Gaussian Power Density Research Articles

Transient and periodic steady-state characteristics of the local heat transfer measurement by thermal perturbation with Gaussian power density distribution

The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation – usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation) elaborated in comparison with the analytical model for dimensional analysis. The statistically more robust technique that relies on the linearity of the spatial phase distribution of the test point array was favored when the target Biot number approaches unity in terms of its order of magnitude. The preferred upper limit for thermographic scanning was discussed as the simplification of later data processing is concerned. Nonetheless, the time elapsed for an acceptable periodic steady state, which in principle leans to the higher end of the target Biot number spectrum in a log scale, indicates the benefit from the time series of pointwise temperature measurement – as in the conventional single-blow testing, where the effect of spikiness, as well as that of the location of individual test point, holds. Note that the vicinity as the target Biot number approaches unity was again observed with higher preference.

A metallurgical and thermal analysis of Inconel 625 electron-beam welded joints

Inconel 625 is a nickel-based superalloy that finds application in many industrial sectors thanks to its high strength, excellent fabricability, and outstanding corrosion resistance. It is characterized by a good weldability and often used in the as-welded conditions. In the following, a metallurgical and thermal analysis of Inconel 625 Electron-Beam welded joints is described. The thermal analysis was supported by a numerical model that uses a superimposition of a spherical and a conical shape heat source with Gaussian power density distribution in order to reproduce the nail-shape of the fusion zone. The heat source parameters were calibrated by using experimental data coming from metallurgical observations and temperature measurements. Numerical and experimental results were found in good agreement.

Double-pass microwave photonic sensing system based on low-coherence interferometry.

In this Letter, we propose and experimentally demonstrate, to the best of our knowledge, a novel high-performance microwave photonic sensing system employing a reflective double-pass spectrum-slicing sensing scheme, based on low-coherence interferometry in combination with a dispersive medium. The setup is implemented by configuring a double-pass spectrum slicing sensing scheme, which significantly increases the output power level of a low-coherence optical source by approximately 12dB to compensate for the optical loss of the system. Moreover, since the light passes through the same optical path twice, the conversion efficiency between the applied optical path difference and the dependent radiofrequency (RF) resonance shift is doubled compared to the conventional approaches. It is also possible to realize a very high resolution thanks to the broad bandwidth of the semiconductor optical amplifier (SOA) spectrum. In addition, this SOA-based scheme enables the future realization of a fully integrated sensing system. As an application example, a highly sensitive displacement sensor was investigated, and the experimental results presented a highly linear relationship between the applied OPDs and the RF frequency shifts. The proposed sensing system successfully achieved a high conversion slope of 5.56GHz/mm and a nearly constant resolution of approximately 124μm using a Gaussian power density spectrum.

Numerical study of influence of J × B force on melt layer under conditions relevant to ITER ELMs**Project supported by the Scientific Research Foundation of Liaoning Province, China (Grant No. 2016J027), the Open Research Project of Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education (Grant No. KF1705), and the National Key Research and Development

The influence of the J × B force on the topographical modification of W targets during a type-I-like ELM in ITER has been studied numerically. A two-dimensional (2D) fluid dynamics model is employed by solving liquid hydrodynamic Navier-Stokes equation with the 2D heat conduction equation in addition to driving forces for surface topography, such as surface tension and pressure gradient, the J × B force is particularly addressed. The governing equations are solved with the finite volume method by adequate prediction of the moving solid-liquid interface. Numerical simulations are carried out for a range of type-I ELM characteristic parameters. Our results indicate that both the surface tension and the J × B force contributes to the melt motion of tungsten plates when the energy flux is under , the surface tension is a major driving force while the pressure gradient is negligible. Our results also indicate that the J × B force makes the small hills grow at different rates at both the crater edges under a type-I-like ELM heat load with a Gaussian power density profile.

A Numerical and Experimental Analysis of Inconel 625 Electron-Beam Welding – Thermal Aspects

Inconel 625, a nickel based superalloy, finds application in many fields. It is known to have a good weldability and it is often used in the as-welded conditions, heat treatments could be necessary to relief stresses. Numerous variables are known to affect the residual stresses field: welding process, joined geometry and clamping conditions. Since experimental measurements based on X-ray diffraction are not straightforward, expensive experimental work could be substituted by numerical simulation. Before performing an elastoplastic simulation, thermal analysis results are needed, first.This paper focus on the thermal analysis procedure. The analysis has been validated by means of macrographs and with thermocouples data. The heat source was successfully modelled using a superimposition of a spherical and a conical shape heat source with Gaussian power density distribution in order to reproduce the nail shape of the fusion zone. Heat source parameters were chosen so that the model would match with experimentally determined weld pool shape and temperatures. Preliminary results of the metallurgical analysis are also presented.

Numerical study of thermal erosion and topographical change of divertor target plates induced by type-I edge-localized modes

The high-Z material tungsten (W) is a promising candidate of the plasma facing components (PFCs) for the future tokamak reactors due to its high melting point (3683 K), low tritium retention and low sputtering yield. However, there are still many problems about W PFCs. One of them is the material melting under off-normal transient heat fluxesit is one of the most outstanding open questions associated with the use of W divertor targets in international thermonuclear experimental reactor (ITER). This requires us urgently to understand the W melting behavior under high power flux deposition condition. In this paper, a two-dimensional (2D) fluid dynamic model is employed by solving the liquid hydrodynamic Navier-Stokes equation together with the 2D heat conduction equation for studying the erosion of the divertor tungsten targets and its resulting topographical modification during a type I-like edge-localized mode (ELM) in ITER with a Gaussian power density profile heat load. In the present model, major interaction forces, including surface tension, pressure gradient and magnetic force responsible for melt layer motion, are taken into account. The simulation results are first benchmarked with the calculated results by other code to validate the present model and code. Simulations are carried out in a wide range of fusion plasma performance parameters, and the results indicate that the lifetime of W plate is determined mainly by the evolution of the melt layer. As a consequence of the melt layer motion, melted tungsten is flushed to the periphery, a rather deep erosion dent appears, and at the dent edges two humps of tungsten form during the ELM. The humps at both edges are almost at the same height. Calculated results show the topographical modification becomes noticeable when the W plate is exposed to a heat flux of 2000 MWm-2 for 0.8 ms (in the simulation, the parameter k=ə/əT is taken to be -9.010-5 Nm-1K-1, where is the surface tension coefficient and T is the temperature). The values of the humps are both about 2.1 m, and the surface roughness is about 1.1 m. The longer the duration of the ELM, the more rapidly the humps rise. The melt flow may account for the higher surface temperature at the pool periphery, and for the larger melt thickness. It is found that when the energy flux is under 3000 MWm-2 the surface tension is a major driving force for the motion of melt layer. Under the same heat flux, the bigger the k used in the simulation, the more severe the surface topography of the target becomes; while at the same k, the higher the heat flux, the more severe the surface topography of the target becomes. In addition, a modified numerical method algorithm for solving the governing equations is proposed.

Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics

This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. The investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. It allows the partial derivatives involved in the formulation to be analytically expressed. To illustrate the method, two examples of offset single reflectors shaped to radiate a Gaussian power density within a superelliptical contoured beam are presented. The results are validated by Physical Optics analysis with equivalent edge currents.

Experimental Approbation of Selective Laser Melting of Powders by the Use of Non-Gaussian Power Density Distributions

Experimental results on laser beam modulation at selective laser melting (SLM) are presented. The modulation is a possible way to improve the efficiency of the SLM process. The optical diagnostics shows the energy loss up to 30%. This could be a consequence of high thermal gradients in the melt pool resulted by the Gaussian power density distribution. The Gaussian distribution can be changed to the flat-top one or to the inverse-Gaussian (donut) one. An experimental stand with a 200W laser source was developed. Twenty single tracks for each of the three modes were obtained for a Co-Cr alloy. The samples were studied by scanning electronic microscopy (SEM) on irregularity. Optical diagnostics by high velocity camera (HVC) shows that the use of the non-Gaussian laser beam distributions can significantly reduce the width of the free-of-powder consolidation zone, which is considered as the main reason for irregularity of single tracks. A better metallurgical bonding of the single tracks with the substrate was obtained by the use of the flat-top laser beam. Both of these facts show a significant influence of the laser beam energy distribution on the energy loss at SLM, especially for high power laser sources. The observed escape of granules shows a possible influence of the dynamic factor. The use of the non-Gaussian distributions can enhance 3D parts, for example, improve the geometrical tolerance and decrease the residual porosity.

Analytical solution of temporary temperature field in half-infinite body caused by moving tilted volumetric heat source

In this work, analytical solution of temporary temperature field in half-infinite body caused by moving heat source tilted towards the direction of motion is presented. In solution is assumed volumetric heat source with Gaussian power density distribution with respect to depth. Calculations of temperature field in cubicoidal steel element have been conducted for three tilt angles between heat source and perpendicular to the surface of object: −30°, 0 and 30°. Results of calculations are presented in the form of temporary and maximum temperature fields in sections of element and thermal cycles at selected point.

Continuous wave synthetic low-coherence wind sensing Lidar: motionless measurement system with subsequent numerical range scanning

A continuous wave (CW) Lidar system for detection of scattering from atmospheric aerosol particles is presented which is useful in particular for remote sensing of wind velocities. It is based on a low-coherence interferometric setup powered by a synthetic broadband laser source with Gaussian power density spectrum. The laser bandwidth is electronically adjustable and determines the spatial resolution which is independent of range. The Lidar system has no moving parts. The location to be resolved can be shifted numerically after the measurement meaning that a single measurement already contains the full range information. The features of constant resolution and numerical range scanning are in sharp contrast to ordinary CW Lidar systems.

A Three-Dimensional Angular Scattering Response Including Path Powers

In this paper, the angular power spectrum exhibited under a three-dimensional (3-D) Gaussian scattering distribution at fixed observation points in space is investigated. Typically, these correspond to the mobile and base units, respectively. Unlike other spatial channel models, the derived model accounts for the distance to each scatterer from the observation point, and transforms distances into power values under the assumption of free-space propagation. The proposed 3-D spatial channel model follows a non-central approach in terms of the scatterer distribution in space, which means that the angular power field at the base unit need not be due to a scatterer distribution centered exactly at the mobile. Derivations are provided for the angular and power domains. As shown, by conditioning the distance, the angular field reduces to the von-Mises Fisher distribution. Most importantly, this work provides a theoretical backup to the Gaussian angular power spectrum observed in radio propagation channel measurements, introducing a formal theoretical framework consistent with the experimental investigations found in literature. More specifically, our findings show that a Gaussian scatterer distribution in space gives rise to a Gaussian-like angular power spectrum and a Gaussian angular power density in the azimuth and elevations fields. By introducing the notion of distance into the framework, the proposed 3-D spatial channel model can be used to evaluate performance of current and future multi-element wireless communication networks.

Computer simulation for calculating the second-order correlation function of classical and quantum light

We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for bunched light was based on a previous publication, the one for antibunched light was developed by master students attending a Quantum Optics course at our University.

3D thermal finite element analysis of single pass girth welded low carbon steel pipe-flange joints

This paper presents a detailed computational procedure for predicting the complete thermal history including transient temperature distribution during girth welding and subsequent post weld cooling of low carbon steel pipe flange joints. Using the FE code ABAQUS, 3-dimensional non-linear heat transfer analysis is carried out to simulate gas metal arc welding (GMAW) process. ANSI Class #300 flange is used with a 6 mm thick, 200 mm long and 100 mm nominal diameter pipe. Joint type is a single ‘V-groove’ butt joint with a 1.2 mm root opening. FORTRAN subroutine is utilized for the application of volumetric heat flux from the weld torch using Goldak’s double ellipsoidal heat source model, which is based on Gaussian power density distribution. Temperature dependent thermal properties as well as phase change effects have also been accounted. Apart from comprehensive discussion on the thermal history, in-depth analysis of the axial temperature profile at four different sections on both sides of the weld joint is presented. The simulated results showed that the temperature distribution around the implemented heat source model is steady when the weld torch moves around the circumferential joint. The present simulation model can be used as a proper tool to investigate the effect of different GMAW process parameters.

Influence of Beam Incidence Angle in Laser Welding of Austenitic Stainless Steel using Finite Element Analysis

This paper presents the influence of beam incidence angle on austenitic stainless steel sheet subjected to a high density laser beam having Gaussian power density distribution. Bead‐on trials are conducted on 3.15 mm thick commercial AISI 304 austenitic stainless steel sheet using a Nd:YAG laser source with a maximum output of 2kW in the continuous wave mode. The effects of beam incident angle on the weld bead geometry are studied using finite element analysis. Experiments are conducted with 600, 1000 and 1400W laser power and 800, 1400 and 2000mm/min welding speed. A three dimensional finite element model is developed for the simulation of non‐linear transient thermal analysis of the weld bead geometry for different beam incident angles using the finite element code ANSYS. The result reveals that by increasing the beam incident angle with constant beam power and welding speed, there is a considerable reduction in the depth of penetration‐to‐width ratio (d/w). Further, it is noticed that the process enters into conduction mode of welding from the keyhole mode of welding as the beam angle is increased beyond 10o. The comparison of the simulation results and the experimental data for weld bead geometry with different beam incident angles show good agreement.

Modeling cast IN-738 superalloy gas tungsten arc welds

A three-dimensional finite-element thermal model has been developed to generate weld profiles, and to analyze transient heat flow, thermal gradients and thermal cycles in cast IN-738 superalloy gas tungsten arc welds. Outputs of the model (cooling rates, the thermal gradient G and the growth rate R) were used to describe solidification structures found around the weld pool for three different welding speeds at constant heat input. Calculations around the weld pool indicate that the cooling rate increases from the fusion line to the centerline at all welding speeds. It was also observed that the cooling rate (G×R) and the ratio G/R fall with welding speed. For instance, as the welding speed is increased, the cooling rates at the centerline, fusion line and penetration depth decrease. Moreover, it was observed that as the power and welding speed both increase (but keeping the heat input constant), the weld pool becomes wider and more elongated, shifting from circular to elliptical shaped. The calculations were performed using ABAQUS® FE code on the basis of a time-increment Lagrangian formulation. The heat source represented by a moving Gaussian power density distribution is applied over the top surface of the specimen during a period of time that depends on the welding speed. Temperature-dependent material properties and the effect of forced convection due to the flow of the shielding gas are included in the model. Numerically predicted sizes of the melt-pool zone and dendrite secondary arm spacing induced by the gas tungsten arc welding process are also given.

Investigation of electron-beam welding in wrought Inconel 706—experimental and numerical analysis

Electron-beam welding (EBW) is commonly employed in the aeroengine industry for the welding of high integrity components, fabricated from high-strength superalloys. For such applications, it is important to predict distortions and residual stresses induced by the process. Melt run trials have been carried out on nickel-base superalloy Inconel 706 plates using the EBW technique in order to analyse the effects of welding parameters on geometrical characteristics and microstructure of the bead. Butt-welded plates have been then investigated by means of tensile tests, microstructural analysis, and X-ray diffraction measurements. A finite element model of the process has been set up using an uncoupled thermal–mechanical analysis. The heat source was modelled using a superimposition of a spherical and a conical shape heat source with Gaussian power density distribution in order to reproduce the nail shape of the fusion zone (FZ). The parameters of the source were chosen so that the model would match with experimentally determined weld pool shape and temperatures, measured with thermocouples. Subsequently, the thermal analysis was used to drive the non-linear mechanical analysis. The predicted residual stresses were then compared with X-ray diffraction measurements. It was found that the correct thermal and residual stresses prediction is influenced by the shape of the fusion zone, the highest thermal tensile stress arising under the nailhead of the fusion zone where microfissuring can be observed.

Temperature distributions in laser-heated biological tissue with application to birthmark removal.

The time-dependent temperature distributions produced within thermally homogeneous media heated by a moving laser beam with Gaussian and uniform power density profiles are examined using a time-domain method based on Green's functions. Regions of finite length, width, and depth within the medium having exponential power absorption are considered. The temperature distribution is written as a single integral with respect to time of simple functions and the resulting expressions have been used to model the heating of blood vessels for birthmark (port-wine stain) removal. The temperature distributions obtained are in good agreement with those produced using Monte Carlo optical and finite difference thermal models.

Theory of randomly inhomogeneous waveguides with slight material dispersion: II. Parabolic graded-index fibres

This paper, following directly from Part I, continues to demonstrate the use of the paraxial approximation in solving the time-dependent wave equation for the propagation of signals in slightly dispersive optical materials with some Gaussian randomness of the permittivity. With the same emphasis as in Part I, a path-integral formulation is employed. Attention is focused on a parabolic graded-index fibre with ⟨1/nk 0( r )⟩=(1+αr 2 ⊥/2)/n¯k 0, α>0. Arising from the possibility of replacing the autocorrelation function of the permittivity by a quadratic function, some final concise expressions are derived. It is shown that if a signal begins propagating with a Gaussian power density ⟨|u( r , 0)|2⟩, the Gaussianity of the function ⟨|u( r , t)|2⟩ is maintained at all later times t. The longitudinal shape of the function ⟨|u( r , t)|2⟩ exhibits attenuation and broadening dependent on the dispersiveness of the optical medium under consideration. The perpendicular shape of the function ⟨|u( r , t)|2⟩ oscillates with the angular frequency Ω⊥=[cvx (k 0α/n¯ k 0 ]1/2 where c and vx (k 0) are, respectively, the velocity of light in vacuum and the axial group velocity of light corresponding to kx =k 0. Special attention is devoted to the limiting case when α→0, i.e. to propagation in a bulk dispersive optical medium.

On the formation of the keyhole and its temperatures

A thermodynamically based model has been developed to calculate the size and temperature of the ‘keyhole’ through the thickness of the weldment. The model is based on calculating the power loss resulting from evaporation of an element in the chemistry of the plate and a minimum power density required to produce a keyhole. The evaporative power loss is set equal to the Gaussian power density, which is used to represent the laser beam. The result is a temperature distribution across the keyhole. Absorption of the laser power in the keyhole is calculated based on inverse Bremsstrahlung absorption, which can be calculated based on Sana's equation and the average Gaunt factor. The results indicate that peak powers below the minimum peak power density yield temperatures that are indicative of melting only; peak powers equal to a minimum power density yield temperatures that reach the evaporation temperature of the element; and that peak powers greater than the minimum power density yield temperatures greater than the evaporation temperature of the element. The results are used to explain the ‘nail head’ appearance of the fusion zone which is quite common in laser beam welds. The results also explain some visual observations of laser beam welds.

Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light

A time-domain method is used to derive simple expressions for temperature distributions within media heated by a moving laser beam with a Gaussian power density profile. Various medium-absorption functions are considered. The solutions are given as single integrals with respect to time of simple functions. The expressions can be applied to multilayer media consisting of layers with different optical (light-absorbing) properties, provided that the layers have similar thermal properties. A number of optical recording examples have been examined in detail, and the results compared with those obtained by use of a more general (fast-Fourier-transform-based) approach.