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ME 525: Combustion Lecture 27: Carbon Particle Combustion Carbon surface reactions. One-film model. Two-film model.

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Combusting Carbon Particle: Surface Reactions

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Combusting Carbon Particle: One-Film Model Temperature and Species Profiles, One-Film Model

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Combusting Carbon Particle: One-Film Model Assume: 1.Particle burns in quiescent, infinite medium containing O 2 and inert N 2 initially. 2.Burning process is quasi-steady. 3.Reaction 1 is dominant at the surface (not a good assumption). 4.Particle has uniform temperature, radiates as a gray body. 5.No diffusion of gas-phase species into particle. 6.Le = 1 in the gas phase 7.k g, c Pg, D g, g are constants evaluated at some mean temperature.

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Combusting Carbon Particle: One-Film Model rsrs r

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Following the same procedures as for the evaporating droplet :

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Combusting Carbon Particle: One-Film Model rsrs TsTs Y O2, T Y O2,s Y CO2,s From a consideration of the chemical kinetics at the carbon particle surface we obtain:

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Combusting Carbon Particle: One-Film Model, Diffusion and Kinetic Resistances Burning of the carbon particle is controlled by matching of the reaction rate and diffusion rate of oxygen to the surface. To analyze these effects we develop expressions for the kinetic and diffusive resistances

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The kinetic resistance is : Combusting Carbon Particle: One-Film Model, Diffusion and Kinetic Resistances For the diffusive resistance, note that the typical value of the transfer number B O,m is typically <<1 [ln (1+x) x for x<<1]:

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Combusting Carbon Particle: One-Film Model, Diffusion and Kinetic Resistances Combining these two relations:

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Combusting Carbon Particle: Two-Film Model Temperature and Species Profiles, Two-Film Model

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Combusting Carbon Particle: Two-Film Model Assume: 1.Particle burns in quiescent, infinite medium containing O 2 and inert N 2 initially. 2.Burning process is quasi-steady. 3.Reaction 3 is dominant at the surface. 4.Particle is surrounded by a flame sheet. 5.At the flame sheet, CO reacts in stoichiometric proportion with O 2 to produce CO 2. 6.Particle has uniform temperature, radiates as gray body. 7.No diffusion of gas-phase species into particle. 8.Le = 1 in the gas phase 9. k g, c Pg, D g, g are constants evaluated at some mean temperature

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Combusting Carbon Particle: Two-Film Model rsrs rfrf

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At the particle surface:

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Combusting Carbon Particle: Two-Film Model At the flame sheet:

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Combusting Carbon Particle: Two-Film Model In this problem analysis: Knowns: Unknowns: rfrf rsrs TsTs TfTf Y O2, T Y CO2,s Y I, Y CO2,f Y I,f

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Combusting Carbon Particle: Two-Film Model Regarding the surface temperature T s and flame temperature T f as known quantities for the moment, we obtain the following four relations by considering the species balances:

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Combusting Carbon Particle: Two-Film Model rfrf rsrs TsTs TfTf Y O2, T Y CO2,s Y I, Y CO2,f Y I,f Rearranging these expressions gives us a relation between the burning rate and

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Combusting Carbon Particle: Two-Film Model Another relation between and is provided by the chemical kinetic equation for the surface reaction:

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Combusting Carbon Particle: Two-Film Model The rate coefficient k 3 is given by For reaction 3 the enthalpy of combustion is given by

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Combusting Carbon Particle: Two-Film Model rfrf rsrs TsTs TfTf Y O2, T Y CO2,s Y I, Y CO2,f Y I,f The enthalpy of combustion is negative - the reaction is endothermic! The energy needed to drive the reaction comes from the reaction of CO and O 2 at the flame sheet.

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Combusting Carbon Particle: Two-Film Model Often assumed that the particle burning process is in the diffusion-controlled regime: In the diffusion-controlled regime, surface chemical kinetics are fast compared to diffusion times and the CO 2 reacts as soon as it gets to the particle surface. For burning carbon particles, the process will be diffusion controlled at high pressures, when the surface temperature is high, and/or when the particle is large.

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Combusting Carbon Particle: Two-Film Model Up to now we have assumed that the surface and flame temperatures are known. Two more equations to determine these temperatures are provided by energy balances at the flame sheet and at the particle surface. Solution for the whole problem is found by iteration in the quantities

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Combusting Carbon Particle: Two-Film Model rsrs At the particle surface:

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Combusting Carbon Particle: Two-Film Model The temperature gradient is found from the same temp profile expression that we obtained for the burning liquid droplet:

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Combusting Carbon Particle: Two-Film Model The energy equation at the surface becomes:

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Combusting Carbon Particle: Two-Film Model, Diffusion and Kinetic Resistances We can develop expressions for the diffusive and kinetic resistances for the two-film model in analogy with the one-film model. Recall the two expressions that we developed previously for the burning rate:

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Combusting Carbon Particle: Two-Film Model, Diffusion and Kinetic Resistances The kinetic resistance is found immediately: For the diffusive resistance, we note that the typical value of the transfer number B CO2,m is typically :

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Combusting Carbon Particle: Two-Film Model, Diffusion and Kinetic Resistances The diffusive resistance is thus given by:

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