Instantaneous Source Research Articles

Development of a source-term migration model for a large bubble formed in a core disruptive accident

Because sodium-cooled fast reactors are designed with high inherent safety in mind, the probability of a core disruptive accident (CDA) is extremely low. However, from a defense-in-depth perspective, the study of CDA sequences is still worthwhile to assure the safety and reliability of reactors. During a CDA, a large bubble rapidly expands inside the sodium pool, rises from the core, and covers the gas region, providing a potential migration path for source terms (radioactive materials present within the containment barriers). Source terms released initially within the cover-gas region after a few hundred milliseconds are called instantaneous source terms. We propose here an instantaneous source-term migration model that provides a simplified evaluation of the amount of source terms absorbed by coolant sodium during the ascent of the CDA bubble. In the model, the particle motion within the CDA bubble obtained from the basic momentum equation is used to calculate the amount of source terms escaping from the bubble interface. In addition, a model analogous to aerosol scavenging by precipitation is used to assess the amount of source terms absorbed by droplets present in the bubble, especially the entrained sodium droplets that form during rapid expansion of the CDA bubble. The model is further validated by a previous source term migration experiment in which a large high-pressure bubble expands and rises in a sodium pool. Good agreement with the measured retention factor of a source term demonstrates the reliability of the developed model. Given these results, some key parameters are selected for a sensitivity analysis.

Migration of copper(II) ions in humic systems—effect of incorporated calcium(II), magnesium(II), and iron(III) ions

The mobility of heavy metals in natural soil systems can be affected by the properties and compositions of those systems: the content and quality of organic matter as well as the character of inorganic constituents. In this work, the diffusion of copper(II) ions in humic hydrogels with incorporated calcium(II), magnesium(II), and iron(III) ions was investigated. The methods of instantaneous planar source and of constant source were used. Experimental data yielded the time development of the concentration in hydrogels and the values of effective diffusion coefficients. The coefficients include both the influence of the hydrogel structure and the interaction of diffusing particles with the hydrogel. Our results showed that the presence of natural metal ions such as calcium, magnesium, or iron can strongly affect the diffusivity of copper in humic systems. They indicate that the mobility of copper ions depends on their concentration. The mobility can be supported by higher contents of copper in the system. While the incorporation of Ca and Mg resulted in the decrease in the diffusivity of copper ions, the incorporation of Fe(III) into humic hydrogel resulted in an increase in the diffusivity of Cu(II) in the hydrogel in comparison with pure humic hydrogel.

Exceptional load-bearing capability of Al FPCB/Cu FPCB lap joints using instantaneous laser-based large area facial soldering: Experimental and numerical investigations

This study introduces a novel method for integrating aluminum flexible printed circuit boards (FPCBs) and copper FPCBs into battery management systems (BMS) using and instantaneous large area facial laser source soldering. Achieving a robust bonding strength of 65 MPa involved applying 600 W of laser power for 2 s, enhancing atom diffusion and promoting intermetallic compound (IMC) growth. Finite Element Method (FEM) simulations revealed variations in heat transfer between Al and Cu, affecting IMC thickness at interfaces. Formation of the (Cu, Ni)3Sn4 phase within solder, and variations in laser output significantly influenced solder joint orientation and Al electrode nucleation. Excessive laser power (>800 W) caused critical damage, such as delamination at the Al-PI interface, altering fracture modes and bonding strength. Furthermore, with a detailed examination of the laser soldering phenomenon through both experimental and numerical investigations, this study provides a thorough understanding of the different soldering mechanisms in conventional reflow soldering compared to instantaneous uniform large-area heat source laser soldering. These insights provide new design and material considerations to replace the conventional wiring harness with Al/Cu FPCB lap joints which optimize the circuitry and reducing BMS volume.

Studying the Effect of the Instantaneous and Continuous Pollutants Sources on the Advection-diffusion Equation and Its Applications

This study investigates instantaneous and continuous sources as point, line, and area sources. Gaussian concentration in the case of the puff model with an instantaneous point source inhomogeneous longitudinal diffusion is investigated. The concentration is calculated using different dispersion parameters to get the proposed normalized concentration of the puff model at ground level around the centerline, which is compared with observed data by the Copenhagen experiment and previous work [1]. Also, the continuous point source is used to get the Gaussian plume model in three dimensions using dispersion parameters to compare with the observed concentration data measured by the Egyptian Atomic Energy Authority for Iodine-135 (I135) in an unstable condition.

Characterizing suspended particle dispersion in wetland flows: Impact of settling velocity and vegetation factor

Predicting the dispersion process of suspended particles with settling velocity in wetland flows holds significant implications for various ecological and environmental applications. This study analytically investigates the dispersion process of fine settling particles in wetland flows due to an instantaneous release source through the asymptotic expansion method. The effect of high-order terms is incorporated. The impact of vegetation factor and settling velocity on characteristic coefficients (including mass retained in the flow, advection velocity, longitudinal dispersion coefficient, skewness, and kurtosis), vertical mean, and two-dimensional concentration distribution are analyzed. Analytical solution is validated by numerical result through random displacement method. Results demonstrate that the vegetation factor does not influence the vertical mass distribution, and a larger settling velocity results in a higher concentration of mass in the bed wall layer. The longitudinal dispersion coefficient does not exhibit a monotonic relationship with the settling velocity. The position of mass centroid of the vertical mean concentration is biased more to the upstream with the larger settling velocity. At larger times, the vertical mean concentration approximates a normal distribution, with skewness and kurtosis nearing zero. Under the influence of settling velocity, the bed wall layer exhibits a high concentration zone in the two-dimensional concentration distribution. These results can help the understanding of sediment dynamics, nutrient cycling, pollutant transport associated with the wetland flows.

A DiffeRential Evolution Adaptive Metropolis (DREAM)-based inverse model for continuous release source identification in river pollution incidents: Quantitative evaluation and sensitivity analysis

The identification of continuous pollution sources for rivers is of great concern for emergency response. Most studies focused on instantaneous river pollution sources and associated incidents. There is a dire need to address continuous pollution sources, as pollutant discharge may impose a major impact on the water ecosystem. Therefore, in this study, a novel inverse model is proposed to identify the continuous point sources in river pollution incidents that would estimate the source strength, location, release time, and spill time. The proposed inverse model combines the advanced DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and the forward transport advection-dispersion equation to infer the posterior probability distribution of source parameters for quantifying uncertainties. In addition, the performance of the DREAM-based model is compared with those of the Metropolis-Hastings (MH)-based and genetic algorithm (GA)-based models. The results show that the DREAM-based model performs accurately for both the hypothetical and the field tracer cases. The comparative analysis shows that the DREAM-based model performs better in saving computation time, improving the accuracy of results, and reconstructing pollutant concentrations. Observation errors significantly influence the accuracy of the identification results from the DREAM-based model. In addition, a comprehensive sensitivity analysis of the DREAM-based model is conducted. The identification results from the DREAM-based model are sensitive to the dispersion coefficient and river velocity. The accuracy of the inverse model could be improved by increasing the monitoring number and by monitoring locations closer to the spill site. The findings of this study can improve decision-making during emergency responses to sudden river pollution incidents.

Simulation of thermal processes in a half-space under heating by a moving source with a uniformly distributed heat flow

Using the method of applying instantaneous point sources, a solution was obtained to the problem of heat conduction during surface heating of a body in the form of a half-space by a uniformly distributed highly concentrated heat flux moving at a constant speed along a rectilinear trajectory with a different shape of the heating spot at constant thermophysical characteristics of the material. The effect of temperature loading modes and the shape of the heating spot on thermal processes in the heat-affected zone is studied. The surfaces and lines of the temperature level are constructed for different moments of time and speed loading modes in different planes of the heating zone. Time dependences of temperatures, heating and cooling rates for body points are given. The shortcomings of the methods used for linear thermal conductivity, the lack of direct consideration in the design scheme of the surface melt zone of the material do not allow one to reliably assess the effect of heat treatment modes on changes in material properties, focusing only on the level of the maximum design temperature. In this regard, the structure formation of metal in the zone of thermal action is proposed to be associated with a thermal impulse, i.e. the total thermal energy perceived by the material at a given point of the body, as well as with the effective structurization impulse introduced into consideration, which characterizes the energy spent on the process of structural transformations of the material, and the structurization time at a point and some volume of the body. The dependencies of these values on the speed of movement and the shape of the heating spot are presented. The considered approaches can be applied to various metals and alloys. The research results can be used to develop more effective methods for determining the optimal modes of surface hardening of metal products with a high-energy source.

Diffusion of 22Na, 137Cs, 133Ba, 152+154Eu and 131I in Argillaceous Clays of Cuddapah Supergroup, Andhra Pradesh, India

Abstract The safety assessment of Deep Geological Repository (DGR) for high level nuclear waste disposal requires the evaluation of transport and retardation parameters of radionuclides. Therefore, the apparent diffusion coefficient (Da) of Cs(I), Ba(II) and Eu(III) in argillaceous clay rock of Tadpatri Formations of Cuddapah Supergroup, one of the proposed host rock in the Indian geological repository, have been determined by instantaneous planar source method. Moreover, Da of Eu(III) in presence of sulphate and picolinate have also been deduced. Da of Cs(I), Ba(II) and Eu(III) shows trend, Da(Ba) >Da(Cs) > Da(Eu). In presence of complexing anions, Da of Eu(III) increases and follows the order, Da (Eu- picolinate) >Da(Eu-sulphate) >Da(Eu).

A maximum temperature rise model of the shear band in bulk metallic glasses

Based on mechanisms applicable to bulk metallic glasses (BMGs), such as a superposition principle of an instantaneous finite surface heat source temperature field and a flow model about the shear-band velocity, a maximum temperature rise model of shear bands in BMGs was deduced, ΔTmax=σycpΔupl·vSB2πα. The model describes the dependence of the maximum temperature rise on the yield strength and the shear-band velocity in BMGs. It can be calculated that the maximum temperature rise of BMGs is between 1 K ∼ 30 K at room temperature through these two parameters. A critical temperature, TC, of almost 0.8∼0.9Tg is introduced, at T<TC, the change of the yield strength with temperature in BMGs basically conforms a cooperative shear model (CSM), and at T>TC, a significant reduction of the yield strength in BMGs can be attributed to avoiding failure due to localized material softening.

Source Parameters of Strong Turkish Earthquakes on February 6, 2023 (&lt;i&gt;M&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; = 7.8 and &lt;i&gt;M&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; = 7.7) from Surface Wave Data

Abstract—Based on the amplitude spectra of surface waves, the source parameters of the strong Turkish earthquakes of February 6, 2023 (Mw = 7.8 and Mw = 7.7) were calculated in two approximations: an instantaneous point source and an elliptical shear dislocation. As a result, rupture planes were identified, data were obtained on the scalar seismic moment, moment magnitude, focal mechanism, and source depth of the considered seismic events, and the integral parameters characterizing the rupture geometry and its development in time were estimated. It is shown that the sources of the earthquakes under study were formed under the influence of the regional stress field and their focal mechanisms were left lateral faults with a strike direction close to the strike of the East Anatolian fault zone for the first event and close to the strike of the Sürgü-Çardak fault system for the second. For the first earthquake, our estimates of the rupture duration and its length (t = 52.5 s, L = 180 km) probably refer not to the entire rupture, but only to its main phase, confined to the northeastern segments of the East Anatolian fault and characterized by maximum displacements and values of the released seismic moment. The values of t = 30 s and L = 180 km that we obtained for the second earthquake fully characterize the entire rupture.

Dynamics and acoustics of bubbly plumes

Transient bubbly plume dynamics including their effects on the free surface were studied numerically using a simple numerical model based on integral theory [1, 2] and Eulerian–Eulerian coupled large Eddy simulation (EE-LES) method. The EE-LES model was validated with the interfacial closures evaluated for drag, lift and virtual mass forces. The simulation data showed good agreement with both numerical predictions and experimental measurements in the literature. The spectrum of the surface pressure fluctuations and acoustical pressure induced by a bubbly plume were extracted from numerical simulations [3]. The effect of interaction of two plumes is discussed. [1] B.R. Morton, G.I. Taylor, J.S. Turner, Turbulent gravitational convection from maintained and instantaneous sources, Proc. R. Soc. Lond. A234, 1–23 (1956) [2] A. Skvortsov, T. DuBois, M. Jamriska, M. Kocan, Scaling laws for extremely strong thermals, Phys. Rev. Fluids 6, 053501 (2021) [3] S.J. Zhu, A. Ooi, R. Manasseh, A. Skvortsov, Prediction of gas holdup in partially aerated bubble columns using an EE-LES coupled model, J. Chem. Eng. Science 217, 115492 (2020)

Influence of a low viscosity zone on the evolution of post-eruption deformation: A case study of the crustal deformation of Aira Caldera after the 1914 eruption of Sakurajima Volcano

Spatial viscosity variations in the crust can be inferred from geophysical imaging and may be essential for interpreting volcano deformations that show more complex behaviours than what simple uni-viscous models predict. In southern Kyushu, Japan, recent seismic imaging implies the presence of a low viscosity zone (LVZ) beneath Aira Caldera, and geodetic data in and around the caldera require uni-viscous model to have lower and higher viscosities earliest and later, respectively, in the period following the 1914 eruption of Sakurajima Volcano. Here, we use a 3D finite element model comprising an elastic layer underlain by a linear Maxwell viscoelastic layer to examine the influence of a LVZ on ground surface displacement in response to two different deformation source modes, i.e., instantaneous source deflation during a major eruption and subsequent continuous source inflation due to magma recharge. A LVZ is introduced into the viscoelastic layer by gradually reducing its viscosity towards the centre. The behaviour of the LVZ model quantified by comparison with the behaviour of a uniform viscosity (UNV) model reveals that, for a given LVZ structure, an apparent UNV model that best represents the LVZ model displacement in response to the instantaneous deflation has lower viscosity than that in response to gradual inflation, i.e., the rate-controlling viscosities of the LVZ model are those in the inner and outer parts of the LVZ for the instantaneous source deflation and subsequent continuous inflation, respectively. Such LVZ model behaviour, for a LVZ spatial extent comparable with the imaged low velocity anomaly, explains well the geodetic data in and around Aira Caldera at any stage after the 1914 eruption, as the predominant viscoelastic response changes with time from that to the instantaneous deflation to that to the subsequent continuous inflation. This study highlights the need for interdisciplinary investigations that integrate geodetic and geophysical datasets to better understand volcanic unrest.

Transient Temperature Distribution in a Half-Space Due to Local Surface Heating Via Non-Fourier Fractional Dual-Phase-Lag Model

Abstract The non-Fourier heat transfer in a half-space is analyzed under sudden heating or cooling on a local surface. The non-Fourier heat transfer effect is described by the time-fractional dual-phase-lag (DPL) model, where the fractional derivative without singular kernel is used. An axisymmetric mixed initial-boundary value problem is solved by the use of the Hankel and Laplace transforms. Two typical cases of sudden temperature rising on a circular zone of the surface or an instantaneous surface heat source are analyzed. For sudden temperature rises, the heat flux and temperature gradient exhibit an inverse square-root singularity near the boundary of the heating zone and their dynamic intensity factors are computed numerically in the time domain. For the instantaneous surface point heat source, an exact solution of the transient temperature at any position in the Laplace domain is obtained. The effects of the fractional order and relaxation time on the temperature distribution and heat flux response are elucidated. The singular behavior of the transient thermal response and the non-Fourier effect of heat transfer are shown.

Investigation of the pulsed neutron source method measuring the fission decay properties of a subcritical assembly with low-Z reflectors

The pulsed neutron source (PNS) method measuring the fission decay properties of a subcritical system with reflectors was analyzed numerically. Using the Monte Carlo code JMCT, a spherical subcritical assembly with a low atomic number (low-Z) reflector was modeled, and the neutron and photon transport process initiated by an instantaneous neutron source was simulated. The time dependence of the leakage photon count rate and the neutron populations in the fissile region and the reflector was obtained. It is indicated that the neutron population in the assembly is dominated by that in the reflector after a relatively short period, the length of which is mainly dependent on the reflector's thickness. That is to say, the neutron population in the assembly is more affected by the reflector than by the fissile region. The leakage photon count rate is approximately proportional to the neutron population in the fissile region during the specific time window of hundreds of nanoseconds after the source pulse. The fission decay properties of the fissile region can therefore be approximately derived from the leakage photon count rate based on the PNS method. The reason for the existence of the above time window was analyzed, and the effective time range of leakage photon count rate was discussed.

Diffusion of radioisotopes in Fe-montmorillonite relevant to geological disposal of HLW

Bentonite clay is proposed as backfill or buffer materials in the engineered barrier system for high-level nuclear waste (HLW) disposal in a deep geological repository (DGR). The major clay mineral of bentonite, montmorillonite (Mt), is expected to undergo alteration owing to its interaction with corrosion products from overpack/canister over a long period of time. As a typical and simple altered clay mineral, we used Fe(II)−Mt and Fe(III)−Mt for preliminary investigation on the diffusion behavior of various radioisotopes relevant to HLW. Instantaneous planar source method was used to determine the apparent diffusion coefficient (Da) using compacted (ρd = 1.6 g/cm3) and water saturated Fe−Mt. In Fe(III)−Mt, the Da values in m2/s for 137Cs+ = (3.9 ± 0.2) × 10−12, 133Ba2+ = (1.1 ± 0.6) × 10−12, 152+154Eu3+ = (2.2 ± 0.5) × 10−12 and 131I− = (5.5 ± 0.1) × 10−12. In Fe(II)−Mt, the Da values in m2/s for 22Na+ = (2.0 ± 1.2) × 10−11, 137Cs+ = (3.0 ± 0.4) × 10−12, 133Ba2+ = (1.4 ± 0.4) × 10−11, 152+154Eu3+ = (4.0 ± 0.7) × 10−12 and 131I− = (4.8 ± 1.0) × 10−12. In general, similar Da values are obtained for Fe(II)−Mt and Fe(III)−Mt. This is the first extensive study to report the diffusion behavior of radioisotopes in Fe−Mt.

Modeling of tsunami generated in stratified oceans by sub-aquatic volcanic eruptions

In this paper, we develop a model by introducing ambient stratification in the ocean to study the surface waves generated by sub-aquatic volcanic eruptions. The developed equations with the initial and boundary conditions were linearized. The linearized equations were solved using the joint Laplace and Hankel transform Green's function method. The solutions were computed, and the surface elevation was obtained for an instantaneous Duffy source function, revealing a beating phenomenon in the stratified ocean. A clear understanding of the sub-aquatic volcanic eruption and its effect on surface waves will help avoiding large-scale damage to communities and infrastructures in coastal areas.

Analysis of the Role of Water Saturation Degree in HTO, 36Cl, and 75Se Diffusion in Sedimentary Rock

The aim of this study was to analyze HTO, 36Cl, and 75Se(IV) diffusion behavior in a sedimentary rock, which was obtained from the site initially selected for the emplacement of centralized temporal disposal of radioactive waste in Spain. Different experimental methodologies were used to analyze radionuclide diffusion in this rock: the through-diffusion (TD) method and the instantaneous planar source (IPS) methods. For the conservative tracers HTO and 36Cl, the effective diffusion coefficients, De, were obtained by the TD method, which was applied to the consolidated material taken at different orientations with respect to the bedding plane (parallel and normal). This revealed a negligible anisotropy of the rock. To analyze the effect of the water saturation degree, the IPS method was used, which was shown to be very suitable for evaluating these effects. For these tests, the samples were crushed, adequately hydrated, and compacted. The apparent diffusion coefficient, Da, was determined for all the tracers at five different water saturation degrees. For each of the tracers investigated, the results indicated that, when the water saturation decreased from 100% to 60%, the Da also decreased by at least one order of magnitude: for HTO, this decrease was from 1.5 × 10−9 to 2.3 × 10−10 m2/s; that for 36Cl was from 4.6 × 10−10 to 2.8 × 10−11 m2/s; and that for 75Se was from 3.6 × 10−11 to 8.3 × 10−13 m2/s. The experimental diffusion profiles of HTO and 36Cl could be satisfactorily fitted considering a unique diffusion coefficient, whereas the profiles of 75Se could not. This behavior is related to the existence of different species of selenium in the system, or to different retention mechanisms.

Chloride penetration and binding behavior in unsaturated alkali-activated slag mortars

A comprehensive study from detailed microstructure analyses to mass transport investigations was implemented to explore chloride penetration of unsaturated alkali-activated slag (AAS) mortars accounting for chloride binding behaviors. Unsaturated chloride penetrations reflected from diffusion cases of instantaneous plane source and sorption cases of wetting-drying exposure were elaborated in relation to solid hydrates and pore structure features. It is found that the specimen with lower saturation has a slower chloride diffusion but a larger chloride penetration under wetting-drying cycles. Slag mortars with sodium hydroxide activation exhibit higher chloride binding capacity owing to more hydrotalcite-like phases and higher Ca/Si ratio of C-(N-)A-S-H gels in the outer product zones as compared to sodium silicate activated slag mortars, regardless of the saturation. Accelerations of the chloride penetration under the wetting-drying exposure are limited in saturated AAS specimens while for unsaturated AAS specimens more wetting-drying cycles result in the inner layers to be gradually diffusion-controlled. The chloride binding capacity of AAS specimens follows Langmuir's isotherm and clearly decreases with a lower saturation. It is advised to consider the electrical double layer effect within narrow pores when applying rapid chloride migration tests for AAS systems.

CFD simulations of instantaneously released liquefied gas in urban areas: A case study of LPG tank truck accident in Wenling, China

The accidental release and ignition of flammable liquefied gas can cause catastrophic events, such as flash fires, vapor cloud explosions, and boiling liquid expanding vapor explosion, which severely endanger urban residents and the environment. In the current study, a method for simulating liquefied gas instantaneous release accidents was established to explore the vapor cloud diffusion behavior in urban areas. The rare liquefied petroleum gas instantaneous release accident in Wenling, China is considered as a test case. To this end, an instantaneous release source model that considers the gas phase, liquid pool, and droplets was developed. The CFD model was validated using the damage distribution at the accident site. The simulation results revealed that droplets in the release source, terrains, and large obstacles significantly affected the dispersion behavior and extension distance of the vapor cloud. The evaporation of droplets resulted in a mushroom-shaped cloud. In addition, when the cloud was ignited, the area covered by the LFL was 1.94 and 2.07 times larger in the cases with droplets than those without. The method developed in this study is applicable to developing hazardous chemical transportation and emergency response measures in urban environments to maintain the sustainable cities development.

Plane and linear blow-up and source

Nonrelativistic equations of continuum mechanics are invariant with respect to space translations and Galilean translations. These symmetries form the 6-parameter group. The 3-dimensional subgroup of the general type containing the Galilean subgroup produces invariant solutions with the blow-up and the instantaneous source. The subgroup generating the solutions with the plane and linear blow-up and source or with both singularities together is considered. Gas particles move along a straight line for the invariant solutions and along plane curvilinear trajectories for the partially invariant solutions with special state equations. The classification of the state equations for these solutions with constant entropy is obtained. Simple solutions for the polytropic gas and the specific gas are found.