General External Flow Characteristics

General External Flow Characteristics in Flow Over Immersed Bodies

When a body is immersed in a moving fluid, it experiences forces due to the interaction between the body and the fluid. These interactions can be described in terms of lift and drag forces, which are critical in the design and analysis of vehicles, structures, and other objects subjected to fluid flow. Here are some key characteristics and concepts related to external flow over immersed bodies:

Flow Classification

• Two-Dimensional Flow: Flow characteristics are uniform in one direction, simplifying analysis.
• Axisymmetric Flow: Flow around bodies with rotational symmetry, such as cylinders or spheres.
• Three-Dimensional Flow: Flow around bodies with complex shapes, requiring comprehensive analysis.

Body Shape

• Streamlined Bodies: Designed to minimize flow separation and reduce drag. Examples include airfoils and streamlined car bodies.
• Blunt Bodies: Have significant flow separation, leading to higher drag. Examples include flat plates and cylinders.

Forces on Immersed Bodies

• Drag (D): The force component in the direction of the upstream velocity. It consists of:
  • Pressure Drag: Due to pressure differences around the body.
  • Friction Drag: Due to shear stresses from the fluid's viscosity.
• Lift (L): The force component perpendicular to the upstream velocity, primarily due to pressure differences.

Boundary Layer Characteristics

• Boundary Layer: A thin region near the body's surface where viscous effects are significant.
• Boundary Layer Thickness (δ): The distance from the body surface to where the flow velocity reaches 99% of the free stream velocity.
• Transition and Separation: The boundary layer can transition from laminar to turbulent flow and may separate from the body, affecting drag and lift.

Dimensionless Numbers

• Reynolds Number (Re): Indicates the relative importance of inertial forces to viscous forces. High Re implies inertial forces dominate, while low Re implies viscous forces dominate.
• Mach Number (Ma): The ratio of the flow velocity to the speed of sound, important in compressible flows.
• Froude Number (Fr): Relevant in flows with a free surface, such as ship hulls.

Flow Past Different Bodies

• Flat Plate: Flow characteristics vary with Reynolds number, from laminar to turbulent boundary layers.
• Circular Cylinder: Exhibits complex flow patterns, including boundary layer separation and wake formation.

Lift and Drag Coefficients

• Lift Coefficient (C_L): Non-dimensional measure of lift, defined as \( C_L = \frac{L}{0.5 \rho U^2 A} \).
• Drag Coefficient (C_D): Non-dimensional measure of drag, defined as \( C_D = \frac{D}{0.5 \rho U^2 A} \).