Displacement thickness

Definition

Displacement thickness is a measure of the reduction in flow area due to the presence of a boundary layer in fluid flow, which effectively displaces the outer inviscid flow. This concept is crucial in understanding how the boundary layer affects the overall flow characteristics, particularly in laminar and turbulent flows. By quantifying the thickness of the boundary layer, displacement thickness helps in calculating parameters like drag and lift for bodies moving through a fluid.

5 Must Know Facts For Your Next Test

1. Displacement thickness can be calculated using the integral of the velocity profile across the boundary layer, showing how much fluid has been displaced by viscous effects.
2. In Blasius solution, displacement thickness is derived specifically for laminar flow over a flat plate and is expressed as a function of distance along the plate.
3. Displacement thickness plays a significant role in determining drag force on objects moving through fluids by impacting the effective flow area around them.
4. As displacement thickness increases, it indicates a thicker boundary layer, which usually corresponds to increased skin friction drag on surfaces.
5. The relationship between displacement thickness and other boundary layer characteristics, like momentum and energy thickness, helps engineers design more efficient aerodynamic shapes.

Review Questions

• How does displacement thickness relate to the overall flow characteristics in a boundary layer?
  • Displacement thickness is directly linked to how much the boundary layer affects the outer inviscid flow by reducing the effective flow area. It represents the distance by which the outer flow is 'displaced' due to viscous effects near solid surfaces. As fluid flows past an object, this reduction in effective area changes parameters like velocity distribution and pressure gradients around that object.
• Compare and contrast displacement thickness with momentum thickness in terms of their significance in fluid dynamics.
  • Displacement thickness measures how much the outer flow is reduced by viscosity near a surface, while momentum thickness focuses on how momentum is lost within that same boundary layer. Both are important for understanding drag forces but highlight different aspects; displacement thickness directly impacts effective area calculations, whereas momentum thickness relates to energy considerations in flow behavior. Understanding both concepts together provides a comprehensive view of boundary layer effects.
• Evaluate the implications of increasing displacement thickness on drag forces for aerodynamic surfaces and how this affects design considerations.
  • Increasing displacement thickness indicates a thicker boundary layer, leading to higher skin friction drag on aerodynamic surfaces. This can significantly impact vehicle performance, requiring designers to consider ways to minimize displacement thickness through streamlined shapes or surface modifications. If not addressed, excessive drag can reduce efficiency and increase fuel consumption, making it crucial for engineers to optimize designs based on these fluid dynamic principles.

Related terms

boundary layer: A thin region adjacent to the surface of a body where the effects of viscosity are significant and fluid velocity transitions from zero at the surface to nearly free-stream velocity.

momentum thickness: A measure related to the velocity profile of the boundary layer, defined as the thickness at which the momentum deficit relative to the free stream is equal to that of the actual boundary layer.

laminar flow: A smooth, orderly flow regime where fluid moves in parallel layers, with little or no disruption between them, typically characterized by low Reynolds numbers.