Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-29T14:54:33.163Z Has data issue: false hasContentIssue false
  • English
  • Français

The inverse problem for incompressible internal flows

Published online by Cambridge University Press:  04 July 2016

P. Laidler  and
D. F. Myring
P. Laidler
Affiliation:
Department of Mathematics
D. F. Myring
Affiliation:
Department of Aeronautical and Mechanical Engineering, University of Salford
Get access Rights & Permissions [Opens in a new window]

Extract

A duct design algorithm is presented by which duct wall shapes are produced directly from prescribed wall friction velocity distributions. The method is based on matched axisymmetric core flow and integral boundary layer solutions in which the flow is assumed to be in viscid in the core, turbulent in the boundary layer and incompressible throughout. An inverse boundary layer analysis is based on Coles profiles coupled with momentum and entrainment equations. Wall friction velocity is used as the major boundary condition which leads to the calculation of the required core velocity at the boundary layer edge. This velocity distribution is simultaneously employed as the major boundary condition in an inverse core flow calculation which is based on an inverted form of the Stokes-Beltrami equation. The displacement surface method is used to match boundary layer and core solutions which together lead to a predicted duct shape. Numerical results are presented, some of which include separated boundary layer flows. An assessment of the influence of wall friction velocity distribution on duct shape and wall pressure field is included.

Type
Rolls-Royce European Symposium 1983
Information
The Aeronautical Journal , Volume 88 , Issue 872 , February 1984 , pp. 38 - 45
Copyright
Copyright © Royal Aeronautical Society 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Coles, D. J. Fluid Mech, 1956, 1, 191–226.Google Scholar
Green, J. E., Weeks, D. J. and Brooman, J. W. F. RAE TR-72231, 1973.Google Scholar
Head, M. R. ARC R & M 3152, 1960.Google Scholar
Lighthill, M. J. ARC R & M 2112, 1945.Google Scholar
Livesey, J. L. and Heravi, M. AIAA 20th Aerospace Sciences Meeting, Florida, 1982. Paper No AIAA-82-0132.Google Scholar
Lock, R. C. and Firmin, M. C. P. Numerical Methods in Aeronautical Fluid Dynamics. Academic Press (Roe, P. L. ed.) 1982. 337–430.Google Scholar
Mikhail, M. N. AIAA J. 1979, 17, no 5, 471.Google Scholar
Pratap, V. S. and Spalding, D. B. Int. J. Heat Mass Transfer. 1976, 19, 1183.Google Scholar