Natural Convection in a Two-Dimensional Cell Filled with a Porous Medium: A Direct Numerical Simulation Study

ABSTRACT

Natural convection in a two-dimensional cell filled with a porous medium was investigated using two direct numerical simulation (DNS) methods. The cell was heated at the lower wall and cooled at the upper wall. The buoyancy force was modeled by the Boussinesq approximation. The Rayleigh numbers ranged from 50  to  20, 000. The DNS results from both DNS methods indicate the linear relationship between Nu and Ra. However, the numerical methods have some effects on the small flow structures. The fish bone structures are clearly identified by the space-time plots of the temperature in a slice close to the boundary layer. Four motion patterns showing mega-plumes and proto-plumes can be observed in the fish bone structures. The characteristic length, velocity, and temperature scales in the boundary layer were studied based on the DNS results.

Acknowledgment

The authors gratefully acknowledge the support of this study by the DFG (Deutsche Forschungsgemeinschaft).

Additional information

Notes on contributors

Patrick Udo Kränzien

Patrick Udo Kränzien is a master student on “Energy- and Environmental Engineering” at Hamburg University of Technology, Germany. His bachelor thesis was about decentralized solutions for phosphor retention in porous filter systems. He has also participated in the project of “Near Field Radiative Heat Transfer.” He is currently working on his master project which is about interfacial mass transfer of single deformable bubbles. His research interests include scientific computing, direct numerical simulation, interfacial mass transfer, natural convection within porous media, mirco- and nano-scale thermal phenomena, retention and recovery of phosphor in decentralized waste-water systems based on porous media substrates, etc.

Yan Jin

Yan Jin is a Privatdozent (senior lecturer) at Institute of Engineering Thermodynamics, Hamburg University of Technology. He received his Ph.D. at Department of Thermal Engineering, Tsinghua University in 2002. In 2014, he passed his Habilitation (professor qualification in Germany) in Thermo-fluid Dynamics at Hamburg University of Technology. In 2016, he was awarded the title of “DFG-Heisenberg Fellow.” His teaching and research interests cover broadly fluid mechanics, turbulence, heat transfer, thermodynamics, and turbomachinery.