Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) T-S Leu May. 3, 2018 Chapter 5: Phenomena of laminar-turbulent boundary layer transition (including free shear layers) Reading assignments: 1. White, F. M., Viscous fluid flow. McGraw-Hill, 1974, Chapter 5-4~5-5. 2. Schubauer, G. B., and Skramstad, H. K., Laminar-boundary-layer oscillations and transition on a flat plate. NACA Report No. 909, 1948. 3. Emmons, H. W., The laminar-turbulent transition in a boundary layer- Part I, Journal of the Aeronautical Sciences, Vol. 18, pp. 490-498, 1951. 4. An Album of Fluid Motion, ed. M. van Dyke, 1982. The process of laminar-turbulent transition is very complex, featuring the non-linear growth of disturbances, cascading different stages of flow evolutions. In this chapter, examples are given concerning the laminarturbulent transition phenomena of boundary layer, jet, mixing layer and wake flows. 1
Tollmien-Schlichting wave Frank White, Viscous fluid flow, third edition, P377 Fig 5 28 (a) Linear Stability Theory Linear instability analysis can only predict the laminar boundary layer for Re<Re crit. It doesn t predict the onset of turbulence if Re>Re crit. 2
Historical Review of Transition Process 50y 20y 10y -Laminar-turbulent transition in a turbulent boundary layer Laminar-turbulent transition is influenced by a number of factors. For instance, 1. Pressure gradient: boundary layers with adverse pressure gradient are much more unstable than zero pressure gradient boundary layer. 2. Disturbance level of the freestream (Bypass Transition): higher level the free stream turbulence intensity, shorter is the distance for on-set of flow instability and transition. 3. Surface roughness: higher the surface roughness, shorter is the distance for onset of flow instability and transition. 3
Hot-wire measurement of Schubauer and Skramstad (1947) regarding the boundary-layer transition Wind Tunnel of Transition Experiment ( Schubauer & Skramstad 1947) T. I.=0.032% settling chamber Disturbances development is critically depending on the free stream turbulence and the roughness of the wall surface. Experiments were made in the 4.5-foot wind tunnel at the National Bureau of Standards. The area reduction from settling chamber to test section is 7.1:1. The guide vanes ahead of the settling chamber were made finer than the others in order to reduce the scale of the turbulence and to permit as much reduction in turbulence through decay as possible. Since directional fluctuations in the horizontal plane were found to be large, closely spaced straighteners were placed at right angles to and on top of the fine guide vanes. This combination was in effect a honeycomb and resulted in great improvement in the steadiness of the stream. Further reduction of turbulence was obtained by installing damping screens in the settling chamber. Without screens, the turbulence in the test section was 0.27 percent at 100 ft per second and, with seven screens was 0.032 percent. 4
ABRI Wind Tunnel T. I.=0.3%~0.4% 5
Cited from Schubauer and Skramstad (1948), the last paragraph in Conclusion: It is possible that boundary-layer oscillations may arise from internal disturbances as well as from external disturbances- that is, from surface irregularities and vibration of the surface. A randomly distributed small roughness may produce effects similar to small amounts of turbulence in the air stream. Small ridges or waves in the surface may start oscillations when the spacing is near some wavelength. Vibration of the surface, like sound, may produce oscillations, especially when the frequency is near some amplified oscillation frequency. An investigation of these and other phases of the problem will throw additional light on the important problem of transition. 6
Overall Picture of Natural Transition Process 7
The observations of Emmons spots (Emmons, 1951, p. 491) A New Observation from water table visualization: The mechanics of transition could be clearly observed, since the turbulent motion of the thin layer of water disturbed the water surface and, hence altered the appearance of the surface in both reflected and transmitted light. Fig. 4. At some instant and at some point (both random), a tiny spot of turbulence appeared at S. The spot was small and of irregular shape. These tiny turbulent origins will be called turbulent sources. Sources could be increased in density and frequency at a given location on the plate either by increase the water velocity or adding disturbances. 8
An Album of Fluid Motion, ed. M. van Dyke, 1982 9
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Bypass Transition In many fluid flows, transition of boundary layers from laminar to turbulence is forced by free-stream perturbations. This phenomenon is called Bypass Transition https://engineering.jhu.edu/zaki/research/bypass-transition/ The clip below shows iso-surfaces of streamwise velocity perturbations, and vertical plane shows the free-stream turbulence. The flow is initially laminar and characterized by long characterized by long streamwise perturbations the boundary layer streaks also known as Klebanoff distortions. A turbulent spot is observed downstream, followed by the fully turbulent boundary layer. The inception of turbulent spots or patches is sporadic, both in space and time. Its frequency and propensity dictate the length of the transitional region. https://engineering.jhu.edu/zaki/research/bypass-transition/ 11
Researchers have also developed novel structure identification and tracking algorithms that enable us to examine the entire temporal and spatial evolution of the pre-transitional streaks, and to extract the particular streaks that break down into spots. These streaks are generally much high amplitude than the rest of the population, and are often two- to three-times higher in magnitude than the average streak. https://engineering.jhu.edu/zaki/research/bypass-transition/ Beyond the secondary instability of the steaks, the emergent turbulent spots can be tracked as well. This enable us to examine the development of turbulence and the dynamics of the laminar-turbulence interface. The video below shows the spot tracking as the turbulent patch expands and occupies a larger volume within larger volume within the boundary layer, and ultimately merge with the with the downstream fully-turbulent flow. https://engineering.jhu.edu/zaki/research/bypass-transition/ 12
To aid in transition modeling, researchers have performed detailed direct numerical simulations (DNS) of bypass transition over a wide range of conditions. These computational experiments were only possible through the development and implementation of efficient, scalable algorithms. The example below compares transition onset at different levels of streamwise pressure gradient, starting with a favorable, then zero and finally two finally two progressively more adverse pressure gradients. favorable zero adverse pressure gradients https://engineering.jhu.edu/zaki/research/bypass-transition/ Forcing (Artificial) Perturbation An Album of Fluid Motion, ed. M. van Dyke, 1982 13
An Album of Fluid Motion, ed. M. van Dyke, 1982 Development of Spanwise Vorticity (T-S Waves) 14
-Turbulent boundarylayer flow An Album of Fluid Motion, ed. M. van Dyke, 1982. Laminar-turbulent transition in a jet or mixing layer -linear instability: this shear flow is always unstable -vortex pairing: large scale flow structures (coherent flow structures), every effective for momentum mixing -self-preserving region: the normalized velocity profile and turbulent intensity profiles are invariant downstream 15
Mixing Layer Vortex Pairing Mechanism the mechanism of turbulent mixing-layer growth at moderate Reynolds number A mixing layer is formed by bringing two streams of water, moving at different velocities. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. Vorticity contours of a two-dimensional subsonic mixing layer with velocity ratio 0.6, density ratio 1, Reynolds number 50000. Computed with parabolized stability equations using 16 frequency modes. Aaron Towne, 2011. https://www.youtube.com/watch?v=r5xv5lt1edi 16
-Turbulent mixing layers at different Reynolds numbers An Album of Fluid Motion, ed. M. van Dyke, 1982. 17
-Jet flow at low Reynolds number An Album of Fluid Motion, ed. M. van Dyke, 1982. -Jet of high Reynolds number (Hover Dam, U. S.) 18
-subsonic and supersonic turbulent jet flows An Album of Fluid Motion, ed. M. van Dyke, 1982. Laminar-turbulent transition in a wake flow -linear instability: -vortex shedding: -turbulent wake 19
-Comparison of turbulent wakes at high and low Reynolds numbers An Album of Fluid Motion, ed. M. van Dyke, 1982. -Turbulent wake in the far downstream region An Album of Fluid Motion, ed. M. van Dyke, 1982. 20