Publication Date:
2019
Description:
〈div data-abstract-type="normal"〉〈p〉Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor–Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (〈span〉Phys. Fluids〈/span〉, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline1.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉(corresponding to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline2.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉) to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline3.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline4.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉). We focus on the influence of the roughness height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline5.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline6.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 up to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline7.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline8.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 and by the friction factor 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline9.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline10.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 is calculated to be 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline11.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline12.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (〈span〉VDI-Forsch.〈/span〉, vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline13.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉 with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline14.gif"〉
〈span data-mathjax-type="texmath"〉
〈/span〉
〈/span〉〈/span〉.〈/p〉〈/div〉
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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