Stochastic modeling of fluid acceleration on residual scales and dynamics of suspended inertial particles in turbulence

Sabelnikov, Vladimir; Barge, Alexis; Gorokhovski, Mikhael

doi:10.1103/physrevfluids.4.044301

Cited by 8 publications

(11 citation statements)

References 29 publications

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“…= ̅ + ′ (9) The filtered Navier Stokes equations and the liquid volume fraction transport equation are given by Eq. (10)(11).…”

Section: = ∫ ( )mentioning

confidence: 99%

“…Based on similar principles, in this paper an attempt is made to present the LES of primary atomization of a diesel spray jet using VOF method accounting for intermittency effects on sub-grid scale liquid/gas interface dynamics. The principal idea is to obtain a full realization of the velocity field by forcing 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 as outlined in [9][10][11]. This approach is referred to as LES-SSAM (stochastic sub-grid scale method).…”

Section: Introductionmentioning

confidence: 99%

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Stochastic sub-grid scale acceleration model (SSAM) for LES of primary atomization using iso-advector VOF method for ECN Spray-A

Oruganti

Gorokhovski

2021

ICLASS

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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.

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“…= ̅ + ′ (9) The filtered Navier Stokes equations and the liquid volume fraction transport equation are given by Eq. (10)(11).…”

Section: = ∫ ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic sub-grid scale acceleration model (SSAM) for LES of primary atomization using iso-advector VOF method for ECN Spray-A

Oruganti

Gorokhovski

2021

ICLASS

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“…Equations (18)- (20) require stochastic equations for unit vector of the droplet acceleration direction (ẽ p ) and for powers of viscous dissipation i.e., e 1 2 and e 2 3 . The Ornstein-Uhlenbeck process forẽ p and the method of its integration is taken from [28]. While the stochastic equations for e 1 2 and e 2 3 are derived by Ito transformation of stochastic log-normal process [31] as described in [32].…”

Section: Standard Sgs Model For Dispersionmentioning

confidence: 99%

“…The model for orientation vector of droplet acceleration is based on random walk over a unit sphere. While in [28], the stochastic equation for the orientation vector on the unit diffusion sphere is based on Ornstein-Uhlenbeck (OU) process, this approach is retained in our current study.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of LES-STRIP approach for modeling of droplet dispersion in diesel-like sprays

Oruganti¹,

Millet²,

Gorokhovski³

2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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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 () "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 choice of one of the approaches, i.e., the stochastic drag or the stochastic forcing, follows the classical condition for drag coefficient based on the droplet Reynolds number (Re p ). The non-vaporizing spray experiments from Engine Combustion Network (ECN) are used as test cases. In addition to the comparison of the spray penetration length, spreading angle and spray structure with the experimental data, a qualitative analysis of the statistics of the droplet acceleration and gas phase velocities is presented. It was shown that the new approach is much more effective in modeling the spray dynamics on relatively coarser mesh. Consequently, the new approach in the framework of two-way coupling may predict the preferential concentration effects better, which is important for spray combustion.

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Model for the dynamics of micro-bubbles in high-Reynolds-number flows

2019

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We propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and fluid inertia forces in a homogeneous and isotropic turbulent flow. This model, that depends on the Stokes number, Reynolds number and the density ratio, reproduces the evolution of the acceleration variance as well as the relative importance and alignment of the two forces as observed from direct numerical simulations (DNS). We also report that the bubble acceleration statistics conditioned on the local kinetic energy dissipation rate are invariant with the Stokes number and the dissipation rate. Based on this observation, we propose a stochastic model for the instantaneous bubble acceleration vector accounting for the small-scale intermittency of the turbulent flows. The norm of the bubble acceleration is obtained by modelling the dissipation rate along the bubble trajectory from a log-normal stochastic process, whereas its orientation is given by two coupled random walks on a unit sphere in order to model the evolution of the joint orientation of the drag and inertia forces acting on the bubble. Furthermore, the proposed stochastic model for the bubble acceleration is used in the context of large eddy simulations (LES) of turbulent flows laden with small bubbles. To account for the turbulent motion at scales smaller than the mesh resolution, we decompose the instantaneous bubble acceleration in its resolved and residual parts. The first part is given by the drag and fluid inertia forces computed from the resolved velocity field, and the second term refers to the random contribution of small unresolved turbulent scales and is estimated with the stochastic model proposed in the paper. Comparisons with DNS and standard LES, show that the proposed model improves significantly the statistics of the bubbly phase.

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Stochastic modeling of fluid acceleration on residual scales and dynamics of suspended inertial particles in turbulence

Cited by 8 publications

References 29 publications

Stochastic sub-grid scale acceleration model (SSAM) for LES of primary atomization using iso-advector VOF method for ECN Spray-A

Stochastic sub-grid scale acceleration model (SSAM) for LES of primary atomization using iso-advector VOF method for ECN Spray-A

Assessment of LES-STRIP approach for modeling of droplet dispersion in diesel-like sprays

Model for the dynamics of micro-bubbles in high-Reynolds-number flows

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