0
Research Papers

Differential Equation Specification of Integral Turbulence Length Scales

[+] Author and Article Information
Richard J. Jefferson-Loveday

e-mail: rjj32@cam.ac.uk

Paul G. Tucker, V. Nagabhushana Rao

Whittle Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge, CB3 ODY, UK

John D. Northall

Rolls-Royce, PLC,
Derby, DE24 8BJ, UK

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received April 10, 2012; final manuscript received August 16, 2012; published online March 25, 2013. Editor: David Wisler.

J. Turbomach 135(3), 031013 (Mar 25, 2013) (8 pages) Paper No: TURBO-12-1030; doi: 10.1115/1.4007479 History: Received April 10, 2012; Revised August 16, 2012

A Hamilton–Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee–Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in re-attachment length is improved by 180% compared with the steady RANS k-ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case, the HJ–NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Contours of vorticity magnitude at two cross-stream locations for high-order LES calculation

Grahic Jump Location
Fig. 2

Schematic of wake-flow behind cube

Grahic Jump Location
Fig. 3

Schematics of case (I) and case (II)

Grahic Jump Location
Fig. 4

Contour plots (a) standard wall distance, (b) L˜ distribution

Grahic Jump Location
Fig. 5

Length scales along cylinder centerline, standard wall distance: dashed line, L˜ distribution: solid line

Grahic Jump Location
Fig. 6

Cavity length scale contours (a) standard wall distance, (b) L˜ distribution

Grahic Jump Location
Fig. 7

Vector plots of cylinder wake region (a) k-ω, (b) time averaged URANS SA, (c) HJ–NK (d) experimental measurements [14]

Grahic Jump Location
Fig. 8

Centerline velocity versus axial distance for URANS-SA: dotted curve, Menter BL model: dashed curve, Wilcox k-ω model: dashed-dotted curve and HJ–NK model: solid curve, Exp [14]: ○

Grahic Jump Location
Fig. 9

Mean velocity at x/D = 1.0, key as in Fig. 8

Grahic Jump Location
Fig. 10

Streamlines for URANS-SA flow field

Grahic Jump Location
Fig. 11

Comparison of u/U, v/U, and −u′v′/U2, experimental measurements of Ref. [15]: ○ LES: solid curve

Grahic Jump Location
Fig. 12

LES instantaneous vorticity magnitude contour plots at different time moments for case (II)

Grahic Jump Location
Fig. 13

Comparison of u/U, experimental measurements of Ref. [15]: ○, RANS-SA: dashed curve, HJ–NK: solid curve, k-ω: dashed-dotted curve, Menter BL: dashed-double dotted curve

Grahic Jump Location
Fig. 14

Comparison of v/U, experimental measurements of Ref. [15]: ○, RANS-SA: dashed curve, HJ–NK: solid curve, k-ω: dashed-dotted curve, Menter BL: dashed-double dotted curve

Grahic Jump Location
Fig. 15

Streamline plots of cavity mean flow field

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In