Boundary conditions, free stream turbulence

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

The form of Eq. 6.241 applies for Re, < 4 x 106, where the Blasius skin friction equation (Eq. 6.16) is reasonably accurate and 2 St cf = PrM and Pr-04 for laminar and turbulent flow, respectively. It also uses the laminar reference enthalpy approach to define p p /pcpc (see the section on uniform free-stream conditions) and uses the turbulent boundary layer transfor-... 

Detachment of Particles Situated in a Laminar Boundary Layer. The action of an air stream on adherent particles under the conditions of a laminar boundary layer (see Fig. X.l. a) or a laminar boundary sublayer (see Fig. X.l. b) have certain features in common but others that differ. The common feature is that there is a linear velocity distribution across the thickness of the laminar layer or sublayer (line c). The difference is that the laminar boundary layer is in direct contact with an air flow having a velocity of Uoo. In the case of a turbulent boundary layer, there is no direct contact between the laminar sublayer and the free stream, which are separated by a buffer layer 3 and a turbulent core 4 (see Fig. X.l.b). These features do affect the drag. 

Let us now compare calculations based on Eqs. (X.18) and (X.33), characterizing the drag under conditions of laminar and turbulent boundary layers. The drag forces F j. and will depend on the same quantities, i.e., on the density p and viscosity v of the stream, the free-stream flow velocity Uoo, the diameter of the adherent particles d, and the position of the adherent particles relative to the length of the flow surface x. The values of the exponents applicable to these quantities, however, will be different for the two cases so that the forces will be different. 

As can be seen from these data, the drag under turbulent boundary layer conditions, for a given free-stream velocity, was approximately 2 orders of magnitude greater than the drag realized for detachment of particles in a laminar boundary layer. These relationships between F j>i and Fdrt have also been confirmed for other free-stream velocities from 5 to 30 m/sec, and for irregularly shaped particles [277]. 

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