# Is it possible to have the laminar flow above $Re=10^7$?

For pipe flow I came across the information that the onset of turbulent flow occurs at approximately $$Re=10^3$$ to $$Re=10^4$$, while for boundary layers on the airfoil the onset occurs in between $$Re=10^5$$ and $$Re=5\cdot 10^6$$. Therefore, since the onset of turbulent flow ranges greatly, is theoretically still possible in some cases to have the laminar flow above $$Re=10^7$$ on the airfoil, disregarding the laminar sublayer in every turbulent flow above the surface?

Any reference to books would be highly appreciated.

• Only in a favorable pressure gradient, or when suction is applied to keep the boundary layer fresh. May 4 '20 at 15:50

The airfoil always starts with a laminar boundary layer; at some point on the airfoil surface, the boundary layer may transition to turbulent. In a uniform free-stream, two modes of transitions dominate:

• Natural transition
• Forced transition

## a. Natural transition

Natural transition is the transition mechanism that we typically associate with Reynolds number. As flow moves along the airfoil, the local Reynolds number increases and any initial disturbances amplify. When the amplification increases past the maximum threshold that a laminar boundary layer can tolerate, the flow separates locally (laminar separation bubble) and reattaches as turbulent boundary layer.

The following graph (Ref. Drela, Flight Vehicle Aerodynamics) shows the growth of the local Reynolds number ($$Re_\theta$$) and the instability parameter ($$\tilde{N}$$) for a flat plate. Once $$\tilde{N}$$ increases past the critical value ($$N_{crit}$$), then laminar-turbulent transition occurs. Notice also how the point of transition is affected by the free-stream Reynolds number ($$Re_\infty$$): the higher the free-stream Reynolds number (which is what your OP is asking), the earlier the natural transition.

Image ref: Drela, Flight Vehicle Aerodynamics

Since the shape of the airfoil affects the pressure distribution, it also affects the boundary layer shape. You can modify the airfoil shape to delay the transition as much as possible in order to minimize skin friction drag. This is the design objective of Natural Laminar Flow (NLF) airfoils. But even on NLF-0215F at a $$C_l$$ of 0.65, for example, transition occurs at 61% chord on the upper surface, at a free-stream Reynolds number of 5 million.

## b. Forced transition

Forced transition occurs when there is irregularity or protuberance on the airfoil surface. This can be due to manufacturing tolerances, contamination, or by design. Contamination can be due to rain, ice-buildup or even collision with insects.

Thus in practice, actual transition would occur much earlier than predicted via natural transition.

The Reynolds number is the ratio of a characteristic velocity and a characteristic dimension (never mind the viscosity for now). The key is the choice of the characteristic quantities. So, the onset of turbulence around Re=2300, what you often find in fluid dynamics textbooks, applies only to pipe flow, with the pipe diameter used as characteristic length scale.

The flow around airfoils is fundamentally different to the flow in a pipe.