SCIENTIFIC REPORT – 2022

Transfer phenomena in special porous media

(PN-III-P4-PCE-2021-0993)

The first part of the project aims at the mathematical modeling of transfer phenomena in bidisperse porous media (BDPM). Thus, mathematical models were obtained for convective flows in bidisperse porous media with high porosity, for convective flows at high speeds and for convective flows with internal heat generation.

Between June and December 2022, the following was achieved:

1. Obtaining physical models and real physical parameters (BDPM)
– In the case of porous media with high porosity, the diffusive term was added in the two moment equations
– For flows at high speeds, a quadratic term is added to the moment equation
– Internal heat generation requires modification of the energy equation.

2. Obtaining the mathematical model and studying the dimensionless parameters (BDPM)

– For large porosities, the mathematical model based on the Brinkman equations was obtained.
– For flows at high speeds, the mathematical model based on the Forchheimer-Darcy equations was obtained.
– In the case of internal heat generation, a mathematical model based on Darcy’s equations and the local thermal balance was obtained.

3. Study of the existence of analytical solutions and studies of existence and uniqueness (BDPM)

– The existence of solutions of coupled equations of the Navier-Stokes type was analyzed theoretically using variational approaches.

4. Obtaining the numerical model and numerical simulations (BDPM)

– Systems of partial differential equations with boundary values were discretized using central finite differences. Systems of algebraic equations were linearized and solved iteratively.

5. Validation of results, interpretation of results, preparation of results for publication/communication – works published/sent for publication or in progress:

i) D. Breaz, T. Grosan, F. Patrulescu, C. Revnic, Free convection in a square cavity filled by a bidisperse porous medium. Effect of internal heat generation, Acta Universitatis Apulensis, 71, 117-125, 2022.
ii) T. Grosan, F. Patrulescu, Natural convection in a bidisperse porous medium. Effect of internal heat generation, 14th Joint Conference on Mathematics and Computer Science (MaCS) 2022, November 24–27, Babeș–Bolyai University, Cluj-Napoca, Romania – presentation.
iii) F. O. Patrulescu, S. R. Pop, C. Berghian-Grosan, T. Grosan, I. Pop, Natural convection in a differentially heated cavity filled with a Brinkman bidisperse porous medium, Int. J. Num Methods Heat&Fluid Flow, submitted for publication.
iv) M. Kohr, R. Precup, Analysis of Navier-Stokes models for flows in bidisperse porous media, Nonlinear Analysis: Real World Applications, submitted for publication
v) T. Grosan, F. Patrulescu, C. Revnic, M. Sheremet, Non-Darcy free convection in a square cavity filled with a bidisperse porous medium, in progress
vi) T. Grosan, F. Patrulescu, I. Pop, Mixed convection from a vertical flat plate embedded in a bidisperse porous medium, in progress