Transition Modelling - A Review

Rapport, 2006

This review article discusses the phenomenon of laminar to turbulence transition in general and transition due to elevated freestream disturbances in particular. The motivation of the study is primarily the increased demands from the gas turbine industry of accurate heat transfer predictions in high and low pressure turbines. In these devices the trends of the last decade, e.g. the development of smaller turbines and turbines with higher by-pass ratios (to reduce noise), lead to engines operating at lower Reynolds number conditions and, thus, delayed and larger transitional flow regions. Three different modes of transition are discussed--natural, by-pass and separation induced transition. Natural transition is (fortunately) not an issue in gas turbine design, nor suitable to statistical modelling, which indeed is the closure level the authors intend to adopt, and is therefore not dealt with in detail. By-pass and separation induced transition on the other hand are probably about equally important to gas turbine flows. The body of literature dedicated to the latter is, however, not as considerable as that dealing with by-pass transition. This is one of the reasons why this article sometimes is biased towards by-pass transition modelling. The other reason is that this is the transition mode best suited to be described with a statistical approach, which has tempted many authors to apply well established ideas from the vast field of turbulence modelling. After an introductory description of the different transition modes some early work on transition is discussed. The turbulent spot concept Emmons (1951), followed by a derivation of the Dhawan & Narasimha (1958) intermittency distribution, is of coarse included. With the introduction of intermittency, there was soon a need for a theoretical analogue to the experimental technique `conditional sampling', i.e. a measure to treat, or model, turbulent and laminar flow portions separately. Conditional averages were introduced by Libby (1974) and it was not long before full transport equations for the intermittency factor was derived. Discussed is also the prospect of using so called low Reynolds number modelling of both near wall turbulence and transition. Thereafter follows a description of two recent transition modelling approaches and the review ends with a section collecting numerous modelling attempts, ranging from simple algebraic correlations to complex transport equations for the intermittency factor, all aiming to improve predictions of the intriguing physics of transitional flows.