Example 8: Fluctuation Field Generation

This example demonstrates the utilities for generating synthetic turbulence, which can be either from a pre-trained DRD model, or based on some well-known spectra models. DRDMannTurb provides several utilities for plotting the resulting fields through Plotly, which can be done in several contexts as well as utilities for saving to VTK for downstream analysis in, e.g., ParaView.

This example may take a few seconds to load. Please be patient if using Plotly, as it requires some time to render 3D graphics.

Import packages

First, we import the packages we need for this example.

from pathlib import Path

import numpy as np
import torch

from drdmannturb.fluctuation_generation import (
    plot_velocity_components,  # utility function for plotting each velocity component in the field, not used in this example
)
from drdmannturb.fluctuation_generation import (
    GenerateFluctuationField,
    plot_velocity_magnitude,
)

path = Path().resolve()

device = "cuda" if torch.cuda.is_available() else "cpu"

if torch.cuda.is_available():
    torch.set_default_tensor_type("torch.cuda.FloatTensor")

Setting Physical Parameters

Here, we set the physical parameters of the environment in which the synthetic wind field is generated: the friction velocity \(u_\mathrm{red} = 11.4\) roughness height \(z_0=0.02\) and reference height of \(90\). The physical domain is determined by dimensions in 3D as well as the discretization size (grid levels) in each dimension.

z0 = 0.02
zref = 90
uref = 11.4
ustar = uref * 0.41 / np.log(zref / z0)
plexp = 0.2  # power law exponent
windprofiletype = "PL"  # choosing power law, use log with "LOG" here instead

L = 0.593 * zref  # length scale
Gamma = 3.89  # time scale
sigma = 0.052  # magnitude (σ = αϵ^{2/3})

Lx = 720
Ly = 64
Lz = 64

nBlocks = 2
grid_dimensions = np.array([Lx / 4, Ly, Lz])

grid_levels = np.array([6, 4, 4])

seed = None

Generating Fluctuation Field from Mann Model

Fluctuation fields are generated block-by-block, rather than over the domain entirely. Please see section V, B of the original DRD paper for further discussion. Here, we will use 4 blocks.

Type_Model = "Mann"  ### 'Mann', 'VK', 'DRD'

Physical Parameters

The Mann model requires three parameters, length scale, time scale, and spectrum amplitude scale, which are defined above

gen_mann = GenerateFluctuationField(
    ustar,
    zref,
    grid_dimensions,
    grid_levels,
    length_scale=L,
    time_scale=Gamma,
    energy_spectrum_scale=sigma,
    model=Type_Model,
    seed=seed,
)

fluctuation_field_mann = gen_mann.generate(
    nBlocks, zref, uref, z0, windprofiletype, plexp
)

Adding the mean velocity profile

The mean velocity profile follows the power law profile

\begin{align}\left\langle U_1(z)\right\rangle= U_{\text{ref}}\left( \frac{z}{z_{\text{ref}}} \right)^\alpha\end{align}

where \(U_{\text{ref}}\) is the reference velocity and \(z_{\text{ref}}\) is the reference height.

spacing = tuple(grid_dimensions / (2.0**grid_levels + 1))

fig_magnitude_mann = plot_velocity_magnitude(
    spacing, fluctuation_field_mann, transparent=True
)

# this is a Plotly figure, which can be visualized with the ``.show()`` method in different contexts. While these utilities
# may be useful for quick visualization, we recommend using Paraview to visualize higher resolution output. We will cover
# saving to a portable VTK format further in this example.

fig_magnitude_mann  # .show("browser"), or for specific browser, use .show("firefox")

Evaluating Divergence Properties and Plotting

DRDMannTurb provides utilities for computing the divergence of the resulting fluctuation field as well as visualizing results. At the continuum level, the DRD model should yield an approximately divergence-free fluctuation field, which we observe to within a reasonable tolerance. Also, the divergence is expected to decrease as the resolution of the fluctuation field is improved.

spacing = tuple(grid_dimensions / (2.0**grid_levels + 1))

gen_mann.evaluate_divergence(spacing, fluctuation_field_mann).max()

0.27897498697330936

Saving Generated Fluctuation Field as VTK

For higher resolution fluctuation fields, we suggest using Paraview. To transfer the generated data from our package, we provide the .save_to_vtk() method.

filename = str(
    path / "./outputs/IEC_simple"
    if path.name == "examples"
    else path / "./outputs/IEC_simple"
)

gen_mann.save_to_vtk(filename)