Natural Transition of Boundary Layers—The Effects of Turbulence, Pressure Gradient, and Flow History

Abstract

Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient histories typical of turbomachinery blades without separation. Empirical relationships are proposed for the prediction of the start and end of transition, as well as the development of the boundary layer during transition. These relations are based on the recent measurements made with a hot-wire anemometer, and augmented, mainly for the start of transition, by results of previously reported research. Finally, these experimental relationships are used in conjunction with well established methods to predict the entire unseparated boundary layer. To utilize the prediction, all that is required is a knowledge of the free-stream turbulence level and the free-stream velocity distribution, which itself can be derived from potential flow theory.

Growth of boundary-layer streaks due to free-stream turbulence

“…The high-frequency disturbances therefore remain confined in the outer portion of the shear layer. As the breakdown mechanism is still unclear, prediction of transition subjected to free-stream turbulence for aeronautical and turbomachinery applications relies heavily on empirical models based mainly on experimental data [35,34,1].…”

Transition Modelling for Turbomachinery Flows

“…Based on boundary layer analysis a shape factor of 2.3 corresponds to a pressure gradient parameter ( θ ) of approximately 0.06. Since the majority of experimental data on transition in favorable pressure gradients falls within that range (see for example reference [17]) the relative error between momentum thickness and vorticity Reynolds number is not of great concern under those conditions.…”

“…However, the trend with experiments is that adverse pressure gradients reduce the transition momentum thickness Reynolds number. In practice, if a constant transition momentum thickness Reynolds number is specified, the transition model is not very sensitive to adverse pressure gradients and an empirical correlation such as that of AbuGhannam and Shaw [17] is necessary in order to predict adverse pressure gradient transition accurately. In fact, the increase in vorticity Reynolds number with increasing shape factor can actually be used to predict separation induced transition.…”

An experimental study on laminar-turbulent transition at high free-stream turbulence in boundary layers with pressure gradients

“…It also shows that rms amplitude is higher when Re is higher. According to Abu-Ghannam and Shaw [4], transition can be expressed in terms of Reynolds number based on the momentum thickness and the shape factor. For a certain flow condition, their paper shows that the transition onset is at the point where the shape factor starts decreasing.…”

“…This phenomenon was termed intermittency and later on, Kovasznay et al [3] introduced the intermittency factor to identify turbulence, so that it is one when the fluid is turbulent and zero otherwise. The effect of pressure gradients and turbulence levels on transition is best investigated by Abu-Ghannam and Shaw [4] proposing methods to calculate the momentum thickness Reynolds number for the start and the end of the transition zone, defined by them as the region in which the intermittency factor ranges between 0.25 and 0.75. Walker and Gostelow [5] carried out experiments under high turbulence levels and adverse pressure gradients and found that close to the wall region within the boundary layer, a turbulent pattern was found to be not much affected by the free-stream conditions.…”