Two-phase Flow Large Eddy Simulation Research Articles

Numerical study on spray characteristics of liquid jets in supersonic crossflow

The spray characteristics of liquid jets in supersonic crossflow at different injection jet-gas momentum ratios are investigated numerically. The compressible two-phase flow large eddy simulation (LES) method is based on the Eulerian-Lagrangian scheme. The average droplet volume fraction is defined to quantify spray concentration distribution, which can also reflect the oscillation boundary of the spray. The LES predicted the spray boundaries at different injection jet-gas momentum ratios in the central and cross-sectional planes, which agree reasonably well with the experiment. Two sets of counter-rotating vortex pair (CVP) are in the gas-liquid mixing region. As injection momentum ratio q increases, the upper CVP increases. Still, the absolute size of the wall CVP remains almost unchanged, which means that the relative size of the wall CVP to the upper CVP becomes smaller. As q increases, the spray's overall distribution position is generally upward, and the number of droplets entering the near-wall region becomes small. Thus, droplet-wall interactions are weakened. The spray body increases with the increase of q, while the spray foot decreases gradually. In the central plane, the coherent structures near the wall are mainly composed of splashed droplets, and this phenomenon gradually weakens as q increases. Although the increase of q can increase the total droplet mass flow rate, the proportion of the droplet mass flow rate in the near-wall region to the total mass flow rate decreases, and the droplet mass flow rate in the near-wall region decreases.

The spray distribution of a liquid jet in supersonic crossflow in the near-wall region

The gas–liquid mixing process of a liquid jet in supersonic crossflow with a gas–liquid momentum ratio of 7.67 in the near-wall region is investigated numerically. The two-phase flow large eddy simulation is based on the Eulerian–Lagrangian approach and considers the droplet–wall interaction. The results indicate the penetration depth and the lateral extension width, which are in good agreement with the experimental data. The Ω shape, especially the spray foot structure of spray in the cross-sectional plane, is captured well. The transport process of spray toward the wall and the formation of spray foot are systematically studied. Under the influence of the upper CVP (counter-rotating vortex pair), partial droplets in the center region of the spray are transported to the near-wall region and move toward both sides when encountering the wall CVP. Under the current gas–liquid momentum ratio, droplets collide with the wall mainly in the central region at the bottom, which will produce splashed droplets. Affected by the horseshoe vortex, the instantaneous distribution of droplets on both sides near the wall shows stripes shape. The spray foot structure forms the shape that is narrow on the top and wide on the bottom and is mainly formed by splashed droplets. Some splashed droplets in the low-speed boundary layer constitute the lower half of the spray foot; meanwhile, some splashed droplets enter mainstream and constitute the upper half of the spray foot. Moreover, the spray is mainly distributed in the core region, and the spray concentration is very sparse in the spray foot region.

Fragmentation and atomization characteristics of near-orifice liquid jet under transverse gas film

In order to understand the fragmentation and atomization characteristics of the liquid jet in transverse gas film, a pintle injection element using air and water as simulants is designed. The two-phase flow large eddy simulation and backlight imaging are used to study the liquid-jet breakup process and spray-field dynamic characteristics in the nearorifice area of pinte injection element under the atmospheric environment. The primary fragmentation process of the liquid jet dominated by surface wave is obtained by large eddy simulation, which reveals the establishment process of the spray field in near-orifice area of the gas-liquid pintle injector. After the subsonic airflow leaves the slit, it expands and accelerates into supersonic state. Then the deceleration and pressurization phenomenon occurs once the supersonic airflow passes through the detached bow shock upstream of the liquid jet. The liquid jet bends downstream due to the difference in pressure between upstream and downstream, and the Rayleigh-Taylor (R-T) unstable surface wave appears on the jet windward surface. As the surface wave develops, the penetration of the wave trough by airflow causes the continuous liquid jet to fragment. Proper orthogonal decomposition (POD) method can effectively reconstruct spray snapshot. The POD mode shows that the low-frequency spray oscillation in near-orifice area is caused by the overall expansion/contraction process of the spray field, while the high-frequency one is due to the “impact wave” movement of the liquid block or liquid mist group on the windward side. The latter is produced by the R-T unstable surface wave before the jet breakup, and can be categorized as traveling wave structure. The dimensionless traveling wave wavelength has a power-law relationship with Weber number.

A new LES approach to trans-critical mixing and combustion processes in high-pressure liquid-injectant engines

The understanding of flame holding mechanism is very important for combustor design. To elucidate the flame holding mechanism at the injector exit in liquid rocket engines, it is indispensable to know the underlying physics of trans-critical mixing process, because the flame holding location is exactly where trans-critical mixing process, which is still veiled, takes place. In the present paper, a new Large Eddy Simulation (LES) method is developed by gaining deeper physical insights into possible sub-grid-scale (SGS) thermodynamic and fluid dynamic instabilities excitable at thin large-density-gradient-magnitude portions to describe trans-critical processes. The presence of thin large-density-gradient-magnitude portions in trans-critical mixing process is troublesome for numerical stability of supercritical fluid flow LES from various points of view. Our idea is to utilize an SGS model functioning at the crossover between the liquid-like and gas-like supercritical fluids in a hybrid scheme of Lagrangian particle tracking and two-phase flow LES. Reduced dynamic viscosity at high pressure may cause SGS thermodynamic and hydrodynamic instabilities in the trans-critical mixing flow field. They are (1) phase separation due to thermodynamic instability, (2) Landau's hydrodynamic instability occurring at the pseudo-boiling location within a heated injector, and (3) Rayleigh–Taylor instability at the pseudo-boiling location, which is induced by Kelvin–Helmholtz instability vortices. These are analyzed and organized into new SGS models characterizing the trans-critical jet mixing process.

A three-dimensional Cartesian cut-cell/volume-of-fluid method for two-phase flows with moving bodies

A three-dimensional Cartesian cut-cell method for the large-eddy simulation of two-phase flows with moving bodies is presented in this study, which combines a volume-of-fluid method to capture the air-water interface and a moving body algorithm on a stationary, non-uniform, staggered, Cartesian grid. The filtered Navier–Stokes equations are discretised using the finite volume method with the PISO algorithm for velocity-pressure coupling and the dynamic Smagorinsky subgrid-scale model is employed to compute the effect of the unresolved (subgrid) scales of turbulence on the large scales. In the present study, the small cut-cells are unmodified and due to the use of an implicit time integration no instabilities occur during the computations. The versatility and robustness of the present two-phase flow model is illustrated via various two- and three-dimensional flow problems with fixed/moving bodies, such as dambreak flows with and without a square cylinder, a moving cylinder in a quiescent fluid, dambreak flow over a wet bed with a moving gate, water entry and exist of a circular cylinder, and landside-generated waves. Good agreement is obtained between the numerical results and the corresponding experimental measurements.

A-Priori Assessment of Interfacial Sub-grid Scale Closures in the Two-Phase Flow LES Context

Due to the continuous increase in available computing power, the Large Eddy Simulation (LES) of two-phase flows started to receive more attention in recent years. Well-established models from single-phase flows are often used to close the sub-grid scale convective momentum transport and recently some modifications have been suggested to account for the jump of density and viscosity at the interface of multi-phase flows. However, additional unclosed terms in multi-phase flows, which are absent in single-phase flows, often remain ignored. This paper focuses on the crucial gaps in literature, namely the modeling of volume fraction advection and surface tension effects on sub-grid level. An a-priori analysis has been conducted for this purpose, i.e. the Direct Numerical Simulation of an academic two-phase flow configuration (single wobbling bubble in a turbulent background flow) has been explicitly filtered (corresponding to implicit filtering in actual LES) for varying filter width and the corresponding sub-grid terms have been compared to potentially suitable model expressions. Besides other approaches, adequately formulated models based on the scale similarity principle emerged to be promising candidates for both sub-grid volume fraction advection as well as sub-grid surface tension effects. In this context, special attention has to be paid to the secondary filter. Owing to the nature of the quasi-singular surface tension term, surface-weighted filtering may be more appropriate and robust than standard volume filtering.

Numerical study of mechanisms of air-core vortex evolution in an intake flow

The mechanism of the generation and evolution of the air-core vortex formed between a free surface and a horizontal flow intake is investigated using large-eddy simulation of two-phase flows, with the air-water interface captured by a coupled level-set and volume-of-fluid method. The simulation provides a detailed description of the flow features of the air-core vortex formation. Based on the simulation data, the flow patterns and the underlying vorticity dynamics at different stages of the vortex formation are analyzed. It is found that the development of the air-core vortex is associated with the evolution of the vertical component of the vorticity. Analyses of the vorticity evolution dynamics reveal the fundamental mechanism of the air-core vortex generation, which is the amplification of the free-surface vertical vortices due to the vertical stretching effect above the intake associated with the pipe suction. Initially, weak vertical vortices caused by the spanwise disturbance of streamwise flows are randomly distributed near the surface and are enhanced by the stretching effect. Then, these randomly distributed vortices interact with each other and evolve into a dominant vortex, which eventually draws air into the intake and creates a fully-developed air-core vortex. The mechanism responsible for maintaining the fully-developed air-core vortex is still the vertical stretching effect in the core. The tilting from streamwise and spanwise vortices to vertical vortices, albeit large in the presence of the fully-developed vortex, nearly cancel each other and has negligible influence on sustaining the vortex.

Large eddy simulation of multiphase flows using the volume of fluid method: Part 1—Governing equations and a priori analysis

Compared to Large Eddy Simulation (LES) of single-phase flows, which has become a mature and viable turbulence modelling technique, the LES of two-phase flows with moving immiscible interfaces is at a rather early development stage. There is no standard set of governing equations for two-phase flow LES, but rather a variety of different formulations, all with advantages and disadvantages. This paper discusses and analyses in detail the governing equations for two-phase flow LES in the context of the Volume of Fluid method, as well as suitable Subgrid Scale closures for the different unknown terms. A particular focus is on the Favre filtered one fluid formulation of the momentum equations, but a comparison with the filtered and the volume averaged version of the balance equations is made as well. Differences and commonalities between the different approaches are discussed and, based on a priori analysis of explicitly filtered Direct Numerical Simulation data, suitable closure models for a posteriori analysis are identified.

LES of primary breakup of pulsed liquid jet in supersonic crossflow

The injection of a pulsed liquid jet into supersonic air flow is a promising approach to improving the fuel atomization performance in a Scramjet engine. Therefore, the primary breakup of a pulsed liquid jet in supersonic crossflow is numerically investigated in the present paper. A two-phase flow Large Eddy Simulation (LES) algorithm is developed for simulations of liquid jet atomization in supersonic gas flow. A coupled Level Set and Volume of Fluid (VOF) method is used to track the interface deformation and disintegration. The supersonic gas flow is solved using a compressible flow solver while the liquid phase is solved by an incompressible flow solver. Appropriate boundary conditions are specified at the interface for both solvers to correctly capture the interaction between the gas and liquid phases. The primary atomization of a steady liquid jet with the same average mass flow rate as the pulsed jet is also simulated as a benchmark test case. The liquid velocity pulsation produces a very different primary atomization morphology in comparison with the steady liquid jet, which significantly enhances the primary breakup process. It is observed that Rayleigh-Taylor instability dominates the development of surface waves for the steady liquid jet. For the pulsed liquid jet, the liquid column deformation induced by the liquid velocity pulsation determines the wavelength of the surface waves and thus the liquid jet breakup location. In comparison with the steady liquid jet, the penetration of the pulsed liquid jet increases by 20%, and the width of the wake zone expands by 25%, resulting in improved atomization and mixing performance.

Large-Eddy Simulation of Kerosene Spray Ignition in a Simplified Aeronautic Combustor

The current work presents the Large Eddy Simulation (LES) of a kerosene spray ignition phase in a simplified aeronautical combustor for which detailed experimental data are available. The carrier phase is simulated using an unstructured multi-species compressible Navier-Stokes solver while the dispersed liquid phase is modeled with a Lagrangian approach. An energy deposition model neglecting the presence of a plasma phase in the very first instants of the energy deposition process, a reduced kinetic scheme and a simplified spray injection model are combined to achieve both a reasonable computational expense and a satisfactory overall accuracy. Following a brief description of the validation of these models, non reactive gaseous and two-phase flow LES’s of the target combustor are performed. Excellent agreement with experiments is observed for the non reactive gaseous simulations. The dispersed phase velocity fields are also well reproduced while discrepancies appear for the spatial size distribution of the particles. Finally, numerical snapshots of a successful ignition phase are shown and discussed.

Detailed SGS atomization model and its implementation to two-phase flow LES

A novel turbulent atomization model, which is physically closed itself and free of case-by-case parameter tuning using experimental data, has been formulated and demonstrated in the framework of turbulent spray combustion large-eddy simulation (LES). Based on our accumulated research findings that elementary droplet/ligament generation is a deterministic phenomenon, not something random as considered in the conventional understanding, the model describes two dominant modes of turbulent atomization, i.e. the turbulent resonant mode and the Rayleigh–Taylor (RT) mode, in a physically straightforward manner. Extending the baseline theory proposed in Umemura (2016), to a hybrid turbulent spray LES formulation which includes both an Eulerian liquid jet core and Lagrangian droplets, the subgrid-scale (SGS) atomization characteristics are completely detailed in this study. Using the LES-resolved turbulent Weber and Bond numbers on the liquid core surface, the atomization mode and the SGS atomization characteristics such as droplet size, number, ejection velocity and core regression velocity are all identified locally, and the information is transferred back to the LES code as input information. Test cases of Diesel fuel jets demonstrate that the present formulation well reproduces the turbulent spray behavior. Thanks to the obtained detailed data, the spray formation process can be tracked both temporally and spatially, from the initial head formation with edge atomization to the later core atomization and spray spreading. It is essentially featured that the present turbulent atomization model works well without ambiguous user input, contrary to the conventional way of spray simulation. This is a significant breakthrough to urge paradigm shift in spray simulation, from unclosed/unpredictable to closed/predictable, which enables drastic improvement in the accuracy of spray simulation and may exert a large impact on both research studies and industrial applications.

Large Eddy Simulation of liquid sheet breakup using a two-phase lattice Boltzmann method

A two-phase flow Large Eddy Simulation (LES) model is developed within the framework of phase-field lattice Boltzmann methods (LBM). The proposed model is based on a standard Smagorinsky model for subgrid closure and uses the Multiple-Relaxation-Time (MRT) collision operator. Relevant test cases are considered to demonstrate the capability and accuracy of the new model in dealing with two-phase flows at wide range of density contrasts. These include the Rayleigh–Taylor instability at two distinct density ratios, the breakup of a turbulent liquid column, and assisted breakup of a liquid layer. The validated model is then utilized to examine a liquid sheet emerging from a nozzle into a stagnant gas at different Reynolds numbers ranging from 1000 to 6000. The influence of jet injection velocity on the flow structure, variation of the jet centerline velocity, and jet area is also investigated. This work reports for the first time the extension of the Smagorinsky model for LES to the binary fluid model of Fakhari & Lee [1] and its application in simulation of turbulent liquid sheet breakup at the density ratios as high as 250.

Large eddy simulation of liquid jet primary breakup in supersonic air crossflow

The paper proposed a two-phase flow Large Eddy Simulation (LES) algorithm for atomization in supersonic gas flow. A coupled Level Set and Volume of Fluid (VOF) interface tracking method is used. The supersonic gas flow is solved using a compressible flow solver, and the liquid phase is solved using an incompressible flow solver. Appropriate boundary conditions are specified on the interface for both solvers to correctly capture the interaction between the gas and liquid. The water jet primary breakup in a supersonic air crossflow is well predicted, with the shock waves ahead of the liquid column and drops/ligaments properly captured. Two kinds of vortices respectively relating to surface breakup and column breakup are observed. Surface waves on the windward side of the liquid jet are numerically reproduced, and the wavelength is well correlated to an effective Weber number which is determined by the gas flow behind the shock. As gas flow goes across the strong shock wave ahead of liquid column, the disintegrating aerodynamic force is weakened. Rayleigh–Taylor instability is found to be responsible for the development of surface waves which causes column breakup. It is demonstrated that LES can produce almost the same breakup morphology as an under-resolved DNS.

Turbulent atomization subgrid model for two-phase flow large eddy simulation (theoretical development)

Current spray combustion simulators work when an initial spray (consisting of point droplets) is prescribed as input data to the spray equation. Two-phase flow Large Eddy Simulation (LES), combined with such a reactive system treatment, could be a promising tool for simulating industrial spray combustion, if a subgrid model describing local turbulent atomization from any possible bulk liquid surface element could be incorporated. In the present study, theoretical considerations were made to develop a turbulent atomization subgrid model, which comprises the following two models. (i) Interfacial turbulence model compatible with the isotropic turbulence concept adopted in LES. Using local interfacial shear stress and liquid inertia force determined from LES, this model characterizes unresolved liquid- and gas-phase turbulent states realizable in each interfacial LES grid cell. (ii) Turbulent atomization model, which judges the occurrence of local atomization based on the interfacial turbulence model data and predicts the mean diameter, ejection velocity and number density of resulting atomized droplets. Thus, the proposed subgrid model provides instantaneous input data to the spray equation where atomization is judged to occur, and recedes the resolved interface by the volume corresponding to the locally atomized droplets.

LES of turbulent liquid jet primary breakup in turbulent coaxial air flow

A robust two-phase flow Large Eddy Simulation (LES) algorithm has been developed and applied to predict the primary breakup of an axisymmetric water jet injected into a surrounding coaxial air flow. The high liquid/gas density and viscosity ratios are known to represent a significant challenge in numerical modelling of the primary breakup process. In the current LES methodology, an extrapolated liquid velocity field was used to minimise discretisation errors, whilst maintaining sharp treatment of fluid properties across the interface. The proposed numerical approach showed excellent robustness and high accuracy in predicting coaxial liquid jet primary breakup. Since strong turbulence structures will develop inside the injector at high Reynolds numbers and affect the subsequent primary breakup, the Rescaling and Recycling Method (R2M) was implemented to facilitate generation of appropriate unsteady LES inlet conditions for both phases. The influence of inflowing liquid and gas turbulent structures on the initial interface instability was investigated. It is shown that liquid turbulent eddies play the dominant role in the initial development of liquid jet surface disturbance and distortion for the flow conditions considered. When turbulent inflows were specified by the R2M technique, the predicted core breakup lengths at different air/water velocities agreed closely with experimental data.

Two-phase flow LES of the sedimentation process of a particle cloud

To predict the sedimentation process practically with high resolution, a large eddy simulation (LES) is performed. A solid/liquid two-phase flow model based on the Euler–Lagrange coupling is developed. Then the discrete element method is applied to calculate inter-particle forces during individual particle motion. The computational grid scale of the Eulerian fluid method is less than the particle diameter to simulate a wake induced by settling particles. Comparison of the simulated and experimental results for the particle sedimentation process verified the performance of the developed numerical model. Finally, the mechanism of the inner structure of the settling particles is investigated from a computational point of view. Consequently, the positive relationship between the turbulence-energy production rate and the inter-particle collisions would be shown.

Advances in LES of Two-phase Combustion (II) LES of Complex Gas-Particle Flows and Coal Combustion

Large-eddy simulation (LES) is under its rapid development and is recognized as a possible second generation of CFD methods used in engineering. Large-eddy simulation of two-phase flows and combustion is particularly important for engineering applications. Some investigators, including the present authors, give their review on LES of spray combustion in gas-turbine combustors and internal combustion engines. However, up to now only a few papers are related to the state-of-the-art on LES of gas-particle flows and combustion. In this paper a review of the advances in LES of complex gas-particle flows and coal combustion is presented. Different sub-grid scale (SGS) stress models and combustion models are described, some of the main results are summarized, and some research needs are discussed.