Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the parameters <svg height="10.925" id="M281" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 12.7 10.925" width="12.7" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.76,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg> (thin curves) and <svg height="10.925" id="M282" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 12.7 10.925" width="12.7" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.76,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg> (bold curves) on the Reynolds-averaged combustion progress variable, calculated for <svg height="10.9125" id="M283" 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> and <svg height="13.8" id="M284" 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> using the R-2<svg height="10.7375" id="M285" 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 1) and the 2<svg height="10.7375" id="M286" 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). </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 7