Preprocessing#

The first section of the tutorial focuses on the geometry and mesh generation. The geometry model is built in Engineering Sketch Pad (ESP). The basic wing model CAD generation file we will use can be found in this BET_tutorial_wing.csm file. The surface and volume mesh parameters input files are discussed below.

This tutorial is meant to be used with the Flow360 Python API V2. All of the mentioned code will be using an import convention:

import flow360 as fl

Information on how to install the API can be found in Python API Guide.

In this tutorial the SI unit system will be used. To ensure correct handling of units, any code blocks where dimensional quantities are defined are enclosed witihin an appropriate with block.

with fl.SI_unit_system:
    ...

While the mesh can be generated manually using numerous meshing software, we will be using our automated meshing toolchain, which takes an ESP CAD model from a CSM file as an input. To use the automated meshing framework, at least one no-slip wall must be present in the simulation and should not cross-over the BET disk region. This can be either a hub for isolated rotor simulations or other vehicle elements such as a wing, tail etc.

For best practices and recommendations on how to generate meshes for BET simulations, please see the Knowledge Base.

The first step to setting up a pipeline is to define a project - an entity described in more detail in Cloud assets. In this case, the base asset will be a geometry:

project = fl.Project.from_geometry("./BET_tutorial_wing.csm", "BET_tutorial")

Accessing the geometry entities is done using the project.geometry attribute.

The BET disk should be placed in a specific refinement region. The XV-15 rotor blade has a radius of 3.81 meters, with the root of the blades at 0.3429 meters radius. Hence, following the recommendations mentioned above, our rotor disk refinement region should have the following dimensions:

• Radially, we want the refinement region in the mesh to start at the disk center and go beyond 1.1 * the rotor disk radius to about 4.25 meters.

• In the axial (thickness) direction, we should chose a value between 10% and 15% of the rotor radius; so we picked a 12% rotor radius value for the actual BET disk thickness in the simulation. Because the mesh refinement region should be slightly larger then the BET disk we will assume a value of 16% rotor radius thickness for the refinement region in the mesh. Hence, our refinement region will be 3.81 * 16% ~= 0.6m thick in the x-axis direction.

The extent and the placement of the refinement region is defined using a Cylinder object:

refinement_extent = fl.Cylinder(
                        name="refinement_extent",
                        inner_radius=0,
                        outer_radius=4.25,
                        height=0.6,
                        axis=(1,0,0),
                        center=(-2,5,0)
                    )

The spacing is defined as follows:

• Since we want at least 20 nodes across the BET disk thickness we use a spacing of 0.02, which leads to 30 nodes across the refinement region in the mesh.

• To maintain a good aspect ratio, the spacing in the radial direction is set to 0.03, leading to approximately $\frac{4.25}{0.03}=142$ nodes in the radial direction in the refinement region.

• In the circumferential direction, we use a spacing of 0.06 leading to approximately 445 nodes along the perimeter.

• For the hub we will implement it directly within the BET/AD formulation. This means defining polars and blade geometry all the way to the center of the propeller at r=0.

The object used to describe the refinement volume zone is an AxisymmetricRefinement, which in this case is defined as:

axi_refinement =  fl.AxisymmetricRefinement(
                    spacing_axial=0.02,
                    spacing_radial=0.03,
                    spacing_circumferential=0.06,
                    entities=[refinement_extent]
                )

The surface and volume meshing parameters are then defined as usually, more on meshing can be found in Automated Meshing.

geometry = project.geometry
farfield = fl.AutomatedFarfield(name="farfield", method="auto")
meshing = fl.MeshingParams(
        defaults=fl.MeshingDefaults(
            surface_max_edge_length=0.5,
            surface_edge_growth_rate=1.2,
            curvature_resolution_angle=30*fl.u.deg,
            boundary_layer_first_layer_thickness=1e-06,
            boundary_layer_growth_rate=1.15
        ),
        volume_zones=[
            farfield,
        ],
        refinements=[
            fl.SurfaceEdgeRefinement(name="edge_refinements1",
                                     entities=[geometry["wingLeadingEdge"],
                                               geometry["wingTrailingEdge"]],
                                     method=fl.HeightBasedRefinement(value=0.0003)),
            fl.SurfaceEdgeRefinement(name="edge_refinements2",
                                     entities=[geometry["rootAirfoilEdge"],
                                               geometry["tipAirfoilEdge"]],
                                     method=fl.ProjectAnisoSpacing()),
            fl.SurfaceRefinement(name="tip_refinement",
                                 faces=[geometry["tip"]],
                                 max_edge_length=0.01),
            fl.UniformRefinement(name="refinement", spacing=0.1,
                                 entities=[
                            fl.Cylinder(
                                name="refinement_cylinder",
                                outer_radius=4.4,
                                height=5,
                                axis=(1,0,0),
                                center=(0,5,0)
                            )
            ]),
            axi_refinement
        ]
    )

Flow360 BET Configuration#

The next step is to define BETDisk object to be used as a volume zone in the SimulationParams object.

bet_file = fl.XROTORFile(file_path="xv15_rotor_26deg.xrotor")
bet_disk = fl.BETDisk.from_xrotor(
    file=bet_file,
    rotation_direction_rule="rightHand",
    omega=460*fl.u.rpm,
    chord_ref=0.3556,
    n_loading_nodes=20,
    entities=[
        fl.Cylinder(
            name="bet_disk",
            outer_radius=3.81,
            height=3.81*0.12,
            axis=(-1,0,0),
            center=(-2,5,0)
        )
    ],
    length_unit=fl.u.m,
    angle_unit=fl.u.deg,
)

Running the case#

The last parameters to define are some standard ones required to run any simulation.

operating_condition=fl.AerospaceCondition.from_mach(mach=0.182, alpha=5*fl.u.deg)
models = [
    fl.Freestream(surfaces=farfield.farfield),
    fl.Wall(surfaces=[geometry["wing"], geometry["tip"]]),
    fl.SlipWall(surfaces=[farfield.symmetry_planes]),
    fl.Fluid(
        navier_stokes_solver=fl.NavierStokesSolver(absolute_tolerance=1e-10),
        turbulence_model_solver=fl.SpalartAllmaras(absolute_tolerance=1e-10)
    ),
    bet_disk
]
time_stepping=fl.Steady(max_steps=20000)
outputs = [
    fl.VolumeOutput(
        output_fields=[
            "primitiveVars",
            "betMetrics",
            "qcriterion"
        ]
    ),
    fl.SurfaceOutput(
        output_fields=[
            "primitiveVars",
            "Cp",
            "Cf",
            "CfVec"
        ],
        surfaces=[geometry["wing"], geometry["tip"]]
    )
]

Finally all of the building blocks come together to form a SimulationParams object.

params = fl.SimulationParams(
    meshing=meshing,
    operating_condition=operating_condition,
    models=models,
    time_stepping=time_stepping,
    outputs=outputs
)

With SimulationParams the only thing left to do is to run the case:

project.run_case(params=params, name="BETTutorial")

Output and postprocessing#

The first thing to check when postprocessing a simulation is its convergence. Getting the Nonlinear Residuals to below 1e-10 is the target for simulation accuracy. Figure Fig. 6.3.4 below shows the convergence plot for this simulation, which achieves our convergnece target.

As mentioned in our quickstart section, To download the surface data and the entire flow field, use the following command lines, respectively:

case = project.get_case()
results = case.results
    results.download(
        nonlinear_residuals=True,
        surface=True,
        volume=True,
        overwrite=True
    )

Once downloaded, you can postprocess these output files in either Tecplot or ParaView. You can specify the exported data you want in the outputs section of the SimulationParams object.

If the BET disk configuration is simulated for the first time, it is useful to examine the flow field solution, with a particular emphasis on the BET disk metrics. Flow360 outputs BET specific volumeOutput metrics to help evaluate the BET solution. This helps to make sure that the BET disk input is correct and that the volumetric mesh refinement regions are aligned with expectations. For example, by looking at the contours of the BET metric betMetric_AlphaRadians, which is zero outside the BET disk, we can see in Fig. 6.3.2 and Fig. 6.3.3 above that, as expected, the BET disk in the simulation is slightly thinner and slightly smaller in radius than the refinement region.

Example visualizations of the BET disk angle of attack are shown in Fig. 6.3.5 and Fig. 6.3.6 below.

The qcriterion output is a very good method for visualizing vorticity and generally better understand where propeller wakes are flowing. As we can see in Fig. 6.3.1 the vortices being shed by the BET disk are clearly visible. Please note that as the BET disk generates a smooth shear layer once past the initial sharp wake contraction, it is not very well resolved in this relatively coarse mesh.

For BET simulations, the Forces and Moments (F&M) values seen in the WebUI as well as reported in the total_forces_v2.csv and surface_forces_v2.csv files only include forces on no-slip walls present in the simulation, they do NOT include the BET disk F&M.

The BET disk F&M are only located in the bet_forces_v2.csv file. To obtain dimensionalized values of the Forces and Moments the to_base method can be used.

results.bet_forces.to_base("SI")
results.bet_forces.to_file("bet_forces_in_SI.csv")

In order to get the forces on the whole vehicle, care must be taken to combine the components from the no-slip walls with the components from the BET Disk.

For more details on how to post process BET forces, please see this case study.