Laminar-turbulent transition
Encyclopedia
The process of a laminar boundary layer
becoming turbulent is known as boundary layer transition. This process is an extraordinarily complicated process which at present is not fully understood. However, as the result of many decades of intensive research, certain features have become gradually clear, and it is known that the process proceeds through a series of stages.
The second stage of the process, is the exponential growth of the few unstable disturbances. Since this stage is linear, it can be well-described by linear stability theory by following the most unstable mode. It is generally accepted that for subsonic
incompressible boundary layers, these initial instabilities which cause transition and ultimately lead to turbulent flow, take the form of Tollmien–Schlichting waves.
In the third stage, the amplitudes of the disturbances now become large enough to introduce non-linearity effects. In low Reynolds number flows, the initial amplitude of the disturbances are insufficient to cause immediate transition
. These waves must first develop within the boundary layer over a finite distance to trigger non-linear effects characteristic of the transition process. Here the uniform spanwise mean flow begins to become modulated by the non-linear interaction of the disturbances. In this third phase, the mean boundary layer profile now begins to become distorted and the boundary layer thickness varies strongly in the streamwise direction.
Due to the distortion of the boundary layer, inflexional mean profiles develop and a fourth stage is reached, where the boundary layer becomes unstable to three-dimensional high-frequency disturbances. The frequencies observed in this phase are typically an order-of-magnitude greater than those observed in the initial stages, and this is generally referred to as secondary instability. Finally, an explosive growth of these high-frequency disturbances initiates the fifth and final phase, the breakdown into turbulence.
Numerous experiments in recent decades have revealed that the extent of the amplification region, and hence the location of the transition point
on the body surface, is strongly dependent not only upon the amplitude and/or the spectrum of external disturbances but also on their physical nature. Some of the disturbances easily penetrate into the boundary layer and turn into Tollmien
-Schlichting
waves, whilst others do not. Consequently, the concept of boundary layer transition is a complex one and still lacks a complete theoretical exposition.
Usually, the Reynolds number of 500.000 it is taken as the transitional flux between laminar and turbulent boundary layer.
Boundary layer
In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...
becoming turbulent is known as boundary layer transition. This process is an extraordinarily complicated process which at present is not fully understood. However, as the result of many decades of intensive research, certain features have become gradually clear, and it is known that the process proceeds through a series of stages.
Transition stages
The initial stage of the natural transition process is known as the receptivity phase and consists of the transformation of external disturbances in the outer freestream flow over the boundary layer (such as freestream turbulence, surface roughness, acoustic noise etc.) into internal instability oscillations within the boundary layer. Upon entering the boundary layer, a wide spectrum of disturbances are present. Many of these disturbances decay, however, and only a limited number become amplified with further downstream development.The second stage of the process, is the exponential growth of the few unstable disturbances. Since this stage is linear, it can be well-described by linear stability theory by following the most unstable mode. It is generally accepted that for subsonic
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
incompressible boundary layers, these initial instabilities which cause transition and ultimately lead to turbulent flow, take the form of Tollmien–Schlichting waves.
In the third stage, the amplitudes of the disturbances now become large enough to introduce non-linearity effects. In low Reynolds number flows, the initial amplitude of the disturbances are insufficient to cause immediate transition
Laminar-turbulent transition
The process of a laminar boundary layer becoming turbulent is known as boundary layer transition. This process is an extraordinarily complicated process which at present is not fully understood...
. These waves must first develop within the boundary layer over a finite distance to trigger non-linear effects characteristic of the transition process. Here the uniform spanwise mean flow begins to become modulated by the non-linear interaction of the disturbances. In this third phase, the mean boundary layer profile now begins to become distorted and the boundary layer thickness varies strongly in the streamwise direction.
Due to the distortion of the boundary layer, inflexional mean profiles develop and a fourth stage is reached, where the boundary layer becomes unstable to three-dimensional high-frequency disturbances. The frequencies observed in this phase are typically an order-of-magnitude greater than those observed in the initial stages, and this is generally referred to as secondary instability. Finally, an explosive growth of these high-frequency disturbances initiates the fifth and final phase, the breakdown into turbulence.
Numerous experiments in recent decades have revealed that the extent of the amplification region, and hence the location of the transition point
Transition point
In the field of fluid dynamics the point at which the boundary layer changes from laminar to turbulent is called the transition point. Where the boundary layer becomes turbulent, drag due to skin friction is relatively high. As speed increases, the upper surface transition point tends to move...
on the body surface, is strongly dependent not only upon the amplitude and/or the spectrum of external disturbances but also on their physical nature. Some of the disturbances easily penetrate into the boundary layer and turn into Tollmien
Walter Tollmien
Walter Tollmien was a German fluid dynamics engineer.-Life:Walter Tollmien studied from the winter semester 1920–1921 mathematics and physics with Ludwig Prandtl in Göttingen and then from 1924 onwards worked under Prandtl at Kaiser Wilhelm Institute...
-Schlichting
Hermann Schlichting
Hermann Schlichting was a German fluid dynamics engineer.-Life and work:Hermann Schlichting studied from 1926 till 1930 mathematics, physics and applied mechanics at the University of Jena, Vienne and Göttingen...
waves, whilst others do not. Consequently, the concept of boundary layer transition is a complex one and still lacks a complete theoretical exposition.
Usually, the Reynolds number of 500.000 it is taken as the transitional flux between laminar and turbulent boundary layer.