Computational domain

The computational domain used for this experiment is the same as the one used byHargreeves

& Wright (2007). It has dimensions of 5000m X 100m X 500m. The domain is meshed

with 500x50x5 cells and the mesh is expanded in the the vertical direction in such a way that the the size of nearest cell to the ground is 1m. This satisfied the Yp > Ks criterion for roughness conditions ofz0 = 0.01m. A reference wind speed of 10m/s at a height of 6m is used. Different boundary conditions at the ground surface, inlet and top of the domain are tested until

4.1. Complexity0: Empty domain 79

a horizontally homogeneous flow is obtained using k-epsilon turbulence model. Hargreeves

& Wright used commercial CFD software CFX and Fluent to demonstrate the problem of

ABLsimulations on an empty fetch. Boundary conditions are modified progressively through user defined functions (UDF) until a horizontally homogeneous flow is obtained for all flow quantities (U,k and). Here similar procedure is followed to check if the software developed in this work can overcome the problem.

4.1.2

Boundary conditions

Boundary conditions are very important for anyCFDsimulation because they are cutoffplanes that divide the area we are interested in simulating from that we do not want to include in the simulation. In other words they are used to incorporate the influence of the surrounding to our model. The type of boundary condition also affects the placement of the cutoffplanes relative to the central region where obstacles are placed. For example, it is well known that use of symmetry boundary condition at the top and sides of the domain introduces artificial accelerations unless blockage ratio is kept to a minimum. The computational domain is usually divided into three regions (Blocken et al. 2007), namely, the central region where the obstacle is modeled as best as possible, and the upstream and downstream regions where the effect of obstacles is modeled by regular roughness elements. The other issue concerns consistency of boundary conditions with the wind profiles specified at the inlet and the turbulence model

(O’Sullivan et al. 2011,Richards & Hoxey 1993).

At the inlet of the computational domain fully developed equilibrium velocity and turbu- lence intensity profiles are applied. The inlet profiles should be consistent with the upstream surface roughness characteristics (Miller & Davenport 1998,Wieringa 1993), and they should be maintained within the computational domain until the flow reaches the face of the test build- ing. This is very important for determination of wind load on buildings, that will be signifi- cantly different if, for instance, a uniform velocity profile is used instead of logarithmic profile. A peculiar problem in ABL simulations is that maintaining horizontal homogeneity is very difficult to achieve with current breed of CFDsoftware. Richards & Hoxey (1993) have in- vestigated this problem thoroughly and suggested boundary conditions (Eqs. 4.1-4.3) to be specified at the inlet that will ensure horizontal homogeneity for the standard k-epsilon turbu- lence model. Their formulas have been used by the wind engineering community for many years. However, it is not enough to specify just inlet conditions to get a stream-wise homoge- neous flow. The wall functions used at the surface should be compatible with the roughness of the upstream fetch outside the domain. Otherwise an internal boundary layer will develop

starting from the inlet at which the roughness change occurs. u= u∗ κ ln z+z0 z0 (4.1) k = u∗ 2 √ Cµ (4.2) = _κ(u∗3 z+z0) (4.3)

Richards & Hoxeyfound that the transport equations for the standard k-epsilon model can be

satisfied with above relations only when a differentσ is used than the standard value of 1.3.

The formula for calculatingσ given vonKarman constant is

σ = κ 2 (C2−C1) p Cµ (4.4)

Nikurdase’s modified log-law equations4.5-4.6are used as rough wall functions in manyCFD

code. As described inBlocken et al.(2007), the first cell’s center should be placed higher than the equivalent sand grain roughness height i.e. Yp > Ks. This constraint is in conflict with using a fine mesh close to walls where high velocity gradients are present.

u+= 1

κln(Ey+)−∆B (4.5)

∆B= 1

κ ln(1+CksKs+) (4.6)

For a horizontally homogeneous flow, i.e. one in which same velocity profile is maintained, the wall function should approximately yield the same profile as the inlet profile as specified by Richards and Hoxey.

u+ = 1_κ lnz+z0

z0 , Inlet

u+ = 1_κ ln(₁₊Ey_C+

ksKs+) , Wall (4.7)

Equating the above two equations we get relations betweenKsandz0 z+z0

z0

= Ey+

4.1. Complexity0: Empty domain 81 z z0 = Ey CksKs Ks= Ez0 Cks Ks∼ 20z0 (4.8)

At the sides and top of the domain, a symmetry boundary condition that prevents inflow or outflow is usually applied. This boundary conditions results in a parallel flow at the boundary which could sometimes lead to artificial acceleration if enough space is not provided between the obstacles and the boundary plane. To solve this problem the domain is sized in such a way that blockage ratio is set at a certain limit below which the effect is minimal. Another solution is to replace the boundary condition with one that allows flow outwards through the boundary

(Franke & Hirsch 2004).

The common use of symmetry boundary condition at the top of the boundary is rather unfortunate since it ignores the contribution of geo-strophic wind in driving the ABL flow. Many researchers have noted that use of symmetry boundary condition results in stream-wise gradients of velocity profile. However there are many reasons why symmetry is assumed in many wind engineering problems. The major physical reason is that log layer in the ABL

extends only up to a certain depth above which the gradient of velocity becomes zero. Also it is not known a priori what the values would be set at the top if symmetry boundary condition is not used. A shear stress boundary condition (τ = ρu2) should be applied at the top to get a homogeneous (non-decaying) profile (Hargreeves & Wright 2007, Richards & Hoxey 1993). Another approach used byBlocken et al.(2007) is to apply Dirichlet boundary condition for velocity and turbulence quantities at the top.