1. Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for WindSim 4.5

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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 

13. Giorgio Crasto University of Cagliari - ITALY

14. Giorgio Crasto University of Cagliari - ITALY

15. Giorgio Crasto University of Cagliari - ITALY

16. 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 

17. 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 ce2 1.92 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