and the hard sphere glass transition.

We investigate the dynamics of polydisperse hard spheres at high packing fractions ϕ. We use extensive numerical simulations based on an experimentally-realistic particle size distribution (PSD) and compare to commonly-used PSDs such as Gaussian or top hat distribution. We find that the mode of kinetic arrest depends on the PSD's shape and not only on its variance. For the experimentally-realistic PSD we find ageing dynamics even though the density correlators decay fully to zero for ϕ ≥ 0.59. We observe substantial decoupling of the dynamics of the smallest and largest particles. While the smallest particles remain diffusive in all our simulations, a power-law describes the largest-particle diffusion, suggesting an ideal arrest at ϕc ∼ 0.588. The latter is however averted just before ϕc, due to the presence of the mobile smallest particles. In addition, we identify that a partial aging mechanism is at work, whose effects are most pronounced for the largest particles. By comparing our results with recent experimental observations of ergodic behavior up to ϕ ∼ 0.6 in a hard-sphere system, we argue that this is an effect of polydispersity, which smears out the glass transition.

The analysis of the optimal two dimensional pump energy distribution for narrower electro-optically Q-switched pulse׳s width

The pump energy distribution in the cross section of the gain medium of a LDA side pumped laser and the effect of the initial gain spatial distribution on the electro-optically (EO) Q-switched pulse׳s width are numerical studied in this paper. The simulation results show that the relatively high energy distribution at the edge of the gain medium will lead to a longer pulse width. And two ideal pump distributions, top-hat distribution and Super Gaussian distribution at part of the cross section are also analyzed. It shows that a uniform pump region at the medium center with around 50% of the medium׳s cross section area leads to narrower pulse width than other pump distributions with the same max initial population inversion density.

Picosecond Laser Induced Selective Removal of Functional Layers on CIGS Thin Film Solar Cells

Abstract Picosecond laser pulses provide a controlled laser based removal used for micro structuring of functional layers, such as copper-indium-gallium-diselenide (CIGS), due to a reduced thermal penetration depth, compared to nanosecond pulses. It is shown that with 7 ps pulse width at a wavelength of 532 nm the P2 and P3 processing of thin film solar cells on glass substrates and flexible polyimide substrates is possible. A Gaussian as well as a top-hat energy distribution were utilized for the experiments. With adjusted laser and processing parameters they allow for the fabrication of precise isolation trenches (width

Prototypes and modulation functions of classical and novel configurations of optical chopper wheels

Optical choppers with rotating wheels are some of the most used macroscopic optomechatronic devices for the controlled modulation, attenuation or obscuration of light in a wide area of applications. We discuss and compare the modulation functions produced by two types of chopper wheels: the classical device, with windows with linear edges, and the eclipse chopper (with windows with circular edges) that, to the best of our knowledge, we have introduced. This discussion is based on the analysis and the design we have previously developed for these various devices, for top-hat (constant over the entire section) light beam distributions. While the comparison of the different shapes of transmitted signals allows for the proper choice of the most appropriate device and parameters to obtain the modulation function that is fit for a certain application, the present work also presents the mechanical setup we have designed and manufactured for testing choppers with rotating wheels. A series of prototype wheels with different, optimized profiles were obtained for the purpose. The simulation and the electro-erosion programs for the wire electro-erosion of aluminum plates to manufacture the wheels are presented. An advantageous double wheel solution has been developed to obtain wheels with windows of different shapes and sizes, and the testing of this final assembly concludes the study.

Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds

We present a statistical cloud scheme based on the subgrid-scale distribution of the saturation deficit. When analyzed in large-eddy simulations (LES) of a typical cloudy convective boundary layer, this distribution is shown to be bimodal and reasonably well-fitted by a bi-Gaussian distribution. Thanks to a tracer-based conditional sampling of coherent structures of the convective boundary layer in LES, we demonstrate that one mode corresponds to plumes of buoyant air arising from the surface, and the second to their environment, both within the cloud and sub-cloud layers. According to this analysis, we propose a cloud scheme based on a bi-Gaussian distribution of the saturation deficit, which can be easily coupled with any mass-flux scheme that discriminates buoyant plumes from their environment. For that, the standard deviations of the two Gaussian modes are parametrized starting from the top-hat distribution of the subgrid-scale thermodynamic variables given by the mass-flux scheme. Single-column model simulations of continental and maritime case studies show that this approach allows us to capture the vertical and temporal variations of the cloud cover and liquid water.

Coherent backscattering cone shape depends on the beam size

Coherent backscattering (CBS) is a beautiful physical phenomenon that takes place in a highly scattering medium, which has potential application in noninvasive optical property measurement. The current model that explains the CBS cone shape, however, assumes the incoming beam diameter is infinitely large compared to the transport length. In this paper, we evaluate the effect of a finite scalar light illumination area on the CBS cone, both theoretically and experimentally. The quantitative relationship between laser beam size and the CBS cone shape is established by using two different finite beam models (uniform top hat and Gaussian distribution). A series of experimental data with varying beam diameters is obtained for comparison with the theory. Our study shows the CBS cone shape begins to show distortion when beam size becomes submillimeter, and this effect should not be ignored in general. In biological tissue where a normal large beam CBS cone is too narrow for detection, this small beam CBS may be more advantageous for more accurate and higher resolution tissue characterization.