Papers by Mikhael Gorokhovski
Proceedings of the Combustion Institute, 2009
Large-eddy simulation of an atomizing spray issuing from a gas-turbine injector is performed. The... more Large-eddy simulation of an atomizing spray issuing from a gas-turbine injector is performed. The filtered Navier-Stokes equations with dynamic subgrid scale model are solved on unstructured grids to compute the swirling turbulent flow through complex passages of the injector. The collocated grid, incompressible flow algorithm on arbitrary shaped unstructured grids developed by Mahesh et al. (J. Comp. Phys. 197 (2004) 215-240) is used in this work. A Lagrangian point-particle formulation with a stochastic model for droplet breakup is used for the liquid phase. Following Kolmogorov's concept of viewing solid particle-breakup as a discrete random process, the droplet breakup is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. The size and number density of the newly produced droplets is governed by the Fokker-Planck equation for the evolution of the pdf of droplet radii. The parameters of the model are obtained dynamically by relating them to the local Weber number and resolved scale turbulence properties. A hybrid particle-parcel is used to represent the large number of spray droplets. The predictive capability of the LES together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail by comparing it with the spray patternation study for the gas-turbine injector. The present approach is computationally efficient and captures the global features of the fragmentary process of liquid atomization in complex configurations.
Afin de prendre en compte les effets d'intermittence aux petites échelles de sous-maille, not... more Afin de prendre en compte les effets d'intermittence aux petites échelles de sous-maille, notre proposition est la suivante. Nous remplaçons l'équation de type LES par une équation restituant une approximation du champ de vitesse non-filtrée à l'aide d'un modèle stochastique d'accélération associée au champ résiduel. Ce modèle a été bâti en cohérence avec la connaissance (en majeure partie expérimentale) sur les propriétés spécifiques de l'accélération lagrangienne dans un champ turbulent à grand nombre de Reynolds. Les calculs de la turbulence de type box 3D, homogène isotrope stationnaire, reproduisent qualitativement les observations expérimentales. Abstract : In the present work, in order to take into account the intermittency phenomena, we proposed a new approach to the LES of constant-density flows. In this approach, the main step is to reconstruct an approximation for unfiltered velocity field based on stochastic simulation of non-resolved (unknown) fl...
Multi-hole gasoline direct injection (GDI) injector sprays have been studied numerically and expe... more Multi-hole gasoline direct injection (GDI) injector sprays have been studied numerically and experimentally. This study is an extension of previous work performed by Rossella Rotondi [1]. The main part of this work fo-cuses on air entrainment and droplet size prediction in the spray plumes under non-evaporating and evaporating conditions, which can have a significant effect on jet to jet interactions, spray propagation and mixture formation. For this purpose, several Continental's special XL gasoline direct injector geometries have been studied includ-ing a 3-hole 90° Cone Angle (CA) and 6-hole 60° CA injectors. The droplet size distributions of 3-hole injector under non-evaporating conditions show sufficient droplets' breakup. Spray penetrations and the air entrainment fields of 3-hole and 6-hole injectors from simulation and experiments under evaporating conditions are quite comparable. Furthermore, the vapour and the air entrainment fields of the 6-hole spray suggest that...
This paper is devoted to the further modification of the level set approach, introduced by Sussma... more This paper is devoted to the further modification of the level set approach, introduced by Sussman et al. (1994). In this method, if the flow velocity in the transport level set equation is not constant, the gradient of the level set scalar may grow rapidly with time. This leads to a strong distortion of the level set function, with loss of accuracy in numerical integration. In level set methods, this problem is remedied by a re-initialization procedure, providing the satisfaction of Eikonal equation by iterations at each time step. In this paper, we modified the level set equation in such a way that the Eikonal equation is satisfied directly from the modified form of the equation. In various tests problems (interface deformation by vortex flow, advection of Zalesak's rotating disk, oscillating circle test, interface subjected to strain and vorticity), this modification allowed to enhance significantly the numerical efficiency and even the numerical accuracy when the velocity field was functional of the level set function. This paper provides the comparative analyses of the interface location error, of the mean deviation from the signed distance property, and of errors of the interface curvature for standard and modified level set equation. The proposed modification of the level set equation is easy to implement into any level set approach.
In this paper, the new extension to the stochastic simulation of primary air-blast atomization is... more In this paper, the new extension to the stochastic simulation of primary air-blast atomization is introduced, and it is assessed by comparison with measurements. The idea of this extension is as follows. In LES of the gas flow, the primary atomization zone (liquid core, network of filaments and detached primary blobs) is viewed as immersed porous solid body with the stochastic structure. Namely, such a composite body is flowing with the inlet parameters for the liquid jet, and it is changing randomly its configuration. The statistics of configuration of this immersed body are used as boundary conditions in LES of the gas flow, thereby it is assumed that the jet fragmentation process is faster than the typical time resolved scale in the gas flow. The statistical structure of the immersed body is defined by specifically introduced stochastic particles, moving in the space, and identifying the random position, outwards normal and curvature of the interface between the liquid and the ga...
This paper is devoted to further modification of the Level Set approach, which is well-known for ... more This paper is devoted to further modification of the Level Set approach, which is well-known for simulation of gas-liquid flows with the interface. In our development, we addressed to the case of a strong velocity gradient at the free interface. This is a typical situation, for example, when this interface interacts with the turbulent flow. In this case, the gradients of the level set scalar, in the vicinity of the interface, increase with time very rapidly. In order to maintain the accuracy of the numerical solution, the Level Set methods are combined usually with the Eikonal equation for a signed distance function from the zero level set. In the standard procedure (Sussman et al., J. Comput. Phys. 114, 1994), in order to be consistent with evolutional type of the Level Set equation, the nonevolutional Eikonal equation is replaced by quasi-evolutional one, with the artificial time providing iterations at each time step. Our idea is to modify the Level Set equation, in such a way th...
International Conference on Liquid Atomization and Spray Systems (ICLASS)
At high Reynolds and Weber numbers typical of diesel-like sprays, the finest turbulent structures... more At high Reynolds and Weber numbers typical of diesel-like sprays, the finest turbulent structures are highly intermittent in nature, resulting in intense fluctuations in gas phase velocities and can significantly contribute to the atomization process. In order to account for their influence on breakup of spray droplets, we introduce a new stochastic breakup model to be used in conjunction with large eddy simulation (LES) for the gaseous flow. The model is based on a stochastic parent-to-child relaxation of droplets, whose parameters are linked to the viscous dissipation rate on residual scales "seen" by a droplet along its trajectory. In order to introduce the intermittency effects on the droplet breakup, this dissipation rate is simulated stochastically, in the framework of log-normal process. The non-reacting "Spray-A" experiment from Engine Combustion Network (ECN) is used to assess the performance of the new stochastic breakup model in comparison to the standard hybrid KH-RT breakup model in terms of evolution of liquid penetration length and droplet size statistics. The results clearly show that in comparison to the hybrid KH-RT model the stochastic breakup model gives a more accurate prediction of different parameters with relatively less sensitivity to the grid resolution.
International Conference on Liquid Atomization and Spray Systems (ICLASS)
Primary atomization at high Weber numbers evolves in highly sheared gas flow. The latter is chara... more Primary atomization at high Weber numbers evolves in highly sheared gas flow. The latter is characterized by energetic intermittent turbulent structures on small length-scales. Although the effects of turbulent flow dynamics on small scales may strongly correlate with wrinkling of the liquid/gas interface, the residual scales are usually discarded in reduced simulations. In this paper, we present the large eddy simulation (LES) of primary atomization of a diesel spray jet using VOF method accounting for intermittency effects on sub-grid scale liquid/gas interface. The principal idea of this approach is to force the filtered Navier Stokes equation by the subgrid acceleration, which is modelled in a way to represent the main statistical properties of intermittency in the high Reynolds number flows. Earlier, this approach was referred to as LES-SSAM (stochastic subgrid acceleration model). In this approach, the statistics of acceleration on residual scales is modelled by two independent stochastic processes i.e., one for the norm and the other for the unit orientation vector. The both are modelled by Ornstein-Uhlenbeck process: while the norm is modelled by a long-correlated log-normal process, the acceleration orientation vector is modelled by diffusion on the unit sphere with relaxation towards the local vorticity field, and with correlation on the short Kolmogorov time. The resulting stochastic velocity field is then used for reconstruction of the liquid/gas interface in the framework of iso-advector geometrical VOF method. The approach is applied to simulate the primary atomization of ECN Spray-A injector. A qualitative comparison of liquid/gas interface evolution with the under-resolved LES-VOF approach is provided.
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles
In this paper, the stochastic equations of droplet motion in turbulent flow, proposed recently by... more In this paper, the stochastic equations of droplet motion in turbulent flow, proposed recently by Gorokhovski and Zamansky (2018, Phys. Rev. Fluids 3, 3, 034602), are assessed for turbulent spray dispersion in diesel like conditions along with Large Eddy Simulation (LES) for the gaseous flow. For droplets above the Kolmogorov length scale, this model introduces the concept of the stochastic drag, independently of laminar viscosity. For droplets below the Kolmogorov length scale, the model equation does depend on the laminar viscosity through the Stokes drag but the particle motion is stochastically forced. Both the stochastic drag and the stochastic forcing of the Stokes drag equation are based on the simple log-normal stochastic process for the viscous dissipation (ϵ) “seen” along the droplet trajectory. In this paper, this model is applied in the framework of two-way coupling, wherein the turbulence generated by the spray inturn controls the spray dispersion. The criterion for the...
Physical Review Fluids
In numerical simulations with highly turbulent flows, the smallest scales are filtered; thereby, ... more In numerical simulations with highly turbulent flows, the smallest scales are filtered; thereby, the effects of intermittency on those scales are neglected. When the flow is loaded by heavy small particles, the decimation of rapid changes in the velocity may lead to wrong results. This paper provides an approach to take account of subfiltered events of strong velocity jumps on the motion of heavy small particles. The idea is to force the filtered Navier-Stokes equations by a stochastic acceleration term with statistical properties identified by experiments and DNS. To this end, the stochastic model for supplemented acceleration contains the lognormal stochastic process for its norm (with long-range correlations) and the new stochastic model for the acceleration direction (with shortrange correlations). The latter represents the Ornstein-Uhlenbeck process in Cartesian coordinates with relaxation to the local direction of the resolved vorticity; thereby, the geometry of highly stretched vortical structures is introduced in the designed model. Both stochastic processes depend on the local Reynolds number. The proposed flow model is applied for simulation of the background turbulence in which heavy particles are released and tracked. The assessment of single and two-time statistics of the particle acceleration and velocity clearly illustrates the advantage of the proposed flow model.
International Journal of Multiphase Flow
Journal of Turbulence, 2016
Volume 1: Symposia, Parts A and B, 2006
ABSTRACT
International Journal of Multiphase Flow, 2003
A stochastic subgrid model for large-eddy simulation of atomizing spray is developed. Following K... more A stochastic subgrid model for large-eddy simulation of atomizing spray is developed. Following KolmogorovÕs concept of viewing solid particle-breakup as a discrete random process, atomization of liquid blobs at high relative liquid-to-gas velocity is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. KolmogorovÕs discrete model of breakup is rewritten in the form of differential Fokker-Planck equation for the PDF of droplet radii. Along with the Lagrangian tracking of spray dynamics, the size and number density of the newly produced droplets is governed by the evolution of this PDF in the space of droplet-radius. The parameters of the model are obtained dynamically by relating them to the local Weber number with two-way coupling between the gas and liquid phases. Computations of spray are performed for the representative conditions encountered in idealized diesel and gas-turbine engine configurations. A broad spectrum of droplet sizes is obtained at each location with coexistence of large and small droplets. A novel numerical algorithm capable of simultaneously simulating individual droplets as well as a group of droplets with similar properties commonly known as parcels is proposed and compared with standard parcels-approach usually employed in the computations of multiphase flows. The present approach is shown to be computationally efficient and captures the complex fragmentary process of liquid atomization.
Springer Proceedings in Physics, 2009
ABSTRACT The fragmentation equation describes the evolution in time of particles system, when par... more ABSTRACT The fragmentation equation describes the evolution in time of particles system, when particles break up. The turbulent eddy decay is an example of such fragmentation. A collection of tangled trajectories of fluid particle, associated with a turbulent concentrated structure, resembles a “wool ball” of a typical scale r. Once a fluid particle is subjected to an intense acceleration, a new “wool ball” is formed, containing a part of total energy of flow. The population of newly appeared “wool balls” is assumed to be governed by the fragmentation equation, requiring conservation of the total kinetic energy injected on large scales. The question raised is how this energy is distributed in statistical ensemble of such “wool balls”. In this paper, the renormalized form of the fragmentation equation is obtained for arbitrary functions for the spectrum and for frequency of fragmentation. If the frequency of fragmentation is a power function of size, a simple exact solution to this equation is obtained, providing for stationary flux of energy, from large scales towards zero scales. A simple stochastic generation of random field with presumed fractal properties is illustrated. Also, presuming the spectrum of breakup and its frequency in the form of power functions, the exact self-similar solution is obtained on the basis of specifically introduced scaling transformations. Here the specific case is considered, when the breakup frequency is decreasing with decreasing of r. This work contributes to the group-theoretical description of statistically homogeneous turbulence, developed recently by authors in [1, 2, 3].
37th Aerospace Sciences Meeting and Exhibit, 1999
38th Aerospace Sciences Meeting and Exhibit, 2000
Lecture Notes in Computational Science and Engineering, 2007
In this paper, the turbulent cascade with intermittency is presented in the framework of universa... more In this paper, the turbulent cascade with intermittency is presented in the framework of universalities of eddy fragmentation under scaling symmetry. Based on these universalities, the stochastic estimation of the velocity increment at sub-grid scales is introduced in order to simulate the response of light solid particle to inhomogeneity of the flow at small spatial scales. The LES of stationary box turbulence was performed, and the computed Lagrangian statistics of tracking particle was compared with measurements. The main effects from recent experimental study of high Reynolds number stationary turbulence are reproduced by computation. For the velocity statistics, the numerical results were in agreement with classical Kolmogorov 1941 phenomenology. However the distribution of velocity increment, computed at different time lag, revealed the strong intermittency: at time lag of order of integral time scale, the velocity increment was distributed as Gaussian, at small time lags this distribution exhibited the long stretched tails.
Atomization and Sprays, 2001
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Papers by Mikhael Gorokhovski