I know for boundary-layer, adverse pressure gradient (dp/dx>0) is a necessary condition for flow separation. Also, when the wall-friction becomes zero ( τw=µ ∂u/ ∂y=0) , the flow separates, and turbulence happens. Am I right? Are these criteria, only for boundary-layer, or for any fluid-flow?
Separation of a streamline does not automatically implies turbulence...
Yes. But it can be applied to all fluid flow. B.L may be also caused due to wave, acoustic noise, pressure fluctuations.
Dear Saeb,
maybe this can help you
https://www3.nd.edu/~powers/vv.presentations/reed.pdf
Franco
dear Manigandan and dear Franco. Thank you for your answers. Saeb.
Separation of a streamline does not automatically implies turbulence...
Transition to turbulence can occur even there is no adverse pressure or zero friction. Adverse pressure is a necessary condition for separation not Transition however, separation can lead to turbulence. The condition of zero friction is an induced condition when boundary layer separates not vice versa.
In my ResearchGate section I have uploaded material on turbulence and other fluid flow matters that explain the mechanism of turbulent flow development. You may be helped by its use.
Reynold number greater than or equal to 2150 in actual sense...
Reynolds number is the main parameter for the flow to be changed from laminar to turbulent. Other parameters like adverse pressure gradient, streamline curvature, free stream turbulence, heat transfer rate, surface roughness and flow divergence or convergence may affect the flow condition.
In the most general sense, we can obtain the conditions for the transition to turbulence by finding the bifurcation points of the modal amplitude equation. The literature on this subject is extensive. One of the interesting aspects of this approach is the connection with the theory of pattern formation. A good discussion was presented by van Hecke and Hohenberg in the article "Amplitude equations for pattern forming systems”
http://wwwhome.lorentz.leidenuniv.nl/~saarloos/Papers/altenberg.pdf
Please pay attention to the disclaimer at the beginning, which states that the document is dated; I believe, however, that the paper is very useful as a general illustration. The advantage of the bifurcation analysis is that we can obtain an explicit algebraic expression for the transition to turbulence, which includes the main parameters characterizing the system (geometry, velocity, viscosity, heat flow).
A good illustration of topological methods that can be used to analyze the departure from laminar flow is shown in Figs. 3, 5, 8 and 10 of the article: "Topological fluid mechanics of the formation of the Karman-Vikhr street"
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F5A1FF5886583B755A428C913DA38654/S0022112016007928a.pdf/div-class-title-topological-fluid-mechanics-of-the-formation-of-the-karman-vortex-street-div.pdf
As many fellow researchers have pointed out, there are quiet a few phenomena's which could lead to turbulent flow (by separation, adverse pressure gradient, zero friction, surface roughness & ...) But non of the mentioned can be seen as a definite criteria to determine whether the flow is laminar or turbulent.
The best criteria used so far for determination of turbulent flow, is the actual Reynolds number in the local region; at least as far as i know
I would point out that we can talk about transition from laminar to turbulent state in few controlled flow problem as well as from a theoretical aspects of the fluid dynamics.
However, the reality is that we usually encouter flow motion wherin laminar, transitional and turbulent states coexist. Be very carefull to use the Reyolds number as it depends on the choice of lenght and velocity reference quantity. For example, in a fully developed turbulent flow you can use lenght scales such as Taylor microscale or Kolmogorov scale, having also Re=O(1) in a turbulent flow.
Thank you all for participation in this discussion. We can conclude that, as fluid dynamics is semi-empirical, no exact confident and certain criteria exists for too many phenomena as transition from laminar to turbulent flow.
The transition from laminar to turbulent is not subtle and consists of several processes, each subject to intense research interests on their own right. The transition and stability of the laminar flow seem to be dependent on a critical value of Reynolds number < 2300. Beside that, other factors contributing to transition from laminar to turbulent flow in a fluid are pressure gradient, surface temperature, and surface roughness.
Experiments in controlled laboratory environments have shown that several distinctive stages are involved in the transition from laminar flow to turbulence. In two-dimensional channel and pipe flows, transition to turbulence occurs more suddenly and explosively over the whole length of the channel or pipe as the Reynolds number is increased beyond its critical value. In an initially non turbulent flow, the onset of turbulence may occur suddenly through a breakdown of streamlined flow in certain localized regions (turbulent spots).
Also I would suggest you to follow this paper
Article Laminar‐turbulent transitional flow phenomena in isosceles t...
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