One-dimensional flow with heat addition: Difference between revisions
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When the heat addition reaches $q^\ast$ the flow becomes sonic and the flow is said to thermally choked. Thermal choking is illustrated in Figure~\ref{fig:TSPV:d}, where the curve representing the energy equation (the blue line in the <math>p\nu</math>-diagram) is tangent to the Rayleigh line and if more heat is added the blue line will move to the right of the Rayleigh line and thus there are no solutions for <math>q>q^\ast</math>. So what happens if more heat is added to the flow after thermal choking is reached. The answer is different if the flow is subsonic or supersonic. For a subsonic flow, the upstream flow will be adjusted such that the slope of the Rayleigh line changes and the energy equation curve becomes tangent to the Rayleigh line. This means that the massflow per unit area (<math>C</math>) is reduced and <math>q^\ast</math> is increased such that <math>q^\ast</math> equals the heat added to the flow. Note that the upstream total conditions will not be changed in this process (see Figure~\ref{fig:thermal:choking:sub}). | When the heat addition reaches $q^\ast$ the flow becomes sonic and the flow is said to thermally choked. Thermal choking is illustrated in Figure~\ref{fig:TSPV:d}, where the curve representing the energy equation (the blue line in the <math>p\nu</math>-diagram) is tangent to the Rayleigh line and if more heat is added the blue line will move to the right of the Rayleigh line and thus there are no solutions for <math>q>q^\ast</math>. So what happens if more heat is added to the flow after thermal choking is reached. The answer is different if the flow is subsonic or supersonic. For a subsonic flow, the upstream flow will be adjusted such that the slope of the Rayleigh line changes and the energy equation curve becomes tangent to the Rayleigh line. This means that the massflow per unit area (<math>C</math>) is reduced and <math>q^\ast</math> is increased such that <math>q^\ast</math> equals the heat added to the flow. Note that the upstream total conditions will not be changed in this process (see Figure~\ref{fig:thermal:choking:sub}). | ||
{{ | {{InfoBox|<math> | ||
M_{1^\prime} = f(q^\ast) | M_{1^\prime} = f(q^\ast) | ||
</math><br><br><math> | </math><br><br><math> | ||
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</math><br><br><math> | </math><br><br><math> | ||
u_{1^\prime} = M_{1^\prime}a_{1^\prime} | u_{1^\prime} = M_{1^\prime}a_{1^\prime} | ||
</math> | </math>}} | ||
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