Tower CFD model

In order to perform the CFD analysis the computational domain needs to be divided according to a volume mesh.

The CFD code build up the domain putting together many blocks, the tower mesh block and the background mesh block.

Mesh and boundary conditions

First of all the cylindrical surface of the tower has been created in POINTWISE with those geometrical characteristics:

Tower bottom radius [m]

Tower top radius [m]

Tower height [m]

Table 5.2: Tower geometrical properties

In order to set the mesh parameters like y+ is necessary to decide the boundary conditions of the simulation:

Wind speed 6.1 m/s Reference length

[top tower chord] 2.5 m

Density 1.231 kg/m³

Dynamic viscosity 1.789E-05 N · s/m² Reynolds number 1.04E+06

y (y+ = 1) 5.62E-05 m

Table 5.3: Simulation settings for the tower

We are now able to set the O-type mesh topology parameters taking into account to impose a wall distance lower than the one computed before.

y (y+ < 1) 2.9E-05 m

Growth rate 1.10

Horizontal distance

from the tower 11.15 m

Vertical distance from

the tower 11.15 m

Boundary condition

on the surface non-slip wall Number of cells 3870720

Table 5.4: Mesh settings for the tower

(a) Mesh tower top (b) y+ tower top

Figure 5.4: Top view O-type mesh topology and y+ values

(a) Mesh tower side (b) y+ tower side

Figure 5.5: Side view O-type mesh topology and y+ values

Once we have defined the mesh around the tower it’s time to create the background using the before mentioned tool and the next parameters:

Height of the domain 4 · Rotor diameter Width of the domain 8 · Rotor diameter Length of the domain 10 · Rotor diameter Minimum spacing (CHIMERA region) 0.25 m

Boundary condition on the ground EulerWall Boundary condition on the outer

surface Farfield

Number of cells 1515520

Table 5.5: Mesh settings for the tower-background

Figure 5.6: Background mesh for tower simulation

The Chimera interpolation method was applied in the overlapping area between the meshes.

CFD settings

Once the computational domain is created, the next step is to set the solver.

In the previous chapter we have described the solver setting that are also valid for this one with the only exception for the spatial discretization scheme:

CFD code FLOWer (IAG-DLR)

Equations URANS

Spatial discretization scheme for

the FULL MODEL background WENO (5th order accurate) Spatial discretization scheme for

other volumes

Jameson-Schmidt-Turkel (2nd order accurate)

Time integration scheme explicit hybrid 5-stage Runge-Kutta (central discretization)

Turbulence model k − ω SST

Table 5.6: CFD solver settings

In order to perform the CFD simulation and obtain a converged solution the follow-ing strategy has been used:

Figure 5.7: Solution strategy

The basic idea is to let converge the steady solution in order to have a basic and starting configuration for the unsteady process which is necessary to be performed in order to capture the unsteady effect of the flow around a tower of finite length placed on one side on a flat plate.

Inside the unsteady simulation two parameters needs to be defined:

ˆ physical timestep that represents the real time that experiences a flow par-ticle inside the domain. In the first step the time value is the one required by a fluid particle to travel from the upstream to downstream of the top of the tower. In the second and last step the time is 1/3 of the previous one.

ˆ Inner iterations represents the number of iteration that the code perform in order to achieve a pseudo steady state for every single timestep.

One the set up of the code is ended and the simulation reaches a converged and

”steady” solution the results can be analysed.

Results

First of all is necessary to ensure the convergence of the simulation by looking at the residuals and the force coefficients.

Figure 5.8: Residuals

Figure 5.9: Lift coefficient values

Figure 5.10: Drag coefficient values

From Figure 5.10 is clearly to see how the switch between steady and unsteady computation has increased the residuals due to the more complex flow to describe but at the same time confirm the necessity to analyse in that way this case.

By looking at Figure 5.9 and Figure 5.10 we can conclude that the flow has an unsteady behaviour along the lift direction (z-axis) and the drag direction (x-axis) because the forces coefficients change in time and therefore is necessary to analyse more in detail which phenomena occur.

Our investigation of the flow around a tower starts by looking at a simpler case like a flow around a cylinder of infinite length.

The Reynolds number of our test case is 1.04E + 06 and therefore we expect to have a fully turbulent wake with the beginning of a vortex sheet.

In the literature some experimental analysis have been made over the years and one interesting investigation on 3D wake structures for flow over a wall-mounted short cylinder was performed.

In order to check and compare the fluid dynamic around the tower some CFD visu-alization tools have been used.

Figure 5.11: Regimes of fluid flow across a smooth tube [74]

Figure 5.12: 3D wake structures for flow over a wall-mounted short cylinder [75]

The pressure coefficients shows us the stagnation point on the front view and how the flow accelerates on the sides of the tower while the rear view displays another stagnation point and two blue zones where the air accelerate due to the tip vortices.

Also on the top of the top we can see two recirculation zones.

From the previous picture we can see not only the vortices that arises from the top and the bottom of the tower but also the down wash and up wash effects.

(a) Front view (b) Rear view

Figure 5.13: Pressure coefficient and flow visualization on the TOP of the TOWER

(a) TOP of the TOWER

(b) BOTTOM of the TOWER

Figure 5.14: Side view streamlines

On the other side from the top view by visualizing the streamlines at different height (Figures 5.15) we can see how the vortices are not on the same side but switch from one side to the other.

The last Figure (5.16) resume what explained until now and give a sight on the vor-tex structure by catching the iso-surfaces of a certain values by using the Lambda2

(a) TOP tower section at z=25m (b) TOP tower section at z=35m Figure 5.15: TOP tower section at z=35m

Figure 5.16: Vortex core structures detected by the lambda2 criterion

After have examined the fluid dynamic behaviour around the tower it’s time to quantify the forces acting along it and at different sections.

Before presenting (next page) and commenting the results is important to under-stand that the SECTIONAL LOADS represents a force per unit length along the tower height and are therefore not sensitive to the distances between the sections of the modelled beam.

The ”drag” (Fx) of the tower behave like the one of an infinite cylinder close to the bottom and the values decrease moving towards the top because the cross section shrink.

Close to the top the so called tip vortices increment the drag as they for example do on the aircraft’s wings.

0 10 20 30 40 50 60 z [m]

-40 -20 0 20 40 60

Fx [N/m]

Fy [N/m]

Fz [N/m]

(a) Forces

0 10 20 30 40 50 60

z [m]

-1.5 -1 -0.5 0 0.5 1

Mx [Nm/m]

My [Nm/m]

Mz [Nm/m]

(b) Moments Figure 5.17: Sectional loads along the tower

The force along the y-direction oscillates across the 0 value because the flow is un-symmetrical due to the vortex shedding.

The forces along the height of the tower are close to zero and the moments reflect the nature of the forces since they are computed starting from those one for local reference system.

The SECTIONAL LOADS gave a great overview but can’t be easily implemented into the FEM code for the structural analysis and the solution was to compute forces and moments on sections along the tower that corresponds with the nodes of our FEM model (INTEGRATED SECTIONAL LOADS).

0 10 20 30 40 50 60

z [m]

-100 0 100 200 300 400 500

Fx [N]

Fy [N]

Fz [N]

(a) Forces

0 10 20 30 40 50 60

z [m]

-30 -20 -10 0 10 20 30

Mx [Nm]

My [Nm]

Mz [Nm]

(b) Moments

Figure 5.18: Integrated sectional loads along the tower

Rather than the SECTIONAL LOADS, the INTEGRATED SECTIONAL LOADS are difficult to be interpreted because they represents the integrated value of forces and moments across a section but depend on the distances between the nodes of our beam model.

Before moving to the structural response of the tower a last comment to the global loads is necessary.

Fx 1.6929492e+03

Fy 1.1154125e+02

Fz 7.0796337e+02

Mx -5.5223034e+03

My 1.6929492e+03

Mz 2.2885258e-02

Table 5.7: Global tower loads

In order to validate the results of the CFD analysis in the literature can be found a lot of experimental results for an infinite cylinder.

Figure 5.19: Variation of cylinder drag coefficient with Reynolds number [76]

The drag coefficient calculated from the line load of the tower is:

C_D = F_x

0.5 ρ V²· cREF

= 0.489 (5.3)

where c_REF = 3.35m is the mean chord.

The crag coefficient is slightly bigger than the one from the theory because we are dealing with a finite cylinder with a free tip.