Jawaharlal Nehru Technological University Hyderabad B.Tech II Year AERODYNAMICS I Previous Question Paper (August/September - 2022 - R15)

The aspect ratio (AR), defined as the square of the span divided by the wing area, significantly influences the aerodynamic performance of an aircraft, primarily through its effect on induced drag. A higher aspect ratio wing is long and slender, while a lower aspect ratio wing is short and stubby.

The primary effects of increasing the aspect ratio include:

• Reduction in Induced Drag: Induced drag is inversely proportional to the aspect ratio. Higher AR wings reduce the strength of wingtip vortices because the pressure difference between the upper and lower surfaces is distributed over a longer span, leading to a more efficient lift distribution and lower drag for a given lift coefficient.
• Increase in Lift-Curve Slope: Increasing the aspect ratio increases the lift-curve slope (dC_L/dα). This means that for a given change in angle of attack, a high-AR wing produces more lift than a low-AR wing, allowing the aircraft to operate at lower angles of attack for cruise conditions.
• Stall Characteristics: High-AR wings often exhibit more abrupt stall characteristics compared to low-AR wings. Low-AR wings are less susceptible to flow separation at high angles of attack due to the stabilizing effect of the strong vortex flow generated at the leading edges.

Surface friction drag is caused by the viscosity of the fluid acting on the surface of the body, resulting in shear stress. It is the integral of the tangential stress components over the entire wetted surface area. Form drag (or pressure drag) arises from the pressure distribution around the body, which is significantly influenced by the shape of the object and the presence of flow separation. When flow separates, the pressure recovery at the rear of the body is incomplete, creating a pressure imbalance between the front and rear, resulting in a net force in the direction of the flow.

Yes, the surface friction coefficient (C_f) is a direct function of the Reynolds number (Re). This relationship exists because the Reynolds number dictates the state of the boundary layer (laminar or turbulent). For a laminar boundary layer, the friction coefficient decreases as Re increases according to the Blasius solution:

For a turbulent boundary layer, the friction coefficient also decreases with increasing Reynolds number, but at a slower rate, typically expressed as:

As the Reynolds number increases, the boundary layer thickness changes and the velocity gradient at the wall is altered, directly modifying the wall shear stress and thus the friction coefficient.