In fact, the heating is produced by the gas going through a shock. This isn't heating by compression. Adiabatic compression is a reversible process; going through a shock is irreversible. Entropy is generated at the shock.
In more detail: at the shock, the conditions of the gas change over a distance on the order of a mean free path. This means that, locally, the gas is out of thermodynamic equilibrium, with fast molecules running into slow ones. The extremely high gradient of gas conditions causes extremely rapid relaxation to an equilibrium state, a process that very rapidly produces entropy.
As Mach number increases, the density jump across the shock approaches an asymptotic limit, but the heating increases without bound.
As you compress a gas, its temperature rises. The air at the leading edge of the machine is static, meaning its compressed. (This is how pitot tubes measure airspeed - they are simply pressure sensors.)
The temperature rise from the compression matches what one predicts from PV=NkT
A shock wave is unnecessary. It happens with subsonic flow, too. In fact, it's how refrigerators work.
(In ME101 Fluid Mechanics, the Prof showed how a re-entering satellite would melt even if the atmosphere was a frictionless gas.)
> The temperature rise from the compression matches what one predicts from PV=NkT
That's a null statement, since that holds for any (ideal) gas regardless of how it got into its current state.
If you mean, the temperature rise is the same as if it were adiabatically compressed to the density or pressure the gas has after the shock, then that is not true.
If you compress a gas, even an ideal frictionless gas, its temperature rises. Like I said, that's how refrigerators work. As for compression in flight, that's how pitot tubes measure airspeed. It has nothing to do with friction.
On a wing, the temperature rise is highest at the static point on the leading edge, where there is no motion of the air. The temperature declines from there back as the airflow speeds up. If friction was the source of the heat, you'd expect the temperature to be the lowest at the static point, and would increase towards the trailing edge.
BTW, how a diesel engine works is by compressing the air/fuel mixture until it heats up enough to ignite. A gas engine will sometimes "diesel" on after the ignition is turned off.
The point I am making is that gas going through a shock is a fundamentally different process than a gas being adiabatically compressed. The former causes an increase in entropy; the latter ideally does not. While a shock isn't "friction" per se, like friction there is dissipation (and at entry speeds, quite a lot of dissipation).
The paper does talk about heat from friction, but not at the stagnation point. It also talks about the heating of the surface being less than predicted by adiabatic compression, but that is the heating of the surface, not the heating of the air at the stagnation point.
I have argued with @pfdietz about this before. In the zeal to make the point the majority of leading edge heating arises from the dissipative effects of shocks, they make statements that have to be very carefully parsed to be correct.
You are right. Isentropic compression will result in a higher temperature of the compressed fluid. This is undergraduate gasdynamics. In these supersonic flowfields with high shock strength though, the shock acts as a very dissipative compression mechanism. Behind the shock is a compressed fluid that is much hotter than it would be if compressed to the same pressure isentropically. Shocks are dissipative, like friction, but shocks and friction are not the same thing.
So unless you remove heat from a perfect compressible fluid being compressed (i.e., via a non-adiabatic process), it will always be hotter post-compression. It's just that the compression and heating that shocks effect causes much greater heating than the isentropic case.
In what we call "acreage" where the forward-facing area is limited (e.g., upper surfaces of wings and vehicle bodies), other effects, including turbulent skin friction heating, can dominate the local heating rate.
That paper doesn't appear to have much to do with what we're talking about here. The transfer of heat to the vehicle from the hot shocked gas is another issue entirely.
Anyway, it's foundational supersonic fluid physics that shocks create entropy.
Reentry with blunt bodies works because most of the dissipation is occurring at the shock, at some distance away from the vehicle, allowing most of the heat (that must be produced from the kinetic energy of the vehicle as it slows) to be carried away.
In more detail: at the shock, the conditions of the gas change over a distance on the order of a mean free path. This means that, locally, the gas is out of thermodynamic equilibrium, with fast molecules running into slow ones. The extremely high gradient of gas conditions causes extremely rapid relaxation to an equilibrium state, a process that very rapidly produces entropy.
As Mach number increases, the density jump across the shock approaches an asymptotic limit, but the heating increases without bound.