Here, a brief explanation of the main procedure is written. This explanation is based on the "A Quick Visualization of the Project's Network" in which we have shown the simulation network.
1) To create any of those networks, first, we create two individual 2D Cubic networks for free flow and washcoat. Next, we connect these networks with the "stitch" tool in OpenPNM. In the case of using a single-porosity network, we can skip step 2.
2) For dual-porosity networks, to create a hierarchical structure in macroscale, we use the adopted method in the previous paper. In contrast, we do not physically create the internal structure of microparticles because it can highly increase the computational cost. Instead, since these microparticles have already been studied in the previous paper, we treat them as non-porous particles and use their effective properties to consider their porous structure.
3) We define three distinct geometries for free-flow, washcoat, and their interconnecting throats and a phase and three physics for those geometries. For free flow, we set the throats' length equal to zero to create a non-porous medium.
4) Next, we use the "hagen_poiseuille_2d" model to calculate the "throat.hydraulic_conductance" for the entire domain. Also, since we want the washcoat to be impermeable, we set the "throat.hydraulic_conductance" of interconnecting throats equal to zero.
5) Now is the time to run the "stokes flow" algorithm and extract the pressure field. The boundary conditions are atmospheric pressure at the outlet (101,325 Pa) and an inlet reactant volumetric flow rate that can give us the inlet pressure by using the Hagen-poiseuille equation.
6) We have to be prepared for running the advection-diffusion algorithm by calculating the "throat.diffusive_conductance" and "throat.ad_dif_conductance" with "mixed_diffusion" and "ad_diff" models.
a) In a single-porosity network, we use the phase’s default “pore.diffusivity" to calculate the "throat.diffusive_conductance" and "throat.ad_dif_conductance."
b) In dual-porosity networks, we must consider microparticles' internal structure in the simulation. As mentioned in step 2, to reduce the computational cost, we give their effective diffusivity as the "pore.diffusivity" to the models above. Microparticles' effective diffusivity can be calculated from the previous paper.
7) In this step, the important part of our simulation arrives, and we have to apply source terms to nanopores. Furthermore, we do not apply source terms to micropores and macropores, and they are only some highways that facilitate reactant diffusion.
a) In a single-porosity network, we apply an appropriate source term to nanopores.
b) In dual-porosity networks, we have to apply source terms to microparticles' nanopores. In this regard, since we have not physically created microparticles' internal network, it is impossible to give source terms to the nanopores. Hence, by using the previous paper, we define a function that can determine each microparticle's performance based on its diameter, boundary condition, microstructure, and operating condition (similar to Fig. 6 of the paper), and we use it as a source term function.
8) Finally, by applying a specific concentration ("Value_BC") to the inlet side and applying the "outflow" condition to the outlet side, we can run the advection-diffusion algorithm and extract the concentration contour and conversion, total reaction rate, and other interesting graphs.
One of the main goals is to compare the results of dual-porosity and single-porosity washcoats and conclude which type of washcoat structure is optimal.
Here, a brief explanation of the main procedure is written. This explanation is based on the "A Quick Visualization of the Project's Network" in which we have shown the simulation network.
1) To create any of those networks, first, we create two individual 2D Cubic networks for free flow and washcoat. Next, we connect these networks with the "stitch" tool in OpenPNM. In the case of using a single-porosity network, we can skip step 2.
2) For dual-porosity networks, to create a hierarchical structure in macroscale, we use the adopted method in the previous paper. In contrast, we do not physically create the internal structure of microparticles because it can highly increase the computational cost. Instead, since these microparticles have already been studied in the previous paper, we treat them as non-porous particles and use their effective properties to consider their porous structure.
3) We define three distinct geometries for free-flow, washcoat, and their interconnecting throats and a phase and three physics for those geometries. For free flow, we set the throats' length equal to zero to create a non-porous medium.
4) Next, we use the "hagen_poiseuille_2d" model to calculate the "throat.hydraulic_conductance" for the entire domain. Also, since we want the washcoat to be impermeable, we set the "throat.hydraulic_conductance" of interconnecting throats equal to zero.
5) Now is the time to run the "stokes flow" algorithm and extract the pressure field. The boundary conditions are atmospheric pressure at the outlet (101,325 Pa) and an inlet reactant volumetric flow rate that can give us the inlet pressure by using the Hagen-poiseuille equation.
6) We have to be prepared for running the advection-diffusion algorithm by calculating the "throat.diffusive_conductance" and "throat.ad_dif_conductance" with "mixed_diffusion" and "ad_diff" models. a) In a single-porosity network, we use the phase’s default “pore.diffusivity" to calculate the "throat.diffusive_conductance" and "throat.ad_dif_conductance." b) In dual-porosity networks, we must consider microparticles' internal structure in the simulation. As mentioned in step 2, to reduce the computational cost, we give their effective diffusivity as the "pore.diffusivity" to the models above. Microparticles' effective diffusivity can be calculated from the previous paper.
7) In this step, the important part of our simulation arrives, and we have to apply source terms to nanopores. Furthermore, we do not apply source terms to micropores and macropores, and they are only some highways that facilitate reactant diffusion. a) In a single-porosity network, we apply an appropriate source term to nanopores. b) In dual-porosity networks, we have to apply source terms to microparticles' nanopores. In this regard, since we have not physically created microparticles' internal network, it is impossible to give source terms to the nanopores. Hence, by using the previous paper, we define a function that can determine each microparticle's performance based on its diameter, boundary condition, microstructure, and operating condition (similar to Fig. 6 of the paper), and we use it as a source term function.
8) Finally, by applying a specific concentration ("Value_BC") to the inlet side and applying the "outflow" condition to the outlet side, we can run the advection-diffusion algorithm and extract the concentration contour and conversion, total reaction rate, and other interesting graphs.
One of the main goals is to compare the results of dual-porosity and single-porosity washcoats and conclude which type of washcoat structure is optimal.