Homogeneous Concentration Research Articles

Particle transport and deposition in wall-sheared thermal turbulence

We studied the transport and deposition behaviour of point particles in Rayleigh–Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number ( $Ra$ ) in the range $10^{7} \leq Ra \leq ~10^9$ with a fixed Prandtl number $Pr = 0.71$ , while the wall-shear Reynolds number ( $Re_w$ ) is in the range $0 \leq Re_w \leq ~12\,000$ . With the increase of $Re_w$ , the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number ( $St$ ), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium $St$ particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large $St$ particles, the turbulent flow structure had a minor influence on the particles’ motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium $St$ particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small $St$ particles settle with an exponential deposition ratio and large $St$ particles settle with a linear deposition ratio. For medium $St$ particles, where complex particle–turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$ .

Numerical Study of Detonation Waves in Gas Suspensions with Spatially Inhomogeneous Particle Concentration Distribution in Sharply Expanding Pipes

The article presents some results of a numerical study of detonation waves in gas suspensions with a spatially inhomogeneous distribution of particle concentration in sharply expanding pipes obtained by the large particle method. The purpose of the research is to study the influence of pipeline geometry and longitudinally spatially inhomogeneous distribution of particle concentration on the propagation of detonation waves in gas suspensions. It is shown that the size of the narrow and wide parts of the pipeline, as well as, the spatially inhomogeneous distribution of particle concentrations, qualitatively and quantitatively affect this process. Three detonation modes have been identified: continuous wave propagation, complete cessation, and partial disruption with subsequent recovery. It has been established that, at a fixed total mass of suspension, a layer with a linearly decreasing law of change in the concentration of unitary fuel particles better attenuates detonation waves than with a linearly increasing and homogeneous one.

Compressive behaviors and deformation mechanism of carbon fiber reinforced epoxy composites: A microscopic and molecular dynamics perspective

AbstractInvestigating the macro‐mechanical properties of polymer composites at the nanoscale is a challenging topic. Here we report the compressive performances of carbon fiber‐reinforced epoxy composites using molecular dynamics (MD) simulations. The evolution of microstructure and microscopic energy, including free volume, radius of gyration, dihedral angle, potential energy, and interaction energy, has been investigated to characterize compressive behaviors at the nanoscale. Molecular chains gradually bend, and the movement space of the molecular chains decreases during compression loading. The radius of gyration and dihedral angle are deformed into a state of irreversible plasticity to accommodate the microstructural transformation. The interaction energy increases and subsequently declines as the carbon fiber/epoxy interface gets closer, reflecting the transition of the internal structure. The inhomogeneity and interfacial concentration distribution of stress, and local molecular stiffness under various strains have been obtained to reveal the nanoscopic mechanism of epoxy failure and interface delamination during compression. This study reveals the compression behaviors and deformation mechanism of carbon fiber‐reinforced epoxy composites at the molecular level, providing directions and possibilities for molecular design and structural optimization of composites.Highlights The nanoscopic compression deformation of CFRP composites is studied. Microstructural evolution and conformation transformation are revealed. The evolution and transition of microscopic energy are analyzed. Micro‐mechanism of epoxy deformation and interface delamination is elucidated.

Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

Study of the features of concentration inhomogeneities during the on ground-based processing of the space experiment of the Ge(Ga) crystals growth

The article presents the results of the preparation and ground testing of the space experiment for growing Ge (Ga) crystals, planned on board the multifunctional laboratory module as part of the ISS RS. Under the conditions simulating microgravity, the features of the formation of concentration inhomogeneity in the form of growth bands when growing crystals under various thermal conditions (in the presence or absence of a free melt surface (Marangoni convection)), as well as when changing technological parameters (variations in growth rate) were investigated. Based on the obtained results of metallographic and electrophysical studies, conclusions were made about the peculiarities of the influence of the technological parameters of the crystallization process on the structural perfection of the grown crystals under microgravity conditions

Mathematical Models of Diffusion in Physiology.

Diffusion is a mass transport phenomenon caused by chaotic thermal movements of molecules. Studying the transport in specific domain is simplified by using evolutionary differential equations for local concentration of the molecules instead of complete information on molecular paths [1]. Compounds in a fluid mixture tend to smooth out its spatial concentration inhomogeneities by diffusion. Rate of the transport is proportional to the concentration gradient and coefficient of diffusion of the compound in ordinary diffusion. The evolving concentration profile c(x,t) is then solution of evolutionary partial differential equation deltac/deltat=DDeltac where D is diffusion coefficient and Delta is Laplacian operator. Domain of the equation may be a region in space, plane or line, a manifold, such as surface embedded in space, or a graph. The Laplacian operates on smooth functions defined on given domain. We can use models of diffusion for such diverse tasks as: a) design of method for precise measurement of receptors mobility in plasmatic membrane by confocal microscopy [2], b) evaluation of complex geometry of trabeculae in developing heart [3] to show that the conduction pathway within the embryonic ventricle is determined by geometry of the trabeculae.

Development of the full Lagrangian approach for modeling dilute dispersed media flows (a review)

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, “folds” and “puckers” of the phase volume may arise, and “caustics” (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows. This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of “gas-particle” media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media.

Void Evolution on the Li-Solid Electrolyte Interface in Solid-State Batteries: A Parametric Study Under Varied Mechanical and Electrochemical Conditions

Void growth during the plating and stripping process is an important interfacial phenomenon that hinders the development of Li-metal solid-state batteries (SSBs) because it can potentially result in inter-component delamination or growth of Li dendrites. Behind the void growth is the complex interaction between electrochemistry and mechanics. Voids usually grow from micro- or nanoscale initial imperfections on the Li-solid electrolyte (SE) interface. It is, therefore, important to analyze the stress concentration at the initial void tips, which largely determines the growth/shrinking of the void as well as the consequent changes in the internal resistance and overall battery efficiency. Recently, the development of in situ operando experimental technology has enabled the electro-chemo-mechanical characterization of the void growth phenomenon on the Li-SE interface. In this study, we explore how voids in SSBs evolve with a multi-physics model in COMSOL Multiphysics. Based on this model, we perform a systematic parametric study in the space of the mechanical stack pressure and the applied current density. The simulation results show different deformation patterns and potential failure mechanisms under different combination of stack pressure and current density. To better understand the phenomena, we develop an analytical solution to understand the void deformation induced by the inhomogeneous Li-ion concentration field under stack pressure. This analytical approach offers a complementary and intuitive perspective on the mechanical aspect of our simulation findings. By combining the simulation and analytical solutions, we depict a phase diagram, in which we identify the “safe zone” that will not result in void growth. The new insights of this research hold the promise of guiding the development of stabilized SSB interfaces.

XPS depth profiling of nano-layers by a novel trial-and-error evaluation procedure

In spite of its superior chemical sensitivity, XPS depth profiling is rarely used because of the alteration introduced by the sputter removal process and the resulting inhomogeneous in-depth concentration distribution. Moreover, the application of XPS becomes increasingly challenging in the case of the analysis of thin layers, if the thickness is in the range of 2–3 inelastic mean free paths (IMFP) of the photoelectrons. In this paper we will show that even in these unfavorable cases the XPS depth profiling is applicable. Herein the XPS depth profiling of a model system tungsten-carbide-rich nano-layer of high hardness and corrosion resistance is presented. We will show that the problems arising because of the relatively high IMFP can be corrected by introducing a layer model for the calculation of the observed XPS intensities, while the alteration, e.g. ion mixing, compound formation and similar artefact, introduced by the sputter removal process can be handled by TRIDYN simulation. The method presented here overcomes the limitation of XPS depth profiling.

Diffusion-induced stress amplification in phase-transition materials for electrodes of lithium-ion batteries

This work sheds the light on the stress amplification in active material particles of electrodes caused by the localized lithium concentration inhomogeneity due to phase transitions. This is a significant issue usually neglected in the literature, as generally the ideal Fickian diffusion model is used to describe the lithium diffusion, which particularly fails when dealing with phase change materials, resulting in the underestimation of the stress. In turn, this results in the underestimation of the fracture behavior of the electrode and the battery degradation, ultimately.To overcome these limitations, this work proposes a mechanical-transport model where the lithium transport is modeled according to the non-ideal solution theory with an equivalent diffusion coefficient depending on the potential of the host material vs Li/Li+. The results show that the proposed model correctly describes the concentration distribution within the particle of phase-change materials (graphite is chosen as a case study), in agreement with the existent experimental measurements. The differences with respect to the traditional Fickian diffusion model is substantial as the stress is up to 85% higher with the proposed model and the concentration distribution can capture the inhomogeneity caused by phase transitions.

Reduced internal stress of quasi-single crystalline Na4Fe3(PO4)2P2O7 electrode enhancing sodium-ion kinetics

A NASICON-type quasi-single crystalline Na4Fe3(PO4)2P2O7 (SC) cathode material was successfully synthesized via a freeze-drying method. The as-optimized SC sample displays both outstanding rate performance (107.9 and 88.5 mAhg−1 at 0.1C and 5C, respectively) and excellent cycling stability (88.1 % of capacity retention after 1000 cycles at 1C). Reduced sodium ion migration path of as-prepared SC cathode material effectively enhanced the kinetics of Na+ upon cycling. More importantly, the SC structure could suppress nearly 50 % of internal strain, prodigiously reducing the local stress accumulation accompanied by the inhomogeneous sodium concentration gradient during the charging/discharging processes. The smaller the stress accumulation, the more stable the crystal structure would be obtained, which maintained a more superb mechanical stability of the SC cathode material. At the same time, a high-spin state of Fe in the SC sample was confirmed by both of electron paramagnetic resonance and temperature-dependent magnetization susceptibility, indicating that the eg orbital occupation of Fe2+ could be regulated to optimize the bond strength between the reduction and oxidation processes. As a consequence, the band gap of SC material has decreased from 1.66 to 1.45 eV, and the electronic conductivity has increased from 6.0 to 32.4 μS/cm. It is believed that the SC cathode material could be a competitive candidate material for sodium ion batteries.

Research on the hazards of gas leakage and explosion in a full-scale residential building

The gas explosion in residential building has always been a highly concerned problem. Explosions in homogeneous mixtures have been extensively studied. However, mixtures are often inhomogeneous in the practical scenarios due to the differences in the densities of methane and air. In order to investigate the effects of gas explosions in inhomogeneous mixtures, experimental studies involving gas leakage and explosion are conducted in a full-scale residential building to reproduce the process of gas explosion. By fitting the dimensionless buoyancy as a function of dimensionless height and dimensionless time, a distribution model of gas in large-scale spaces is established, and the mechanism of inhomogeneous distribution of methane is also be revealed. Furthermore, the stratified reconstruction method (SRM) is introduced for efficiently setting up inhomogeneous concentration fields in FLACS. The simulation results highlight that for the internal overpressure, the distribution of methane has no effect on the first overpressure peak (ΔP1), while it significantly influences the subsequent overpressure peak (ΔP2), and the maximum difference between the overpressure of homogeneous and inhomogeneous distribution is 174.3%. Moreover, the initial concentration distribution also has a certain impact on the external overpressure.

The significance of partial volume effect on the estimation of hypoxic tumour volume with [18F]FMISO PET/CT

BackgroundThe purpose of this study was to evaluate how a retrospective correction of the partial volume effect (PVE) in [18F]fluoromisonidazole (FMISO) PET imaging, affects the hypoxia discoverability within a gross tumour volume (GTV). This method is based on recovery coefficients (RC) and is tailored for low-contrast tracers such as FMISO. The first stage was the generation of the scanner’s RC curves, using spheres with diameters from 10 to 37 mm, and the same homogeneous activity concentration, positioned in lower activity concentration background. Six sphere-to-background contrast ratios were used, from 10.0:1, down to 2.0:1, in order to investigate the dependence of RC on both the volume and the contrast ratio. The second stage was to validate the recovery-coefficient correction method in a more complex environment of non-spherical lesions of different volumes and inhomogeneous activity concentration. Finally, we applied the correction method to a clinical dataset derived from a prospective imaging trial (DRKS00003830): forty nine head and neck squamous cell carcinoma (HNSCC) cases who had undergone FMISO PET/CT scanning for the quantification of tumour hypoxia before (W0), 2 weeks (W2) and 5 weeks (W5) after the beginning of radiotherapy. Here, PVE was found to cause an underestimation of the activity in small volumes with high FMISO signal.ResultsThe application of the proposed correction method resulted in a statistically significant increase of both the hypoxic subvolume (171% at W0, 691% at W2 and 4.60 × 103% at W5 with p < 0.001) and the FMISO standardised uptake value (SUV) (27% at W0, 21% at W2 and by 25% at W5 with p < 0.001) within the primary GTV.ConclusionsThe proposed PVE-correction method resulted in a statistically significant increase of the hypoxic fraction (HF) with p < 0.001 and demonstrated results in better agreement with published HF data for HNSCC. To summarise, the proposed RC-based correction method can be a useful tool for a retrospective compensation against PVE.

Chemical Vapor Deposition of Tantalum Carbide in the TaBr5–CCl4–Cd System

The tantalum carbide coatings were deposited on substrates made of 12Kh18N10T steel, ZhC6 alloy, and molybdenum by reduction of TaBr5 and CCl4 vapors with cadmium vapors at temperatures of 950–1000 K. The average deposition rate of coatings on molybdenum was ~5 μm/h, on ZhC6 alloy was ~6 μm/h, and on 12Kh18N10T steel was ~8 μm/h. The coatings were formed as columnar grains on the substrate surface and as a diffuse layer in the substrate material. The surface layers contained mainly tantalum monocarbide TaCy (y = 0.72–0.86) and a small fraction of tantalum. The coatings on the surface of ZhC6 alloy and 12Kh18N10T steel flaked off with increasing thickness, which was due to different thermal expansion of the coating and substrate, as well as concentration inhomogeneity and phase transitions in the substrate material during coating deposition and during the heating and cooling processes.

Prediction model for vertical distribution of oil particles under thermal plume and displacement ventilation in a machining workshop

Oil particle concentrations exhibit an inhomogeneous distribution in large-space machining workshops with a displacement ventilation system. The inhomogeneous distribution can lead to variations in the required supply air volume used to control the indoor particle concentration at different heights. To rapidly calculate the particle concentration distribution in the vertical direction, this study established a zonal particle concentration prediction model based on the mass and energy balance by considering the interaction between the heat source thermal plume, wall thermal plume, and supply airflow. An experiment was conducted in a scaled chamber to validate the proposed prediction model. The result showed that the relative error between the prediction model and experiment ranged from −17% to 10%. A case study was performed to demonstrate the applicability of the prediction model to the control of a displacement ventilation system. Using the prediction model, the control system can maintain the particle concentration in the work area below 0.5 mg/m³with variable particle source emission rates and reduce the supply air volume by at least 24% and 55% compared with the variable and constant air volume systems, respectively, neither of which can address the inhomogeneous distribution of oil particle concentration. The prediction model can also be used for the design of displacement ventilation systems when the inhomogeneous particle concentration distribution is considerable.

Effect of hydrogen ratio on leakage and explosion characteristics of hydrogen-blended natural gas in utility tunnels

Based on computational fluid dynamics technology, the effect of hydrogen blending ratio (HBR) on the concentration distribution of leaked gas diffusion in utility tunnels was investigated, and based on this, the explosion characteristics of hydrogen-blended natural gas (HBNG) were studied in an inhomogeneous concentration field. The results showed that the concentration field of HBNG gradually stabilized in the downstream of the leak site, and the peak concentration increased linearly with HBR. When HBR≤5%, a high concentration region above the upper explosive limit is formed inside the gas cloud. This characteristic of the distribution induces secondary combustion in utility tunnels. The maximum flame velocity and steady acceleration distance increase with the increase of HBR. The flame shape is significantly affected by the concentration field distribution. The explosion overpressure induced by the real concentration field created multiple peak structures that exacerbated the explosion disaster complexity. The first overpressure peak at the ends was formed by the superposition of the precursor shock wave and its reflected wave, and those at other locations are caused by the shock waves. However, all maximum overpressure peaks are formed by the superposition of multiple reflections of the explosion wave. The maximum peak overpressure at both ends of the tunnel is higher than that in the middle. The explosion overpressure induced by the inhomogeneous gas cloud is lower than that caused by homogeneous gas cloud under the same volume. The research results can provide an effective reference for the anti-explosion design and risk assessment of utility tunnel.

The Feasibility of Static Shoulder Friction Stir Welding in Joining Dissimilar Metals of Al6061 and Ti6Al4V

In this study, static shoulder friction stir welding (SSFSW) is innovatively employed to join Al6061 and Ti6Al4V, aiming to minimize material mixing and intermetallic formation, significantly influencing the interfacial microstructure and joint strength. The results revealed that SSFSW reduced the intermetallic layer thickness at the interface, improving joint quality. The mutual interdiffusion of Al and Ti at the interface was influenced by an exothermic chemical reaction, forming an Al5Ti2–Al3Ti sequence due to the diffusion of Al into the Ti matrix. The microstructural analysis demonstrated better interfacial microstructural homogeneity in SSFSW joints than conventional FSW (CFSW), with finer titanium particle distribution. The larger particles resulted in coarser grains in CFSW, affecting the mobility of dislocations, which potentially led to the inhomogeneous concentration of dislocations at the interface. Recrystallization mechanisms varied between CFSW and SSFSW, with the Ti interface showing equiaxed and recrystallized grains due to the dynamic recovery driven by adiabatic shear bands. The tensile testing results of SSFSW exhibited a joint efficiency of 88%, demonstrating a 20.2% increase compared to CFSW, which can be attributed to differences in fracture modes. This study contributes to an understanding of dissimilar Al-Ti joining and provides insights for industries seeking to leverage the benefits of such combinations in lightweight and high-performance structures.

Enhanced RBE of Particle Radiation Depends on Beam Size in the Micrometer Range.

High-linear energy transfer (LET) radiation, such as heavy ions is associated with a higher relative biological effectiveness (RBE) than low-LET radiation, such as photons. Irradiation with low- and high-LET particles differ in the interaction with the cellular matter and therefore in the spatial dose distribution. When a single high-LET particle interacts with matter, it results in doses of up to thousands of gray (Gy) locally concentrated around the ion trajectory, whereas the mean dose averaged over the target, such as a cell nucleus is only in the range of a Gy. DNA damage therefore accumulates in this small volume. In contrast, up to hundreds of low-LET particle hits are required to achieve the same mean dose, resulting in a quasi-homogeneous damage distribution throughout the cell nucleus. In this study, we investigated the dependence of RBE from different spatial dose depositions using different focused beam spot sizes of proton radiation with respect to the induction of chromosome aberrations and clonogenic cell survival. Human-hamster hybrid (AL) as well as Chinese hamster ovary cells (CHO-K1) were irradiated with focused low LET protons of 20 MeV (LET = 2.6 keV/µm) beam energy with a mean dose of 1.7 Gy in a quadratic matrix pattern with point spacing of 5.4 × 5.4 µm2 and 117 protons per matrix point at the ion microbeam SNAKE using different beam spot sizes between 0.8 µm and 2.8 µm (full width at half maximum). The dose-response curves of X-ray reference radiation were used to determine the RBE after a 1.7 Gy dose of radiation. The RBE for the induction of dicentric chromosomes and cell inactivation was increased after irradiation with the smallest beam spot diameter (0.8 µm for chromosome aberration experiments and 1.0 µm for cell survival experiments) compared to homogeneous proton radiation but was still below the RBE of a corresponding high LET single ion hit. By increasing the spot size to 1.6-1.8 µm, the RBE decreased but was still higher than for homogeneously distributed protons. By further increasing the spot size to 2.7-2.8 µm, the RBE was no longer different from the homogeneous radiation. Our experiments demonstrate that varying spot size of low-LET radiation gradually modifies the RBE. This underlines that a substantial fraction of enhanced RBE originates from inhomogeneous energy concentrations on the µm scale (mean intertrack distances of low-LET particles below 0.1 µm) and quantifies the link between such energy concentration and RBE. The missing fraction of RBE enhancement when comparing with high-LET ions is attributed to the high inner track energy deposition on the nanometer scale. The results are compared with model results of PARTRAC and LEM for chromosomal aberration and cell survival, respectively, which suggest mechanistic interpretations of the observed radiation effects.

Experimental study on the effects of ignition position and inhomogeneous concentration on vented hydrogen deflagrations in a 7 m3 chamber

Vented inhomogeneous hydrogen deflagrations are conducted in a 7 m3 chamber. The effects of ignition position and inhomogeneous concentration are studied. The results show that a coupling flame structure of jet fire and flame bubble is first observed. In the case of top ignition, a M-shaped flame structure forms for average hydrogen concentration C¯H2≤ 10.14 vol%. In the cases of center ignition and bottom ignition, the flame bubble rapidly expands towards the walls and the horizontal propagation speed of upper part of flame bubble is obviously higher than that of lower part of flame bubble for C¯H2≥ 11.27 vol%. Moreover, the speed of horizontal flame front quickly decreases as the flame front moves away from the centerline of hydrogen jet. Three overpressure peaks appear in all scenarios, namely Popen, Phel and Pvib, which results from the vent failure, Helmholtz-type oscillations and thermo-acoustic oscillations respectively. The maximum overpressure dominated by Popen is nearly insensitive to C¯H2for top ignition. However, the maximum overpressure induced by center ignition or bottom ignition significantly increases when C¯H2≥ 10.14 vol%. For a given C¯H2, Pvib induced by bottom ignition is always the largest.

Quantifying the spatial inhomogeneity of ice concentration in mixed-phase stratiform cloud using airborne observation

The distribution of ice particles strongly affects the microphysical processes in mixed-phase clouds, but the inhomogeneity of ice distribution is not well understood. In this paper, based on airborne in-situ measurements from three flights on May 31, 2021 in Hulun Buir, China, the inhomogeneity and clustering of ice distribution in a stratiform cloud is quantitatively analyzed using the pair correlation function (PCF). The results show that ice clusters on scales of a few kilometers dominate the inhomogeneity of the ice distribution. Due to the cumulative impact of ice clusters on different scales, the probability of finding relative high ice concentration within a lag of 80 m can be enhanced by 0.1 to 3.5 times. On average, the scale of ice cluster is ∼100 m for a sampling distance of 1 km, and increases to 3.2 km for a sampling distance of 20 km. It is also found that the ice growth is not fast enough to cluster the ice water content (IWC), and the inhomogeneity of IWC is strongly influenced by ice generation in addition to ice growth in the observed cloud. The results are helpful to better understand the distribution of ice in mixed-phase cloud, and provide potentially important information to improve the parameterizations of microphysics in models.