Simulation of multiple cases with a virtual Wind tunnel

First we consider an approach of simulating a whole boundary layer wind tunnel similar to that done in section4.3.5.2 but without using spires and barrier as shown in Fig. 4.21. Also

the V-BLWTused for this case is from Wang & Stathopoulos’s study, Concordia University

BLWT. Roughness blocks are used to model suburban and urban roughness, while carpet is used for open country roughness. Some of theV-BLWTsetups for multiple roughness patches are shown in AppendixA. We do not incorporate spires,barriers or grids to the models to save on simulation time. Fully developed boundary layer velocity and turbulence intensity profiles are applied at the inlet of theV-BLWTinstead. The wind tunnel has a length of 12.2m, width of 1.8m and height of 1.8m. Open country roughness is is directly incorporated by the use of wall functions. This method has a limitation in that the nearest cell to the wall should be big enough, but sincez0 = 0.024 is small the requirement is satisfied. For the suburban and urban roughness blocks are used as shown in Fig. 4.19. The blocks used inWang & Stathopoulos’s study were 1in cubes for suburban (S), and 1.5in cubes for urban (U). This results in too many roughness elements for the simulation, so it is decided to double the size of the cubes to 2 in and 3 in respectively. The number of roughness blocks is as a result reduced by four times. This is in accordance with formulas that use area density ratios to determine average roughness characteristics. The modified block sizes result in the same planar and frontal area density ratios as the original, hence they are equivalent. For this simulations we consider blocks to be the only roughness features, and no spires, grids or barriers are used. Instead of a uniform wind profile as used at wind tunnel inlet, anABLboundary layer profile is applied. The inlet velocity

(a) Velocity contour details close to spires, barrier and roughness blocks

(b) Contour of U at mid vertical section

(c) Contour of U at height of blocks

4.3. Complexity2: Inhomogeneous roughness evaluation 103 0 2 4 6 8 10 0 0.5 1 1.5 2 U(m/s) z(m) 0 20 40 60 80 0 0.5 1 1.5 2 Iu(%) z(m) No roughness features Blocks Spires+Barrier+Blocks

Figure 4.18: Comparison of U and Iu profiles for different roughness features

profile is logarithmic with the gradient height fixed at 600mm andUg = 12.5m/s. The length scale of the BLWTsimulations is 1:400 and time scale is 3:400. A preliminary simulation is

Figure 4.19: Open country(OC), Suburban(S) and Urban(U) roughness representation carried out on an open country roughness. A sand grain roughness of Ks = 20z0 = 0.48 is used for the wall function.The result is shown in Fig. 4.20. There are two problems with this simulation. First the first cell height Yp = 0.48 is too high compared to the boundary layer thickness δ = 0.6m. The problem of matching roughness in wind tunnel problems is a well known problem. For the simulation of the 69 cases of Wang & Stathopoulos a much lower roughness is assumed for the carpet so that theYp > Kscondition is met. The first simulations we carried out withKs= 0.48 for open carpet turned out to be bad where a bulge in the velocity profile is observed close to the ground. Using a lower roughness for OC corrected this problem much better fit are obtained except for the cases where open country roughness dominates the other patches. Second one should not expect horizontal homogeneity as the case of an empty domain because of the no-slip boundary conditions used at the top and side walls.

0 5 10 15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 U(m/s) z(m) U_inlet U outlet

Figure 4.20: Inlet and outlet horizontal velocity profiles for open surface roughness

The results for the 69 cases are given in the following pages and Appendix A. We can observe that in most of the cases the V-BLWT fits the data much better than ESDU model. This is in contrast to the result found byWang & Stathopoulosusing numerical model with 2D simulations, which gave closer result to theESDUmodel. The reason for this difference is not the simplified 2D model rather the difference in the shear stress modeling at the wall. Wang

& Stathopoulos assumed a model of shear stress variation with fetch suggested by Bradley

(1968).

u∗(x) ∼ x−0.1 (for S-R) (4.35)

Garrat(1989) found that the shear stress initially increase to about twice its equilibrium value

for S-R change, and decreases to about half its final value for R-S change.

u∗(x) ∼ 2x−0.1u∗ (for S-R)

u∗(x) ∼ 0.4x−0.1u∗ (for R-S)

(4.36)

These equations were directly incorporated inWang & Stathopoulos’s numerical model. Our approach does not model shear stress but let it develop from the simulation. Also we should note that it is difficult to incorporate Wang’s numerical approach into an existingCFDsoftware due to the shear stress model. The other difference concerns turbulence models. Wang’s numer- ical model uses linear eddy viscosity (mixing length) model for turbulence closure, while the current approach uses two equationReynolds Averaged Navier-Stokes (RANS)model, namely standardk− model. We believe that these two differences , primarly the shear stress model, are the reasons for better result found from virtual wind tunnel simulations.

4.3. Complexity2: Inhomogeneous roughness evaluation 105