Reynolds number and transition from laminar to turbulent boundary layer

Reynolds number is a dimensionless quantity that plays a significant role in determining the type of flow regime that develops over a surface. It is used to predict whether the flow is laminar or turbulent. Reynolds number is given by

Re = ρVD/μ
where,
ρ = density of the fluid,
V = velocity of the fluid,
D = characteristic length of the object/surface,
μ = dynamic viscosity of the fluid.

Laminar and turbulent flow

Laminar flow is a smooth, consistent flow regime where the fluid travels in parallel layers with no mixing between them. It is characterized by low Reynolds numbers. On the other hand, turbulent flow is a chaotic, unpredictable flow regime where the fluid is highly mixed and exhibits eddies and vortices. It is characterized by high Reynolds numbers.

Transition from laminar to turbulent boundary layer

The boundary layer is the region of fluid near a surface where the velocity of the fluid is affected by the presence of the surface. At low Reynolds numbers, the boundary layer is laminar, with smooth and predictable flow. However, as the Reynolds number increases, the boundary layer becomes unstable and transitions to a turbulent regime.

Critical Reynolds number

The critical Reynolds number is the value of Reynolds number at which the transition from laminar to turbulent flow occurs. It varies depending on the surface conditions and the type of flow. For external flows, such as flow over a flat plate or a cylinder, the critical Reynolds number is typically taken as 5 x 105.

Importance of critical Reynolds number

Knowing the critical Reynolds number is important in predicting the behavior of fluid flow over a surface. It helps in designing and optimizing the performance of various devices, such as aircraft wings, turbines, and heat exchangers. Designing these devices with the correct Reynolds number in mind can lead to more efficient and effective performance.