- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2021-04-08 15:18:19+12:00
- Desc:
- modified svg
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/994dbbb88a761fe3a62bfaf8352da94103650bb2/BG Tutorial Fluid Systems/pv_type.cellml
<?xml version='1.0'?>
<model name="pv_type" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="J_s_per_m3">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m6_per_J">
<unit exponent="6" units="metre"/>
<unit exponent="-1" units="joule"/>
</units>
<units name="m3_per_s">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_m3">
<unit units="joule"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="J_s_per_m6">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-6" units="metre"/>
</units>
<units name="J_s2_per_m6">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-6" units="metre"/>
</units>
<units name="J_s2_per_m5">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-5" units="metre"/>
</units>
<component name="pv_type">
<variable name="t" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s2_per_m5"/>
<variable initial_value="0.4e+6" name="E" units="J_per_m3"/>
<variable initial_value="0.2" name="l" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable initial_value="0.002" name="r" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<!-- State Variables-->
<variable initial_value="1.0" name="u_in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable initial_value="1.0" name="v_out" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>
