# Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain

## Abstract

Two-dimensional (2D) and three-dimensional (3D) numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out in the present work. The Boussinesq approximation is made in the formulation of the problem, and Neumann boundary conditions for temperature and concentration are adopted, respectively, on vertical and horizontal walls of the cavity. The used numerical method is based on the control volume approach, with the third order quadratic upstream interpolation scheme in approximating the advection terms. A semi implicit method algorithm is used to handle the velocity-pressure coupling. To avoid the excessively high computer time inherent to the solution of 3D natural convection problems, full approximation storage with full multigrid method is used to solve the problem. A wide range of the controlling parameters (Rayleigh-Darcy number Ra, lateral aspect ratio Ay, Lewis number Le, and the buoyancy ration N) is investigated. We clearly show that increasing the depth of the cavity (i.e., the lateral aspect ratio) has an important effect on the flow patterns. The 2D perfect parallel flows obtained for small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motionmore »

- Authors:

- Laboratoire LTPMP, Fac GMGP, USTHB, BP 32, Alia, Bab Ezzouar, Algiers (Algeria)
- LMT-ENS Cachan, 61 av. du président Wilson F-94235 Cachan Cedex (France)

- Publication Date:

- OSTI Identifier:
- 22311236

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ADVECTION; ALGORITHMS; APPROXIMATIONS; ASPECT RATIO; BOUNDARY CONDITIONS; CAVITIES; COMPUTERIZED SIMULATION; COMPUTERS; COUPLING; DIFFUSION; FLOW MODELS; INTERPOLATION; LEWIS NUMBER; NATURAL CONVECTION; POROUS MATERIALS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; VELOCITY; WALLS

### Citation Formats

```
Mimouni, N., Chikh, S., Rahli, O., and Bennacer, R., E-mail: Rachid.Bennacer@ens-cachan.fr.
```*Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain*. United States: N. p., 2014.
Web. doi:10.1063/1.4886801.

```
Mimouni, N., Chikh, S., Rahli, O., & Bennacer, R., E-mail: Rachid.Bennacer@ens-cachan.fr.
```*Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain*. United States. doi:10.1063/1.4886801.

```
Mimouni, N., Chikh, S., Rahli, O., and Bennacer, R., E-mail: Rachid.Bennacer@ens-cachan.fr. Tue .
"Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain". United States.
doi:10.1063/1.4886801.
```

```
@article{osti_22311236,
```

title = {Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain},

author = {Mimouni, N. and Chikh, S. and Rahli, O. and Bennacer, R., E-mail: Rachid.Bennacer@ens-cachan.fr},

abstractNote = {Two-dimensional (2D) and three-dimensional (3D) numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out in the present work. The Boussinesq approximation is made in the formulation of the problem, and Neumann boundary conditions for temperature and concentration are adopted, respectively, on vertical and horizontal walls of the cavity. The used numerical method is based on the control volume approach, with the third order quadratic upstream interpolation scheme in approximating the advection terms. A semi implicit method algorithm is used to handle the velocity-pressure coupling. To avoid the excessively high computer time inherent to the solution of 3D natural convection problems, full approximation storage with full multigrid method is used to solve the problem. A wide range of the controlling parameters (Rayleigh-Darcy number Ra, lateral aspect ratio Ay, Lewis number Le, and the buoyancy ration N) is investigated. We clearly show that increasing the depth of the cavity (i.e., the lateral aspect ratio) has an important effect on the flow patterns. The 2D perfect parallel flows obtained for small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complex flow pattern and the usually considered 2D parallel flow model cannot be applied.},

doi = {10.1063/1.4886801},

journal = {Physics of Fluids (1994)},

number = 7,

volume = 26,

place = {United States},

year = {Tue Jul 15 00:00:00 EDT 2014},

month = {Tue Jul 15 00:00:00 EDT 2014}

}