Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for WindSim 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 WindSim 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 – h c The canopy is discretized with a caertain number of cells (uniform grid?) Underwood roughness length – z 0 Porosity – Drag coefficients – C1 and C2
Giorgio Crasto University of Cagliari - ITALY Concept of Porosity Given a generic volume occupied by fluid and solid phases, its porosity is defined as the ratio
Giorgio Crasto University of Cagliari - ITALY Given a surface partially permeable, also a porosity for a 2D windbreak can be defined as Concept of Porosity
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 and S x EAST z HIGH Darcy’s velocity
Giorgio Crasto University of Cagliari - ITALY On the concept of Darcy’s velocity The Darcy’s velocity is the velocity that would occur if the whole volume was occupied by the fluid porous region
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 WindSim Sinks of momentum [N/m 3 ]: two terms viscous force pressure force Since the high Reynolds numbers pressure >> viscous forces
Giorgio Crasto University of Cagliari - ITALY In the canopy model of WindSim 4.5 is possible to set the drag coefficients C1 and C2 where Present model
Giorgio Crasto University of Cagliari - ITALY How to estimate the porosity k? The relation k vs. is proposed: In this way it’s possible to estimate the value of the drag coefficient C1 starting from a given value of porosity
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 C1 and C2 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
Giorgio Crasto University of Cagliari - ITALY Additional sources in the transport equations of k and epsilon (to be tested) S k = dens*0.5*Cd*a*abs(u)*u 2 Where Cd can be taken equal to C2+C1/u a is the area of foliage per unit of volume S e = ce4*dens*(eps/ke)*0.5*Cd*a*abs(u)*u 2 ce4 of the same order of ce1 and ce2 where ce1=1.44 and ce The two additional sources in the tke and tdr transport eq.ns are meant to account for the total work eddies do against foliage drag