Atmospheric turbulent layer simulation for cfd unsteady inlet conditions

Atmospheric turbulent layer simulation providing unsteady inlet conditions for large eddy simulation
Berthaut-Gerentès, Julien*1), Delaunay, Didier1), Sanquer, Stéphane1)
1) Meteodyn, Nantes, France
*) presenting author, julien.berthaut-gerentes@meteodyn.com
ABSTRACT
The aim of this work is to bridge the gap between experimental approaches in wind tunnel testing and numerical computations, in the field of structural design against strong winds. This paper focuses on the generation of an unsteady flow field, representative of a natural wind field, but still compatible with CFD inlet requirements. A simple and “naïve” procedure is explained, and the results are successfully compared to some standards.
1 INTRODUCTION
Inlet conditions for Large Eddy Simulations are of the utmost importance, as it determines a large part of the fluid behaviour within the computational domain. Tabor and Baba-Ahmadi (2010) gave a good overview of the different techniques, classifying them as synthesised turbulence methods and precursor simulation methods.
The first category presents the critical limitation of not achieving a flow field inlet 100% compatible with CFD requirements (temporal and spatial fluctuations, divergence-free, spectrum). For instance, the method developed by Jin et al. (1997) is not divergence-free. These requirements are of great importance when the purpose of the computations is to generate pressure fields on obstacles. Some regularisation methods have to be introduced, as for instance the Synthetic Eddy Method (Jarrin et al. (2006)).
The second category of techniques is due to Spalart and Leonard (1985). The idea of these methods is to generate inflow condition using CFD itself, as a genuine simulation of turbulence. The inflow of this precursor domain is obtained through a rescaling of the flow field extracted from a downstream location. Nevertheless, even with different stages of simplification (Lund et al., (1998), Nakayama et al (2012)), those techniques are still complicated and not easy to implement. Additionally, they seem more adequate to small scale turbulence (Re about 2.103)), which does not correspond to structural design against strong winds (Re about 4.107).
This paper deals with a more “naïve” precursor model. The idea is to draw inspiration from the wind tunnel testing community, with the use of roughness blocks lying on the floor. The large x-axis dimension of the wind tunnel is replaced by a short cyclic domain, in order to convert the large domain issues into a duration matter. Similarly to atmospheric turbulent layer which is driven by geostrophic wind (instead of a horizontal pressure gradient), our flow is naturally driven by the upper boundary condition, acting as a conveyor belt. Re-introducing a flow field extracted downstream becomes straightforward.
The final aim of the method being building dimensioning to high winds, our reference will be an international code concerning these issues: Eurocode I (EN-1991-1-4): “Actions on structures – Wind actions”. This code proposes a systematic approach to describe some of the wind characteristics; we will focus on these characteristics in order to validate –or not– the approach.

2 DESCRIPTION OF THE METHOD
2.1 Aim of the simulation
In order to compute the extreme loads on a building, CFD calculations have to immerse it in a turbulent atmospheric air flow. Eurocode I (EN-1991-1-4) proposes a systematic and simple approach to describe this air flow: a log-law profile for the mean wind speed, associated with an inverse log-law profile for turbulence intensity. ( ) ( )
(1) ( ) ( )
(2)
Wind speeds distributions are Gaussian and the spectrum of turbulence is driven by a modified Von Karman model:. ( ) ( ) ( ( )) ⁄
With ( ) ( ) ( )⁄ (3)
The turbulence scale is also given by Eurocode: ( ) ( ) ( )
(4)
There is no mention of correlation length within the Eurocode. Another regulation, the English code ESDU 75001, gives the correlation lengths: ( ) ( ) ( ) ( ) ( )
With (5a) (5b) (5c)
Our target is to generate an unsteady flow corresponding to this wind model, with a roughness length equal to 5 cm.
2.2 Geometry and boundary conditions
The domain used is a 20x10x20m3 box. On the ground, the roughness is modelled by random cubic elements: their size and density are given by some “rule of the thumb” from the experimental wind- tunnel community ( between and , area density around 10%). Special attention is focused on the lateral homogeneity (the largest cubes mustn’t be grouped on the left or on the right). Figure 1 shows the roughness cubes at the bottom of the computational domain for this study.
Figure 1: Geometry of the roughness-cubes lying on the floor

Boundary conditions are no slip on the ground and on the roughness-cubes. Because the cubes are randomly located, a lateral force can appear on the ground. In order to compensate this force and to guide the flow within the x-axis, the lateral boundaries have to block the flow: symmetry boundary condition is chosen on these boundaries. Concerning the inlet and outlet, cyclic is used to re-introduce the flow field as it is. The upper-boundary condition is also no slip on the “roof”, but with a moving wall (67.5 m/s instead of 0 m/s on the ground). This value of 67.5 m/s has been obtained through a try- and-error process (the flow being Reynolds quite independent, the results of the simulation are proportional to this moving roof speed). Figure 2 sums up these boundary conditions.
Figure 2: Boundary conditions
2.3 Running OpenFOAM
The mesh density is uniform with a 25cm grid step. In order to slightly reduce the cells number, a pinch of grading is introduced in the upper half space (last upper cell is 50cm; see Figure 3 Left).
Figure 3: x-projection of computational domain: Left: meshing and roughness cubes. Right: probe locations

Pimplefoam is run in order to optimize the time step: max Co is 10, with a time step close to 4.10-2 s. Time scheme is Crank-Nicholson, spatial scheme is Gauss Linear (and Gauss LinearUpWindV GradU ). Subgrid turbulence model is oneEqEddy. Solver for pressure is GAMG, and PBiCG DILU for and . Initial condition is a uniform field equal to 67.5 m/s.
3 RESULTS
3.1 Spatial and temporal extraction method
Many probes are placed onto a -constant plane in order to evaluate the success of the method to generate an atmospheric boundary layer: three vertical lines to estimate the flow homogeneity and the vertical gradient, and a uniform horizontal line to assess the horizontal homogeneity and correlations (see Figure 3 Right).
A time span of 300 seconds is first run. During this first period, the flow is rapidly decreasing (from uniform 67,5m/s), starting to brake from the ground. 300 seconds turns out to be a good time span in order to achieve a global equilibrium. Then the statistics are evaluated over a 300s window, which is half the meteorological international standard.
3.2 First check
Visual inspection (Figure 4) shows a first validation: the flow field looks like one could expect.
Figure 4: Instant wind field sections in the computational domain.
3.3 Results; comparison with Eurocode
The flow is quite homogeneous: at 10m high, the mean wind speed and turbulence intensity do not depend of the lateral position (see Figure 5), at least in the central part of the flow (one half centered span).
30m/s
0m/s
20m/s
10m/s

Figure 5: Horizontal gradient of mean wind speeds (left) and turbulence intensities (right).
Blue: u-component; red: v-component; purple : z-component
Densities are found symmetric, close to Gaussian (Figure 6).
Figure 6: normalized distribution of u, v and w fluctuating components.
First line: 16 m high. Second line: 1m high
Left: 5m to left wall. Middle: center of computational domain. Right: 5m to right wall.
Vertical gradients (mean wind speed, Figure 7, and turbulence intensity, Figure 8) exhibit excellent fit
with the Eurocode model. In those figures, the results from LES are compared with the Eurocode
gradients (equations (1) and (2)), with a roughness length of cm and a based velocity equal to
31.6 m/s. This based velocity is found to be directly proportional to the top boundary condition speed.
Figure 7: vertical gradient of mean wind speed. Blue stared: LES results. Black line: Eurocode
-10 -5 0 5 10
-10
0
10
20
30
40
GRADIENT HORIZONTAL
Vitesse [m/s]
550s
-10 -5 0 5 10
0
5
10
15
20
25
30
Turbulence [%]
Statistiques sur 300s
0 5 10 15 20
-0.5
0
0.5
1
Corrélations spatiales
Horizontale
0 5 10 15 20
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Verticale
-10 -5 0 5 10
-10
0
Vitesse 550s
-10 -5 0 5 10
0
5
10
15
20
25
30
Turbulence [%]
0 -0.5
0
Horizontale
0 -0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Verticale
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté gauche
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Centre veine
561s
-5 0 5
0
2
4
6
8
10
12
14
16
18
20
Coté droit
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
Left, 16m Center, 16m Right, 16m
Left Center Right
Mean wind speeds [m/s]
Turbulence intensities [%]
Lateral position [m] Lateral position [m]
Altitude [m]
Mean wind spead [m/s] Mean wind spead [m/s] Mean wind spead [m/s]

Figure 8: vertical gradient of turbulence intensity. Blue stared: LES results. Black line: Eurocode
Power density spectra are computed at different locations within the domain. Results are plotted
Figure 9 (blue line), as well as Eurocode model (bold black line, equation (3)). The peak of energy is
slightly shifted to low frequencies, corresponding to a turbulence length scale slightly larger than the
one proposed by Eurocode (equation (4)). Nevertheless, the global balance between high and low
frequencies is not accurately reproduced: low frequencies are over estimated whereas high frequencies
are underestimated. This behaviour might be linked with the LES filtering of high frequencies.
Figure 9: Normalized power densities versus reduced frequency
Close to ground (5m high), there is a second peak energy at a reduced frequency around 4. This might
be the “signature” of the domain size: 10 m long, about 28m/s, makes a cycling frequency equal to
2.8 Hz, corresponding to a reduced frequency (equation (3) and (4)) of
.
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
471s
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 10 20 30 40
0
5
10
0 0.1 0.2 0.3 0.4
0
5
10
15
20
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
A 10m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
451s
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
A 5m de haut
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
10
-2
10
-1
10
0
10
1
0
0.05
0.1
0.15
0.2
0.25
0.3
Left Center Right
Altitude [m]
Turbulence intensity [-] Turbulence intensity [-] Turbulence intensity [-]

3.4 Correlations; comparison with ESDU
Streamwise correlation length is evaluated thanks to Taylor hypothesis: the temporal correlation (of
fluctuating component u, v, and w) is calculated and compared with a negative exponential (Figure
10). The parameter of this negative exponential is given by formulae (5a) (135m at 10 m high, 105m at
5 meter high), divided by the local mean wind speed (given on Figure 7).
Figure 10: Stream wise correlation analysis
Top: 10m high. Bottom: 5m high. Left/middle/right = left/center/right
Agreement is very good for axial component u, especially at the middle of the domain. For the other
two components (v and w), situation is not so satisfactory: for ESDU, correlation lengths are different
for different axis (equations (5b) and (5c)), whereas in our LES calculation they seem to be the same.
Figure 11: Lateral and vertical correlation for the three components
Blue for u-component; Red for v-component; Purple for w-component
Lateral and vertical correlation lengths are much smaller: we can estimate from Figure 11 around 5m,
which is a quarter of the width and height of the domain. These correlation lengths seem limited by the
domain size much more than any other aspect.
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Coté gauche
A 10m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
135m
Centre veine
501s
0 5 15
0
0.2
0.4
0.6
0.8
1
135m
Coté droit
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
A 5m de haut
0 5 10 15
0
0.2
0.4
0.6
0.8
1
105m
0 5 15
0
0.2
0.4
0.6
0.8
1
105m
10
10
0 5 10 15 20
-0.5
0
0.5
1
Horizontale
0 5 10 15 20
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Verticale
-10 -5 0 5 10
-10
0
10
20
30
40
GRADIENT HORIZONTAL
Vitesse [m/s]
550s
-10 -5 0 5 10
0
5
10
15
20
25
30
Turbulence [%]
0 5 10 15 20
-0.5
0
0.5
1
Horizontale
0 5 10 15 20
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Verticale
Vertical Horizontal gap [m] gap [m]

4 CONCLUSIONS
A new solution for generating unsteady inlet conditions for Large Eddy Simulation is presented in this paper. This solution, which draws its inspiration from the wind tunnel testing community, is as simple as possible and straightforward to implement using OpenFoam. The flow field generated can be directly used as inlet conditions for Large Eddy Simulations.
The results are compared with international standards concerning wind engineering (Eurocode 1 and ESDU 75001). Densities are found symmetric, close to Gaussian, and the flow is homogeneous (no lateral fluctuations). Vertical gradients of mean wind speed and turbulence intensity exhibit excellent fit with the Eurocode model. Stream-wise correlation length is about 120m which agrees with ESDU; lateral and vertical correlations are much smaller (about 4~5m). The main discrepancies concern the power spectral density: low frequency domain is a bit over energetic while there is a lack of high frequencies. This misbalance might be linked with the LES filtering of high frequencies.
Acknowledgements
The author greatly acknowledges Alberto Passalacqua for his GeekoCFD live distribution. Thanks also to Bernhard Gschaider for his kind help using swak4foam, and all the CFD online community for their discussions and nice exchanges.
References
Jarrin, N., Benhamadouche, S., Laurence, D., Prosser, R. (2006). A synthetic eddy-method for generating inflow conditions for large-eddy simulations, Int. J. Heat Fluid Flow 27, 585, 2006
Jin, S., Lutes, L.D., Sarkani, S. (1997). Efficient simulation of multidimensional random fields, Journal of Engineerings Mechanics, ASCE, Vol 123, n°10, pp 1082-1089 Nakayama, H., Takemi, T., Nagai, H. (2012). Large-eddy simulation of urban boundary-layer flows by generating turbulent inflows from mesoscale meteorological simlations, Atmos.Sci.Let 13: 180-186 (2012)
Lund, T.S, Wu, X., Squires, K.D. (1998). Generation of turbulent inflow data for spatially-developing boundary layer simulations. Journal of Computational Physics 140, 233-258 (1998)
Robert. S. (2013), Wind Wizard: Alan G. Davenport and the Art of Wind Engineering, Princeton university Press. (2013)
Spalart, P.R., Leonard, A. (1985). Direct numerical simulation of equilibrium turbulent boundary layers, in Proc. 5th Symp. On Turbulent Shear Flows, Ithaca, NY, 1985.
Tabor, G.R., Baba-Ahmadi, M.H. (2009). Inlet conditions for large eddy simulation: A review. Computers & Fluids 39 (2010) 553-567.

Atmospheric turbulent layer simulation for cfd unsteady inlet conditions

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