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A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).
In fluid dynamics, Blasius theorem states that [1] [2] [3] the force experienced by a two-dimensional fixed body in a steady irrotational flow is given by F x − i F y = i ρ 2 ∮ C ( d w d z ) 2 d z {\displaystyle F_{x}-iF_{y}={\frac {i\rho }{2}}\oint _{C}\left({\frac {\mathrm {d} w}{\mathrm {d} z}}\right)^{2}\mathrm {d} z}
The thin shear layer which develops on an oscillating body is an example of a Stokes boundary layer, while the Blasius boundary layer refers to the well-known similarity solution near an attached flat plate held in an oncoming unidirectional flow and Falkner–Skan boundary layer, a generalization of Blasius profile.
Paul Richard Heinrich Blasius (9 August 1883 – 24 April 1970) was a German fluid dynamics physicist.He was one of the first students of Prandtl.. Blasius provided a mathematical basis for boundary-layer drag but also showed as early as 1911 that the resistance to flow through smooth pipes could be expressed in terms of the Reynolds number for both laminar and turbulent flow.
Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell. [1] [2]
The boundary layer thickness, , is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity, .Prior to the development of the Moment Method, the lack of an obvious method of defining the boundary layer thickness led much of the flow community in the later half of the 1900s to adopt the location , denoted as and given by
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This equation can be integrated and the fluid velocity at free surface can be obtained either by extrapolation from the interior or by using dynamic boundary condition. For the calculation of flow, FV method is widely used. The steps for a fully conservative FV method of this type are: