Comparison of Presumed PDF Models of Turbulent Flames

<table>Dependencies of the normalized mean heat release rate on the Reynolds-averaged combustion progress variable, calculated for the beta-function PDF (curves 1), the R-2<svg height="10.7375" id="M238" 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)">
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</svg>-PDF (curves 2), and the 2<svg height="10.7375" id="M239" 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">
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<g transform="translate(72,-63.41)">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝛿</tspan>
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</svg>-PDF (curves 3). <svg height="10.9125" id="M240" 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>
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</svg>. (a) <svg height="13.8" id="M241" 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">
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<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>
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</svg>, (b) <svg height="13.8" id="M242" 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>
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</svg>, (c) <svg height="13.6125" id="M243" 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>.  </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 5