Giorgio Crasto University of Cagliari ITALY Forest Modelling

Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for Wind. Sim 4. 5

Giorgio Crasto University of Cagliari - ITALY Why the need for a canopy model

Giorgio Crasto University of Cagliari - ITALY § In the new canopy model of Wind. Sim the Canopy Layer is solved by the use of porosity and drag forces (sinks of momentum) § The canopy is described by: § Height of the canopy – hc § The canopy is discretized with a caertain number of cells (uniform grid? ) § Underwood roughness length – z 0 § Porosity – b § Drag coefficients – C 1 and C 2

Giorgio Crasto University of Cagliari - ITALY Concept of Porosity § Given a generic volume occupied by fluid and solid phases, its porosity b is defined as the ratio

Giorgio Crasto University of Cagliari - ITALY Concept of Porosity § Given a surface partially permeable, also a porosity for a 2 D windbreak can be defined as

Giorgio Crasto University of Cagliari - ITALY Concept of Porosity § Once done an hypothesis on the structure of the porous region, there is a relation linking b and b. S z HIGH x EAST Darcy’s velocity

Giorgio Crasto University of Cagliari - ITALY Every element of the canopy introduces in the flow a sink of momentum § So inside the canopy the momentum RANS equations present an additional term Advection Diffusion Additional forces: pressure gradient, gravity, adittional sources

Giorgio Crasto University of Cagliari - ITALY The sinks of momentum depend upon porosity and velocity § A classical approach (for high porous materials) is to consider the sinks of momentum proportional to the velocity § In the Darcy’s law the advective and diffusive terms are neglected, so the gravity Darcy’s law

Giorgio Crasto University of Cagliari - ITALY Sinks of momentum implemented in the new version of Wind. Sim § Sinks of momentum [N/m 3]: two terms Since the high Reynolds numbers viscous force pressure >> viscous forces

Giorgio Crasto University of Cagliari - ITALY Present model § In the canopy model of Wind. Sim 4. 5 is possible to set the drag coefficients C 1 and C 2 where

Giorgio Crasto University of Cagliari - ITALY How to estimate the porosity k? § The relation k vs. b is proposed: In this way it’s possible to estimate the value of the drag coefficient C 1 starting from a given value of porosity b

Giorgio Crasto University of Cagliari - ITALY

Giorgio Crasto University of Cagliari - ITALY

Giorgio Crasto University of Cagliari - ITALY

Giorgio Crasto University of Cagliari - ITALY Conclusions § With the proposed canopy model is possible to estimate properly the dissipation of momentum and the production of turbulence inside a forest § Further validations are needed in order to state more precise guidelines for the choice of the parameters C 1 and C 2 used together § Masts inside forests § Wind farms close to forests § A possible treatment of a canopy would be with additional sources in the transport equations of k and e