- Open Access
- Access by Xinjiang University
Triple-deck analysis of the steady flow over a rotating disk with surface roughness
Phys. Rev. Fluids 6, 014103 – Published 19 January, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.014103
Abstract
The effect of surface roughness on the steady laminar flow induced by a rotating disk submerged by fluid otherwise at rest is investigated here theoretically and numerically. A theory is proposed where a triple-deck analysis is applied leading to a fast evaluation of the steady-flow modification due to the rough surface. The theory assumes that the roughness is much smaller than the boundary-layer height and is characterized by a significantly longer length scale (slender roughness). Only the leading-order correction is developed here, corresponding to a velocity-field correction that is linear with the roughness height. The proposed theory neglects some curvature terms (here partially accounted by means of a stretching of the radial coordinate and of a scaling of the dependent variables). Numerical simulations performed with different roughness geometries (axisymmetric roughness, radial grooves, and localized bumps) have been used to validate the theory. Results indicate that the proposed theory leads to a good quantification of the flow modifications due to surface roughness at a very low computational cost. A demonstration of the capabilities of the theory is finally proposed where the statistical effects on the flow due to a random (but statistically known) roughness distributed on the surface of a rotating disk are characterized.
Physics Subject Headings (PhySH)
Article Text
References (21)
- T. von Kármán, Über laminare und turbulente Reibung, Z. Angew. Math. Mech. 1, 233 (1921).
- N. Gregory, J. T. Stuart, and W. S. Walker, On the stability of three dimensional boundary layers with application to the flow due to a rotating disk, Philos. Trans. R. Soc. London 248, 155 (1955).
- M. R. Malik, The neutral curve for stationary disturbances in rotating-disk flow, J. Fluid Mech. 164, 275 (1986).
- T. C. Corke and K. F. Knasiak, Stationary traveling crossflow mode interactions on a rotating disk, J. Fluid Mech. 355, 285 (1998).
- E. Appelquist, S. Imayama, P. H. Alfredsson, P. Schlatter, and R. J. Lingwood, Linear disturbances in the rotating-disk flow: A comparison between results from simulations, experiments and theory, Eur. J. Mech. B/Fluids 55, 170 (2016).
- R. J. Lingwood, Absolute instability of the boundary layer on a rotating disk, J. Fluid Mech. 299, 17 (1995).
- T. Corke, E. H. Matlis, and H. Othman, Transition to turbulence in rotating-disk boundary layers-convective and absolute instabilities, J. Eng. Math. 57, 253 (2007).
- M. Miklavčič and C. Y. Wang, The flow due to a rough rotating disk, Z. Angew. Math. Phys. 55, 235 (2004).
- M. S. Yoon, J. M. Hyun, and J. S. Park, Flow and heat transfer over a rotating disk with surface roughness, Int. J. Heat Fluid Flow 28, 262 (2007).
- S. J. Garrett, A. J. Cooper, J. H. Harris, M. Özkan, A. Segalini, and P. J. Thomas, On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness, Phys. Fluids 28, 014104 (2016).
- A. J. Cooper, J. H. Harris, S. J. Garrett, M. Özkan, and P. J. Thomas, The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer, Phys. Fluids 27, 014107 (2015).
- B. Alveroglu, A. Segalini, and S. J. Garrett, The effect of surface roughness on the convective instability of the bek family of boundary-layer flows, Eur. J. Mech. B/Fluids 56, 178 (2016).
- A. Segalini and S. J. Garrett, On the non-parallel instability of the rotating-sphere boundary layer, J. Fluid Mech. 818, 288 (2017).
- A. Segalini and S. Camarri, Flow induced by a rotating cone: Base flow and convective stability analysis, Phys. Rev. Fluids 4, 084801 (2019).
- F. T. Smith, R. I. Sykes, and P. W. M. Brighton, A two-dimensional boundary layer encountering a three-dimensional hump, J. Fluid Mech. 83, 163 (1977).
- A. H. Nayfeh, Triple-deck structure, Computers Fluids 20, 269 (1991).
- A. Segalini, J. D. Rüedi, and P. A. Monkewitz, Systematic errors of skin-friction measurements by oil-film interferometry, J. Fluid Mech. 773, 298 (2015).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series - 55 (National Bureau of Standards, Washington DC, 1972).
- www.freefem.org.
- https://nek5000.mcs.anl.gov.
- D. Xiu and G. Em Karniadakis, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, Computer Methods Applied Mechanics Engineering 191, 4927 (2002).
