The Hydrodynamic and Thermal boundary layers

[Urmi Roy]

Hi,

I'm doing 'Heat and Mass transfer' at college and we're covering the topic on the hydrodynamic and thermal boundary layers.

I have a couple of questions, the answers to which are not given explicitly in any of my textbooks.

1. During open flow, why does laminar flow eventually have to become turbulent and why does that involve an increase in thickness of the layer?

2. Viscosity is due to 1. exchange of molecules from one layer to another in a fluid(momentum exchange) and 2. force of cohesion.

Therefore in laminar flow, where the flow is a lot more organized, and the adjacent layers stick to each-other, there would be larger force of cohesion. However, in turbulent flow, there is a lot of mixing of the molecules, so it would contribute to the create of large viscous forces.

Therefore, is the force of viscosity greater in laminar or in turbulent flow?

3. Heat exchange is greater in the turbulent layer, but so is the force of friction. So in practical life, would we prefer turbulent flow or laminar? ( So far I have formed an impression that the turbulent boundary layer is disadvantageous and unpredictable because its so 'messy' so I'll be really surprised if it turns out to be the better option').

 

[RandomGuy88]

A laminar boundary layer will become unstable due to instabilities in the flow. Disturbances such as free stream turbulence, surface roughness, surface vibration, noise ... Will excite instability modes within the boundary layer and cause the flow to transition. It is a very complicated process that is still not fully understood.

As for the thickness, because of the random velocity fluctuations momentum transport is significantly increased in a turbulent boundary layer. This results in the boundary layer growing at a much higher rate when the flow is turbulent.

When a flow is turbulent, viscous forces are less important than the effects of turbulence. It is not really correct to say viscous forces are weaker in laminar flows. Although the maximum shear stress will likely be less in a laminar flow (because of smaller velocity gradients) but the actual viscosity does not change. Turbulent velocity fluctuations are signicantly more effective at transporting momentum than viscous diffusion is and as a result viscous stresses can usually be ignored in turbulent flows except very close to a wall.

Whether or not a laminar or turbulent boundary layer is preferred depends on the situation. It is true that turbulent boundary layers are harded to predict but they do have many advantages. If I want a large amount of heat transfer than a turbulent boundary layer is better. If I want a high rate of mixing to say quickly and efficiently mix air and fuel than turbulent is better. Turbulent boundary layers are also usually better at resisting separation. However like you said the friction is larger and this can be a significant source of drag for vehicles such as aircraft.

 

[Urmi Roy]

Thanks for the reply!

When a flow is turbulent, viscous forces are less important than the effects of turbulence. It is not really correct to say viscous forces are weaker in laminar flows. Although the maximum shear stress will likely be less in a laminar flow (because of smaller velocity gradients) but the actual viscosity does not change. Turbulent velocity fluctuations are signicantly more effective at transporting momentum than viscous diffusion is and as a result viscous stresses can usually be ignored in turbulent flows except very close to a wall.

Hmm...I still don't completely get this...I mean the molecules of the fluid in turbulent flow will have too much kinetic energy to be able to maintain organised layers (as in laminar flow). This seems to be kind of analogous to the effect of temperature rise in a liquid (viscosity decreases with increase in temperature)

On the other hand, for gases, as temperature increases, the viscosity increases. So, for transition of a gas from laminar to turbulent, the viscosity would actually increase? Lol, this doesn't make sense!

 

[RandomGuy88]

The viscosity does NOT change when the flow transitions from laminar to turbulent. Your argument of the molecules having more kinetic energy in a turbulent flow is essentially saying that viscosity depends on the bulk velocity of the fluid, which would mean even if a laminar flow was accelerating the viscosity would be changing. Which is not true except perhaps at high speeds when there are large temperature changes. As the speed increases the bulk kinetic energy of the fluid would change but not the kinetic energy of the molecules relative to other molecules. The length scale of the turbulent fluctuations is significantly larger than the mean free path of the molecules so it does not effect motion on a molecular scale.

As a flow accelerates the relative importance of viscosity compared to inertial forces decreases. This is characterized by the Reynolds numbers which is the ratio of inertial to viscous forces. The Reynolds number of turbulent flows is typically fairly high so the transport of momentum by inertial forces is significantly stronger than transport by viscous forces.

 

[Urmi Roy]

Thanks,that was a really good explanation!

 

[boneh3ad]

I'd also like to point out that viscosity decreases with increasing temperature only in a liquid. In a gas, it is the opposite.