Evaporation/condensation around a wetted cylinder confined between two parallel walls

Mixed convection flows in presence of condensation and evaporation phenomena have crucial role in several natural and technological processes, in particular in those involving drying and wetting of solid surfaces. Although such flows are quite common in engineering applications, their knowledge is far from being complete. The complex physics involved can be briefly sketched as follows: wetted solid bodies exchange heat with the liquid laying on their surfaces; the liquid phase exchange mass and heat with the surrounding gas through change of phase; the consequent diffusion of temperature and vapor concentration results in density variations that greatly impact the gaseous flow introducing buoyancy forces. In the present study we will focus on the liquid-gas interaction and we study how evaporation and condensation over solid wetted surfaces take place in an archetypal problem. To the best of our knowledge, in literature this problem has been mostly faced, through numerical modelling (see for example [1], [2]), since uncertainties in experimental approaches may come from the difficulties to control the parameters ruling the process. The mathematical model usually adopted consists of the incompressible Navier- Stokes equations where the buoyancy forces are taken into account by means of the Boussinesq approximation; at the wetted wall the thin liquid film is modelled as semi-permeable boundary condition which prescribes a Dirichlet condition for temperature and consequently for the saturated vapor concentration. This condition permits evaporation/condensation of the liquid/vapor phase through the evaluation of the Stefan flow at the liquid-gas interface. The set of equations and the boundary conditions are implemented within an unsteady incompressible Navier-Stokes solver developed using the openFOAM library. The new solver has been validated against literature numerical results of [3] in the case of laminar plane channel flow. Recent literature studies have been focused on the study of the flow moving within a straight channel with different conditions at wetted walls (among the others see [1]). In the present study we consider a more complex situation. The flow develops in a straight channel of length L and width H. A cylinder of diameter D = 0.2H is placed inside the channel at a distance equal to L/10 from the inflow section. In order to enlighten the different interaction mechanism between the walls and the bluff body two different distances of the cylinder from the bottom wall are investigated, respectively d = H/2 and d = H/4. At the inlet uniform temperature T0 and vapor concentration C0 are prescribed along with a parabolic velocity profile with a mean velocity U0 such that the Reynolds number Re = U0 H/ν is 500, being ν the kinematic viscosity. At the outlet a zero gradient condition is imposed together with a sponge region where fluid viscosity, thermal and concentration diffusivity are artificially increased according to an exponential law. Moreover in the sponge region the concentration is treated as a passive scalar. The liquid film interface on the wetted cylinder has temperature Tc and concentration Cc such to allow liquid evaporation. The channel walls can be either adiabatic and impermeable or wetted with fixed temperature Tw and concentration Cw , the latter allowing vapor condensation. Preliminary results are here very briefly discussed and more comprehensive results will be shown at the work-shop. For the case with adiabatic and impermeable walls, the different cylinder positions yield to small differences in the Stefan flow in the overall evaporation process. The latter appears substantially steady and the evaporation fluxes around the surface are quite homogeneous with a defect in the rear of the body. The vapor flows in the upper part of the domain and two regions of different concentration level are clearly visible. The velocity field develops in unsteady vortices without a clear dominant size. The wetted walls condition, on the other hand, seems to greatly impact the process and especially the heat and mass transfer one. The buoyancy force and hence the characteristic velocity is increased. Downstream the body the velocity field develops in well defined vortical structures of the size of the channel width. Near the cylinder the flow is greatly unsteady and poorly organized making the vapor well mixed. In this condition evaporation process is non homogeneous and unsteady. On the average the whole surface of the cylinder permits higher Stefan flow rates. This study encourages further developments in order to include the liquid thin film dynamic into the model.