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dc.contributor.authorCheng, Wan
dc.contributor.authorPullin, Dale I.
dc.contributor.authorSamtaney, Ravi
dc.date.accessioned2019-12-19T12:47:27Z
dc.date.available2019-12-19T12:47:27Z
dc.date.issued2019-08-19
dc.identifier.urihttp://hdl.handle.net/10754/660704
dc.description.abstractWe present wall-resolved large-eddy simulations (LES) of the incompressible Navier-Stokes equations together with empirical modeling for {turbulent} Taylor-Couette {(TC)} flow where the inner cylinder is rotating with angular velocity $\Omega_i$ and the outer cylinder is stationary. A simple empirical model of the turbulent, TC flow is developed consisting of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. The model is closed by a proposed scaling relation concerning the thickness of the wall layer on the inner cylinder. Model results include the Nusselt number $Nu$ (torque required to maintain the flow) and various measures of the wall-layer thickness as a function of both the Taylor {number} $Ta$ and $\eta$. These agree reasonably with experimental measurements, direct numerical simulation (DNS) and the present LES over a range of both $Ta$ and $\eta$. In particular, the model shows that, at fixed $\eta<1$, $Nu$ grows like $Ta^{1/2}$ divided by the square of the Lambert, (or Product-Log) function of a variable proportional to $Ta^{1/4}$. This cannot be represented by a power law dependence on $Ta$. At the same time the wall-layer thicknesses reduce slowly in relation to the cylinder gap. This suggests an asymptotic, very large $Ta$ state consisting of constant angular momentum in the cylinder gap with $u_\theta = 0.5\,\Omega_i\,R_i^2/r$, where $r$ is the radius, with vanishingly thin turbulent wall layers at the cylinder surfaces. An extension of the model to rough-wall turbulent wall flow at the inner cylinder surface is described. This shows an asymptotic, fully rough-wall state where the torque is independent of $Re_i/Ta$, and where $Nu\sim Ta^{1/2}$.
dc.description.sponsorshipThis work was partially supported by the KAUST baseline research funds of R.S.. The Cray XC40, Shaheen, at KAUST was utilized for all the reported LES.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/1908.06577
dc.rightsArchived with thanks to arXiv
dc.titleLarge-eddy simulation and modeling of Taylor-Couette flow with an outer stationary cylinder
dc.typePreprint
dc.contributor.departmentFluid and Plasma Simulation Group (FPS)
dc.contributor.departmentMechanical Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionGraduate Aerospace Laboratories, California Institute of Technology, CA, 91125, USA
dc.identifier.arxivid1908.06577
kaust.personCheng, Wan
kaust.personSamtaney, Ravi
refterms.dateFOA2019-12-19T12:49:26Z
kaust.acknowledged.supportUnitCray XC40
kaust.acknowledged.supportUnitKAUST baseline research
kaust.acknowledged.supportUnitShaheen


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