Two-Dimensional Slope
*********************

.. html metadata
.. meta::
   :description: Two-Dimensional Slope
   :keywords: Digital Wind Tunnel, Validation, Two-Dimensional Slope

.. Public Project
.. ==============
.. .. link to insight page
.. `AeroSim Web App`_

.. .. _AeroSim Web App: https://insight.aerosim.io/cp/TODEFINE/


.. animations, surfaces and contours
.. figure_expand:: /_static/vel_turb/slope/visuals_1.png
   :alt: Two-Dimensional Slope
   :figwidth: 100%
   :align: center

1. Project Description
=======================

.. short description of the project

The objective of this project is to reproduce the wind flow properties over the two-dimensional slope, as measured in wind tunnel by :footcite:p:`bowen1977wind`.
One convective time scale is defined as :math:`CTS = H / U_{H}`.

.. reference

**Source of target results:**

.. footbibliography::

The configurations chosen to be adressed were:

.. list of analyzed cases
.. csv-table:: Slope Configurations
   :file: /_static/vel_turb/slope/cases.csv
   :widths: 25, 25, 25, 25
   :header-rows: 0

2. Simulation Setup
===================

The Synthetic Eddy Method (SEM) boundary condition is applied at the inlet of the computational domain. 
Solid fins are distributed across the floor to ensure the desired velocity and turbulence profiles during flow development length. 
A Neumann boundary condition is applied at the remaining boundaries.
 
The position 0 of the slope is positioned  :math:`144H` from inlet, and 5 grid refinement levels (:math:`lvl\,0` to :math:`lvl\,4`) were adopted:

.. ilustration of the grid
.. figure_expand:: /_static/vel_turb/slope/geometry.svg
   :alt: Two-Dimensional Slope
   :max-width: 640px
   :align: center

A 1:2 refinement ratio is estabilished between levels, and the simulation parameters at grid :math:`lvl\,4` were:


.. constant simulation parameters
.. csv-table:: Dimensionless Parameters
   :file: /_static/vel_turb/slope/params.csv
   :widths: 80, 20
   :header-rows: 0

The equivalent parameters in full scale are:

.. full scale parameters
.. csv-table:: Full-scale Parameters
   :file: /_static/vel_turb/slope/full_scale.csv
   :widths: 80, 20
   :header-rows: 0

The computational resources required were:

.. hardware and execution aspects
.. csv-table:: Computational Resources
   :file: /_static/vel_turb/slope/perf.csv
   :widths: 28, 24, 24, 24
   :header-rows: 0

3. Inflow
=========

The inflow profile is taken at position :math:`-5H`.
The spectrum is read at inflow position for at height :math:`H`.

.. profiles of velocity, turbulence and integral lenght scale
.. figure_expand:: /_static/vel_turb/slope/inflow_profile.svg
      :alt: Inflow Profile
      :max-width: 640px
      :align: center

4. Results: Velocity and Turbulence Profiles
============================================

The Speed-up factor is the ratio between the velocity at the given position and the reference inflow velocity at the same height relative to the ground. 

**Slope 1-1** 
-------------

**Speed-up Factor - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_1-1/upstream_S1.svg
  :alt: slope_1-1 - S1 Upstream
  :figwidth: 100%
  :align: center

**Speed-up Factor - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_1-1/downstream_S1.svg
  :alt: slope_1-1 - S1 Downstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_1-1/upstream_Iu.svg
  :alt: slope_1-1 - Iu Upstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_1-1/downstream_Iu.svg
  :alt: slope_1-1 - Iu Downstream
  :figwidth: 100%
  :align: center

**Slope 2-1**
-------------

**Speed-up Factor - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_2-1/upstream_S1.svg
  :alt: slope_2-1 - S1 Upstream
  :figwidth: 100%
  :align: center

**Speed-up Factor - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_2-1/downstream_S1.svg
  :alt: slope_2-1 - S1 Downstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_2-1/upstream_Iu.svg
  :alt: slope_2-1 - Iu Upstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_2-1/downstream_Iu.svg
  :alt: slope_2-1 - Iu Downstream
  :figwidth: 100%
  :align: center

**Slope 4-1**
-------------

**Speed-up Factor - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_4-1/upstream_S1.svg
  :alt: slope_4-1 - S1 Upstream
  :figwidth: 100%
  :align: center

**Speed-up Factor - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_4-1/downstream_S1.svg
  :alt: slope_4-1 - S1 Downstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Upstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_4-1/upstream_Iu.svg
  :alt: slope_4-1 - Iu Upstream
  :figwidth: 100%
  :align: center

**Turbulence Intensity - Downstream**:

.. figure_expand:: /_static/vel_turb/slope/slope_4-1/downstream_Iu.svg
  :alt: slope_4-1 - Iu Downstream
  :figwidth: 100%
  :align: center


Changelog
=========

* **30 Oct 2024**: Added scattering plots