**TURBULENT, THERMAL BOUNDARY- AND TRANSITION-LAYERS ABOVE AND WITHIN POROUS MEDIA**

Many environmental and industrial situations involve thermal, turbulent boundary- and transition - layers above and within porous bodies.These include gravel beds of natural streams, atmospheric boundary layers over snow or vegetation, bio-heat transfer in human tissues (Khaled & Vafai, 2003), the development of innovative and compact heat exchangers (Kasaeian, Daneshazarian, Mahian, Kolsi, & Chamkha, 2017)and many others.

When a turbulent flow takes place through and above a slab of porous, solid material, and a temperature difference is maintained between them, a thermal, turbulent boundary layer develops at the interface between the solid and the *free*-fluid regions. The surface of the porous material splits the whole flow domain into a surface and a subsurface flow region. When either of these two flow regions exists on its own, flow characteristics are reasonably well understood. Indeed there is a large body of literature on both boundary layers over rough (and smooth) impermeable walls and traditional porous media flows. This is not the case whenever surface flows and porous media interact. A so called *transition layer*develops in the upper part of the subsurface flow where mean velocities deviate from the typical constant profile of undisturbed porous media. Moreover, within the surface flow, some authors have noticed that the wall permeability can significantly affect the flow resistance of both laminar and turbulent boundary layers (Kuwata & Suga, 2017).

The interplay between the thermal properties of the fluid and the porous layer affect the intensity of the turbulent, thermal fluctuations at the interface and, consequently, impact on the resulting interfacial heat transfer rate. The actual values of the equivalent thermal conductivity and the equivalent, specific heat capacity of the porous matrix determine whether there is a substantial thermal equilibrium between the matrix and the interstitial fluid.

The proposed project aims to characterize the turbulent, thermal boundary layer developing at the interface between a *free*fluid, namely a gas species with Prandtl number close to 1, and a porous matrix and to contribute to the advancement of closure models for the volume-averaged energy equation. The assumption of thermal equilibrium between the fluid and the solid matrix will be critically addressed and the error induced by this approximation will be related to the thermal and hydraulic properties of the porous layer. Focusing on relatively low Reynolds numbers, we propose to carry out micro-scale, direct numerical simulations (DNS henceforth) of turbulent flow and heat transfer on a plane channel partially filled with a *synthetic *porous matrix consisting of either a regular or an irregular arrangement of regularly- or irregularly-shaped obstructions (e.g., therandom geometry YADE model created by (Dyck, 2014)): the details of the flow throughout the inter-granular spaces will be captured (see, e.g., (Piller, et al., 2009), (Piller, Casagrande, Schena, & Santini, 2014)). The results of the aforementioned DNSs will be up-scaled and used as reference to validate and possibly improve existing models for, e.g., the shear stress and the heat transfer coefficient over porous surfaces and to assess the validity of the thermal equilibrium assumption under different combinations of fluid and solid materials.

**References**

Dyck, N. (2014). Digital Generation and Radiation in Spherical Void-Phase Porous Media. (W. University, Ed.) London, Ontario, Canada.

Kasaeian, A., Daneshazarian, R., Mahian, O., Kolsi, L., & Chamkha, A. (2017). Nanofluid flow and heat transfer in porous media: A review of the latest developments. *International Journal of Heat and Mass Transfer, 107*, 778–791.

Khaled, A.-R., & Vafai, K. (2003). The role of porous media in modeling flow and heat transfer. *International Journal of Heat and Mass Transfer, 46*, 4989-5003.

Kuwata, Y., & Suga, K. (2017). Direct numerical simulation of turbulence over anisotropic porous media. *Journal of Fluid Mechanics, 831*, 41-71. doi:10.1017/jfm.2017.619

Piller, M., Casagrande, D., Schena, G., & Santini, M. (2014). Pore-scale simulation of laminar flow through porous media. *Journal of Physics: Conference Serie, 501*(1), 012010. doi:10.1088/1742-6596/501/1/012010

Piller, M., Schena, G., Nolich, M., Favretto, S., Radaelli, F., & Rossi, E. (2009). Analysis of hydraulic permeability in porous media: From high resolution x-ray tomography to direct numerical simulation. *Transport in Porous Media, 80*(1), 57-78. doi:10.1007/s11242-009-9338-9