dc.contributor.author Cheng, Wan dc.contributor.author Pullin, Dale I. dc.contributor.author Samtaney, Ravi dc.date.accessioned 2019-12-19T12:47:27Z dc.date.available 2019-12-19T12:47:27Z dc.date.issued 2019-08-19 dc.identifier.uri http://hdl.handle.net/10754/660704 dc.description.abstract We 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.sponsorship This 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.publisher arXiv dc.relation.url https://arxiv.org/pdf/1908.06577 dc.rights Archived with thanks to arXiv dc.title Large-eddy simulation and modeling of Taylor-Couette flow with an outer stationary cylinder dc.type Preprint dc.contributor.department Fluid and Plasma Simulation Group (FPS) dc.contributor.department Mechanical Engineering Program dc.contributor.department Physical Science and Engineering (PSE) Division dc.eprint.version Pre-print dc.contributor.institution Graduate Aerospace Laboratories, California Institute of Technology, CA, 91125, USA dc.identifier.arxivid 1908.06577 kaust.person Cheng, Wan kaust.person Samtaney, Ravi refterms.dateFOA 2019-12-19T12:49:26Z kaust.acknowledged.supportUnit Cray XC40 kaust.acknowledged.supportUnit KAUST baseline research kaust.acknowledged.supportUnit Shaheen
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