2. Thermal Decomposition of Nitrous Oxide
- The continuity equation
- The Navier–Stokes equation with buoyant forces (G).
- The infinitesimal balance of heat transfer, based on the Fourier’s law, including effects of natural convection and viscous dissipation.
- The linear Bousinesq equation of state.
- The gaseous fluid (air and different species involved in the thermal decomposition of the laughing gas) is incompressible and Newtonian.
- The thermal conductivity, viscosity, coefficient of thermal expansion and coefficient of diffusion of chemical species are all constant throughout the studied temperature range.
- The variation of density is only significant in terms of buoyant forces.
- Viscous dissipation is negligible.
- The Reynolds number is small (for Bénard–Poiseuille flow).
- The laughing gas decomposition is the only chemical reaction that takes place in the system.
- In the top and bottom plates, temperature is constant. This means that the heat generated by the chemical reaction is assumed to be efficiently removed from the system.
- In the bottom plates, there are two heat sources (or hot spots) for both the opened and closed channels at a higher temperature than the low constant temperature set in 7. These heat sources trigger the (N2O decomposition) reaction.
- The concentrations of chemical species are kept sufficiently small so that they dominate the properties of air during the phenomenon of natural convection.
3. The Lattice Botlzmann Model
3.1. Open Channel
- For the top plate, bounce back boundary conditions for the fluid dynamic LBE and a low constant isothermal boundary conditions for the thermic LBE are used.
- Inlet and outlet periodic boundary conditions, for the moment and thermal LBE, are set.
- For the bottom plate, bounce back boundary conditions are imposed in all the nodes for the hydrodynamic LBE, while for thermal LBE we used bounce back conditions as well, except in the heat sources sites where Dirichlet boundary conditions are set.
- Top and bottom bounce back boundary conditions.
- Invariable concentration in the inlet of the channel.
- Null gradient concentration in the outlet of the channel (von Neumann condition).
3.2. Closed Channel
- Bounce back boundary conditions at all the sites for the fluid and thermal LBE on all borders, except at the heat’s sources.
- Diritchlet boundary conditions at all high temperature sites (heat sources).
- Initial state with uniformly distributed nitrous oxide in the closed vessel, with initial concentration C0 and initial temperature T0, smaller than the temperature of the sources.
- Bounce back boundary conditions at all the sites for the reaction-diffusion LBE on all borders.
4. The Lattice Botlzmann Algorithm
4.1. Open Channel
- The distribution functions f and g for the velocity u and temperature T fields, respectively, were evaluated simultaneously in a coupled fashion, taking into account iterative calculations performed by the following steps:
- Propagation (streaming) of the f and g distribution functions.
- Calculation of the distribution functions at equilibrium; feq and geq.
- Actualization of the f and g distribution functions.
- Introduction of thermal and fluid dynamics boundary conditions.
- Calculation of the u and T fields from the new f and g distribution functions.
- Assessment of the new and preceding values of u and T, if they are closed enough, finish the iterations; else, return to step 1.1.
- Once obtaining the steady temperature and velocity profiles, the temporal evolution of the distribution functions hi for each one of the three chemical species is calculated, solving the LBM equations for the reaction-diffusion advection phenomena. This is a non-iterative procedure, structured practically by the same steps as the ones in the thermo-hydrodynamic analysis, except for that in the formulation of the diffusional distribution functions for each chemical species. The chemical kinetics term (Arrhenius law also considered) is introduced, keeping the 1:1:1/2 stoichiometric relationships between reactants and products.
4.2. Closed Channel
5. Results and Conclusions
Conflicts of Interest
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