Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the Reynolds-averaged (curves 1) and Favre-averaged (curves 2) combustion progress variables, associated with the maximum mean heat release rate, on the segregation factor <svg height="9.9375" id="M453" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
</text>
</g>
</g>
</svg>. <svg height="10.9125" id="M454" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 48.712502 10.9125" width="48.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
<tspan style="font-size: 12.50px; " x="11.190185" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="23.230574" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="29.482075" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="32.607822" y="0">0</tspan>
</text>
</g>
</g>
</svg>. Thin and bold curves are associated with <svg height="21.825001" id="M455" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 64.300003 21.825001" width="64.300003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.825)">
<g transform="translate(72,-54.54)">
<text transform="matrix(1,0,0,-1,-71.95,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
<tspan style="font-size: 12.50px; " x="7.4267821" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="16.779026" y="0">,</tspan>
</text>
<g>
<path d="m -49.96,65.21 5.81,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-49.96,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="5.8013921" y="0">,</tspan>
</text>
<g>
<path d="m -38.94,70.71 14.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-38.94,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-33.12,60.24)">
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
<tspan style="font-size: 8.75px; " x="3.47" y="-1.67">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-24.78,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
</text>
</g>
</g>
</svg> and <svg height="21.9125" id="M456" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 90.400002 21.9125" width="90.400002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.9125)">
<g transform="translate(72,-54.47)">
<text transform="matrix(1,0,0,-1,-70.8,59.34)">
<tspan style="font-size: 12.50px; " x="0" y="0"></tspan>
<tspan style="font-size: 12.50px; " x="-1.15" y="2.53">𝑃</tspan>
<tspan style="font-size: 12.50px; " x="8.1397285" y="2.53">(</tspan>
<tspan style="font-size: 12.50px; " x="12.303228" y="2.53">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="17.491974" y="2.53">,</tspan>
<tspan style="font-size: 12.50px; " x="28.494614" y="2.53">̃</tspan>
<tspan style="font-size: 12.50px; " x="22.718227" y="2.53">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="28.519619" y="2.53">,</tspan>
</text>
<g>
<path d="m -37.06,70.71 23.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-37.06,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="6.2765059" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-24.97,60.24)">
<tspan style="font-size: 8.75px; " x="6.4499998" y="-1.67">2</tspan>
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
<tspan style="font-size: 8.75px; " x="2.9756801" y="0"></tspan>
</text>
<text transform="matrix(1,0,0,-1,-13.65,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
</text>
<g>
<path d="m -10.17,65.21 6.27,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-10.17,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="6.2765059" y="0">)</tspan>
</text>
</g>
</g>
</svg>, respectively. </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 13