Hi,
I'm having problems in implementing the two phase transport in the Low-Temperature PEMFC model.
Initially, I built a model composed by the following physics:
1. Secondary Current Distribution;
2. Mixture Flow in the Cathode Channel, GDL and RL;
3. Mixture Flow in the Anode Channel, GDL and RL;
4. Cathode Gas Phase Transport of Concentrated Species: Describes the reactions occurring in the Cathode side between the gas substances and the condensation/evaporation (i.e. passage from the gas to the liquid phase and vice-versa);
5. Anode Gas Phase Transport of Concentrated Species: Describes the reactions between occurring in the Anode side between gas substances and the condensation/evaporation (i.e. passage from the gas to the liquid phase and vice-versa);
Using the Mixture Model developed by C.Y. Wang,, starting from the mixture velocity and pressure I have obtained the velocity and the pressure of the single phases.
I tried this model with imposed values of the saturation (i.e. H2O content divided by the liquid H2O density) and it provides real values.
However when I try to write the equation describing the liquid phase transport the model diverges and no solution is obtained.
To describe the liqui transport i tried two different paths:
1. I have tried to write the equation using the Mathematical Physic:
2. I used the Flow in Diluite Species by substituting to the Diffusion Coefficient the Capillary Diffusion Coefficient.
Both the two paths are not correct.
The last equation that I want to implement is:
eps*d(sl*rhol,t)+div(rhol*Ul)+div(lamdal*lambdag*K/mu*rho*(grad(pc)+(rhol-rhog)*g)))=rw
Where:
- eps: Porosity;
- sl: Liquid Saturation;
- rhol= Liquid Density;
- Ul=Liquid Velocity;
- lambdag, lambdal=Relative mobilties of the gas and liquid phases;
- K: Permeability;
- mu: Viscisity;
- rho: Mixture Density;
- pc: Capillary pressure;
- g: Gravity acceleration;
- rw: Condensation/Evaporation rate [kg/m^3/s]=if(w_H2O*p)>psat_H2O(T),100[s^-1]*eps*sg*(w_H2O*p-psat_H2O(T))*MW_H2O/R_const/T,100[s^-1]*eps*sl*(w_H2O*(p)-psat_H2O(T))*MW_H2O/R_const/T)
- sg=1-sl: Gas phase saturation;
- psat: Saturation Pressure [Pa];
- T: Temperature [K];
THe boundary conditions i have imposed are:
- Dirichlet at the cathode and anode inlet: sl=0;
- No flux in all the other boundaries.
There is someone that has been able to implement this phenomena that wants to help me? If it is required i can send via email the model.
Thank you very much.
In the file i have posted all the equation i have been used and some images to understand better what i did. In the last part of the file there are the coefficients to insert in the Mathematical model to write the equation.
I'm having problems in implementing the two phase transport in the Low-Temperature PEMFC model.
Initially, I built a model composed by the following physics:
1. Secondary Current Distribution;
2. Mixture Flow in the Cathode Channel, GDL and RL;
3. Mixture Flow in the Anode Channel, GDL and RL;
4. Cathode Gas Phase Transport of Concentrated Species: Describes the reactions occurring in the Cathode side between the gas substances and the condensation/evaporation (i.e. passage from the gas to the liquid phase and vice-versa);
5. Anode Gas Phase Transport of Concentrated Species: Describes the reactions between occurring in the Anode side between gas substances and the condensation/evaporation (i.e. passage from the gas to the liquid phase and vice-versa);
Using the Mixture Model developed by C.Y. Wang,, starting from the mixture velocity and pressure I have obtained the velocity and the pressure of the single phases.
I tried this model with imposed values of the saturation (i.e. H2O content divided by the liquid H2O density) and it provides real values.
However when I try to write the equation describing the liquid phase transport the model diverges and no solution is obtained.
To describe the liqui transport i tried two different paths:
1. I have tried to write the equation using the Mathematical Physic:
2. I used the Flow in Diluite Species by substituting to the Diffusion Coefficient the Capillary Diffusion Coefficient.
Both the two paths are not correct.
The last equation that I want to implement is:
eps*d(sl*rhol,t)+div(rhol*Ul)+div(lamdal*lambdag*K/mu*rho*(grad(pc)+(rhol-rhog)*g)))=rw
Where:
- eps: Porosity;
- sl: Liquid Saturation;
- rhol= Liquid Density;
- Ul=Liquid Velocity;
- lambdag, lambdal=Relative mobilties of the gas and liquid phases;
- K: Permeability;
- mu: Viscisity;
- rho: Mixture Density;
- pc: Capillary pressure;
- g: Gravity acceleration;
- rw: Condensation/Evaporation rate [kg/m^3/s]=if(w_H2O*p)>psat_H2O(T),100[s^-1]*eps*sg*(w_H2O*p-psat_H2O(T))*MW_H2O/R_const/T,100[s^-1]*eps*sl*(w_H2O*(p)-psat_H2O(T))*MW_H2O/R_const/T)
- sg=1-sl: Gas phase saturation;
- psat: Saturation Pressure [Pa];
- T: Temperature [K];
THe boundary conditions i have imposed are:
- Dirichlet at the cathode and anode inlet: sl=0;
- No flux in all the other boundaries.
There is someone that has been able to implement this phenomena that wants to help me? If it is required i can send via email the model.
Thank you very much.
In the file i have posted all the equation i have been used and some images to understand better what i did. In the last part of the file there are the coefficients to insert in the Mathematical model to write the equation.