The science of double glazed windows: Valuable insight on the complex physics of natural convection flows in a differentially heated cavity


Buoyancy-driven flows have been a topic of interest in fluid dynamics for decades due to their presence in numerous industrial configurations such as passive cooling processes. Since the early work of Batchelor in the mid-twentieth century, buoyancy-driven flows, especially in heated cavities, have remained a challenging research area. Over the years, three distinct flow regimes were identified: steady laminar, unsteady laminar and fully turbulent. Most of the computational and experimental research work has been focused on the mapping of transitions between these flow regimes as a function of aspect ratio, Rayleigh number and Prandtl number. However, efficient characterization of the turbulent flow regime at high Rayleigh number, which is the most relevant case for industrial applications, has remained a great challenge due to the inappropriate computational resources.

Taking advantage of the growth in the computing technology, some simulations of turbulent flows in differentially heated cavities at increasingly higher Rayleigh numbers have been recently published. However, high order statistical data that could help the turbulence modeling community remain scarce.

To this note, Imperial College London scientists: Dr. Frederic Sebilleau, Professor Raad Issa and Dr. Simon Walker together with Dr. Sylvain Lardeau at CD-Adapco carried out direct numerical simulations on a heated square cavity. Specifically, a square cavity was chosen considering the fact that its configuration was well known for producing the largest degree of discrepancy between turbulence models. The numerical simulation involved using a Prandtl number of 0.71 and Rayleigh number ranging between 108 – 1011. In order to provide insightful data for the turbulence modelling community, they presented the full budgets i.e. Reynold stresses, temperature variances, and turbulent heat fluxes budgets for all the Rayleigh number covered during the experiment. Their work is currently published in International Journal of Heat and Mass Transfer.

The authors observed that the budgets were influenced by the displacement of the temperature variance towards the inner boundary layer. Consequently, a negative production region that increased with the increase in the Rayleigh number was initiated in the budget due to the behavioral difference between the velocity and thermal boundary layers.

In summary, the research team was the first to perform a direct numerical simulation of a differentially heated square cavity at higher Rayleigh number with statistical data that can help understanding the limitations of current turbulence models to simulate buoyancy driven flows. It also gives reference data that will be useful to assess the performance of new turbulence models. The database associated to their paper has been made available to the scientific community on the ERCOFTAC classic database and was chosen as the benchmark case of the 16th SIG15 ERCOFTAC workshop, gathering most of the academic and industrial turbulence modelling research groups in Europe, held in October 2019 in Slovenia. This database will be used again at the next SIG15 ERCOFTAC workshop in France in 2021.

The science of double glazed windows: Valuable insight on the complex physics of natural convection flows in a differentially heated cavity - Advances in Engineering

About the author

Dr Sebilleau gained an Imperial College MSc before joining the Nuclear Engineering Group lead by Dr Simon Walker to complete his PhD in 2016. Under the supervision of Dr Raad Issa and Dr Simon Walker, his research at Imperial focused on the numerical simulation of buoyancy driven flows. This work has led to the creation of a DNS database that has been recognised as a major scientific contribution by the turbulence modelling community. This data has been made available on the ERCOFTAC classic database and has been chosen to be the benchmark case for the next ERCOFTAC workshop of the Turbulence Modelling Special Interest Group.

In 2016, soon after completing his PhD, Dr Sebilleau took over the family owned consultancy company IMF Ingenierie. He is now developing the company towards his area of expertise: high-end numerical simulation tools put to the service of engineering. At the same time, Dr Sebilleau is an academic visitor at Imperial College in the Nuclear Engineering group where he also gives guest lectures. He was recently awarded the the Margaret Fishenden Centenary Memorial Prize for the best PhD thesis over the previous five year period in the Imperial College Mechanical Engineering department.

About the author

Dr. Issa has a Bachelor degree (1969) in Mechanical Sciences from Cambridge University and M.Sc. (1970) and Ph.D. (1974) degrees in Mechanical Engineering from Imperial College. After working in consulting in the UK and USA he rejoined Imperial College on the academic staff, where he is now Professor of Practice in Computational Fluid Dynamics. Dr Issa has been active in research in computational modelling of single and multiphase flow since 1970 and has published over 100 papers in the fields. He was one of the founders and a director (from 1987 to 2000) of Computational Dynamics Ltd. the company that produced the STAR-CD, CFD code (now STAR CCM+).

About the author

Dr Walker has a Bachelor degree (1977) and PhD in Nuclear Engineering (1980) from Imperial College. He rejoined Imperial College as a lecturer after a few years working in industry in the UK and Canada. He is now Head of the Nuclear Research group in the Mechanical Engineering department of Imperial College. This group is composed of 5 academics and about 30 PhD students and post-doctoral researchers working on various aspects of Nuclear power.

Dr Walker has published over 150 technical publications with a particular emphasis on thermal-hydraulics. This has lead him to a number of advisory roles for governmental institutions and companies involved in Nuclear Engineering around the world.

About the author

Dr Sylvain Lardeau is currently a principal developer for the commercial CFD software Siemcenter STAR-CCM+, more specifically in charge of turbulence and turbulence modelling. He obtained his PhD from the University of Poitiers in 2001, under the supervision of Profs. Lamballais and Bonnet. He was research associate at Imperial College London from 2002 to 2004, working on turbulence and transition modeling with Prof. Leschziner in the department of Aeronautics. From 2005 to 2006, he was responsible of CFD methodologies, for external aerodynamics, at PSA Peugeot-Citroen, and then from mid-2006, he went back to Imperial College London as manager of the Wing Technologies Center.

Sylvain Lardeau joined CD-adapco in 2011, to work on turbulence modeling in the development group. He is principal software developer for Siemcenter STAR-CCM+ since 2014.


Sebilleau, F., Issa, R., Lardeau, S., & Walker, S. (2018). Direct Numerical Simulation of an air-filled differentially heated square cavity with Rayleigh numbers up to 1011International Journal of Heat and Mass Transfer, 123, 297-319.

Go To International Journal of Heat and Mass Transfer

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