| Author | Message | ||
     Mohammad Rahmani (mrahmani) Member Username: mrahmani Post Number: 36 Registered: 10-2004 |
Suppose we have a 2D PDE which has been defined on domain "M1" as following: PDE: u*dz(c)=1/r*dr(r*dr(c))-rg where rg=Eta*f(c) Eta has to be calculated from a BVP defined as following: BVP: -del2(S)+rA=0, (del2 is laplacian for curvilinear coordinates) Eta=-2/h^2*(dw(S) @ w=1), w is the spatial variable in the above BVP. This is the typical case in Fixed bed reactors where, BVP defines the mass balance on solid pellets and PDE defines the mass balance in the free fluid. If we define the 2D domain "M1" in FP then, is there any way to calculate "Eta" as a parameter to be used by the solver. I think this is not a real coupled set of DE. It will be more expensive to solve the set as coupled DE, but, how it could be implemented in FlexPDE? Mohammad | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 388 Registered: 06-2003 |
It probably would have been clearer if you had described the physics, instead of some abstract differential equations. Nevertheless, this sounds similar to a problem that came up a couple of years ago. In that case, there was a column packed with spherical pellets, and through which a fluid flowed. The fluid absorbed into the pellets. The absorption into the pellets was a 1D diffusion problem inside the spheres, and the fluid concentration was affected by the absorption at the sphere surfaces. Is this the kind of thing you have here? In that case, the fluid characteristic was considered to depend only on distance down the column, whereas you seem to want a 2D (R,Z) variation of the fluid in the column. For the earlier problem, my suggestion was as follows: 1) Declare a 2D problem, in which the "X" coordinate is distance down the column, and the "Y" coordinate is radius inside a representative sphere at that "X" position. 2) Write an equation for fluid content that depends on X only, with a diffusion term to spread it throughout Y. 3) Write a diffusion equation for the Y dimension with a very small diffusion in the X dimension to kill oscillations. 4) Couple the two dimensions only through boundary conditions at the surface of the spheres. In your case, an analogous system would be a 3D model using X and Y for fluid coordinates and Z for radial position in the spheres. Again, coupling between the two systems is only through boundary conditions at the Z=1 surface. | ||
| Mohammad Rahmani (mrahmani) Member Username: mrahmani Post Number: 37 Registered: 10-2004 |
Robert, That's right. The problem describes the convection-diffusion-reaction in a packed bed reactor where the reaction is only taking place inside pellets. The difference as you have mentioned is the 2D fluid flow in this case. Thanks for your comment. I will try as you advised |