Question about boundary layer growth in convergent and divergent ducts

In summary, the boundary layer in a convergent duct in subsonic flow grows differently compared to a divergent duct in subsonic flow. This is due to the area-velocity relations, where the speed increases in the convergent section and decreases in the divergent section. Pressure gradients also play a role, with a positive pressure gradient in the divergent section leading to an increase in boundary layer thickness and a decrease in wall shear stress. The opposite is true for the convergent section, where an adverse pressure gradient results in a decrease in boundary layer thickness.
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Master1022
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How does a boundary layer grow in a convergent duct in subsonic flow? How does this compare to the growth of a boundary layer in a divergent duct in subsonic flow?
Hi,

I was recently reading about convergent-divergent nozzles and was wondering about how boundary layers grow in them.

Question: How does a boundary layer grow in a convergent duct in subsonic flow? How does this compare to the growth of a boundary layer in a divergent duct in subsonic flow?

Given that we are in subsonic flow, ## M < 1 ## and therefore we know from the area-velocity relations that subsonic flow increases speed in the convergent section and decreases speed in the divergent section. I am not really sure what the next steps would be...

Do I need to make arguments about the pressure gradients in the two sections? For example, in the diverging section, there is a positive (unfavorable). This then decreases the free-stream velocity, increases the boundary layer thickness, and decreases the wall shear stress (source: here). Then we could make the opposite argument for the convergent section where there is an adverse pressure gradient which would decrease the boundary layer thickness.

Is this correct?

Any guidance would be greatly appreciated.
 
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  • #2
That all sounds pretty good to me.
 
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FAQ: Question about boundary layer growth in convergent and divergent ducts

What is a boundary layer?

A boundary layer is a thin layer of fluid that forms along the surface of a solid object in a flow field. It is characterized by a gradual change in velocity and pressure from the surface to the outer flow.

How does the boundary layer grow in convergent and divergent ducts?

In convergent ducts, the boundary layer grows in thickness as the flow accelerates due to the decreasing cross-sectional area. In divergent ducts, the boundary layer thickness decreases as the flow decelerates due to the increasing cross-sectional area.

What factors affect the growth of the boundary layer in ducts?

The growth of the boundary layer in ducts is affected by the shape of the duct, the fluid properties, and the flow conditions. Additionally, the surface roughness of the duct can also impact the growth of the boundary layer.

How does the boundary layer affect the overall flow in ducts?

The boundary layer can significantly impact the overall flow in ducts by causing drag and reducing the efficiency of the flow. It can also lead to flow separation and pressure losses.

Can the growth of the boundary layer be controlled in ducts?

Yes, the growth of the boundary layer can be controlled through various methods such as using surface treatments to reduce roughness, altering the shape of the duct, or introducing turbulence through flow control devices. These methods can help improve the overall performance of the duct flow.

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