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droplet.html
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<!DOCTYPE html>
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<title>droplet — Cortix 0.1.0 documentation</title>
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<h1>Source code for droplet</h1><div class="highlight"><pre>
<span></span><span class="ch">#!/usr/bin/env python</span>
<span class="c1"># -*- coding: utf-8 -*-</span>
<span class="c1"># This file is part of the Cortix toolkit environment.</span>
<span class="c1"># https://cortix.org</span>
<span class="kn">import</span> <span class="nn">pickle</span>
<span class="kn">import</span> <span class="nn">logging</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy.constants</span> <span class="k">as</span> <span class="nn">const</span>
<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="k">import</span> <span class="n">odeint</span>
<span class="kn">from</span> <span class="nn">cortix.src.module</span> <span class="k">import</span> <span class="n">Module</span>
<span class="kn">from</span> <span class="nn">cortix.support.phase</span> <span class="k">import</span> <span class="n">Phase</span>
<span class="kn">from</span> <span class="nn">cortix.support.specie</span> <span class="k">import</span> <span class="n">Specie</span>
<span class="kn">from</span> <span class="nn">cortix.support.quantity</span> <span class="k">import</span> <span class="n">Quantity</span>
<div class="viewcode-block" id="Droplet"><a class="viewcode-back" href="../examples_rst/droplet_swirl_rst/droplet.html#droplet.Droplet">[docs]</a><span class="k">class</span> <span class="nc">Droplet</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Droplet Cortix module used to model very simple fluid-particle interactions.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> Port names used in this module: `external-flow` exchanges data with any other</span>
<span class="sd"> module that provides information about the flow outside the droplet,</span>
<span class="sd"> `visualization` sends data to a visualization module.</span>
<span class="sd"> '''</span>
<div class="viewcode-block" id="Droplet.__init__"><a class="viewcode-back" href="../examples_rst/droplet_swirl_rst/droplet.html#droplet.Droplet.__init__">[docs]</a> <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Attributes</span>
<span class="sd"> ----------</span>
<span class="sd"> initial_time: float</span>
<span class="sd"> end_time: float</span>
<span class="sd"> time_step: float</span>
<span class="sd"> show_time: tuple</span>
<span class="sd"> Two-element tuple, `(bool,float)`, `True` will print to standard</span>
<span class="sd"> output.</span>
<span class="sd"> '''</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">port_names_expected</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'external-flow'</span><span class="p">,</span><span class="s1">'visualization'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="bp">self</span><span class="o">.</span><span class="n">end_time</span> <span class="o">=</span> <span class="mi">100</span>
<span class="bp">self</span><span class="o">.</span><span class="n">time_step</span> <span class="o">=</span> <span class="mf">0.1</span>
<span class="bp">self</span><span class="o">.</span><span class="n">show_time</span> <span class="o">=</span> <span class="p">(</span><span class="kc">False</span><span class="p">,</span><span class="mi">1</span><span class="o">*</span><span class="n">const</span><span class="o">.</span><span class="n">minute</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bounce</span> <span class="o">=</span> <span class="kc">True</span>
<span class="bp">self</span><span class="o">.</span><span class="n">slip</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">species</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">quantities</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="c1"># Create a drop with random diameter up within 5 and 8 mm.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">8</span> <span class="o">-</span> <span class="mi">5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">5</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">const</span><span class="o">.</span><span class="n">milli</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'droplet-diameter'</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'droplet-xsec-area'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span><span class="o">/</span><span class="mf">2.0</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'gravity'</span><span class="p">]</span> <span class="o">=</span> <span class="n">const</span><span class="o">.</span><span class="n">g</span>
<span class="c1"># Species in the liquid phase</span>
<span class="n">water</span> <span class="o">=</span> <span class="n">Specie</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'water'</span><span class="p">,</span> <span class="n">formula_name</span><span class="o">=</span><span class="s1">'H2O(l)'</span><span class="p">,</span> <span class="n">phase</span><span class="o">=</span><span class="s1">'liquid'</span><span class="p">,</span> \
<span class="n">atoms</span><span class="o">=</span><span class="p">[</span><span class="s1">'2*H'</span><span class="p">,</span><span class="s1">'O'</span><span class="p">])</span>
<span class="n">water</span><span class="o">.</span><span class="n">massCC</span> <span class="o">=</span> <span class="mf">0.99965</span> <span class="c1"># [g/cc]</span>
<span class="n">water</span><span class="o">.</span><span class="n">massCCUnit</span> <span class="o">=</span> <span class="s1">'g/cc'</span>
<span class="n">water</span><span class="o">.</span><span class="n">molarCCUnit</span> <span class="o">=</span> <span class="s1">'mole/cc'</span>
<span class="n">species</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">water</span><span class="p">)</span>
<span class="n">droplet_mass</span> <span class="o">=</span> <span class="mi">4</span><span class="o">/</span><span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span> <span class="o">*</span> <span class="n">water</span><span class="o">.</span><span class="n">massCC</span> <span class="o">*</span> \
<span class="n">const</span><span class="o">.</span><span class="n">gram</span> <span class="o">/</span> <span class="n">const</span><span class="o">.</span><span class="n">centi</span><span class="o">**</span><span class="mi">3</span> <span class="c1"># [kg]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'droplet-mass'</span><span class="p">]</span> <span class="o">=</span> <span class="n">droplet_mass</span>
<span class="c1"># Spatial position</span>
<span class="n">x_0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="n">position</span> <span class="o">=</span> <span class="n">Quantity</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'position'</span><span class="p">,</span> <span class="n">formalName</span><span class="o">=</span><span class="s1">'Pos.'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'m'</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="n">x_0</span><span class="p">)</span>
<span class="n">quantities</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">position</span><span class="p">)</span>
<span class="c1"># Velocity</span>
<span class="n">v_0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="n">velocity</span> <span class="o">=</span> <span class="n">Quantity</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'velocity'</span><span class="p">,</span> <span class="n">formalName</span><span class="o">=</span><span class="s1">'Veloc.'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'m/s'</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="n">v_0</span><span class="p">)</span>
<span class="n">quantities</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">velocity</span><span class="p">)</span>
<span class="c1"># Speed</span>
<span class="n">speed</span> <span class="o">=</span> <span class="n">Quantity</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'speed'</span><span class="p">,</span> <span class="n">formalName</span><span class="o">=</span><span class="s1">'Speed'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'m/s'</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
<span class="n">quantities</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">speed</span><span class="p">)</span>
<span class="c1"># Radial position</span>
<span class="n">radial_pos</span> <span class="o">=</span> <span class="n">Quantity</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'radial-position'</span><span class="p">,</span> <span class="n">formalName</span><span class="o">=</span><span class="s1">'Radius'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'m'</span><span class="p">,</span> \
<span class="n">value</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">x_0</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]))</span>
<span class="n">quantities</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">radial_pos</span><span class="p">)</span>
<span class="c1"># Liquid phase </span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span> <span class="o">=</span> <span class="n">Phase</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span><span class="p">,</span> <span class="n">time_unit</span><span class="o">=</span><span class="s1">'s'</span><span class="p">,</span> <span class="n">species</span><span class="o">=</span><span class="n">species</span><span class="p">,</span> \
<span class="n">quantities</span><span class="o">=</span><span class="n">quantities</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'water'</span><span class="p">,</span> <span class="n">water</span><span class="o">.</span><span class="n">massCC</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span><span class="p">)</span>
<span class="c1"># Domain box dimensions: LxLxH m^3 box with given H.</span>
<span class="c1"># Origin of cartesian coordinate system at the bottom of the box. </span>
<span class="c1"># z coordinate pointing upwards. -L <= x <= L, -L <= y <= L, </span>
<span class="bp">self</span><span class="o">.</span><span class="n">box_half_length</span> <span class="o">=</span> <span class="mf">250.0</span> <span class="c1"># L [m]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">box_height</span> <span class="o">=</span> <span class="mf">500.0</span> <span class="c1"># H [m]</span>
<span class="c1"># Random positioning of the droplet constrained to a box sub-region.</span>
<span class="n">x_0</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">box_half_length</span> <span class="o">/</span> <span class="mf">4.0</span>
<span class="n">x_0</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">box_height</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'position'</span><span class="p">,</span> <span class="n">x_0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span><span class="p">)</span>
<span class="c1"># Droplet Initial velocity = 0 -> placed still in the flow</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'velocity'</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">]),</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span><span class="p">)</span>
<span class="c1"># Default value for the medium surrounding the droplet if data is not passed</span>
<span class="c1"># through a conneted port.</span>
<span class="n">medium_mass_density</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="o">*</span> <span class="n">const</span><span class="o">.</span><span class="n">gram</span> <span class="o">/</span> <span class="n">const</span><span class="o">.</span><span class="n">centi</span><span class="o">**</span><span class="mi">3</span> <span class="c1"># [kg/m^3]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-mass-density'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_mass_density</span>
<span class="n">medium_displaced_mass</span> <span class="o">=</span> <span class="mi">4</span><span class="o">/</span><span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span> <span class="o">*</span> \
<span class="n">medium_mass_density</span> <span class="c1"># [kg]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-displaced-mass'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_displaced_mass</span>
<span class="n">medium_dyn_viscosity</span> <span class="o">=</span> <span class="mf">1.81e-5</span> <span class="c1"># kg/(m s)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-dyn-viscosity'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_dyn_viscosity</span></div>
<div class="viewcode-block" id="Droplet.run"><a class="viewcode-back" href="../examples_rst/droplet_swirl_rst/droplet.html#droplet.Droplet.run">[docs]</a> <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
<span class="n">time</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bottom_impact</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">while</span> <span class="n">time</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">end_time</span><span class="p">:</span>
<span class="c1"># Interactions in the external-flow port</span>
<span class="c1">#---------------------------------------</span>
<span class="n">position</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">GetValue</span><span class="p">(</span><span class="s1">'position'</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">send</span><span class="p">(</span> <span class="p">(</span><span class="n">time</span><span class="p">,</span><span class="n">position</span><span class="p">),</span> <span class="s1">'external-flow'</span> <span class="p">)</span>
<span class="p">(</span><span class="n">check_time</span><span class="p">,</span> <span class="n">velocity</span><span class="p">,</span><span class="n">fluid_props</span><span class="p">)</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">recv</span><span class="p">(</span> <span class="s1">'external-flow'</span> <span class="p">)</span>
<span class="k">assert</span> <span class="nb">abs</span><span class="p">(</span><span class="n">check_time</span><span class="o">-</span><span class="n">time</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">1e-6</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'flow-velocity'</span><span class="p">]</span> <span class="o">=</span> <span class="n">velocity</span>
<span class="c1">#medium_mass_density = fluid_props.mass_density # see Vortex</span>
<span class="c1">#medium_dyn_viscosity = fluid_props.dyn_viscosity # see Vortex</span>
<span class="n">medium_mass_density</span> <span class="o">=</span> <span class="n">fluid_props</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">medium_dyn_viscosity</span> <span class="o">=</span> <span class="n">fluid_props</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-mass-density'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_mass_density</span>
<span class="n">medium_displaced_mass</span> <span class="o">=</span> <span class="mi">4</span><span class="o">/</span><span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">droplet_diameter</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span> <span class="o">*</span> \
<span class="n">medium_mass_density</span> <span class="c1"># [kg]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-displaced-mass'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_displaced_mass</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">[</span><span class="s1">'medium-dyn-viscosity'</span><span class="p">]</span> <span class="o">=</span> <span class="n">medium_dyn_viscosity</span>
<span class="c1"># Interactions in the visualization port</span>
<span class="c1">#---------------------------------------</span>
<span class="bp">self</span><span class="o">.</span><span class="n">send</span><span class="p">(</span> <span class="n">position</span><span class="p">,</span> <span class="s1">'visualization'</span> <span class="p">)</span>
<span class="c1"># Evolve droplet state to next time stamp</span>
<span class="c1">#----------------------------------------</span>
<span class="n">time</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__step</span><span class="p">(</span> <span class="n">time</span> <span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">send</span><span class="p">(</span><span class="s1">'DONE'</span><span class="p">,</span> <span class="s1">'visualization'</span><span class="p">)</span> <span class="c1"># this should not be needed: TODO</span>
<span class="k">return</span></div>
<span class="k">def</span> <span class="nf">__rhs_fn</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">u_vec</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
<span class="n">drop_pos</span> <span class="o">=</span> <span class="n">u_vec</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span>
<span class="n">flow_velo</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'flow-velocity'</span><span class="p">]</span>
<span class="n">drop_velo</span> <span class="o">=</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span>
<span class="n">relative_velo</span> <span class="o">=</span> <span class="n">drop_velo</span> <span class="o">-</span> <span class="n">flow_velo</span>
<span class="n">relative_velo_mag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">relative_velo</span><span class="p">)</span>
<span class="n">area</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'droplet-xsec-area'</span><span class="p">]</span>
<span class="n">diameter</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'droplet-diameter'</span><span class="p">]</span>
<span class="n">dyn_visco</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'medium-dyn-viscosity'</span><span class="p">]</span>
<span class="n">rho_flow</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'medium-mass-density'</span><span class="p">]</span>
<span class="c1"># Calculate the friction factor</span>
<span class="n">reynolds_num</span> <span class="o">=</span> <span class="n">rho_flow</span> <span class="o">*</span> <span class="n">relative_velo_mag</span> <span class="o">*</span> <span class="n">diameter</span> <span class="o">/</span> <span class="n">dyn_visco</span>
<span class="k">if</span> <span class="n">reynolds_num</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">:</span>
<span class="n">fric_factor</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="k">elif</span> <span class="n">reynolds_num</span> <span class="o"><</span> <span class="mf">0.1</span><span class="p">:</span>
<span class="n">fric_factor</span> <span class="o">=</span> <span class="mi">24</span> <span class="o">/</span> <span class="n">reynolds_num</span>
<span class="k">elif</span> <span class="n">reynolds_num</span> <span class="o">>=</span> <span class="mf">0.1</span> <span class="ow">and</span> <span class="n">reynolds_num</span> <span class="o"><</span> <span class="mf">6000.0</span><span class="p">:</span>
<span class="n">fric_factor</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">24</span> <span class="o">/</span> <span class="n">reynolds_num</span><span class="p">)</span> <span class="o">+</span> <span class="mf">0.5407</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="k">elif</span> <span class="n">reynolds_num</span> <span class="o">>=</span> <span class="mi">6000</span><span class="p">:</span>
<span class="n">fric_factor</span> <span class="o">=</span> <span class="mf">0.44</span>
<span class="n">drag</span> <span class="o">=</span> <span class="o">-</span> <span class="n">fric_factor</span> <span class="o">*</span> <span class="n">area</span> <span class="o">*</span> <span class="n">rho_flow</span> <span class="o">*</span> <span class="n">relative_velo_mag</span> <span class="o">*</span> <span class="n">relative_velo</span> <span class="o">/</span> <span class="mf">2.0</span>
<span class="n">gravity</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'gravity'</span><span class="p">]</span>
<span class="n">droplet_mass</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'droplet-mass'</span><span class="p">]</span>
<span class="n">medium_displaced_mass</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'medium-displaced-mass'</span><span class="p">]</span>
<span class="n">buoyant_force</span> <span class="o">=</span> <span class="p">(</span><span class="n">droplet_mass</span> <span class="o">-</span> <span class="n">medium_displaced_mass</span><span class="p">)</span> <span class="o">*</span> <span class="n">gravity</span>
<span class="n">dt_u_0</span> <span class="o">=</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="c1"># d_t u_1 = u_4</span>
<span class="n">dt_u_3</span> <span class="o">=</span> <span class="n">drag</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">/</span><span class="n">droplet_mass</span> <span class="c1"># d_t u_4 = f_1/m</span>
<span class="n">dt_u_1</span> <span class="o">=</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="c1"># d_t u_2 = u_5</span>
<span class="n">dt_u_4</span> <span class="o">=</span> <span class="n">drag</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">droplet_mass</span> <span class="c1"># d_t u_5 = f_2/m</span>
<span class="n">dt_u_2</span> <span class="o">=</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span> <span class="c1"># d_t u_3 = u_6</span>
<span class="n">dt_u_5</span> <span class="o">=</span> <span class="p">(</span><span class="n">drag</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">buoyant_force</span><span class="p">)</span><span class="o">/</span><span class="n">droplet_mass</span> <span class="c1"># d_t u_6 = f_3/m</span>
<span class="k">return</span> <span class="p">[</span><span class="n">dt_u_0</span><span class="p">,</span> <span class="n">dt_u_1</span><span class="p">,</span> <span class="n">dt_u_2</span><span class="p">,</span> <span class="n">dt_u_3</span><span class="p">,</span> <span class="n">dt_u_4</span><span class="p">,</span> <span class="n">dt_u_5</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">__step</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="o">=</span><span class="mf">0.0</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">'''</span>
<span class="sd"> ODE IVP problem:</span>
<span class="sd"> Given the initial data at :math:`t=0`,</span>
<span class="sd"> :math:`(u_1(0),u_2(0),u_3(0)) = (x_0,x_1,x_2)`,</span>
<span class="sd"> :math:`(u_4(0),u_5(0),u_6(0)) = (v_0,v_1,v_2) =</span>
<span class="sd"> (\dot{u}_1(0),\dot{u}_2(0),\dot{u}_3(0))`,</span>
<span class="sd"> solve :math:`\frac{\text{d}u}{\text{d}t} = f(u)` in the interval</span>
<span class="sd"> :math:`0\le t \le t_f`.</span>
<span class="sd"> When :math:`u_3(t)` is negative, bounce the droplet to a random height between</span>
<span class="sd"> 0 and :math:`1.0\,x_0` with no velocity, and continue the time integration until</span>
<span class="sd"> :math:`t = t_f`.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> time: float</span>
<span class="sd"> Time in the droplet unit of time (seconds).</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> None</span>
<span class="sd"> '''</span>
<span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">bottom_impact</span><span class="p">:</span>
<span class="n">x_0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">GetValue</span><span class="p">(</span><span class="s1">'position'</span><span class="p">,</span> <span class="n">time</span><span class="p">)</span>
<span class="n">v_0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">GetValue</span><span class="p">(</span><span class="s1">'velocity'</span><span class="p">,</span> <span class="n">time</span><span class="p">)</span>
<span class="n">u_vec_0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">x_0</span><span class="p">,</span><span class="n">v_0</span><span class="p">))</span>
<span class="n">t_interval_sec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">time_step</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="p">(</span><span class="n">u_vec_hist</span><span class="p">,</span> <span class="n">info_dict</span><span class="p">)</span> <span class="o">=</span> <span class="n">odeint</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__rhs_fn</span><span class="p">,</span>
<span class="n">u_vec_0</span><span class="p">,</span> <span class="n">t_interval_sec</span><span class="p">,</span>
<span class="n">args</span><span class="o">=</span><span class="p">(</span> <span class="bp">self</span><span class="o">.</span><span class="n">ode_params</span><span class="p">,</span> <span class="p">),</span>
<span class="n">rtol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">,</span> <span class="n">mxstep</span><span class="o">=</span><span class="mi">300</span><span class="p">,</span>
<span class="n">full_output</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">info_dict</span><span class="p">[</span><span class="s1">'message'</span><span class="p">]</span> <span class="o">==</span><span class="s1">'Integration successful.'</span><span class="p">,</span> \
<span class="s1">'At time: </span><span class="si">%r</span><span class="s1">; state: </span><span class="si">%r</span><span class="s1">; message: </span><span class="si">%r</span><span class="s1">; full output: </span><span class="si">%r</span><span class="s1">'</span><span class="o">%</span>\
<span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">time</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="n">u_vec_0</span><span class="p">,</span> <span class="n">info_dict</span><span class="p">[</span><span class="s1">'message'</span><span class="p">],</span> <span class="n">info_dict</span><span class="p">)</span>
<span class="n">u_vec</span> <span class="o">=</span> <span class="n">u_vec_hist</span><span class="p">[</span><span class="mi">1</span><span class="p">,:]</span> <span class="c1"># solution vector at final time step</span>
<span class="n">values</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">GetRow</span><span class="p">(</span><span class="n">time</span><span class="p">)</span> <span class="c1"># values at previous time</span>
<span class="n">time</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time_step</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">AddRow</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">values</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">bottom_impact</span><span class="p">:</span>
<span class="c1"># Ground impact with bouncing drop</span>
<span class="k">if</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o"><=</span> <span class="mf">0.0</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounce</span><span class="p">:</span>
<span class="n">position</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">GetValue</span><span class="p">(</span><span class="s1">'position'</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">initial_time</span><span class="p">)</span>
<span class="n">bounced_position</span> <span class="o">=</span> <span class="n">position</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">bounced_position</span>
<span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># zero velocity</span>
<span class="c1"># Ground impact with no bouncing drop and slip velocity</span>
<span class="k">elif</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o"><=</span> <span class="mf">0.0</span> <span class="ow">and</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounce</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">slip</span><span class="p">:</span>
<span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># don't bounce</span>
<span class="c1"># Ground impact with no bouncing drop and no velocity</span>
<span class="k">elif</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o"><=</span> <span class="mf">0.0</span> <span class="ow">and</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounce</span> <span class="ow">and</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">slip</span><span class="p">:</span>
<span class="n">u_vec</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># don't bounce</span>
<span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># zero velocity</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bottom_impact</span> <span class="o">=</span> <span class="kc">True</span>
<span class="c1"># Update current values</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'position'</span><span class="p">,</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'velocity'</span><span class="p">,</span> <span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">:],</span> <span class="n">time</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'speed'</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">u_vec</span><span class="p">[</span><span class="mi">3</span><span class="p">:]),</span> <span class="n">time</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">liquid_phase</span><span class="o">.</span><span class="n">SetValue</span><span class="p">(</span><span class="s1">'radial-position'</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">u_vec</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]),</span>
<span class="n">time</span><span class="p">)</span>
<span class="k">return</span> <span class="n">time</span></div>
</pre></div>
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Cortix is a Python library for network modeling and HPC simulation.
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<a href="https://www.uml.edu/Engineering/Chemical/faculty/de-Almeida-Valmor.aspx">Prof. V. F. de Almeida, Ph.D.</a></br>
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<a href="https://www.uml.edu/">UMass Lowell</a><br>
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