Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the parameters of the R-2<svg height="10.7375" id="M374" 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>
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</g>
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</svg> (thin curves) and 2<svg height="10.7375" id="M375" 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 on the Reynolds-averaged combustion progress variable, calculated for <svg height="13.6125" id="M376" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 46.737499 13.6125" width="46.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<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">9</tspan>
</text>
</g>
</g>
</svg> and <svg height="10.9125" id="M377" 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>.  <svg height="13.45" id="M378" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 32.375 13.45" width="32.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="18.741997" y="0">𝛼</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M379" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 36.137501 14.6" width="36.137501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="18.741997" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.02,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M380" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 36.137501 14.6" width="36.137501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="18.741997" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.02,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>. </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 11