Three-dimensional Large Eddy Simulation Research Articles

Internal Nozzle Flow Simulations of the ECN Spray C Injector under Realistic Operating Conditions

<div class="section abstract"><div class="htmlview paragraph">In this study, three-dimensional large eddy simulations were performed to study the internal nozzle flow of the ECN Spray C diesel injector. Realistic nozzle geometry, full needle motion, and internal flow imaging data obtained from X-ray measurements were employed to initialize and validate the CFD model. The influence of injection pressure and fuel properties were investigated, and the effect of mesh size was discussed. The results agreed well with the experimental data of mass flow rate and correctly captured the flow structures inside the orifice. Simulations showed that the pressure drop near the sharp orifice inlet triggered flow separation, resulting in the ingestion of ambient gas into the orifice via a phenomenon known as hydraulic flip. At higher injection pressure, the pressure drop was more significant as the liquid momentum increased and the stream inertia was less prone to change its direction. Two fuels were tested in both experiments and simulations, namely iso-octane and n-dodecane. With the former, the gas species in the low-pressure region consisted of both fuel vapor and non-condensable gas. With n-dodecane, due to its low saturation pressure, fuel vapor was practically absent. Furthermore, it was found that fuel cavitation might not be the only phenomenon able to trigger flow separation, as “pseudo-cavitation” caused by non-condensable gas expansion played a similar role in promoting the conditions that led the flow to detach from the wall. Finally, it was found that a minimum mesh size of 10 μm within the orifice was sufficient to ensure the main flow features were captured. However, it was shown that finer meshes allowed for better resolution of the near-wall gas layer, resulting in more flow features to be resolved.</div></div>

Large-Eddy Simulations of a Reactive Solid Rocket Motor Plume

Large-eddy simulation (LES) of a solid rocket motor plume is performed with a reduced chemical scheme that is able to describe the postcombustion occurring in the multispecies supersonic plume between the unburnt exhaust and ambient air. The reduced chemical scheme is first evaluated on laminar flame cases in conditions representative of those encountered in the LES of the reactive plume. The reduced mechanism is then applied to three-dimensional LES, which provides a more detailed representation of the structure of the solid rocket motor exhaust plume compared with previous studies based on one-dimensional box models or three-dimensional Reynolds-averaged Navier–Stokes simulations. The present chemical model does not include alumina particles, whose effects at the plume scale are still uncertain, yet the simulation offers a prediction of the chlorine species distribution, which is known to produce strong interactions with stratospheric ozone, eventually leading to ozone depletion.

Numerical and experimental studies on the aerodynamics of a 5:1 rectangular cylinder at angles of attack

The aerodynamic behavior of a 5:1 rectangular cylinder at angles of attack (AoA) up to 15° is investigated based on Three-dimensional Large-Eddy Simulations (3D LES) and instantaneous pressure measurements. The numerical results indicate that the separated flow is highly sensitive to AoA and involves two patterns: (i) the flow reattaches to the bottom surface and the length reduces as AoA increases, (ii) the separation bubble around the top surface grows with AoA and does not reattach as AoA≥4°. The relationships between flow topology and the pressure statistics are obtained numerically by addressing their distributions in different flow regimes. With respect to these relationships, the differences between the separated-reattached and fully separated flows are determined. On the basis of these relationships, the influence of AoA on the mean, fluctuation, phase difference and, chordwise and spanwise correlations of pressures are studied experimentally. There is a close correspondence between each parameter and the length of the separation bubble, which involves different fluid phenomena in the chordwise and spanwise directions. Furthermore, a weak low-frequency flapping motion is observed in the separation bubble at large AoAs when the main vortex center behind the tail corner. Finally, the influences of AoA on the unsteady and spanwise features of the total forces are analyzed.

Numerical investigation of the separated and reattaching flow over a 5:1 rectangular cylinder in streamwise sinusoidal flow

Three-dimensional Large-Eddy Simulations (3D LES) are performed to study the separated and reattaching flow over a 5:1 rectangular cylinder in streamwise sinusoidal flow. The ratio of inflow frequency to natural vortex-shedding frequency is varied from 0 to 6 ​at five amplitudes up to 60% of the time-mean velocity. The effect on the two-dimensional (2D) and three-dimensional (3D) characteristics of the separation bubble and surface pressures are reported. The relationship between the time-averaged flow field and the statistics of the chordwise pressure distribution are obtained firstly. The flow-pressure relationships are qualitatively similar in uniform and sinusoidal flows. Then, the amplitude-frequency domain of the sinusoidal flow is divided into three regimes to describe the effects on the mean reattachment length. The simulations capture the interferences between leading-edge vortices and trailing edge vortices for longer separation bubbles. However, the interactions are not observed in shorter separation bubbles due to the diffusions of leading-edge vortices. Finally, the flow three-dimensionality is studied by performing proper orthogonal decomposition (POD) and spanwise correlation analysis on the surface pressures. The oncoming flow oscillations correspond to the most energetic structures dominating the pressure field, which are constant in the spanwise direction. While the local vortical structures mainly influence the 3D features of the flow dynamics.

Computational fluid dynamics approaches to drag and wake of a long-line mussel dropper under tidal current.

Hydrodynamic effects of mussel farms have attracted increased research attentions in recent years. The understanding of the hydrodynamic impacts is essential for predicting the sustainability of mussel farms. A large mussel farm includes thousands of mussel droppers, and the combined drag on the mussel droppers is sufficient to possibly affect the longevity of the entire long-lines. This article intends to study the drag and wake of an individual long-line mussel dropper using computational fluid dynamics approaches. Two equivalent rough cylinders, namely, Curved-Model and Sharp-Model, have been utilized to simulate the mussel dropper, and each rough cylinder is assigned with surface roughness. The porosity is not considered in this article due to its complexity from inhalant and exhalant of mussels. Two-dimensional laminar simulations are conducted at Reynolds number from 10 to 200, and three-dimensional large eddy simulations are conducted at subcritical Reynolds number ranging from 3900 to . The results show that larger drag coefficients and Strouhal numbers are attributed to surface roughness and sharp crowns on the rough cylinder. The obtained drag coefficient ranges from 1.1 to 1.2 with respect to the diameter of the mussel dropper and the peak value of the tidal velocities. Wakes behind rough cylinders fluctuate more actively compared to those of smooth cylinders. This research work provides new insight for further investigations on hydrodynamic interactions between fluid and mussel droppers.

대규모 와 모사에 의한 1피치 소형 나선형 축류홴의 운전부하에 따른 난류유동장 구조에 대한 연구

The unsteady-state, incompressible and three-dimensional large eddy simulation (LES) was performed to analyze the structure of turbulent flow fields according to the operating load of one-pitched small-size helical axial fan (SSHAF). The static pressure coefficient distribution according to the flow coefficient of SSHAF does not include stall, and the maximum static pressure efficiency is about 13% higher than that of conventional small-size axial fan. The typical axial flow developed downstream of SSHAF decreases with increasing operating load, and external axial flow outside the fan center develops radially. There is a reverse flow in the internal flow developed downstream from the hub of SSHAF. As the operating load increases, the absolute velocity of the reverse flow increases and its space gradually increases to approach the hub side. Even with increasing operating load, the flow that develops downstream of SSHAF does not include full radial flow, unlike conventional small-size axial fan.

저선회 모델 연소기의 스월러 코어 막힘률에 따른 난류연소유동장에 관한 수치적 연구

A low swirl combustor is an alternative technology to sustain a stable flame and to meet the required emission restriction of industrial gas turbine engines. The flame is lifted above the combustor front wall due to a balance between the flame speed and the local flow velocity. The present study is on the numerical simulations of reacting flows of a low swirl model combustor. The flamelet-generated manifold (FGM) method, which is one of the combustion chemistry reduction techniques, is coupled with a large eddy simulation solver. For a premixed CH₄ and air inflow at an equivalence ratio of 0.65, the combustion flow field in the combustor is investigated for two kinds of core blockage configurations, using three-dimensional large eddy simulations based on FGM. Compared to conventional swirl combustors, the low swirl model combustor presents turbulent core flow through the center body of the swirler, which turns out to play an important role in producing stable lifted flames.

Large-eddy simulation of the near wake of a 5:1 rectangular cylinder in oscillating flows at Re=670

In this study, three-dimensional Large-Eddy Simulations (3D LES) are conducted to investigate the near-wake characteristics of a 5:1 rectangular cylinder in oscillating flow. The oscillating flow is generated by introducing a sinusoidal velocity perturbation to the smooth flow at a low Reynolds number. It is observed that the dynamics of the vortices on the upper and lower surfaces are synchronously affected by the oscillating flow, and thus interact with the wake flow. Consequently, the vortex shedding patterns that appear are less regular than those in uniform flow, resulting in a non-synchronous phenomenon between the shedding of the wake vortices and the leading-edge vortices. Interestingly, the complex near-wake dynamics in the oscillating flow are characterized by multiple peaks of the wake velocity in the frequency domain. The energy contributions of each frequency component are studied through POD analysis. The results indicate that the flow structures of Modes 1 and 2 are of Kármán vortices which dominate the velocity fluctuations in the wake and exhibit the most prominent peak in the velocity spectra. In contrast, Modes 3 and 4 are controlled by the inflow oscillations. The higher modes result from the interactions between the above two patterns. It is worth noting that the shedding frequency, longitudinal spacing and convective speed of the Kármán vortices are synchronously influenced by the inflow frequency and amplitude.

Channel width, bedform length and turbulence: numerical investigation of flow dynamics over laboratory-scale pool–riffle sequences

Spatial dimensions of bedforms relative to the flow depth are of great interest for both engineers and geoscientists, and continue to be an active area of research. These morphological features are of significant consequence for critical hydrodynamic parameters, which in turn has an impact on sediment and solute transport through the river system. In this study, we present results from three-dimensional large eddy simulation of flows over such bedforms in a straight channel. Rigid three-dimensional pool–riffle structures occupying the full span of the channel were considered as the macro-bedforms. The presence of pool–riffle affects the spatial heterogeneity of the flow parameters such as lateral flow concentration. We observed that the lateral flow concentration increases in convective deceleration (CDF) zone with peak values at the central plane in channels with narrower span. The peak values shift from the central plane towards sidewall in channels with larger width. Flow recovery is found to be faster in narrower channels in the conducted simulations. High-magnitude counter-rotating vortices (HCRVs) in CDF and pool transport the momentum of the flow towards the centre of the channel. Larger channel width ensures persistent presence of HCRV in CDF and pool. Longer riffle length in the streamwise direction is observed to further alter the lateral flow concentration compared to the shorter riffles. Instantaneous bed shear stress mapping reveals the presence of coherent high- and low-velocity streaks on riffles. The coherence of these structures is lost in CDF and pool accompanied with an increase in turbulence represented by an increase in turbulent kinetic energy and Reynolds stress.

A population balance model for large eddy simulation of polydisperse droplet evolution

In the context of many applications of turbulent multi-phase flows, knowledge of the dispersed phase size distribution and its evolution is critical to predicting important macroscopic features. We develop a large eddy simulation (LES) model that can predict the turbulent transport and evolution of size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, and occurring at low volume fraction. We use a population dynamics model for polydisperse droplet distributions specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. We model the number density fields using an Eulerian approach for each bin of the discretized droplet size distribution. Following earlier methods used in the Reynolds-averaged Navier–Stokes framework, the droplet breakup due to turbulent fluctuations is modelled by treating droplet–eddy collisions as in kinetic theory of gases. Existing models assume the scale of droplet–eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. After initial comparisons of the one-dimensional model to measurements of oil droplets in an axisymmetric jet, it is then applied in a three-dimensional LES of a jet in cross-flow with large oil droplets of a single size being released at the source of the jet. We model the concentration fields using $N_{d}=15$ bins of discrete droplet sizes and solve scalar transport equations for each bin. The resulting droplet size distributions are compared with published experimental data, and good agreement for the relative size distribution is obtained. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behaviour.

Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios

Three-dimensional large eddy simulations were carried out to investigate the flow over two tandem square cylinders for a fixed spacing ratio of L/D = 4 and a Reynolds number of 5.3 × 103, where L is the cylinder center-to-center distance between the cylinders and D is the cylinder width. The corners of each cylinder were chamfered with a ratio of ξ = B/D = 0%, 5%, 10%, and 15%, where B is the chamfered corner dimension. The focus is given on how ξ influences the flow structure, wake recirculation bubble, flow separation bubble, Strouhal number (St), aerodynamic force, and phase lag (ϕ) between vortex sheddings from the cylinders. With increasing ξ, the recirculation bubble length and minimum velocity in the wake of the upstream cylinder remain more or less constant and are close to those of a single cylinder, while the minimum velocity in the wake of the downstream cylinder dramatically drops between ξ = 0% and 5%. While the flow over the downstream remains attached on the side surfaces, that over the upstream cylinder forms primary and secondary side-surface bubbles on the side surface, and both shrink with increasing ξ. In addition, the leading chamfered corners are accompanied by corner bubbles that play an important role in the flow structure modification. Therefore, the time-mean drag and fluctuating lift of the upstream cylinder remarkably decrease for 0% ≤ ξ ≤ 5% and remain almost unchanged for 5% < ξ ≤ 15%, whereas those on the downstream cylinder diminish in the whole range of 0% ≤ ξ ≤ 15%. The Strouhal number (St) being identical for the two cylinders grows from 0.104 to 0.132 when ξ is increased from 0% to 15%. Overall, the influence of ξ on the wake structure and aerodynamics is remarkable for 0% ≤ ξ ≤ 5% because of the corner bubbles and is less for 5% < ξ ≤ 15%.

Single-Phase Instability in Non-Premixed Flames Under Liquid Rocket Engine Relevant Conditions

Under rocket-relevant conditions, real-gas effects and thermodynamic nonidealities are prominent features of the flow field. Experimental investigations indicate that phase separation can occur, depending on the operating conditions and on the involved species in the multicomponent flow. During the past decades, several research groups in the rocket combustion community have addressed this topic. In this contribution, a high-fidelity thermodynamic framework comprising real-gas and multicomponent phase-separation effects is employed to investigate liquid-oxygen/methane and liquid-oxygen/hydrogen flames at high pressure. A thorough introduction and discussion on multicomponent phase separation are conducted. The model is validated with experimental data and incorporated in a reacting flow computational fluid dynamics code. Using one-dimensional counterflow diffusion flames, the thermodynamic states and processes are discussed. Both real-gas and phase-separation effects are present and quantified in terms of derived properties. Finally, the method is applied in a three-dimensional Large-Eddy Simulation of a single-element reference test case, and the results are compared to experimental data.

Numerical study of wake and aerodynamic forces on two tandem circular cylinders at Re = 103

Three-dimensional large eddy simulations were carried out to investigate the flow around two tandem circular cylinders at a subcritical Reynolds number of Re = 103. The cylinder center-to-center spacing ratio L/D is varied from 1.25 to 6, where D is the cylinder diameter. In order to enhance the understanding of flow physics around two circular cylinders, particular attention is devoted to fluctuating forces, shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), and phase lag (ϕ) between the fluctuating lift of the two cylinders. The flow structure around the cylinders is highly sensitive to L/D. A change in L/D thus leads to overshoot flow (L/D ≤ 1.25), reattachment flow (1.5 ≤ L/D ≤ 3.5), and coshedding flow (L/D ≥ 4). The boundaries are characterized by drastic changes in the flow structure and a discontinuous drop/rise in St and forces. The St drops at the boundary between overshoot and reattachment flow regimes and jumps at the boundary between reattachment and coshedding flow regimes, while fluctuating forces and ϕ both jump at both boundaries. The flow separation on the downstream cylinder is much delayed (122°–128°) in the reattachment flow regime compared to that on the single cylinder (95°) or upstream cylinder (92°–95.5°). The fluctuating pressure on the entire surface of either cylinder is low for the overshoot flow because the two cylinders are enclosed by the upstream-cylinder-generated shear layers having the longest wake recirculation. The ϕ is almost zero in the overshoot flow. With increasing L/D, ϕ linearly increases in the reattachment and coshedding regimes with different gradients, larger in the latter regime than in the former, by nearly twice.

Resolvent-analysis-based design of airfoil separation control

We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of$23\,000$and a free-stream Mach number of$0.3$are considered at two post-stall angles of attack of$6^{\circ }$and$9^{\circ }$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.

The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Downslope Regime

AbstractThe dynamics of a stratified oceanic bottom boundary layer (BBL) over an insulating, sloping surface depend critically on the intersection of density surfaces with the bottom. For an imposed along-slope flow, the cross-slope Ekman transport advects density surfaces and generates a near-bottom geostrophic thermal wind shear that opposes the background flow. A limiting case occurs when a momentum balance is achieved between the Coriolis force and a restoring buoyancy force in response to the displacement of stratified fluid over the slope: this is known as Ekman arrest. However, the turbulent characteristics that accompany this adjustment have received less attention. We present two estimates to characterize the state of the BBL based on the mixed layer thickness: Ha and HL. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of HL makes use of a newly defined slope Obukhov length Ls that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of Ha can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/Ha that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale Ls can also be used to obtain an expression for the wall stress when the BBL relaminarizes. We validate these relationships using output from a suite of three-dimensional large-eddy simulations. We conclude that the BBL reaches the relaminarized state before the steady Ekman arrested state. Calculating H/Ha and H/HL from measurements will provide information on the stage of oceanic BBL development being observed. These diagnostics may also help to improve numerical parameterizations of stratified BBL dynamics over sloping topography.

Autoignition-cascade in the windward mixing layer of a premixed jet in hot vitiated crossflow

This numerical study builds upon the experimental work of Wagner et al., e.g. [Combust. Flame 176 (2017)], and focuses on the flame stabilization mechanism of a reactive jet in crossflow (RJICF). A 300 K premixed ethylene-air jet (ϕj=1.2) is injected into a hot vitiated crossflow at 1500 K. A compressible three-dimensional (3-D) large eddy simulation (LES) was performed with an analytically reduced chemistry mechanism. Comparisons between LES and experiments are in good agreement in terms of jet trajectories and flow velocities. The LES captures the flame-flow interactions that were experimentally observed in the central plane of the RJICF by means of particle image velocimetry and OH planar laser-induced fluorescence. It gives access to the spatio-temporal evolution of the autoignition process along the windward mixing layer of the RJICF. Chemical explosive mode analysis shows that autoignition is the dominant flame stabilization mechanism on the windward side of the jet. “Low-heat-release” autoignition starts at the front root of the jet, at the “very lean” most reactive mixture fraction, which is the spot where the autoignition time of the mixture is the smallest. Immediately downstream, the released heat is advected and diffuses, contributing to a decrease of autoignition times in the neighboring richer inner side of the jet. Autoignition in this richer layer of the jet is characterized by higher heat release rate that again diffuses toward even richer regions until the stoichiometric layer ignites. This autoignition-cascade mechanism determines the position of the “visible” windward flame. Moreover, a 3-D flame analysis shows that the resulting “high-heat-release” autoignition patches expand within the stoichiometric layer and ultimately merge with the leeward propagating flame while being advected toward the flame tip. It is also shown that the latter layer, and therefore the growing autoignition patches, get wrinkled by the coherent structures that originate from the hydrodynamically unstable front root of the jet in crossflow.

Effect of Nozzle Port Angle on Transient Flow and Surface Slag Behavior During Continuous Steel-Slab Casting

Undesirable flow variations can cause severe instabilities at the interface between liquid mold flux and molten steel across the mold top-region during continuous steel casting, resulting in surface defects in the final products. A three-dimensional Large Eddy Simulation (LES) model using the volume of fluid method for the slag and molten steel phases is validated with plant measurements, and applied to gain new insights into the effects of nozzle port angle on transient flow, top slag/steel interface movement, and slag behavior during continuous slab casting under nominally steady conditions. Upward-angled ports produce a single-roll flow pattern with lower surface velocity, due to rapid momentum dissipation of the spreading jet. However, strong jet wobbling from the port leads to greater interface variations. Severe level drops allow easy entrapment of liquid flux by the solidifying steel shell at the meniscus. Sudden level rises may also be detrimental, leading to overflow of the solidified meniscus region. Downward-angled ports produce a classic double-roll pattern with less jet turbulence and a more stable interface everywhere except near the narrow faces. Finally, the flow patterns, surface velocity, and level predicted from the validated LES model are compared with steady-state standard k-e model predictions.

Numerical investigation of internal solitary waves of elevation type propagating on a uniform slope

Numerous laboratory-scale physical experiments and numerical simulations have been carried out to explore the shoaling dynamics of internal solitary waves (ISWs) on slope topographies. Detailed features during wave breaking have been investigated under relatively low Reynolds numbers, but for real ocean-scale or lake-scale scenarios with a much higher Reynolds number, laboratory-scale modeling is inadequate to capture the three-dimensional turbulent characteristics in the wave shoaling process. As a result, a three-dimensional large-eddy simulation (LES) is performed in the present study to investigate the shoaling process of the elevation-typed ISWs traveling on uniform slopes in a two-layer fluid system. Scale effects due to the Reynolds numbers (varied from 103 to 105) and three-dimensional characteristics during wave shoaling are also explored and discussed. Detailed ISW-slope interaction dynamics, including the typical shoaling features, the characteristics of internal boluses, and both the velocity field and the energy transformation, are systematically obtained and analyzed. It is found that, while reaching the maximum vertical displacement (i.e., maximum run-up height), the frontal part of the heavier lower-layer fluid can evolve into the internal bolus if the internal Iribarren number, Ir, defined as the ratio of the topographic slope and the square root of the incident wave steepness, is less than 0.65. The maximum wave-induced velocities and energy loss are also well related to Ir. Empirical regressed equations for seven important physical parameters during the shoaling process are also proposed. The extreme velocities, wave energy loss, and three-dimensionality of the flow field are all identified to be very sensitive to Reynolds numbers, indicating that traditional two-dimensional laboratory-scale modeling tools may be insufficient to accurately capture the shoaling mechanisms of the ISWs of elevation type.

Broadening of Modeled Cloud Droplet Spectra Using Bin Microphysics in an Eulerian Spatial Domain

Abstract This study investigates droplet size distribution (DSD) characteristics from condensational growth and transport in Eulerian dynamical models with bin microphysics. A hierarchy of modeling frameworks is utilized, including parcel, one-dimensional (1D), and three-dimensional large-eddy simulation (LES). The bin DSDs from the 1D model, which includes only vertical advection and condensational growth, are nearly as broad as those from the LES and in line with observed DSD widths for stratocumulus clouds. These DSDs are much broader than those from Lagrangian microphysical calculations within a parcel framework that serve as a numerical benchmark for the 1D tests. In contrast, the bin-modeled DSDs are similar to the Lagrangian microphysical benchmark for a rising parcel in which Eulerian transport is not considered. These results indicate that numerical diffusion associated with vertical advection is a key contributor to broadening DSDs in the 1D model and LES. This DSD broadening from vertical numerical diffusion is unphysical, in contrast to the physical mixing processes that previous studies have indicated broaden DSDs in real clouds. It is proposed that artificial DSD broadening from vertical numerical diffusion compensates for underrepresented horizontal variability and mixing of different droplet populations in typical LES configurations with bin microphysics, or the neglect of other mechanisms that broaden DSDs such as growth of giant cloud condensation nuclei. These results call into question the ability of Eulerian dynamical models with bin microphysics to investigate the physical mechanisms for DSD broadening, even though they may reasonably simulate overall DSD characteristics.

Analysis of mild ignition in a shock tube using a highly resolved 3D-LES and high-order shock-capturing schemes

A highly resolved three-dimensional large-eddy simulation (LES) is presented for a shock tube containing a stoichiometric hydrogen–oxygen ( $$\hbox {H}_2$$ / $$\hbox {O}_2$$ ) mixture, and the results are compared against experimental results. A parametric study is conducted to test the effects of grid resolution, numerical scheme, and initial conditions before the 3D simulations are presented in detail. An approximate Riemann solver and a high-order interpolation scheme are used to solve the conservation equations of the viscous, compressible fluid and to account for turbulence behind the reflected shock. Chemical source terms are calculated by a finite-rate model. Simultaneous results of pseudo-Schlieren, temperature, pressure, and species are presented. The ignition delay time is predicted in agreement with the experiments by the three-dimensional simulations. The mechanism of mild ignition is analysed by Lagrangian tracer particles, tracking temperature histories of material particles. We observed strongly increased temperatures in the core region away from the end wall, explaining the very early occurrence of mild ignition in this case.