Simulation results for the evolution of boundary layer parameters in steady, incompressible flow over a flat plate with zero-pressure gradient (ZPG)

Overview

Project Goals and Benefits

The simulation data provides insight into the behavior of the boundary layer by analyzing key parameters along a flat plate. Using numerical methods, the study solves the Navier-Stokes equations—five fully coupled, time-dependent 3D partial differential equations—while applying Prandtl's theoretical framework to simplify the problem. This provides insights into the steady-state evolution of boundary layer dynamics, which is crucial for optimizing aerodynamic designs.

The primary focus is on the evolution of boundary layer parameters in steady, incompressible flow over a flat plate with a zero-pressure gradient, in accordance with boundary layer theory. Specifically, the simulation investigates:

• Velocity Profile
• Boundary Layer Thickness
• Displacement Thickness
• Wall Friction

For a detailed overview of the numerical scheme used and the assumptions underlying the model, please refer to the GitHub repository (see related works).

Data Structure

The generated simulation data is stored in a structured text format in the file simulation-data.csv. The file is divided into two main sections:

First Section

This section contains general information about the flow along the streamwise coordinate (in the x-direction). For each x-value (ranging from 0 to N), the following parameters are recorded:

    'Um':             The mean streamwise velocity.
    'Vm':             The mean normal velocity.
    'd':                The displacement thickness.
    'd99':            The boundary layer thickness at which the velocity reaches 99% of the free-stream velocity.
    'tw':              The wall shear stress.

This section is formatted as follows:

    x Um Vm d d99 tw
    0 0.929966 0.000000 0.138634 0.529339 0.005000
    1 0.928717 0.045704 0.141137 0.532872 0.004728
    ...

Second Section

This section contains detailed data for each point in the grid, including both the x- and y-coordinates. For each x-coordinate, the following is recorded:

    'y':               The vertical grid point.
    'u':               The streamwise velocity at the grid point (x,y).
    'v':               The normal velocity at the grid point (x,y).
    'tau_xy':       The shear stress at the grid point (x,y).

This section is formatted as follows:

    x 0
    y u v tau_xy
    0 0.000000 0.000000 0.005000
    1 0.016665 0.000000 0.004999
    ...
    #
    x 1
    y u v tau_xy
    0 0.000000 0.000000 0.004728
    1 0.015761 0.000030 0.004729
    ...
    #
    x 2
    y u v tau_xy
    0 0.000000 0.000000 0.004632
    1 0.015440 -0.000019 0.004631

Extracting the Data

To extract the simulation data, the following pseudo code can be used:

    (1) Open the file raw_simulation_data.csv for reading.

    (2) Initialize variables to store the extracted data:
        'x_values':           A list to store the grid index x-coordinates (from the first section).
        'Um_values':       A list to store the streamwise velocity values (Um) from the first section.
        'Vm_values':       A list to store the normal velocity values (Vm) from the first section.
        'd_values':          A list to store the displacement thickness values from the first section.
        'd99_values':      A list to store the boundary layer thickness at 99% velocity values from the first section.
        'tw_values':        A list to store the wall shear stress values from the first section.
        'flow_data':        A dictionary to store detailed flow data, indexed by grid x and y: 
                                          flow_data[x] = {y: [u, v, tau_xy]}

    (3) While reading the file: 
        a. Read each line. 
        b. If the line starts with "x Um Vm d d99 tw":
            This marks the start of the first section. Skip this line and continue to the next. 
        c. If the line contains a data row like "x Um Vm d d99 tw":
            Parse the values and append them to the corresponding lists: 'x_values', 'Um_values', 'Vm_values', 'd_values', 'd99_values', and 'tw_values'. 
        d. If the line contains "x <value>":
            Parse the grid index x-coordinate from the line and initialize a new entry in flow_data for this grid index. 
        e. If the line contains "y u v tau_xy":
            This marks the start of the detailed grid data. Skip this line and continue to the next. 
        f. If the line contains data like "i u v tau_xy":
            Parse the grid index y value and the corresponding values for u, v, and tau_xy.
            Store these values in 'flow_data[x][y]'.

    (4) Important Transformation:
        When processing the raw simulation data, the grid points (x and y) represent discrete indices. To convert these into physical coordinates, use the following formulas:

            xtrue = x / N * L
            ytrue = y / M * H

        N and M are the grid sizes, and L and H are the physical dimensions of the domain, with the converted values representing the actual coordinates in the flow domain.

    (5) Close the file.

    The extracted data is now organized as follows:
        * 'x_values', 'Um_values', 'Vm_values', 'd_values', 'd99_values', and 'tw_values' contain the general information about the flow along the streamwise coordiante.

        * 'flow_data' is a dictionary where each grid index x is a key, and the corresponding values for u, v, and τxy at each grid index y are stored.

This structure provides easy access to both the overall flow characteristics and the detailed distribution of velocity and shear stress, with the transformation to physical coordinates prepared for further analysis or visualization.

Technical Details

Technical Requirements

    Tools: Any text editor or IDE (e.g., VS Code, PyCharm)

General Information

Authors

Kofler Joshua
- [GitHub]
- [ORCID]

FAQ or Troubleshooting

For any issues or questions, please refer to the GitHub repository (see related works) and check the issues section or open a new issue.

License

This data is licensed under the [CC-BY-4.0].