JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS Previous Question Paper (September - 2020 - R16)

Non-dimensional numbers are fundamental in wind tunnel testing because they allow for the scaling of physical phenomena from a full-scale prototype to a reduced-scale model. Since it is rarely possible to replicate all environmental conditions simultaneously, these numbers ensure that the flow characteristics around the model are dynamically and kinematically similar to the real-world structure.

The primary role of these numbers is to maintain Similitude, which is categorized into three types:

• Geometric Similitude: Ensures the model is a precise scale replica of the prototype, maintaining the same shape and proportions.
• Kinematic Similitude: Ensures that velocity ratios and flow patterns are identical at corresponding points, typically achieved by maintaining the same Strouhal number (St = fL/V) for unsteady flows.
• Dynamic Similitude: Ensures that the ratios of forces (inertial, viscous, gravitational, and elastic) are identical between the model and the prototype.

Key non-dimensional numbers used in wind engineering include:

• Reynolds Number (Re = ρVL/μ): Represents the ratio of inertial forces to viscous forces. In wind tunnel testing, matching the Reynolds number is critical for ensuring that boundary layer behavior, flow separation, and wake characteristics remain consistent.
• Froude Number (Fr = V/√(gL)): Represents the ratio of inertial forces to gravitational forces. This is particularly important for studies involving free-surface flows or density-stratified atmospheric layers.
• Mach Number (M = V/a): Represents the ratio of flow velocity to the speed of sound. While wind engineering typically deals with incompressible flow (low Mach numbers), this becomes relevant for high-speed aeroelastic studies.

In practice, it is often impossible to match all non-dimensional numbers simultaneously (e.g., matching both Reynolds and Froude numbers requires changing the fluid properties). Therefore, wind tunnel engineers prioritize the numbers most relevant to the specific problem, such as the Reynolds number for drag and pressure distribution studies, or the Scruton number for aeroelastic stability analysis. By keeping these ratios constant, researchers can reliably extrapolate model test data to predict the aerodynamic performance, structural loads, and wind-induced vibrations of full-scale buildings and bridges.

The simulation of the Atmospheric Boundary Layer (ABL) in a wind tunnel is essential for accurately modeling wind loads on structures, as the velocity profile and turbulence characteristics of natural wind differ significantly from the uniform flow produced in standard aeronautical wind tunnels. To replicate the ABL, the wind tunnel must simulate the vertical velocity gradient, the turbulence intensity, and the power spectral density of the natural wind.

The following methods are commonly employed to achieve this simulation:

• Passive Simulation Techniques: These involve placing physical devices at the test section entrance to modify the flow. Common devices include:
  • Spires or Wedges: Large triangular or wedge-shaped plates placed at the tunnel entrance to generate large-scale vortices and create a velocity deficit.
  • Roughness Elements: Blocks, cubes, or grids placed on the floor of the wind tunnel to increase surface drag and generate small-scale turbulence, effectively thickening the boundary layer.
  • Barrier Walls: A fence or wall placed at the start of the test section to induce an immediate velocity gradient.
• Long Test Sections: Using a long development length allows the boundary layer to grow naturally over a surface covered with roughness elements. This is the most accurate method but requires a very long wind tunnel.
• Active Simulation Techniques: These involve mechanical systems such as oscillating flaps, jets, or rotating shutters that inject energy into the flow to control turbulence intensity and scale. These are used when passive methods are insufficient to match the required turbulence characteristics.

The success of the simulation is verified by comparing the wind tunnel's mean velocity profile, typically represented by the power law or logarithmic law, and the turbulence intensity profile against full-scale atmospheric data. The power law is expressed as:

where U(z) is the velocity at height z, U_ref is the reference velocity, and α is the power-law exponent dependent on the terrain roughness. Matching these parameters ensures that the aerodynamic forces measured on the model are representative of real-world conditions.