Three-dimensional Eddy Research Articles

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.

Analysis of Rotating Machines by HDDM with Periodic B.C.

This paper deals with an efficient treatment of a periodic boundary condition in parallel environments for a three-dimensional non-steady eddy current analysis of a rotating machine as an example of a parallel finite element analysis including moving bodies. To reduce computation time, analysis domain is often reduced using the periodic boundary condition. In general, high efficiency in parallel computing with the periodic boundary condition is difficult to achieve.

Effect of an Electrically-Conducting Wall on Transient Magnetohydrodynamic Flow in a Continuous-Casting Mold with an Electromagnetic Brake

Large eddy simulation (LES) of transient magnetohydrodynamic (MHD) turbulent flow under a single-ruler electromagnetic brake (EMBr) in a laboratory-scale, continuous-casting mold is presented. The influence of different electrically-conductive boundary conditions on the MHD flow and electromagnetic field was studied, considering two different wall boundary conditions: insulating and conducting. Both the transient and time-averaged horizontal velocities predicted by the LES model agree well with the measurements of the ultrasound Doppler velocimetry (UDV) probes. Q-criterion was used to visualize the characteristics of the three-dimensional turbulent eddy structure in the mold. The turbulent flow can be suppressed by both configurations of the experiment’s wall (electrically-insulated and conducting walls). The shedding of small-scale vortices due to the Kelvin–Helmholtz instability from the shear at the jet boundary was observed. For the electrically-insulated walls, the flow was more unstable and changed with low-frequency oscillations. However, the time interval of the changeover was flexible. For the electrically-conducting walls, the low-frequency oscillations of the jets were well suppressed; a stable double-roll flow pattern was generated. Electrically-conducting walls can dramatically increase the induced current density and electromagnetic force; hence they contribute to stabilizing the MHD turbulent flow.

An irregularly shaped warm eddy observed by Chinese underwater gliders

Mesoscale eddies are important for transporting oceanic energy and matter. We investigated the three-dimensional structure of an irregularly shaped warm eddy using three Chinese underwater gliders and satellite data during May 2015 in the northern South China Sea. The warm eddy lasted for 2 months, remained quasi-steady, and had a mean radius of ~ 70 km from May 10 to May 31. The heat contents observed along the two glider tracks differed markedly, by 2 × 109 J/m2, which reflected an imbalance in the geostrophic and tangential velocity distributions of the eddy. The geostrophic/tangential velocity decreased/increased with depth within the warm eddy. The maximum tangential velocities calculated using the datasets from the two gliders were 0.8 and 0.25 m/s, respectively, confirming that the shape of the warm eddy was horizontally asymmetrical. Large errors can arise when the heat, energy, and matter transport for an irregularly shaped eddy are estimated using a regular circular model. We suggest that more intersecting glider tracks should be used to retrieve the three-dimensional eddy structure, and that those tracks should be better designed. The irregular shape of the warm eddy was likely induced by oceanic currents such as the wind-induced Ekman current. Further study is needed to elucidate the eddy–current interactions and the mechanisms thereof.

Initial dilution equations for wastewater discharge: Example of non-buoyant jet in wave-following-current environment

In this study, three semi-empirical equations are developed to quantify the wave effect on the initial dilution of wastewater discharge, which usually forms a turbulent jet. To develop the equations, data from a non-buoyant jet in a wave-following-current environment, which is realised using a three-dimensional large eddy simulation model, are used with 27 cases in total. The effects of the wave-to-current velocity ratio, jet-to-current velocity ratio, and Strouhal number are considered in the equations. The initial dilution equations, which focused on the jet visual area, cross-sectional minimum dilution, and vertical location of the cross-sectional minimum dilution, have vital relationships with the characteristic length scale. The reliability of the present equations is discussed by comparing them with existing equations for a jet in a crossflow-only environment. The applicability range of the present equations is illustrated by comparing them with data for a jet in a crossflow-only environment and data for other cases of a jet in a wave-following-current environment. The three equations provide references for the conceptual design of wastewater discharge. This study reveals that a surface wave with low energy has a positive effect on the initial dilution of wastewater discharge.

Dynamic Mode Decomposition of a Wing-Body Junction Flow

Junction flows are subject to an intense adverse pressure gradient and three-dimensional separation when encountering a wall-mounted obstacle. A dynamically rich horseshoe vortex system is formed in this region. In this study the junction flow at the interaction of a wing and a flat plate is investigated. The numerical modelling is carried out using the three-dimensional large eddy simulation (LES) approach at the Reynolds number Re = 1.15×105 based on the wing’s maximum thickness T and the free stream velocity Uref. The comparison with the experimental results shows that the numerical simulations fairly accurately reproduce the phenomenon under study. The dynamic mode decomposition (DMD) of the resolved flow field is employed to obtain the coherent dynamics of the flow. To clearly demonstrate the oscillation characteristics and the horseshoe vortex structures of junction flow the velocity field in the plane of symmetry is decomposed with eduction of two dominant DMDmodes. These two DMDmodes are reconstituted and developed, together with the mean flow mode to explain the latent dynamics. Mode 1 reveals the merging of the horseshoe vortices and mode 2 is responsible for the process of fission and stretching.

Autoignition flame dynamics in sequential combustors

This numerical study investigates the linear and non-linear flame dynamics in the second stage of a sequential combustor, with methane fuel injection into vitiated hot gas. It focuses on the heat release rate response of the sequential flame to entropy waves. The response is shown to be very sensitive to small changes in operating condition and excitation amplitude. One-dimensional (1-D) flame simulations were performed to identify transitions between three combustion regimes: autoignition, flame propagation and flame propagation assisted by autoignition. Three-dimensional (3-D) large eddy simulations (LES) were performed for two configurations: one that includes the fuel injector and the mixing section, and one with a perfectly premixed inlet. An analytically reduced chemistry (ARC) mechanism, which allows to account for autoignition chemistry, was used in combination with the dynamic thickened flame (DTF) model. For certain conditions, local autoignition events occur upstream of the flame in the advected “hot” streamwise strata that result from the inlet modulation. These auto-ignited kernels get convected downstream and impinge on the stabilized flame front leading to a sudden increase of heat release rate followed by an abrupt decrease due to flame front merging. This is identified as the driving mechanism for the onset of non-linear flame response characterised by high transfer function gains. In particular, this work shows that the gain of the flame describing function increases beyond a certain threshold of the excitation amplitude.

An Eulerian stochastic field cavitation model coupled to a pressure based solver

Probability density functions (PDF) and the relevant methods have been widely used to describe non-linear phenomena in the realm of turbulence modelling and CFD. In order to solve PDF transport equations, the main trend of previous studies rely on Monte Carlo method with Lagrangian particle tracking. However, as with any Lagrangian based approach, the scalability of the parallelized simulations of such method is less than satisfactory. An Eulerian stochastic field model has been presented recently by Dumond et al. [1] to simulate cavitating flows. Their model uses a fully compressible density based solver. Here we present an adapted version using an iso-thermal cavitation model adopting the homogeneous mixture assumption in a pressure based flow solver which is more relevant to engine simulations. A PDF method is used to represent a distribution of vapour volume fractions, based on which the Eulerian stochastic field (ESF) method is applied to perform a three-dimensional large eddy simulation (LES) of the cavitation phenomena inside an academic fuel injector configuration. The numerical model is based on a volume of fluids approach and coupled with a pressure based solver for the flow field, and is implemented in the framework of the open source C++ toolbox OpenFOAM. The result of the ESF simulation is compared against that from a typical single volume fraction solver for validation. Vortex structures and its correspondence to cavitation are shown, and the behaviour of the PDF at different probe locations at different times are acquired to demonstrate the potential of the ESF model in capturing both transient and stochastically steady cavitation.

Multi-objective optimization for the aerodynamic noise of the high-speed train in the near and far field based on the improved NSGA-II algorithm

With the increased running speed of trains, the aerodynamic noise of trains becomes increasingly obvious. Reducing aerodynamic noises has become one of keys to controlling the noise of high-speed trains. This paper conducted a numerical simulation on the aerodynamic noise of head of the high-speed train. Firstly, this paper established a mathematical-physical model for the three-dimensional turbulent flow field of a high-speed train, adopted standard k-ε equation turbulent model and broadband noise source model to compute the aerodynamic noise sources of the high-speed train and applied three-dimensional transient large eddy simulation (LES) to compute the external unsteady flow field of the high-speed train after obtaining noise sources. Based on the unsteady flow field, then this paper applied FW-H equations to compute the far-field aerodynamic noise of the high-speed train. After obtaining the unsteady fluctuation pressure on the surface of the train, this paper computed the radiation characteristics of aerodynamic noises around the high-speed train based on the boundary element method (BEM). Researched results showed: The main aerodynamic noise sources of the high-speed train were at the nose tip of head train; fluid separation and recombination were main reasons for the aerodynamic noise of the high-speed train; vortexes in the position of head train were striped and horseshoe-shaped or hairpin vortexes were mainly in the area of tail train; in addition, vortexes were symmetrically distributed along the longitudinal symmetry plane of train; dipole noises were mainly distributed in the area of head train, whose main energy was decreased with the increased frequency; the quadrupole noise of aerodynamic noises of the high-speed train was mainly distributed in the wake flow area of tail train; when the high-speed train ran at the speed of 300 km/h, the maximum sound pressure level of far-field observation points was 76.8 dB; additionally, aerodynamic noises in the far field were mainly a broadband noise, whose main energy was within the frequency range of 1250 Hz to 3150 Hz. Finally, the improved NSGA-II algorithm was used to conduct a multi-objective optimization for the head shape. The aerodynamic drag of the high-speed train could be most reduced by 6.74 %, and the dipole aerodynamic noise source could be most reduced by 8.34 dB. The improved NSGA-II algorithm has an obvious effect on the multi-objective optimization of the head shape.

Large eddy simulation (LES) calculations of natural convection in cylindrical enclosures with rack and seeds for crystal growth applications

This paper presents three-dimensional (3D) large eddy simulation (LES) calculations of natural convection in laterally-heated cylindrical enclosures using ANSYS FLUENT. The problem considered here is at a Rayleigh number, (Ra) of 8.8×106, based on a characteristic length scale defined by the ratio of the reactor's volume to the lateral area. The numerical simulations are carried out for three different geometrical configurations: an empty reactor, a reactor with a rack and 32 seeds, and thirdly, a reactor with a rack and 80 seeds mounted inside. The objective of the current study is to understand the effects of the rack and seeds on the flow patterns and thermal distribution inside the reactor. In order to investigate these effects, a comprehensive analysis of velocity and temperature on the selected planes and points inside the domain were performed. Results showed that with an increase in seeds within the reactor, the flow slowed down more, the turbulence intensity reduced, and the extent of temperature inversion increased. These have important implications for the choice of ammonothermal method in terms of acidic or basic, and also for species transport and reactions, which eventually affect the deposition rates of GaN crystals in autoclaves.

Three-dimensional unsteady large eddy simulation of the vortex structures and the mono-disperse particle dispersion in the idealized human upper respiratory system

The present study concerns the three-dimensional unsteady large eddy simulation (LES) in an idealized human mouth-throat under the different inspiration flow rates of 15, 30 and 60L/min. Three-dimensional vortices are observed in both the instantaneous and in the mean flow field in the mouth cavity, pharynx, larynx and trachea as well as in the recirculation zone of the pharynx. In the steady flow field it is found that the barrier caused by the tongue may induce hairpin vortices whereas the barrier glottis may cause horseshoe vortices. With the increase of the inspiration flow rate, the distance between the legs of the hairpin vortices in the mouth cavity decreases, and the length scale of the vortex in the trachea decreases with increasing inspiration flow rate. In the unsteady flow field, the counter-rotating vortices in the pharynx and trachea disappear at the highest inspiration flow rate, but the counter-rotating vortices can still be observed at the lowest inspiration flow rate. The vortex in the unsteady flow field is much more complex compared to the steady situation, and more vortices with smaller length scales are observed in the trachea for the increased flow rate. Lagrangian particle tracking is introduced into the model to investigate the process of particle drug delivery for medical treatment of the human airway. It is found that the mono-disperse particles may follow totally different trajectories depending on their initial release positions and the inspiration flow rates as well as on their size. The particles may follow very complex recirculating movements within the recirculation zone, and they may show a swinging, transverse or helical motion due to the vortex of the gas flow. This may also affect the deposition characteristics of the injected particles.

Benchmarking the mesoscale variability in global ocean eddy-permitting numerical systems

The role of data assimilation procedures on representing ocean mesoscale variability is assessed by applying eddy statistics to a state-of-the-art global ocean reanalysis (C-GLORS), a free global ocean simulation (performed with the NEMO system) and an observation-based dataset (ARMOR3D) used as an independent benchmark. Numerical results are computed on a 1/4 ∘ horizontal grid (ORCA025) and share the same resolution with ARMOR3D dataset. This “eddy-permitting” resolution is sufficient to allow ocean eddies to form. Further to assessing the eddy statistics from three different datasets, a global three-dimensional eddy detection system is implemented in order to bypass the need of regional-dependent definition of thresholds, typical of commonly adopted eddy detection algorithms. It thus provides full three-dimensional eddy statistics segmenting vertical profiles from local rotational velocities. This criterion is crucial for discerning real eddies from transient surface noise that inevitably affects any two-dimensional algorithm. Data assimilation enhances and corrects mesoscale variability on a wide range of features that cannot be well reproduced otherwise. The free simulation fairly reproduces eddies emerging from western boundary currents and deep baroclinic instabilities, while underestimates shallower vortexes that populate the full basin. The ocean reanalysis recovers most of the missing turbulence, shown by satellite products , that is not generated by the model itself and consistently projects surface variability deep into the water column. The comparison with the statistically reconstructed vertical profiles from ARMOR3D show that ocean data assimilation is able to embed variability into the model dynamics, constraining eddies with in situ and altimetry observation and generating them consistently with local environment.

Numerical research on aerodynamic radiation noises of alternators in vehicles

To study the aerodynamic noise characteristics of alternators in vehicles, this paper established a computational model for the aerodynamic noise of an alternator based on computational fluid dynamics (CFD). The alternator adopted a non-scaling model and considered the detailed structure of collectors and other parts. Based on Lighthill acoustic theory, this paper adopted three-dimensional and large eddy simulation (LES) to conduct an unsteady numerical simulation for the flow field around the alternator, and Ffowcs Williams-Hawkings (FW-H) model was then adopted to conduct an unsteady computation for the aerodynamic noise of the alternator in the far field. When the rotational speed of the alternator was 10000 r/min, this paper obtained the aerodynamic noise characteristics of the alternator and the unsteady flow field structure around the alternator. Studied results showed: The main aerodynamic noise sources of the alternator were front fan, rear fan and stator structure; main influence orders of aerodynamic noises were the 6th, 8th, 10th, 12th, 18th, 24th, 30th and 36th orders. Similarly, this paper also conducted an experimental test on the noise of vehicle alternators. The main influence orders of aerodynamic noises of alternators were the 6th, 8th, 10th, 12th, 18th, 24th, 30th and 36th orders, which was consistent with the working condition of numerical simulation. It showed the correctness of computational results in this paper. In addition, this paper adopted the method of vector synthesis and the distribution of fan blades of the alternator to explain the cause of various orders and provided engineering application foundation for further reducing the noise of main orders.

3D hydrodynamic simulations of carbon burning in massive stars

We present the first detailed three-dimensional (3D) hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon burning shell within a 15$\,\textrm{M}_\odot$ one-dimensional stellar evolution model. We consider models with $128^3$, $256^3$, $512^3$ and $1024^3$ zones. The turbulent flow properties of these carbon burning simulations are very similar to the oxygen burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier-Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30% and 10% of the local pressure scale heights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell burning simulations, we observe entrainment at both boundaries in our carbon-shell burning simulations. In the large P\'eclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, Ri$_{\rm B}$ ($\propto $Ri${\rm_B}^{-\alpha}$, $0.5\lesssim \alpha \lesssim 1.0$). We thus suggest the use of Ri$_{\rm B}$ as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing.

A Circuit Equation as a Limit of Eddy Current Equations

We consider a three-dimensional time-harmonic eddy current problem formulated in terms of the magnetic field. We prove that in the case of one thin toroidal conductor, eddy current equations have as a limit Kirchhoff’s algebraic equation for circuits. This approximation is valid in the case of small resistivity and voltage.

Analytical Prediction of 3-D Magnet Eddy Current Losses in Surface Mounted PM Machines Accounting Slotting Effect

This paper presents a novel analytical technique for predicting three-dimensional (3-D) magnet eddy current losses accounting the slotting effect of any pole–slot combinations for a surface mounted permanent magnet machine under any conditions of load. The slotting effect is incorporated from a subdomain model and the 3-D boundary conditions are imposed with the current vector potential to represent the 3-D eddy currents circulating in the magnets. The proposed model in polar coordinate system is demonstrated on a fractional slot rare-earth permanent magnet machine by analyzing its magnet losses as functions of axial and circumferential segmentations. The results have shown an excellent match with 3-D numerical calculations. The analytical prediction has also been validated by experimental tests. The interaction of the armature reaction field with the slotting harmonics is analyzed and their effect on eddy current loss in rotor magnets is established. The proposed technique is employed to evaluate the effect of slotting on magnet loss with increase in field weakening angle.

A large eddy simulation of the breakup and atomization of a liquid jet into a cross turbulent flow at various spray conditions

A three-dimensional large eddy simulation (LES) is conducted to investigate the breakup and atomization of a liquid jet into a cross turbulent flow for several variants of a liquid-gas momentum flux ratio by varying the liquid injection velocity and cross flow temperature. The spray-field dynamics are treated using a combined Eulerian-Lagrangian approach in which the gas phase is discretized using a density-based, finite-volume approach. A Kelvin-Helmholtz and Rayleigh-Taylor (KH-RT) hybrid wave breakup model is implemented to simulate the liquid column and droplet breakup process. While the KH model is applied to the liquid column breakup (primary breakup), the RT model is implemented to the breakup of the small droplets (secondary breakup). The detail flow structures of the counter-rotating vortex pair (CVP) and vortex interaction behind the injector are observed. The spray penetration depth in the crossflow compares well with the experimental data and similar to empirical equations. The Sauter mean diameter (SMD) distribution is analyzed along the flow downstream representing somewhat different, and an analytical correlation model is proposed to pre-evaluate the SMD in the flowfield.

The effect of mountain wind on the falling snow deposition

The air-flow over morphologic prominence is of vital importance for the temporal and spatial variations of snow distribution, which may further affect the hydrological cycle, climate system, ecological evolution as well as other natural processes. Most previous studies have neglected the effect of non-uniform mountain wind on the trajectory of falling snow particle and thus the uneven snow distribution over complex terrain is little known. Here in this paper, we carry out a numerical study on the deposition process of mixed grain size snow particles over mountain terrains. A three-dimensional large eddy simulation (LES) code is used to predict the wind field and the fluid-solid coupling effect is considered, the Lagrangian particle tracking method is employed to track the movement of each falling snow particle. Our results suggest the boundary layer flow over steep slopes or complex terrains exhibits obvious uneven characteristics. The mountain wind has obvious effect on the motion of snow particles and finally results in a non-uniform distribution of snow. This research is of significance to understand the evolution of high resolution snow distribution in cold highland areas.

3D large eddy simulation (LES) calculations and experiments of natural convection in a laterally-heated cylindrical enclosure for crystal growth

The ammonothermal crystal growth technique is one of the most effective methods used for growing Gallium Nitride (GaN) crystals in terms of the final product quality and manufacturing efficiency. Popular applications of GaN crystals include light emitting diodes (LEDs) and high-frequency electronic devices. A laterally-heated cylindrical enclosure with a top to bottom temperature gradient is considered in this study to investigate the fluid mechanics and heat transfer in an ammonothermal crystal growth reactor. Three-dimensional (3D) large eddy simulations (LES) results of natural convection in a laterally heated cylindrical reactor, using the commercial computational fluid dynamics (CFD) software, ANSYS FLUENT, are presented in this paper for a Rayleigh number (Ra) of 8.8×106. The Ra is defined based on a length scale that is equal to the ratio of volume to the lateral area of the cylinder (R/2). In addition, an experiment of a geometrically- and dynamically-similar geometry is developed, and particle image velocimetry (PIV)-based flow visualizations are carried out for the purpose of validating the numerical model. Comparisons between experiments and numerical simulations showed that flow patterns were qualitatively similar, and Fourier transforms of velocity magnitudes at selected points in the domain matched reasonably well. An added interesting observation in the simulation was the existence of temperature inversion, which has potential implications on the choice of mineralizer (acidic/basic).

Simulations of combustion oscillation and flame dynamics in a strut-based supersonic combustor

This paper numerically investigated the dynamic characteristics of combustion in a model scramjet. Three-dimensional compressible large eddy simulation was performed on a hydrogen fueled combustor and pressure fluctuations were recorded. The analysis of pressure data showed that the combustion processes are intrinsically unstable under supersonic air inflow conditions. Flame dynamics were convinced by the fluctuations in flame lift-off distance away from the strut base. Combined with the corresponding time interval, instantaneous flame speed was calculated. Results indicated that pressure oscillations at different locations show difference in amplitude, frequency, and the underlying control mechanism. Flame front oscillation analysis showed that the flame–shock interaction in the strut recirculation zone was responsible for the combustion instability. Flame dynamics were compared with low-speed turbulent lifted flames. The transition between flame propagation just after the strut and shock-induced combustion in the subsonic bubble at the intersection of two wall-reflected oblique shocks made for the flame stabilization.