Comparison of Presumed PDF Models of Turbulent Flames

<table>Data for averaging invoking presumed PDFs. (a) Normalized heat release rates <svg height="13.45" id="M155" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 29.137501 13.45" width="29.137501" 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">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="19.042068" y="0">)</tspan>
</text>
</g>
</g>
</svg> versus combustion progress variable <svg height="7.1875" id="M156" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg>, calculated for various gasoline-air mixtures, with the equivalence ratio being specified in legends. (b) Normalized laminar flame speed <svg height="10.925" id="M157" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.375 10.925" width="15.375" 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">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.45,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐿</tspan>
</text>
</g>
</g>
</svg> (solid curve) and maximum heat release rate <svg height="10.6875" id="M158" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
</text>
</g>
</g>
</svg> (dashed curve) versus equivalence ratio <svg height="10.325" id="M159" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
</text>
</g>
</g>
</svg>. </table>

Journal of Combustion

Comparison of Presumed PDF Models of Turbulent Flames

Figure 2