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Boundary-Layer Parameters

Let's get to know about all the parameters in detail.


Table of Contents:

  1. Introduction

  2. Boundary layer thickness

  3. Displacement thickness

  4. Momentum thickness

  5. Shape factor

  6. Conclusion

  7. Short Video

Introduction

We have already posted two articles on boundary layer formation and separation. Before reading this post, it would be beneficial if you read the related articles beforehand as it will be easier to comprehend.

Engineers are charged with putting to use the scientific knowledge we possess. So, now that we know boundary layer theory, let's put it into practice. Boundary layer concepts can be applied anywhere aerodynamics is present. For example, aircraft, will turbines, rockets, etc. In order to do that we will need to know the numbers and make it more efficient. We will discuss all the parameters relating to boundary layers.

 

Boundary-Layer Thickness


Let's review what the boundary layer is. A Boundary layer can be defined as an imaginary layer of fluid, that is formed when solid and fluid are in relative motion, at a layer where the velocity of the fluid is equal to 99% of free stream velocity.

Boundary-Layer thickness is denoted by a delta.

The boundary layer thickness is the distance normal to the wall to a point where the flow velocity has essentially reached the 99% of the free stream velocity.
Boundary layer thickness
Boundary layer thickness

In other words, it is the thickness from the plate to the fluid velocity almost equal to free stream velocity.

Formula for Boundary layer thickness:

It depends on the nature of the layer, such as if it's laminar or turbulent, on what formulae to use. In order to calculate the boundary layer thickness, the Blasius solution is used for flat-plate, incompressible, laminar boundary layers.


Displacement Thickness

The displacement thickness is the normal distance to a reference plane representing the lower edge of a hypothetical inviscid fluid of uniform velocity that has the same flow rate as occurs in the real fluid with the boundary layer.

As you can see in the image, the shaded areas have equal areas. In the image above the mass deficit is just placed in a different way to make the calculations easy. Imagine all of the mass deficit is transferred as shown from the first to the second figure. The height that it will take up in the Y direction is displacement thickness. Displacement thickness is denoted by delta star.


Formula for displacement thickness:

Displacement thickness
Displacement thickness

Momentum thickness

The momentum thickness, is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an inviscid fluid stream of velocity, or to give the same total momentum as exists between the surface and the reference plane in a real fluid.

Imagine a fluid flowing without any friction and is inviscid. and another fluid, honey. Imagine, comparing the surface covered for both of the flowing fluids. Compared to displacement thickness momentum thickness might be difficult to visualize. But we hope you understand by now. Momentum thickness is denoted by theta.

Formula for momentum thickness:

Momentum thickness
Momentum thickness

Momentum thickness is very useful in determining skin friction drag on a surface.

Similar to the above thicknesses we have energy thickness, which is not used regularly.

Energy thickness
Energy thickness

Shape Factor

A shape factor is used in boundary layer flow to determine the nature of the flow. It helps to differentiate laminar and turbulent flow.

It is the ratio between displacement thickness and momentum thickness, which is denoted by H.

Formula for Shape factor:

Conventionally, H = 2.59 (Blasius boundary layer) is typical of laminar flows, while H = 1.3 – 1.4 is typical of turbulent flows.

 

Summary

  1. The boundary layer thickness is the distance normal to the wall to a point where the flow velocity has essentially reached the 99% of the free stream velocity.

  2. The displacement thickness is the normal distance to a reference plane representing the lower edge of a hypothetical inviscid fluid of uniform velocity that has the same flow rate as occurs in the real fluid with the boundary layer.

  3. The momentum thickness is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an inviscid fluid stream of velocity or to give the same total momentum as exists between the surface and the reference plane in a real fluid.

  4. A shape factor is used in boundary layer flow to determine the nature of the flow. It helps to differentiate laminar and turbulent flow.

 

Short Video

Hello everyone, I feel so good writing back after a long time here! Keep supporting and following us! Did you like the article? Let me know in the comment section!

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