Air flows at 800 m / s through a long duct in a wind...

Air flows at $800 \mathrm{~m} / \mathrm{s}$ through a long duct in a wind tunnel, where the temperature is $20^{\circ} \mathrm{C}$ and the absolute pressure is $90 \mathrm{kPa}$. The leading edge of a wing in the tunnel is represented by the $7^{\circ}$ wedge. Determine the pressure created on its top surface if the angle of attack is set at $\alpha=2^{\circ}$.

Key Concepts

Pressure Distribution

Pressure distribution over an aerodynamic surface is influenced by the flow conditions, geometry of the surface, and phenomena like shock waves or expansion fans. In the context of high-speed flows, variations in surface pressure arise due to the compressibility effects and flow deflections around the surface. Analyzing the pressure distribution is fundamental to predicting aerodynamic forces and designing efficient aerodynamic structures.

Oblique Shock Waves

Oblique shock waves occur when a supersonic flow encounters a sharp change in geometry, such as a wedge or a compression corner, causing the flow to be deflected and compressed. This phenomenon leads to an abrupt increase in pressure, temperature, and density across the shock. Understanding oblique shock relationships is critical for predicting the pressure distribution over inclined surfaces in high-speed flows.

Angle of Attack

The angle of attack is the angle between the oncoming airflow and a reference line on an aerodynamic body, usually the chord line of a wing. It effectively changes the incidence of the airflow on the surface, altering the pressure distribution and aerodynamic forces. Even small variations in the angle of attack can have significant impacts on lift, drag, and surface pressures in high-speed flow conditions.

Compressible Flow

Compressible flow refers to fluid flow in which changes in density become significant, typically at speeds approaching or exceeding the speed of sound. In such flows, pressure, temperature, and density fluctuations are interdependent, and the governing equations must account for variations in these properties. This concept is essential for understanding how high-speed air interacts with surfaces, as seen in wind tunnel experiments and supersonic flight.

Mach Number

The Mach number is a dimensionless parameter defined as the ratio of the flow velocity to the local speed of sound. It determines the regime of the flow—subsonic, transonic, or supersonic—and hence the compressibility effects involved. In high-speed aerodynamic scenarios, accurately calculating the Mach number is crucial because it influences the formation of shock waves and expansion fans.

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