Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of <svg height="23.950001" id="M225" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 18.112499 23.950001" width="18.112499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,23.95)">
<g transform="translate(72,-52.84)">
<g>
<path d="m -71.95,70.71 14.39,0" 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,-71.95,55.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜉</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.91,60.24)">
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
<tspan style="font-size: 8.75px; " x="3.47" y="-1.67">3</tspan>
</text>
</g>
</g>
</svg> on <svg height="18.5875" id="M226" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.6750002 18.5875" width="7.6750002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.5875)">
<g transform="translate(72,-57.13)">
<g>
<path d="m -71.95,70.71 6.04,0" 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,-71.95,59.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜉</tspan>
</text>
</g>
</g>
</svg>, calculated for the beta-function PDF (curves 1), the R-2<svg height="10.7375" id="M227" 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 (curves 2), and the 2<svg height="10.7375" id="M228" 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 (curves 3). (a) <svg height="13.8" id="M229" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 54.549999 13.8" width="54.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8)">
<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
<tspan style="font-size: 12.50px; " x="9.6148071" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.655195" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.906696" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.032446" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.283947" y="0">5</tspan>
</text>
</g>
</g>
</svg>, (b) <svg height="13.8" id="M230" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 54.549999 13.8" width="54.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8)">
<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
<tspan style="font-size: 12.50px; " x="9.6148071" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.655195" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.906696" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.032446" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="37.283947" y="0">5</tspan>
</text>
</g>
</g>
</svg>, (c) <svg height="13.8" id="M231" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 46.737499 13.8" width="46.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8)">
<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
<tspan style="font-size: 12.50px; " x="9.6148071" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.655195" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.906696" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.032446" y="0">5</tspan>
</text>
</g>
</g>
</svg>. </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 4