| Citation: |
Jose Luis Diaz Palencia, Federico Prieto Munoz, Juan Miguel Garcia-Haro. NON-HOMOGENEOUS REACTION IN A NON-LINEAR DIFFUSION OPERATOR WITH ADVECTION TO MODEL A MASS TRANSFER PROCESS[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 179-205. doi: 10.11948/20210096
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NON-HOMOGENEOUS REACTION IN A NON-LINEAR DIFFUSION OPERATOR WITH ADVECTION TO MODEL A MASS TRANSFER PROCESS
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Abstract
It is the objective to provide a mathematical treatment of a non-homogeneous and non-lipschitz reaction problem with a non-linear diffusion and advection operator, so that it can be applied to a fire extinguishing process in aerospace. The main findings are related with the existence and characterization of a finite propagation support that emerges in virtue of the the non-linear diffusion formulation. It is provided a precise assessment on different times associated to the extinguisher discharge process. Particularly, the time required to activate the discharge, the time required for the extinguisher front to cover the whole domain, the time required to reach a minimum level of concentration so as to extinguish a fire and the time required by the agent to reach some difficult dead zones where the extinguisher propagates only by diffusion and no advection. The equation proposed is firstly discussed from a mathematical perspective to find analytical solutions and propagating profiles. Afterwards, the application exercise is introduced.
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Keywords:
- Reaction, non-linear advection /
- non-linear diffusion /
- non-homogenous /
- aerospace
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References
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Jose Luis Diaz Palencia, Federico Prieto Munoz, Juan Miguel Garcia-Haro. NON-HOMOGENEOUS REACTION IN A NON-LINEAR DIFFUSION OPERATOR WITH ADVECTION TO MODEL A MASS TRANSFER PROCESS[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 179-205. doi: 10.11948/20210096
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- Figure 1. Domain representation. Note that the sensors are placed close to each of the sections A, B, C and D
- Figure 2. Extinguisher sensor position and numbering for Section A (left) and Section B (right).
- Figure 3. Extinguisher sensor position and numbering for Section C (left) and Section D (right).
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Figure 4. Extinguisher volumetric concentration evolution upon fire activation procedure that is initiated during the flight test used to validate the postulated diffusion. Each of the coloured lines represent the measurements of a sensor located as described in the previous figures. Note that the horizontal red bar represents a volumetric concentration of
$ 6\% $ . At$ 1.3 $ seconds from the beginning of discharge, half of the sensors reach the$ 6\% $ level. - Figure 5. fire suppressant concentration (H) represented versus the axial variable x (meters)
- Figure 6. Nacelle shape geometry