## ANDREA GALLEGATI

PhD Graduate**PhD program:**: XXXIII

**supervisor**: Prof. Gualtieri

**advisor**: Prof. Casciola

**Thesis title:**Droplet condensation in turbulent jets.

The evaporation and condensation process of liquid droplets, advected by a turbu- lent flow is found in many technological applications - ranging from aeronautical/power- plants engines up to the rather new discipline of Particle Engineering in the biotech industry - and in many natural phenomena, such as cloud formation and meteorology. A better understanding of droplets nucleation, transport, evaporation/condensation and vapour mixing is crucial for the eciency of these devices as well as it would be to improve weather forecasting.
The phase change is a multi-scale phenomena ranging from the nano scale, at which droplets nucleate, to the micro and macro scales where the turbulent flow advects both the droplets and their vapour. Although droplet laden flows have been extensively studied, several issues are still in place, especially when dealing with multi-phase turbulent flows. Many phenomena, such as small scales clustering of droplets (considered as inertial particles) or preferential spatial accumulation, have been observed and understood under the simplifying assumption of the one-way cou- pling regime, where the disperse phase does not modify the carrier fluid. Nonetheless, a deeper understanding of multiphase flows demands at least for two-way coupling eects, accounting for the inter-phase mass, momentum and energy exchanges. Homogeneous nucleation of liquid droplets occurs when a hot vapour stream mixes with a cooler and dry external flow. Even though many applications could benefit from a better understanding of droplet nucleation in turbulence, nowadays it has been investigated only experimentally, given all the aforementioned diculties on modelling the multi-physics phenomena occurring in such a complex turbulent flow. In fact, the nonlinear interplay between turbulent fluctuations and homogeneous nucleation, immediately leads to non-trivial cross-coupling phenomena between the gas and the liquid phase. Their modelling reveals to be crucial for detailed numerical investigations to be reliable.
Classical Nucleation Theory (CNT) prescribes a rate for the homogenous nucleation of droplets, per unit time and volume. It also provides for an estimate of the critical radius at which – eventually – each droplet nucleates. The droplet nucleation itself basically occurs when a stable molecules cluster size is reached, thus everything strongly depends on the local thermodynamical state. While the equations describ- ing mass, momentum and energy exchange, between droplets and the turbulent flow are still formulated on phenomenological ground, a rigorous derivation of the fluid flow equations still lacks. In the present work a first attempt to tackle this challenging physical problem will be presented: modelling the mass, momentum and energy transfer, with appropriate boundary conditions, at the interface between the two phases. Starting from the low-Mach number formulation of the Navier-Stokes equations for the gaseous phase, an analytical decomposition of the flow field allows – within the point particle approximation, for the disperse phase – to reallocate the boundary conditions at the droplets surface as equivalent source/sink terms on the carrier phase, without any ad-hoc assumption. However this methodology still needs an estimate for the fluxes at the droplet surface, at any length-scale. Two different models for the mass transfer, have been tested and employed here to be validated against the available experimental investigations found in literature.
In the present study a full description of the droplet nucleation in a vapour turbulent jet is provided by means of Direct Numerical Simulation (DNS). No turbulence model has been considered, since all the relevant scales of turbulent motion have been resolved on the computational grid. To capture the inter-phase exchanges the so-called Exact Regularised Point-Particle method (ERPP) has been adopted, proving again its suitability for High Performance Computing simulations (HPC) on massively parallel machines, handling billions particles. In the point-particle ap- proximation and within the Eulerian-Lagrangian approach, here adopted to describe respectively the carrier and disperse phase dynamics, each droplets is described as point mass. The relevance of the inter-phase coupling eects is thoroughly discussed, by comparing the results obtained accounting for the droplets back-reaction with those obtained neglecting it. It is already known how a disperse phase does aect the carrier phase dynamics, modulating turbulence, stretching the shape of the jet, but always preserving the (statuary) jet self-similarity found in the one-way coupling regime. Beyond turbulence modulation, the droplets back-reaction is mainly eective on the temperature and vapour fields of the carrier phase, heavily altering the local thermodynamical fluctuations, thus aecting the related droplet nucleation rate. This way, one is able to completely characterise the phase change process, to measure any droplet trajectory followed in a Lagrangian way and to fully characterise any observable from a statistical point of view.
Considerable eects of the droplets back-reaction on the nucleation rate emerged, by decreasing the amount of vapour – due to nucleation/condensation – and heating up, to a lesser extent, the dry environment. Both eects decrease the vapour saturation and the nucleation rate that strongly depends on it. The intensity of these eects is related to the number of back-reacting nucleated droplets, thus at lower concen- trations the nucleation rate is almost insensitive to it. However, for higher vapour concentration, it is not possible to neglect the particles back-reaction, especially being these an additional source of turbulent fluctuations that ultimately impacts on the mean nucleation rate. In fact, the droplets redistribute vapour through condensation/evaporation and temperature by releasing/absorbing heat, along their trajectory. In other words, the particles back-reaction serves as an additional source of fluctuations not to be disregarded. It is reasonable to hypothesise that it is not possible to eectively model the back-reaction eects, discussed so far, rather than to simply evolve each single droplet as it has been done in the present DNS simulations. Under this respect, the present contribution constitutes an absolute novelty in the aerosol community shedding light on the the two-way coupling eects that were revealed to be crucial in the overall nucleation process and turbulent transport of the droplets.

**Research products**

- 11573/1416205 - 2020 - Droplet homogeneous nucleation in a turbulent vapour jet in the two-way coupling regime (02a Capitolo o Articolo)

GALLEGATI, ANDREA; BATTISTA, FRANCESCO; GUALTIERI, PAOLO; CASCIOLA, CARLO MASSIMO - 11573/1592655 - 2021 - Droplet condensation in turbulent jets (07a Tesi di Dottorato)

GALLEGATI, ANDREA