Development of an intermittency transport equation for modeling bypass, natural and separation-induced transition

ABSTRACT

The objective of this paper is to propose a new intermittency transport equation that is naturally capable of capturing the effects of free-stream turbulence and pressure gradient on bypass and natural transition without need for any extra parameters/terms to take into account the free-stream turbulence and the pressure gradient. This new intermittency transport equation is obtained by derivation and, in it, only its production term is modeled via two empirical functions in order to detect the onset location of transition and to control the growth rate of transition process. Only one sensing parameter is used to detect the transition onset for both natural and bypass transition. For the purpose of not altering the original form of the base turbulence model, the effective intermittency factor is used to describe the separation-induced transition. The base turbulence model remains unmodified in conjunction with the effective intermittency factor as a regulator to control the net turbulent generation rate. For the evaluation of model performance, the modeled intermittency equation is tested against (1) the transitional boundary layer on a flat plate with zero and non-zero pressure gradients, (2) the transitional flow over a compressor blade with a laminar separation bubble, and (3) the transitional flow over a wind turbine airfoil at various angles of attack. The present results are also compared to those of the $\gamma$ transition model of Menter et al. [1] and those of the $\gamma -R{e}_{\theta }$ transition model of Langtry and Menter [2]. The evaluation results reveal that the new intermittency transport equation is capable of predicting the bypass, natural and separation-induced transition.

KEYWORDS:

• bypass transition
• natural transition
• separation-induced transition
• intermittency
• transition model

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was funded by King Mongkut’s University of Technology North Bangkok [Contract no. KMUTNB-62-KNOW-03].