Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the normalized burning rate integral <svg height="11.025" id="M294" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 11.575 11.025" width="11.575" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.025)">
<g transform="translate(72,-63.18)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑢</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.02,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑡</tspan>
</text>
</g>
</g>
</svg> on the segregation factor <svg height="21.825001" id="M295" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 82.987503 21.825001" width="82.987503" 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)">
<g>
<path d="m -71.95,70.71 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,-71.95,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.14,60.24)">
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
<tspan style="font-size: 8.75px; " x="3.48" y="-1.67">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.79,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">[</tspan>
</text>
<g>
<path d="m -50.15,65.21 5.82,0" 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,-50.15,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="5.8138952" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="9.9773941" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="19.00456" y="0">−</tspan>
</text>
<g>
<path d="m -19.8,65.21 5.82,0" 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,-19.8,56.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="5.8138952" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="9.9773941" y="0">]</tspan>
</text>
</g>
</g>
</svg>, calculated for various equivalence ratios specified in legends using the beta-function PDF (thin curves) and the 2<svg height="10.7375" id="M296" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 7.9875002 10.7375" width="7.9875002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
<g transform="translate(72,-63.41)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛿</tspan>
</text>
</g>
</g>
</svg>-PDF (bold curves). </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 8