Boundary layer

The boundary layer is an ideal zone of fluid flow where the effects of viscosity caused by the proximity of a surface are much more marked than in an external zone. Usually, this area is identified in a fluid layer in the immediate vicinity of a solid surface. As the fluid moves past an object, the molecules right next to the surface stick to the surface. The molecules just above the surface are slowed down in their collisions with the molecules sticking to the surface. These molecules, in turn, slow down the flow just above them. The farther one moves away from the surface, the fewer the collisions affected by the object surface. This creates a thin layer of fluid near the surface in which the velocity changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the boundary layer because it occurs on the boundary of the fluid.

The theory which describes boundary layer effects was first presented by Ludwig Prandtl in the early 1900s. The general fluids equations had been known for many years, but solutions to the equations did not properly describe observed flow effects (like wing stalls). Prandtl was the first to realize that the relative magnitude of the inertial and viscous forces changed from a layer very near the surface to a region far from the surface. He first proposed the interactively coupled, two-layer solution which properly models many flow problems.

Prandtl indicated as the boundary layer the zone inside which the speed differs at less than 1% from the speed of the external portion of the fluid, assuming for the outside the potential motion model. Prandtl further hypothesized that the size of the boundary layer was small compared to the size of the external motion field, assuming that the layer starts at the leading edge of the surface. Consequently, for the hypotheses made, the current lines remain undisturbed until they intersect the edge of the boundary layer, starting from this point onwards to deflect slightly due to the slowdown of the current.

Boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object.

So the boundary layer gives any object an “effective” shape which is usually slightly different from the physical shape. To make things more confusing, the boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure. Flow separation is the reason for wing stall at a high angle of attack. The effects of the boundary layer on the lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient.

Boundary layer types

Depending on which physical quantity varies in the vicinity of the boundary layer, we speak respectively of:

  • momentum boundary layer: in fluid dynamics, the momentum boundary layer is the fluid layer in the immediate vicinity of a solid surface in which the velocity varies from zero (in contact with the body) to the value of the undisturbed fluid current (in the bulk of the fluid). In hydrostatics, the boundary layer represents the layer of fluid, of comparable thickness with the molecular width, just below the layer where the phase transition occurs;
  • thermal boundary layer: concept used in heat transport;
  • matter boundary layer: concept used in matter transport.

These three concepts are studied by boundary layer theory indistinctly, but cover different applications. The concept of momentum boundary layer is applied in the context of fluid dynamics; the concept of matter boundary layer is applied in the context of reactorics and interphase transport; the concept of heat boundary layer is applied in the context of heat transport.

Velocity boundary layer

The motion of a fluid in the vicinity of a surface can be studied through the concept of the velocity boundary layer(mechanical boundary layer). The mechanical interaction that a fluid undergoes in this “layer” is dissipative, that is, the fluid is slowed down both by the effect of a tangential action opposite to the motion, that is, the friction of the surface and the effect of the kinematic viscosity of the fluid itself, which due to the inertia of the growing mass of fluid involved in the interaction. Therefore, the fluid, during its motion, from the entrance to all subsequent positions changes its velocity profile; while as the internal portion of the fluid increases, the effects of the slowdown wear off leaving the fluid undisturbed.

Velocity boundary layer

So if we identify the points where, at less than 1%, we find a speed equal to that of the entrance, and we connect them with a curve, this will represent the edge of the velocity boundary layer; beyond which the fluid will be undisturbed. The velocity boundary layer, on the other hand, will be represented by the area underlying the curve, in which the effects of the slowdown with non-zero speed gradients occur. The thickness of the velocity boundary layer, therefore, will depend on the effects of the fluid/surface interaction; therefore, the greater the kinematic viscosity value of the fluid, the thicker the velocity boundary layer will be.

Temperature boundary layer

Assuming the hypothesis of a surface at a temperature different from that of the fluid in contact, the thermal interaction that takes place there will be represented by a layer, called the temperature boundary layer, in which the fluid is affected by the thermal interaction and changes its temperature.

Temperature boundary layer

So in the event of a temperature difference, thermal gradients will be generated which will allow a heat flow, which will have an intensity directly proportional to the thermal diffusivity value of the fluid itself.

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