The project addresses the evaporation/condensation of liquid droplets transported by a turbulent flow. In technological applications, e.g. internal combustion engines, aeronautical engines or power plants combustion chambers, the droplet transport, evaporation and vapor mixing is crucial for the overall efficiency of the device.
The phase change in a turbulent flow is a multi-scale phenomena ranging from the nano scales where the vapor is formed at the liquid interface, to the micro and macro scales of the turbulent flow which transports both the droplets and the vapor.
This multi-scale process poses several issues. Nowadays, the set of equations for the carrier phase in presence of mass, momentum and energy transfer is still formulated on phenomenological ground as well as the models which provide the macroscopic mass and energy fluxes.
In this project a rigorous derivation of the fluid flow equations will be carried out. The methodological path starts from the low-Mach number equations for the carrier phase endowed with appropriate boundary conditions at the droplet surface. In the limit of small droplets size, a rigorous decomposition of the flow field in terms of a background plus a disturbance (density, velocity and temperature), allows to reallocate the boundary conditions at the droplet surface as appropriate source terms for the carrier phase. These sources follow from a solution of a five dimensional unsteady Stokes problem without any ``ad hoc'' assumptions.
The methodology still needs mass and energy fluxes at the droplet positions. New models will be pursued starting the investigation at the nano scale where the evaporation/condensation naturally occurs via Molecular Dynamics simulations. The models will be checked against well targeted experiments of a single droplet evaporation/condensation and will be employed in the Direct Numerical Simulation of a droplet laden turbulent jet to be further validated against experimental measurements.
The present project presents many aspects of innovation with respect to the available state of the art literature of multi-phase flows in presence of droplets evaporation/condensation.
The first aspect consists in the derivation of the fully coupled equations system for the carrier phase in presence of mass, momentum and energy transfer due to the disperse phase. Indeed, the source terms in the set of equations for the carrier fluid are still lacking of a rational framework. Starting from first principles, i.e. without any ``ad hoc'' assumptions, a set of equations for the carrier flow is derived which takes into account all the coupling effects at the level of mass, momentum and energy due to the droplets phase change. Briefly, the disturbance fields (density, momentum and energy) due to the droplets evaporation/condensation is evaluated through the solution of a five dimensional unsteady Stokes problem which involve the mass, momentum and energy balance. Then, the solution of the disturbance field, is employed to reallocate the boundary conditions at the particle surface, as appropriate source terms in the carrier phase flow equations.
The second innovative aspect consists in tackling the evaporation/condensation process starting from the nanoscopic scale where it naturally occurs. Under this respect, the data ensuing from Molecular Dynamics simulations will serve as well established benchmark for phenomenological models which necessarily must be used in the macroscopic simulations of WP1. Indeed, the mass and energy fluxes will be directly measured and parametrized in terms of several thermodynamical conditions avoiding any "a priori" assumption. The experimental WP3 will overlap both with WP1 concerning the macroscopic behavior of a turbulent flow in presence of phase change and with WP3 concerning the measurements of the evaporation rate of a single microscopic droplet. This will give the chance to validate the new mass and energy coupling method developed in WP1 and the mass and energy fluxes computed by Molecular Dynamics in WP2.
Overall the present project will advance the theoretical knowledge of multiphase-flows in presence of evaporation/condensation under different aspects. The first one is represented by the theoretical formulation of a new set of equations from first principle, the second concerns the implementation of innovative models for mass and energy fluxes ensuing from Molecular Dynamics data in fluid flow solvers. The reliability of the new models is constantly certified by dedicated experimental measurements.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
REFERENCES
[1] Jenny, P., Roekaerts, D., and Beishuizen, N. (2012). Progress in Energy and Combustion Science, 38(6)
[2] Saito, I., & Gotoh, T. (2018). New Journal of Physics,| 20(2)
[3] Falkovich, G., & Pumir, A. (2007). | Journal of the Atmospheric Sciences,| 64(12)
[4] Balachandar, S., & Eaton, J. K. (2010)| Annual Review of Fluid Mechanics,| 42
[5] Burton, T. M. and Eaton, J. K. (2005). Journal of Fluid Mechanics, 545
[6] Elghobashi, S. (1994). Applied Scientific Research, 52(4)
[7] Balachandar, S. (2009). International Journal of Multiphase Flow, 35(9)
[8] Migdal, D. and Agosta, V. (1967). Journal of Applied Mechanics, 34
[9] Crowe, C., Sharma, M., and Stock, D. (1977). ASME. J. Fluids Eng., 99(2)
[10] Miller, R. S. and Bellan, J. (1999). Journal of Fluid Mechanics, 384:
[11] Okong'o, N. a. and Bellan, J. (2004). Journal of Fluid Mechanics, 499:1-47.
[12] Dalla Barba, F. and Picano, F., (2018) Physical Review Fluids 3(3)
[13] Vreman, A. W. (2015). | Journal of Fluid Mechanics,| 773
[14] Gualtieri, P., Picano, F., Sardina, G., and Casciola, C. M. (2015). Journal of Fluid Mechanics, 773
[15] Gualtieri, P., Battista, F., & Casciola, C. M. (2017). Physical Review Fluids,| 2(3)
[16] F. Battista, P. Gualtieri, J.-P. Mollicone and C.M. Casciola (2018). International Journal of Multiphase Flows, 101
[17] Mashayek, F., Jaberi, F., Miller, R., and Givi, P. (1997). International Journal of Multiphase Flow, 23(2)
[18] Mashayek, F. (1998a). International Journal of Heat and Mass Transfer, 41(17)
[19] Mashayek, F. (1998b). Journal of Fluid Mechanics, 367
[20] Michaelides, E. E. (2003) Journal of Fluids Engineering 125
[21] Abramzon, B. and Sirignano, W. A. (1989) International Journal of Heat and Mass Transfer, 32
[22] Wang, F., Liu, R., Li, M., Yao, J. and Jin, J. (2018),Fuel 211
[23] Lavieille, P., Lemoine, F., Lavergne, G., M. Lebouché, M. (2001), Experiments in Fluids 31
[24] Bazile, R. and Stepowski, D. (1995), Experiments in Fluids 20
[25] Lozano, A., Yip, B. and Hanson, R.K. (1992), Experiments in Fluids 13
[26] Khalitov, D. and Longmire, E. (2002), Experiments in Fluids 32