# Shock-boundry layer

1. Oct 31, 2006

### scott_alexsk

Hello,

In some papers I have come across this term. There are no formal definitions online, but I have a rough idea that it deals with a change in the nature of air in the boundry layer of an aircraft surface after reaching supersonic speeds. About this topic I have several questions. What is the formal defintion of the shock boundry layer? Also does anyone know anything about a responsive aircraft surface to variable speeds?

Thanks,
-scott

2. Oct 31, 2006

### Clausius2

When looking at the supersonic flow over a slender body, there are two main regions. Exclude for a moment what happens at the nose, and focuse on one of the sides of the body. There the bulk flow is also mainly supersonic, even though the leading shock wave has decreased a little bit its velocity (the leading shock wave is a weak Mach wave at this point). Even though the bulk flow is mainly inviscid and isentropic (assuming ionization and dissociation of air negligible at this mach #) and so the Euler Equations are applied there, there is an small region of non uniformity of the Euler Equations, where the flow is slowed down because of the viscosity. This thin region is call boundary layer, and has a non dimensional thickness $$\delta \sim O(M^2/\sqrt{Re})$$, where M is the Mach# and Re is the Reynolds#. In that region the flow has to go from supersonic speeds to subsonic speeds, and as you may know there is no physical way of slowing down a supersonic flow to subsonic unless a shock is produced. Inside the boundary layer there should be a Shock Layer, in which a shock (more or less of the same shape than the boundary layer) is decreasing the flow velocity. This shock layer has a great importance, because it is related to the Entropy Layer. This shock layer is one of the most important causes of the drag of a hypersonic aircraft. And as you may imagine by yourself, the state of the surface of the body is extraordinarily important, because $$\delta<<1$$, and the shock layer may interact with the local compressions-expansions of the fluid caused by a non uniform surface. That is why those planes are also extraordinarily polished.

Last edited: Oct 31, 2006
3. Nov 2, 2006

### scott_alexsk

Thanks Clausius2,

Also what is there to be gained from having an aircraft with a 'variable' surface that can respond to the shock-boundry layer? Has anyone heard of mesoflaps?

Thanks
-scott