Viscous Heating from Alt. Frame of Reference
 

I've come across a logical issue which I am having trouble grasping. Maybe someone could explain why my reasoning is incorrect and enlighten me. :confused:

*This has arisen during supersonic flow simulations*

1. CFD and fluid analysis is predominantly taken from the frame of reference of a "stationary" body with the fluid flowing past it. For supersonic flow, this makes logical sense that it is equivalent to the body flowing through the fluid, compressing the medium it is running into, heating it.

My issue arises in, for example, the skin heating. In the real world, the fluid is brought UP to body speed and not down to the no slip condition as every textbook ever has presented to me. How does this increase in kinetic energy result in heating? Could it be analogous to a shock wave parallel to the surface?

Moreover, a general explanation of the equivalency between the two frames of reference, from the body and from the fluid, would be greatly appreciated! I've been told they are equivalent but not why.

Thanks!

I am not sure to understand this statement ...

however, by means of the Galilean invariance one would say that the body in movement with a certain kinetic energy transfers a part of its kinetic energy to the mass of fluid increasing its kinetic energy but also contributing to the internal energy. The same happens if the body is at the rest, the kinetic energy of the fluid is partly dissipated by the no slip condition. Only transfer by the isotropic part of the work is reversible but the deviatoric part produces entropy and dissipation of energy as heat.

To clarify: My issue was that in the real world, the no slip condition does not slow the fluid being passed through but instead accelerates it to the body's velocity. Therefore, how does this result in a temperature increase.

In response to you FMDenaro: Right so work is done in imparting kinetic energy into the fluid in the boundary layer which under an ideal approximation is reversible. But the actual generation of entropy results in an increase in temp? The boundary layer shouldn't compress or expand the flow, right? So im confused on how / why entropy increases and what that physically means.

Sorry for my ignorance on the topic.

When the fluid hits the surface (regardless of your frame of reference) it experiences compression. The compression of the air results in a temperature rise of the fluid. Look up stagnation point heating for an example.

any type of work due to the deviatoric part of the stress tensor is not reversible and enters into the entropy production
if you compare the equations of kinetic energy and internal energy you will see a coupling term explaining that.
Thus, if the body accelerates the flow by means of the no-slip condition it acts by means of the tangential stress (the deviatoric part) ..

agd: Well say for a flat laminar plate a high speed. Would not only the closest single molecules be impacting the surface, yet the entire boundary layer is hot. So would this be due to diffusion of the higher energy particles perpendicular to the flow or due to the compression of the oncoming fluid into the leading "edge" of the boundary layer?

Why is the boundary layer hot? For a flat plate aligned with the flow, you will get some viscous heating as the fluid is sheared between the plate velocity and the freestream. The bulk of any heating in the boundary layer will occur at a stagnation point, or where the body turns the flow causing compression (assuming that there is no heat transfer from the body itself.) The molecules closest to the boundary are impacting the wall, and lose some energy. As they move back out into the flow, they impact other molecules and cause them to lose a little kinetic energy. The net effect is the boundary layer. But at the leading edge of the plate you have a stagnation point. Over a very small region you get a compression of the flow.

agd: So the initial stagnation point heating and effects are carried downstream through the boundary layer with additional heating as density decreases and boundary layer thickens?

In the absence of other effects, yes.