Published online by Cambridge University Press: 07 October 2011
The Analogy between Unsteady Separation and Separation from a Moving Surface
For the steady fluid motions considered in the preceding chapters, flow separation leads to a change in the flow structure as a whole. The limiting state when the Reynolds number tends to infinity is defined by the Helmholtz–Kirchhoff theory for ideal fluid flows with free streamlines, and the location of the separation point, in accordance with the criterion of Prandtl, coincides with the point where the shear stress at the surface of the body vanishes (see Chapter 1).
The situation is somewhat different if the flow is unsteady. To illustrate this fact we consider the example of flow past a circular cylinder that is set into motion instantaneously from rest. The starting motion of a body in a viscous fluid can be likened to the introduction of the no-slip condition at the surface of a body as it moves through a fluid that has no internal friction. Therefore, at the first instant the flow is potential and is described by the well-known solution for unseparated steady flow past a cylinder with zero circulation. At the body surface, where the no-slip condition is imposed, there arises the process of vorticity diffusion and convection, which leads to the formation of a boundary layer.
Blasius (1908) formulated this problem and gave an approximate solution. It turns out that at a certain instant the point of zero skin friction starts moving upstream along the body surface from the rear stagnation point. At the same time a region of reverse flow appears within the boundary layer (Figure 5.1).
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.