4.7 Article

A model for the effect of pressure gradient on turbulent axisymmetric wakes

期刊

JOURNAL OF FLUID MECHANICS
卷 837, 期 -, 页码 -

出版社

CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2017.864

关键词

general fluid mechanics; turbulent flows; wakes

资金

  1. EOS (Energie Ouest Suisse) Holding
  2. Swiss Federal Office of Energy [SI/501337-01]
  3. Swiss National Science Foundation [200021_172538]
  4. Swiss Innovation and Technology Committee (CTI) within the context of the Swiss Competence Center for Energy Research 'FURIES: Future Swiss Electrical Infrastructure'
  5. Swiss National Supercomputing Centre (CSCS) [s706]

向作者/读者索取更多资源

Turbulent axisymmetric wakes under pressure gradient have received little attention in the literature, in spite of their fundamental and practical importance, for example, in the case of wind turbine wakes over topography. In this paper, we develop an analytical framework to analyse turbulent axisymmetric wakes under different pressure gradient conditions. Specifically, we develop a model to predict how an arbitrary imposed pressure gradient perturbs the evolution of the zero-pressure-gradient wake. The starting point of the model is the basic mean conservation of the streamwise momentum equation. We take advantage of the self-similarity of the wake velocity deficit and the assumption that the ratio of the maximum velocity deficit to the wake width is independent of the pressure gradient; such an assumption is supported experimentally for planar wakes, and numerically for axisymmetric wakes in this study. Furthermore, an asymptotic solution for the problem is also derived. The problem is considered for both an axisymmetric strain and a planar strain. The inputs to the model are the imposed pressure gradient and the wake width in the zero-pressure-gradient case. To validate the model results, a set of large-eddy simulations (LES) are performed. Comparing the evolution of the maximum velocity deficit and the wake width, the model results and the LES data show good agreement. Similarly to planar wakes, it is observed that the axisymmetric wake recovers faster in the favourable pressure gradient compared with the adverse one.

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