Paper Submission
ETC2019 17th European Turbulence Conference





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16:15   Multiphase Flows 3
16:15
15 mins

#125
EVAPORATING DROPLETS IN HOMOGENEOUS SHEAR TURBULENCE
Philipp Weiss, Daniel W. Meyer, Patrick Jenny
Abstract: Turbulent shear flows laden with evaporating droplets appear in various natural and technological systems like atmospheric clouds or fuel sprays. Such flows involve complex and coupled phenomena that are part of ongoing research [5]. The mean shear flow produces turbulent and anisotropic fluctuations in the gas phase [3]. The droplets interact with these fluctuations. First, they cluster in regions of low vorticity and high strain and exert forces that modulate the turbulent kinetic energy of the gas phase [4]. Second, they evaporate and release vapor and energy that mix with the gas phase. These processes lead to the formation of anisotropic clusters that contain many droplets and large amounts of vapor. Important parameters that govern these processes are the Taylor-microscale Reynolds number, the shear rate, the mass loading and the Stokes number [6, 11]. The present work investigates these flows with direct numerical simulations. The gas phase is modeled with the low Mach number approach and resolved from the smallest to the largest relevant scales [2]. The droplets, however, are modeled with the point droplet approach and are only resolved in time. The gas phase and droplets exchange momentum, mass and energy. First, source terms in the gas phase equations transfer momentum, mass and energy from the droplets to the gas phase. Second, local (or seen) gas phase variables in the droplet equations drive the evolution of the droplet velocity, diameter and temperature [7]. The flow configuration is a homogeneous shear flow laden with droplets. The boundary conditions for the gas phase and droplets are shear-periodic in the direction of the mean velocity gradient and periodic in the other two directions [3, 1]. To keep the gas phase temperature and vapor mass fraction stationary, vapor and energy are removed from the gas phase with additional mass and energy sources. To keep the mass loading and mean Stokes number stationary, small droplets that evaporated are replaced by large droplets. These procedures allow us to control the important parameters and to study their effects in terms of time and space averaged statistics [11]. The test cases examine mixtures of air and decane vapor laden with decane droplets. The gas phase and droplets are at temperatures around 350 K and pressures around 10^5 Pa [7]. The gas phase is weakly turbulent with Taylor-microscale Reynolds numbers at around 50 to 80 [9]. The shear rate, mass loading and mean Stokes number are varied and their effects on the clustering of droplets and mixing of vapor are investigated. Voronoï tessellations are used to measure the droplet number density, where the inverse of a Voronoï cell volume is equal the local droplet number density [8, 10]. The spatial scales and orientations of anisotropic clusters are analyzed based on spectra and correlation functions of vapor mass fraction and droplet number density. The droplets and amount of vapor and energy in clusters and voids are analyzed based on probability density functions of droplet diameter, local vapor mass fraction and local gas phase temperature. The probability density functions are conditional on the local droplet number density, where a high or low droplet number density indicates that a droplet is located in a cluster or void [8, 11].
16:30
15 mins

#528
3D-RECONSTRUCTION OF O 2 BUBBLE WAKE CONCENTRATION FIELDS OF TWO CONSECUTIVE BUBBLES
Alexandra von Kameke
Abstract: We present time resolved scanning laser induced fluorescence (TRS-LIF) measurements of pairs of bubbles rising freely in nitrogen saturated fluorophore solution. With our technique the three dimensional oxygen concentration in the bubble wake of a freely rising bubble pairs can be analyzed in order to gain insight of the locally available dissolved gas for a potential chemical reaction. This study is part of the DFG Priority Programme SPP1740 Reactive Bubbly Flows.
16:45
15 mins

#315
Multiscale Lattice Boltzmann simulations of droplet dynamics in turbulent flows
Felix Milan, Luca Biferale, Mauro Sbragaglia, Federico Toschi
Abstract: The deformation and dynamics of a single droplet on the sub-Kolmogorov scale in isotropic turbulence is studied using a Lattice Boltzmann diffuse interface model involving local open boundary conditions to allow for the creation of an external turbulent flow. The external flow field is obtained via pseudo spectral simulation data describing the trajectory of a passive tracer in isotropic turbulence. In this way we combine the microscopic scale of the droplet and the macroscopic scale of the turbulent flow. The results obtained from this fully resolved model are compared to previous studies on sub-Kolmogorov droplet dynamics in isotropic turbulent flows ( L. Biferale, C. Meneveau, R. Verzicco, J. Fluid Mech. 754, 184 (2014)), where an analytical model (P.L. Maffettone, M. Minale, Equation of change for ellipsoidal drops in viscous flow, J. Non-Newtonian Fluid Mech. 78 (1998) 227-241.), which assumes the droplet shape to be an ellipsoid at all times, is used to describe the droplet deformation. In contrast, the Lattice Boltzmann simulations enable us to study the fully resolved turbulent droplet dynamics and deformation of a single droplet, allowing also for the possibility of droplet break up.
17:00
15 mins

#524
ON THE CONSERVATION OF ENERGY FOR INTERFACE-CAPTURING TECHNIQUES FOR MULTIPHASE FLOWS. APPLICATION TO FALLING FILMS.
Nicolas Valle, Francesc Xavier Trias, Jesús Castro
Abstract: The simulation of falling films is a relevant problem of industrial and scientific interest. Their chaotic behavior presents a challenge to which the community has devoted many efforts. Among several possible approaches to multiphase flows, the use of interface capturing schemes is popular and amenable in modern computational architectures. In particular, the use of level-set techniques allows for a flawless treatment of topological changes [1], most notably in atomization processes. The use of interface-capturing schemes involves an Eulerian frame which rretrievably clips the spectra of resolvable interfacial features. Such a limited resolution may break the imbalance between kinetic and surface energies. The aforementioned present a dynamic equilibrium which manifests itself trough the capillary force. While capillary force affects the velocity field trough the pressure jump, the induced transport of the marker may modify the surface morphology, ultimately modifying the curvature. The mathematical responsible of a such a subtle equilibrium is the first variation of area formula.
17:15
15 mins

#183
Analysis and Modeling of Evaporating Dilute Polydispersed Sprays in Isotropic Turbulence
Valentin Giddey, Daniel Werner Meyer, Philipp Weiss, Patrick Jenny
Abstract: The non-trivial tendency of inertial particles or droplets to concentrate in low-vorticity-high-strain regions of a turbulent phase, called preferential concentration, has received a lot of attention in the past and also very recently (see e.g \cite{ Petersen2018, Sumbekova2017}). Aerosol drug delivery methods, the evaporation of liquid fuel in a combustion chamber, or the condensation/evaporation of water droplets in the atmosphere are typical applications motivating studies of this complex phenomenon. Preferential concentration is particularly relevant for the case of evaporating sprays, as droplets in dense clusters experience conditions that are very different from the conditions seen in regions with a low number-density \cite{Jenny2012}. Direct Numerical Simulations (DNS) of droplet-laden turbulent flows have been performed \cite{Elghobashi2019, Weiss2018}, but a modeling effort is required to account for clustering effects in numerical methods able to simulate regimes and problem sizes inaccessible to DNS. Models describing the behavior of non-evaporating inertial particles have been proposed by several authors (see e.g. \cite{Innocenti2018a, Minier2014}). In the present work, we present the development of a new Lagrangian description of droplets which accounts for the effect of preferential concentration on their evaporation. This is done by adding a statistical description of the seen conditions (temperature, mass fraction, and relative velocity) to the state vector describing each Lagrangian computational droplet.The advantage of this formulation is that group effects can be accounted for without having to provide or compute the exact spatial distribution of particles. The computational droplets are independent of each other but they experience the effects of clustering through the modeled seen conditions. In a first step, DNS are performed under different conditions \cite{Weiss2018} to gain insight into the processes controlling the evaporation. Coupled stochastic processes describing the seen conditions along the droplet trajectories are then defined and combined with ordinary differential equations for the droplet liquid temperature and evaporation rate. Gaussian processes are used as approximations of the slip velocity and seen temperature. A Beta process is used for the seen mass fraction. The low-order moments required to fully describe these processes are inferred from DNS data and parametrized as functions of known droplet properties and input parameters such as the Reynolds number, the mean Stokes number, and the mass loading. Simulations using the modeled processes are then performed. Statistics describing the droplet cloud and evaporation properties are averaged over a large number of realizations and compared against DNS references. The contribution of this work is twofold. First, the analysis of Lagrangian DNS data provides interesting information about the evaporation mechanisms of turbulent sprays, and second, we show that a model based on simple stochastic processes is able to capture the evaporation modulation caused by preferential concentration.
17:30
15 mins

#297
On the momentum and heat exchange in wind-wave turbulent flows
Federica Romoli, Lorenzo Silvestri, Andrea Cimarelli
Abstract: The interactions of a turbulent boundary layer with a water surface represents a very fundamental problem for many geophysical and industrial processes. The momentum and heat exchanges across the wind-wave interface in oceans abruptly affects the atmosphere and the understanding of the mechanisms driving these phenomena would certainly improve weather predictions. However, after decades of research efforts, the wind-wave interaction problem is still recognized as extremely elusive. The reason is the multidimensional and multiscale nature of the phenomena involved. Indeed, spatial and temporal scales of the air-turbulent boundary layer are significantly affected by the wavelength and velocity of the water surface waves which in turn are affected by the shear stresses and pressure fluctuations of the air turbulent boundary layer itself. To address these aspects, in this work we present results obtained from the analysis of Direct Numerical Simulation data of an air-water two-phase turbulent open channel. Single-point and two-point statistics are analysed in order to understand the structure of the air turbulent boundary layer and of its self-sustaining processes as a function of the characteristics of the water surface waves and viceversa. To better understand the role of the wave pattern, Direct Numerical Simulation data of a simple turbulent open channel with bottom wall are also considered. The comparison of statistics from the two simulations allows us to appreciate the modifications of the near-wall cycle and of the consequent momentum and heat transfers induced by the presence of water surface waves. Given the dual nature of the problem in the space of scales and positions, we will also present preliminary results based on the analysis of the exact equations for the second-order moments of the two-point velocity and temperature increments, the so-called Kolmogorov and Yaglom equations. Such a study allows us to infer on the multidimensional features of the cascade mechanisms connecting the production to the dissipation regions of the flow with possible repercussions on turbulence closures.
17:45
15 mins

#439
Two-phase homogeneous shear turbulence
Marco Rosti, Zhouyang Ge, Suhas Jain, Michael Dodd, Luca Brandt
Abstract: The understanding of turbulent two-phase flows with bubbles and/or droplets is important in many natural and industrial processes, e.g. rain formation, liquid-liquid emulsion, spray cooling and spray atomization in combustors. In these flows the turbulence is altered by the droplet feedback on the surrounding fluid and by droplet-droplet interactions. We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15200 with a volume of fluid method. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. Using a number of post-processing techniques, we will discuss the turbulence modulation in terms of statistics and flow structures. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady state conditions exhibit reduced Taylor microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small-scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplets size distribution which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering breakup in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.
18:00
15 mins

#23
THE STOCHASTIC SUBGRID MODEL FOR DROPLET VAPORIZATION IN A HIGHLY TURBULENT FLOW
Mikhael Gorokhovski, Surya Kaundinya Oruganti
Abstract: The effect of turbulence on the vaporization rate of droplets moving in a heated gas flow is manifested through two random processes, droplet dispersion and scalar mixing. The former is associated with the residence time of a droplet within a given eddy, whereas the latter is controlled by scalar gradients in the vicinity of the droplet surface. Both these processes are predominantly characterized by the small-scale dynamics in turbulence. The under-resolution of this dynamics in LES, necessitates the modeling of its effect on the droplet vaporization. This has motivated the present work. Recently in simulations of solid particle dispersion [1], the acceleration of individual particle was decomposed into filtered and residual components. The norm of the latter was expressed by the viscous dissipation “seen” by the particle along its trajectory, and thereby was simulated in terms of the lognormal stochastic process. As to the direction of the residual acceleration, a new stochastic equation, describing the Ornstein-Uhlenbeck process on the unit sphere, was proposed and assessed in [2]. This dispersion model, based on [1, 2], is used in the present work. The main contribution of this work is the development and assessment of a new stochastic sub-grid scale (SGS) model for droplet evaporation in turbulent conditions. Our physical concept is simple: the evaporation and the turbulent mixing around the droplet represent two successive processes with the former limiting the latter. This allowed to introduce the turbulent small-scale characteristics in the formulation of the droplet vaporization rate, and to construct the stochastic process for this variable along the droplet trajectory. The performance of the new SGS model is assessed in comparison to the vapor mass fraction and velocity statistics of the spray obtained from the experiments and the standard approach used in the literature. This comparison clearly illustrated the advantage of the proposed SGS model for turbulent vaporization. Additionally, the study also addresses the following question: How intermittent may be the vaporization rate, and what are the main parameters of statistics of the vaporization rate? To answer, we analyzed correlations between the vaporization rate, the local vorticity in the flow and the viscous dissipation “seen” along the droplet trajectory. This analyses was supported by conditional Voronoi Diagrams for segregation of droplets of different size. Also correlations between the vaporization rate and droplet parameters, such as acceleration and diameter, showed typical scales on which the turbulent vaporization rate is more intensive. References [1] M. Gorokhovski and R. Zamansky, Modeling the effects of small turbulent scales on the drag force for particles below and above the Kolmogorov scale, Phys. Rev. Fluids 3, 034602, 2018 [2] V. Sabelnikov, A. Barge and M. Gorokhovski, Stochastic modeling of the fluid acceleration on residual scales and dynamics of inertial particles suspended in turbulence., submitted to Phys. Rev.Fluids in 2018