Boundary layer thickness in partial air vacuum

[GT1]

How does low ambient pressure effect on the thickness of the boundary layer for given flow conditions of gas?

In absolute vacuum the thickness of the boundary layer is 0 of course, but it seems that all the boundary layer thickness correlations use the Reynolds number, which doesn’t change much vs pressure for given flow conditions (the kinematic viscosity of air is roughly independent of pressure).

How can we explain it?

 

[Chestermiller]

Bird, Stewart, and Lightfoot, Transport Phenomena has a derivation for the viscosity of gases based on molecular considerations. It is in Chapter 1.

 

[DoItForYourself]

As pressure decreases, the gas flow decreases because it is the result of ΔP. Consequently, Reynolds number decreases and the boundary layer's thickness tends to be zero when pressure tends to be zero.

 

[GT1]

As pressure decreases, the gas flow decreases because it is the result of ΔP. Consequently, Reynolds number decreases and the boundary layer's thickness tends to be zero when pressure tends to be zero.

And if we have an electric car driving at partial vacuum? -the Reynolds number stays the same. and what about the boundary layer thickness?

 

[DoItForYourself]

In such low pressures (this happens also in higher pressures), kinematic viscosity increases when pressure decreases. Dynamic viscosity does not change significantly but density decreases due to less molecules of air.

I am not sure if the air velocity will be the same in this case, but I think it will decrease.

 

[boneh3ad]

I don't know why you are being advised that a decrease in pressure has any bearing on boundary-layer thickness ($\delta$). The only real dependence $\delta$ has is on $Re$, which does not depend on pressure. Viscosity also does not depend on pressure; it depends on temperature. Density depends on pressure, but also temperature. So, absent additional constraints, the answer is that $\delta$ does not depend explicitly or directly on pressure.

 

[DoItForYourself]

As pressure becomes lower, density becomes lower too (gas flow) and so does Reynolds number ( $Re = \frac {uDd} {μ}$ ).

So, if all conditions remain constant except pressure, the boundary layer thickness will be influenced.

 

[boneh3ad]

However, when you lower pressure, it is unusual for temperature to also be constant such that only density changes. Consider an ideal gas:
$$p = \rho R T\to\rho = \dfrac{p}{RT}.$$
Also consider viscosity. Since we are talking gases, it has a relationship to temperature such that
$$\mu\propto \sqrt{T}.$$
So,
$$Re\propto \dfrac{\rho}{\mu}\propto\dfrac{p}{T^{3/2}}.$$
So if temperature is held constant, then sure, but temperature is rarely constant like that.

The bottom line is that the boundary layer does not directly depend on pressure, and depending on other constraints, notably on temperature, the boundary layer might do a number of things.