JNTU B.Tech IV INDUSTRIAL AERODYNAMICS Previous Question Paper (February/March - 2022 - R18)

Wind variation is primarily driven by the atmospheric boundary layer, where surface friction causes wind speed to decrease near the ground. This variation is described by the power law or logarithmic law profiles. The power law is expressed as:

where α is the power-law exponent depending on surface roughness (e.g., 0.14 for open terrain, 0.40 for urban areas). The effects of this variation are critical in industrial aerodynamics: it dictates the structural wind loads on tall buildings and chimneys, influences the performance and fatigue life of wind turbine blades, and determines the dispersion patterns of pollutants in the atmosphere. Significant vertical gradients lead to shear stress, which impacts the stability of structures and the efficiency of energy extraction systems.

To determine the wind speed variation over a hill, we assume the flow is steady, incompressible, and inviscid (potential flow). The hill acts as a bluff body, causing the streamlines to compress at the crest, which leads to an increase in local wind speed known as the speed-up effect.

Assumptions:

• The hill shape is modeled as a smooth, two-dimensional obstacle.
• The flow remains attached to the surface.
• The upstream wind profile follows a standard power-law distribution.
• The speed-up factor is maximum at the crest and decays exponentially with height above the hill.

At the crest, the wind speed u(z) at a height z is given by u(z) = u_0(z) * (1 + ΔS(z)), where u_0(z) is the upstream velocity and ΔS(z) is the speed-up factor. Starting from the ground (z=0) to 50 ft, the velocity profile shows a sharp peak at the surface due to flow acceleration, converging back to the undisturbed upstream profile as height increases beyond the hill's influence zone.