ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉〈img orientation="portrait" mimesubtype="gif" mimetype="image" position="float" type="simple" href="S0022112019007973_figAb" src="http://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0022112019007973/resource/name/S0022112019007973_figAb.gif?pub-status=live"〉〈/p〉〈/div〉 〈div data-abstract-type="normal"〉〈p〉By means of three-dimensional direct numerical simulations, we investigate the influence of the regular roughness of heated and cooled plates on the mean heat transport in a cylindrical Rayleigh–Bénard convection cell of aspect ratio one. The roughness is introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The considered Prandtl number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 equals 1, the Rayleigh number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 varies from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the number of rings on each plate is 1, 2, 4, 8 or 10, the height of the rings is varied from 1.5 % to 49 % of the cylinder height and the gap between the rings is varied from 1.5 % to 18.8 % of the cell diameter. Totally, 135 different cases are analysed. Direct numerical simulations show that with small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and wide roughness rings, a small reduction of the mean heat transport (the Nusselt number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) is possible, but, in most cases, the presence of the heated and cooled obstacles generally leads to an increase of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, compared to the case of classical Rayleigh–Bénard convection with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 versus 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 scaling first increases with growing 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case.〈/p〉〈/div〉