Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the normalized mean laminar flame speed <svg height="16.0875" id="M484" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.375 16.0875" width="15.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.0875)">
<g transform="translate(72,-59.13)">
<g>
<path d="m -71.95,70.71 5.5,0" 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,-71.95,62.31)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.45,59.18)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐿</tspan>
</text>
</g>
</g>
</svg> on the mean equivalence ratio <svg height="15.4875" id="M485" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.05 15.4875" width="12.05" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.4875)">
<g transform="translate(72,-59.61)">
<g>
<path d="m -71.95,70.71 9.54,0" 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,-71.95,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
</text>
</g>
</g>
</svg>, calculated invoking the beta-function (thin curves) and R-2<svg height="10.7375" id="M486" 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> (bold curves) PDFs for different <svg height="12.975" id="M487" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 15.825 12.975" width="15.825" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.975)">
<g transform="translate(72,-61.62)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.8,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg> specified in legends. <svg height="14.7875" id="M488" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 70 14.7875" width="70" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7875)">
<g transform="translate(72,-60.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">m</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="0">i</tspan>
<tspan style="font-size: 8.75px; " x="9.2421122" y="0">n</tspan>
</text>
<text transform="matrix(1,0,0,-1,-43.72,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.417639" y="0">5</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.7125" id="M489" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 71.8125 14.7125" width="71.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">m</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="0">a</tspan>
<tspan style="font-size: 8.75px; " x="10.694944" y="0">x</tspan>
</text>
<text transform="matrix(1,0,0,-1,-42.26,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">9</tspan>
</text>
</g>
</g>
</svg>. </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 15