# Computing Boundary Layer Thickness in CFD Analysis

### Key Takeaways

Immediate to the surface, there is a low-velocity zone. Boundary layer thickness is calculated as the distance from this surface to the point where the velocity is 99% free-stream.

The complexity of boundary layer thickness calculations varies based on structural geometry and the nature of the flow.

Analysis of boundary layer thickness with CFD solvers facilitates system optimization for improved efficiency.

When pouring water out of a glass, you may notice the layer of water near the surface moves slower than the rest of the bulk fluid. This is because the velocity is affected by the friction between the fluid and the glass surface. Adjacent to the surface, a boundary layer forms. This behavior is observed in all kinds of flow — for instance, when the wind blows over the airplane wings or when water comes in contact with hydrofoil ships. The concern lies in the thickness of this boundary layer and how it affects the flow and fluid system design.

CFD simulation makes boundary layer analysis easier, i.e., you can visualize the flow velocity and pressure distribution, compute the boundary layer thickness in CFD, and optimize the fluid system for maximum efficiency.

## Boundary Layer Thickness

The boundary layer refers to the thin layer of fluid that exists in close proximity to the surface in contact during the flow. The formation of the boundary layer can be accredited to the presence of friction between the surface and the fluid. The friction slows down the normal rate of fluid flow and creates a low-velocity zone – the boundary layer. Thus, the boundary layer can also be characterized by the gradual transition of velocity.

The increase in velocity becomes evident as the fluid moves further away from the surface – from zero at the surface to the free stream velocity. This distance from the surface where the fluid particle velocity is zero to the point where the velocity reaches 99% free-stream is called the **boundary layer thickness.** Generally, the boundary layer thickness increases as:

**➡**Fluid particle velocity decreases**➡**Surface roughness increases**➡**Fluid viscosity increases

The formula for boundary layer thickness greatly depends on whether the flow is laminar or turbulent. Let us consider a fluid flowing on a flat plate. In the laminar boundary layer, the flow is smooth and steady with less friction. In such cases, the boundary layer thickness can be calculated using the Blasius solution:

δ is the boundary layer thickness

x is the length of the flat plate

Re is Reynolds number

The turbulent flow can be associated with excess surface roughness, flow randomness, and increased intensity. As such, the calculation of boundary layer thickness in CFD can simply be an estimate. This is done using the following formula:

In CFD, boundary layer thickness calculations have a critical role in many aerodynamic and hydrodynamic applications. They can be used in the analysis of:

- Drag and lift experienced by airfoils
- Rate of heat transfer from the surface to the fluids
- Flow stability and transitions
- Fluid system performance and efficiency

## Solving Boundary Layer Thickness With CFD Analysis

CFD is the key analysis tool for making detailed flow field analysis — i.e., boundary layer thickness, velocity profile, pressure distribution, etc. These parameters have vital implications for the design and performance of fluid systems. CFD uses Navier-Stokes equations for numerical simulation of fluid flow and boundary layer analysis. The following steps may be involved:

- In a computational domain, choose an appropriate laminar/ turbulence model. Check for the y+ requirement in turbulence modeling.
- Generate a fine grid or mesh and define the geometry of the 3D model for boundary layer analysis. Assign and solve the Navier-Stokes equation to each grid to accurately capture the boundary layer thickness.
- Specify the initial and boundary conditions for the fluid flow. This includes defining the velocity, temperature, surface roughness, heat transfer coefficient, and other physical properties at the wall, inlet, or outlet.
- Solve for boundary layer thickness. Generally, it is the point where 99% freestream velocity has been reached. Validate the boundary condition with other experimental or analytical results.

Through appropriate simulation and precision analysis of boundary layer thickness with CFD, it is possible to get valuable insight into fluid behavior and the boundary layer effects.

## Enhance Fluid System Performance With Boundary Layer Thickness Analysis

The right CFD tools allow for the accurate simulation and analysis of boundary layer thickness to help designers understand fluid flow behavior and optimize the system for maximum efficiency. System designers can make use of Cadence’s CFD tools to compute the governing equations that define the flow profile and boundary layer effects. By referencing the results from high-fidelity simulations and calculations of boundary layer thickness, CFD solvers support design changes to minimize resistance and improve the performance of fluid-engineered structures such as aircraft, wind turbines, and ships.

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