Transient Burning Rate Model for Solid Rocket Motor Internal Ballistic Simulations

<table>Predicted unsteady head-end
pressure-time profile, for SRM undergoing axial combustion instability
symptoms (<svg height="14.7125" id="M3" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 78.862503 14.7125" width="78.862503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.34,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="26.618887" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="32.870388" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="39.121887" y="0">0</tspan>
</text>
</g>
</g>
</svg> s<sup>−1</sup>, <svg height="14.9" id="M4" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 99.375 14.9" width="99.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9)">
<g transform="translate(72,-60.08)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">Δ</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝐻</tspan>
</text>
<text transform="matrix(1,0,0,-1,-52.01,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.19,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="24.543388" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="32.870388" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="39.121887" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="45.373386" y="0">0</tspan>
</text>
</g>
</g>
</svg> J/kg, <svg height="14.725" id="M5" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 53.349998 14.725" width="53.349998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.725)">
<g transform="translate(72,-60.22)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Δ</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝑝</tspan>
</text>
<text transform="matrix(1,0,0,-1,-56.81,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-47.66,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">2</tspan>
</text>
</g>
</g>
</svg> atm).</table>

International Journal of Aerospace Engineering

fig2

Figure 2

Figure 2: Transient Burning Rate Model for Solid Rocket Motor Internal Ballistic Simulations 