PA Residential Building
***********************

.. html metadata
.. meta::
   :description: PA Residential Building
   :keywords: Digital Wind Tunnel, Validation, PA Residential Building

.. 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/surrounded-high-rise/visuals_1.png
   :alt: PA Residential Building
   :figwidth: 100%
   :align: center

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

The current study numerically reproduces a wind tunnel assessment of high-rise building with urban surroundings.
The project was measured in a wind tunnel facility. 
The time histories of forces-by-floor were provided to us, and serve as a basis for comparison

The horizontal reference width of the main building is :math:`B=45.6\mathrm{m}` and its geometry is shown below: 

.. Comprehensive description of the geometries and dimensions
.. figure_expand:: /_static/surrounded-high-rise/geometry.svg
   :alt: Building Geometry
   :figwidth: 100%
   :align: center

The wind directions chosen to be simulated were:

.. list of analyzed cases
.. csv-table:: Wind Directions
   :file: /_static/surrounded-high-rise/cases.csv
   :widths: 10, 6, 6, 6, 6, 6, 6, 6, 6
   :header-rows: 0

With the coordinate system

.. figure_expand:: /_static/surrounded-high-rise/coordinage_system_final.png
   :alt: Building Geometry
   :figwidth: 100%
   :max-width: 640px
   :align: center


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 at the test section.
A Neumann boundary condition is applied at the remaining boundaries.

The building is positioned :math:`6H` from inlet, and 6 grid refinement levels (:math:`lvl\,0` to :math:`lvl\,5`) were adopted:

.. Top and lateral views, indicating the box and body refinements
.. figure_expand:: /_static/surrounded-high-rise/grid.svg
   :alt: Computational Grid
   :figwidth: 100%
   :align: center


A 1:2 refinement ratio is estabilished between levels, and the simulation parameters at the building level were:

.. constant simulation parameters
.. csv-table:: Dimensionless Parameters
   :file: /_static/surrounded-high-rise/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/surrounded-high-rise/full_scale.csv
   :widths: 80, 20
   :header-rows: 0

The computational resources required were:

.. hardware and execution aspects
.. csv-table:: Computational Resources
   :file: /_static/surrounded-high-rise/perf.csv
   :widths: 20, 20, 20, 20, 20
   :header-rows: 0

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

An empty domain simulation is performed to measure the mean velocity and turbulence profiles.
A probe line is placed at the position where the building will be located.
The mean velocities used for calculating the pressure coefficient and convective time scale are taken from this simulation.

Wind Profiles
-------------

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

Wind Spectra
------------
The power spectral density of the velocity components at height :math:`H` are compared with theoretical Von Kármán curves to validate the atmospheric flow.

.. spectra of velocity components
.. figure_expand:: /_static/surrounded-high-rise/inflow/spectrum.svg
      :alt: Inflow Spectrum
      :figwidth: 100%
      :align: center

4. Results: Global Statistics
=============================

The wind effect on the solid building is measured through force and moment coefficients.
The building is divided in 76 floors.
The force coefficient is calculated as:

.. math::
  C_{f\alpha} = \frac{1}{B H}\sum_{i\,\in\,\mathrm{floor}} C_{p, i} A_{i}n_{i\alpha}
  :label: force_coefficient

where :math:`A_{i}` is the tributary area.

For the peak values, the following procedure was applied for both datasets (numerical experimental):

  - The sample is subdivided in sub-samples of duration :math:`T`, and a 3s moving-average is applied to all sub-samples.
  - The smoothed sub-samples are divided in 10 intervals, from which the minimum and maximum values are taken.
  - The max/min values are fitted into a Gumbel distribution, and the mode :math:`U` is rescaled to a duration of 1h.
  - A non-excedence probability of 78% is considered for the extreme values.

Force Coefficient - Mean and Peak
---------------------------------

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_000.svg
  :alt: Mean and Peaks 000
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_040.svg
  :alt: Mean and Peaks 030
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_090.svg
  :alt: Mean and Peaks 090
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_130.svg
  :alt: Mean and Peaks 120
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_180.svg
  :alt: Mean and Peaks 180
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_220.svg
  :alt: Mean and Peaks 210
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_270.svg
  :alt: Mean and Peaks 270
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/mean_peak_310.svg
  :alt: Mean and Peaks 300
  :figwidth: 100%
  :align: center

Force Coefficient - RMS
-----------------------

.. figure_expand:: /_static/surrounded-high-rise/rms_000.svg
  :alt: RMS 000
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_040.svg
  :alt: RMS 030
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_090.svg
  :alt: RMS 090
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_130.svg
  :alt: RMS 120
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_180.svg
  :alt: RMS 180
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_220.svg
  :alt: RMS 210
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_270.svg
  :alt: RMS 270
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/rms_310.svg
  :alt: RMS 300
  :figwidth: 100%
  :align: center


Force Coefficient - Spectrum
----------------------------

.. figure_expand:: /_static/surrounded-high-rise/spectra_0Cf_x.svg
  :alt: Cfx Spectra 000
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_0Cf_y.svg
  :alt: Cfy Spectra 000
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_0Cm_z.svg
  :alt: Cmz Spectra 000
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_40Cf_x.svg
  :alt: Cfx Spectra 030
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_40Cf_y.svg
  :alt: Cfy Spectra 030
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_40Cm_z.svg
  :alt: Cmz Spectra 030
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_90Cf_x.svg
  :alt: Cfx Spectra 090
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_90Cf_y.svg
  :alt: Cfy Spectra 090
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_90Cm_z.svg
  :alt: Cmz Spectra 090
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_130Cf_x.svg
  :alt: Cfx Spectra 120
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_130Cf_y.svg
  :alt: Cfy Spectra 120
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_130Cm_z.svg
  :alt: Cmz Spectra 120
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_180Cf_x.svg
  :alt: Cfx Spectra 180
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_180Cf_y.svg
  :alt: Cfy Spectra 180
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_180Cm_z.svg
  :alt: Cmz Spectra 180
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_220Cf_x.svg
  :alt: Cfx Spectra 210
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_220Cf_y.svg
  :alt: Cfy Spectra 210
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_220Cm_z.svg
  :alt: Cmz Spectra 210
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_270Cf_x.svg
  :alt: Cfx Spectra 270
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_270Cf_y.svg
  :alt: Cfy Spectra 270
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_270Cm_z.svg
  :alt: Cmz Spectra 270
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_310Cf_x.svg
  :alt: Cfx Spectra 300
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_310Cf_y.svg
  :alt: Cfy Spectra 300
  :max-width: 480px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/spectra_310Cm_z.svg
  :alt: Cmz Spectra 300
  :max-width: 480px
  :align: center


Global Loads
------------

The static approach for the calculation of peak moments is given by:

.. math::
  R = \bar{R} + g \sigma_{R}
  :label: static

where :math:`\sigma` is the root-mean-square and we use a peak factor :math:`g=3` in the current analysis.

In the dynamic approach, the structural properties must be considered, and :math:`\sigma_{R}` is broken in a background component :math:`\sigma_{B}`, and a resonant component :math:`\sigma_{RE}`, which results:

.. math::
  R = \bar{R} + g \sqrt{\sigma_{B}^{2}+\sigma_{RE}^{2}}
  :label: dynamic

The background parcel is given by:

.. math::
  \sigma_{B}=\frac{\sigma_{F}}{K}
  :label: background

and the resonant by:

.. math::
  \sigma_{RE}=\sqrt{\frac{\pi}{4}+\frac{1}{\xi_{s}+\xi_{B}}\frac{f_{0}S_{F}\left(f_{0}\right)}{K^{2}}}
  :label: resonant

where :math:`\sigma_{F}` is the root-mean-square of the generalized force, :math:`K` is the generalized stiffness (determined from natural frequency and generalized mass), :math:`\xi_{S}` and :math:`\xi_{B}` are the structural and aerodynamic damping, and :math:`S_{F}\left(f_{0}\right)` the power spectrum of the generalized force at the natural frequency :math:`f_{0}`.

We consider :math:`\xi_{S}=0.02` and :math:`\xi_{B}=0`.
The results for the static and dynamic responses for the bending moments is shown below:

.. figure_expand:: /_static/surrounded-high-rise/global_loads.svg
  :alt: Global Static Loads
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/surrounded-high-rise/global_dyn_loads.png
  :alt: Global Static Equivalent Loads
  :max-width: 640px
  :align: center

Execution Notes
===============

.. csv-table:: Execution Notes
   :file: /_static/surrounded-high-rise/exec.csv
   :widths: 50, 50
   :header-rows: 0

Changelog
=========

* **19 Dez 2024**: Added case