Nicola Suzzi

The recovery of waste heat from post-combustion gases is often limited by sulfuric acid condensation, which promotes severe low-temperature corrosion. Hydrophobic and superhydrophobic coatings promote dropwise condensation rather than filmwise mode, potentially reducing the residence time of the condensed liquid on the surface. However, the dynamics of sulfuric acid dropwise condensation on such surfaces remain poorly understood. To address this gap, an individual-based model is developed to simulate the evolution of the condensing droplet population. Each droplet is tracked from nucleation to shear-driven sliding, accounting for growth by direct condensation and coalescence with other droplets. The heat and mass transfer model, used to evaluate the condensation rate of sulfuric acid for each droplet, includes latent heat transfer at the liquid–vapor interface and convection in the surrounding gas phase. Given its low mole fraction, all the sulfur trioxide is assumed to react with water to form sulfuric acid. Assuming that the wall temperature is below the acid dew point but above the water dew point, the composition of the condensed H₂SO₄-H₂O solution is determined from vapor–liquid equilibrium (VLE). The numerical model is validated against experimental data from the literature. The results show that, compared with hydrophilic surfaces, superhydrophobic surfaces substantially reduce the wet fraction of solid substrate and the residence time of condensed droplets, suggesting a lower risk of low-temperature corrosion.

A probability-based model (PBM) is developed to predict the evolution of a population of impinging droplets on a solid substrate and the eventual transition between dropwise and filmwise regimes. A dedicated heat transfer model is designed, in order to estimate the evaporating mass flux when the solid substrate is heated. Statistical information such as the droplet size distribution and the influence of surface wettability, required by the PBM, are derived using a previously developed high-fidelity individual-based model (IBM). The PBM is verified with the high-fidelity model for a small patch of solid substrate. Then, validation with experimental evidence from the literature is carried out in the case of in-flight ice on the NACA0012 airfoil. Results show that the present PBM is capable of investigating in-flight ice problems and can be integrated with a CFD analysis of the air flow past an airfoil flying through a cloud of supercooled droplets to predict the possible onset of ice accretion on the airfoil surface. Compared to Messinger-like models, the influence of surface morphology on runback water flow is incorporated in the PBM through the modeling of a discontinuous wetting layer, contributing to the design of passive and active anti-icing systems.

A novel droplet growth model is presented in the case of humid air condensation, since an accurate prediction of the droplet growth rate is crucial to develop accurate individual and statistically based models to predict the heat transfer performances of dropwise condensation over an hydrophobic surface. In the present modelization, the thermal resistance correlated to the presence of an hydrophobic coating is added to the conductive resistance through the droplet liquid core, which is derived assuming a spherical droplet with a prescribed contact angle. The implementation of the Knudsen layer allows the modelization of the liquid-gas interface. The combined effect of latent and convective heat fluxes is considered to estimate the heat transfer between the droplet free surface and the undisturbed moist air flow, while only the latent contribution is retained in the literature models (notwithstanding the convective heat flux is of the same magnitude in the case of humid air condensation). The mass transfer rate, which gives the latent heat flux and is usually estimated assuming vapor diffusion around an isolated droplet, is here calculated modeling the influence of neighbor droplets, that affect the local vapor concentration field and, thus, the effective mass transfer rate. To do so, the point-sink superposition method is recast in its integral form, knowing the statistical size distribution of a condensing droplet population. The effect of vapor convection is also integrated with the point-sink superposition method via the imposition of the vapor concentration at a known distance from the solid surface. The developed condensation model is validated with literature experimental data and compared with previous literature modelizations.

Steam condensation over a hybrid hydrophobic–hydrophilic surface is modeled via simplified heat transfer modelization. Filmwise condensation is assumed over the hydrophilic region. The standard film model is improved, accounting for the liquid flow rate crossing the hydrophobic–hydrophilic boundaries. A threshold for flooding occurrence is also presented. Dropwise condensation is assumed over the hydrophobic region. Compared to the heat transfer models in the literature, based on the statistical drop size distribution, a novel correlation is used for the size distribution of small droplets. The correlations of both the liquid flow rate crossing the hydrophobic–hydrophilic boundary and the size distribution of small drops are derived via Lagrangian simulations, using an in-house code previously developed and validated by the authors. The heat transfer model is validated with experimental data in the literature involving a hybrid surface, composed by alternate vertical hydrophobic–hydrophilic stripes. Then, the optimization of the hybrid surface geometry is performed in terms of hydrophobic width and hydrophilic width, with the aim of enhancing the heat flux.

Several engineering systems currently use microchannel heat sinks. In order to increase the performance of these devices, optimisation according to the first and second law of thermodynamics is employed. One way to achieve the goal is to modify the geometry of the cross-section, as is done in this paper for square ducts, having the walls at a uniform temperature which is higher than that of the bulk fluid at the inlet. The effects of both the thermal entry region of the duct and the heat generation due to viscous dissipation are considered. The resulting Graetz–Brinkman problem is solved numerically to obtain the velocity and temperature fields. It is demonstrated that non-negligible viscous heating eventually causes the heat flux to reverse (from fluid to walls), and that, only after this condition is achieved, can the flow become fully developed, which makes the entry region the only useful stretch for real-life applications. The length after which the direction of the heat flux reverses due to viscous heating in the fluid is obtained as a function of the Brinkman number and of the smoothing radius. Optimisation with performance evaluation criteria and entropy generation minimisation was carried out separately, and the results were combined into a single objective function. A comparison with published models highlights how neglecting the entry region and viscous heating yields misleading results. It turns out that smoothing the corners is always profitable in the case of the constrained heated perimeter or area of the cross-section but seldom when the characteristic length or the hydraulic diameter is fixed. With few exceptions, viscous heating amplifies the trends experienced for zero-Brinkman flows. The results are in non-dimensional form, yet they have been obtained starting from plausible dimensional values and are applicable to real-life devices.

Dropwise condensation (DWC) of steam over hybrid hydrophobic–hydrophilic surfaces is numerically investigated via a phenomenological, Lagrangian model. The full non-dimensionalization of the heat transfer model, needed to determine the droplet growth, allows for generalization of computational results. Hybrid surfaces characterized by recursive geometries are implemented via the introduction of proper boundary conditions. The numerical size distribution of both the large and the small droplet populations, crucial for development of simplified, statistically sound models, is compared with empirical and theoretical correlations. Then, the validation with experimental data involving DWC over an hybrid surface is successfully conducted and the heat flux is enhanced under different operating conditions via hybrid geometry optimization.

Current technology has produced a wide range of advanced micro-structured surfaces, designed for achieving the best wettability and adhesion performances for each specific application. In the context of in-flight icing simulations, this opens new challenges since the current most popular and successful ice accretion prediction tools neglect the details of the droplet behavior opting for a continuous film model. Here, a phenomenological model, following, in a Lagrangian approach, the evolution of the single droplets from the impinging to the onset of rivulets, is developed to simulate the performances of super-hydrophobic surfaces in icing application. Possible rebound and droplet spread on the impact, coalescence, single ice bead formation and droplet to rivulet transition are taken into account. The first validation shows how the models are able to predict the anti-icing capability of a super-hydrophobic surface coupled with a heating system.