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14 changes: 7 additions & 7 deletions book/content/modelling/05_combustion/01_fundamentals.ipynb
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"source": [
"## Burning Candle\n",
"\n",
"A buring candle is a good fire example. Here, once ignited, the flame emitts heat radiation which is absorbed by the candle body. The solid melts and the fluid wax is transported through the wick and evaporates in a endotermic reaction. Through diffusion, the vaporised wax mixes with air and conducts an exothermic reaction, the combustion. The hot combustion products rise and enentually lead to further reactions.\n",
"A buring candle is a good fire example. Here, once ignited, the flame emits heat radiation which is absorbed by the candle body. The solid melts and the fluid wax is transported through the wick and evaporates in a endothermic reaction. Through diffusion, the vaporised wax mixes with air and conducts an exothermic reaction, the combustion. The hot combustion products rise and eventually lead to further reactions.\n",
"\n",
"The main zones of this process and the characteristic temperatures are shown in {numref}`fig-comb-candle`, with:\n",
"\n",
"* **Zone I**: Endotermic vaprisation of the wax,\n",
"* **Zone I**: Endothermic vaporisation of the wax,\n",
"* **Zone II + III**: Decomposition of the wax molecules, diffusive mixing with the ambient air and combustion, and\n",
"* **Zone IV**: Hot (large) soot particles emitt thermal radiation. \n",
"* **Zone IV**: Hot (large) soot particles emit thermal radiation. \n",
"\n",
":::{figure-md} fig-comb-candle\n",
"\n",
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"source": [
"## Reaction Rates\n",
"\n",
"A chemical process is the collision and interaction of molecules of the involved species. Therefore the rate at which the reaction takes place is proportional to the collision frequency $\\mf R$:\n",
"A chemical process is the collision and interaction of molecules of the involved species. Therefore, the rate at which the reaction takes place is proportional to the collision frequency $\\mf R$:\n",
"\n",
"$$\n",
"\\mf R = k C_{f}C_{o}\\quad ,\n",
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"source": [
"## Flamability\n",
"\n",
"Not all mixtures of fuel and oxygen / air are flammable. In general there exists a lower (LFL) and an upper flammability limit (UFL), which relate the volume fraction of the fuel to air. Additionally the gas temperature may have a lower limit and there exist an autoignition temperature. A pilot ignition is needed below the autoignition temperature (AIT). The schematics in {numref}`fig-comb-flammability` outline the relevant regions of fuel mixture and gas temperature.\n",
"Not all mixtures of fuel and oxygen / air are flammable. In general there exists a lower (LFL) and an upper flammability limit (UFL), which relates the volume fraction of the fuel to air. Additionally the gas temperature may have a lower limit and there exist an autoignition temperature. A pilot ignition is needed below the autoignition temperature (AIT). The schematics in {numref}`fig-comb-flammability` outline the relevant regions of fuel mixture and gas temperature.\n",
"\n",
":::{figure-md} fig-comb-flammability\n",
"<img src=\"./figs/flamibility.svg\" width=\"80%\">\n",
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" - 500\n",
"```\n",
"\n",
"During the combustion process air’s oxygen is consumed and therefore the situation of an under-ventilated fire (not enough oxygen) is possible. Here the combustion will be reduced, however the fuel is still in the air and may burn at an other place or when oxygen is advected.\n",
"During the combustion process air’s oxygen is consumed and therefore the situation of an under-ventilated fire (not enough oxygen) is possible. Here the combustion will be reduced, however the fuel is still in the air and may burn at another place or when oxygen is advected.\n",
"\n",
"The equivalence ratio $\\mf \\Phi$ relates the real ratio of the mass fractions of fuel $\\mf Y_f$ and air $\\mf Y_a$ to their stoichiometric ratio.\n",
"\n",
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"\n",
"**TODO: Add link to video of a candle flash back**\n",
"\n",
"The following figures illustrate a setup with a pipe, which is closed at one side and filled with a combustible mixture. The velocity at which the flame effectivle moves depends on the ignition location.\n",
"The following figures illustrate a setup with a pipe, which is closed at one side and filled with a combustible mixture. The velocity at which the flame moves depends on the ignition location.\n",
"\n",
":::{figure-md} fig-comb-burning-velocity_1\n",
"<img src=\"./figs/flame_burn_velocity_setup_1.svg\" width=\"80%\">\n",
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