Constant Temperature Anemometry: A Tool to Study Turbulent Boundary Layer Flow

Source: Xiaofeng Liu, Jose Roberto Moreto, and Jaime Dorado, Department of Aerospace Engineering, San Diego State University, San Diego, California

A boundary layer is a thin flow region immediately adjacent to the surface of a solid body immersed in flow field. In this region, viscous effects, such as the viscous shear stress, dominate, and the flow is retarded due to the influence of friction between the fluid and the solid surface. Outside of the boundary layer, the flow is inviscid, i.e., there is no dissipative effects due to friction, thermal conduction or mass diffusion.

The boundary layer concept was introduced by Ludwig Prandtl in 1904, which enables significant simplification to the Navier-Stokes (NS) equation for the treatment of flow over a solid body. Inside the boundary layer, the NS equation is reduced to the boundary layer equation, while outside of the boundary layer, the flow can be described by the Euler equation, which is a simplified version of the NS equation.

Figure 1. Boundary layer development over a flat plate.

The simplest case for boundary layer development occurs on a flat plate at zero angle of incidence. When considering boundary layer development on a flat plate, the velocity outside of the boundary layer is constant so that the pressure gradient along the wall is considered to be zero.

The boundary layer, which naturally develops on a solid body surface, typically undergoes the following stages: first, the laminar boundary layer state; second, the transition state, and third, the turbulent boundary layer state. Each state has its own law(s) describing the flow structure of the boundary layer.

The research into the development and structure of boundary layer is of great importance for both theoretical study and practical applications. For example, boundary layer theory is the basis for calculating the skin friction drag on ships, aircraft and the blades of turbomachines. Skin friction drag is created on the body surface within the boundary layer and is due to the viscous shear stress exerted on the surface through fluid particles in direct contact with it. The skin friction is proportional to the fluid viscosity and the local velocity gradient on the surface in the surface normal direction. Skin friction drag is present on the entire surface, thus it becomes significant over large areas, such as an airplane wing. Additionally, turbulent fluid flow creates more skin friction drag. The macro-turbulent fluid motion enhances the momentum transfer within the boundary layer by bringing fluid particles with high momentum down to the surface.

This demonstration focuses on the turbulent boundary layer over a flat plate, in which the flow is irregular, such as in mixing or eddying, and the fluctuations are superimposed on the mean flow. Thus, the velocity at any point in a turbulent boundary layer is a function of time. In this demonstration, constant temperature hot-wire anemometry, or CTA, will be used to conduct a boundary layer survey. Then, the Clauser chart method will be used to calculate the skin friction coefficient in a turbulent boundary layer.