Does anyone know how pressure-fed/hypergolic rocket engines cool themselves down? Do they regenerativly cool themselves?
Regenerative cooling can be done with pressure-fed rockets just as it is with pump-fed rockets, the only differences are the source of the pressure driving the fuel (and sometimes oxidizer) through the cooling channels, and the lower pressures that are practical when the entire tank must be pressurized.
Hypergolic engines can be either pressure-fed or pump-fed. Some hypergolic propellants might be problematic for use as engine cooling, but N2O4/hydrazine engines have used regenerative cooling.
The space shuttle's Orbital Maneuvering Engines (OMEs) were pressure-fed hypergolic engines burning nitrogen tetroxide and mono-methyl hydrazine.
The combustion chamber was regeneratively cooled by hydrazine flow. The nozzle extension was radiation cooled.
An alternative to regenerative cooling is film cooling.
Film cooling has been in use for small pressure fed thrusters for decades, not least on the Marquardt R4D used on the Apollo Service Module for attitude control - see the photo below. This was a 490N MMH/Mon engine that has also been used on countless other programmes.
The principle has also been used on a wide range of other thrusters in the range 10N to 500N at least and is the default design approach in this class.
The rough principle of operation is that the injector directs some fuel at the combustion chamber wall where it flows along the wall and out to the nozzle. It evaporates along the way, because of the heat developed by adjacent combustion of the fuel and oxidiser in the centre of the chamber, and in doing so it keeps the walls cool.
There have been real life examples of similar thrusters having problems from burn-through and side-jets forming (i.e. the last thing before catastrophic failure) where this film has not completely covered the walls, perhaps because of operation at the wrong mixture ratio or duty cycle. But on the whole it is a extremely well established method of cooling.
Further details of consideration of Marquard film cooled thrusters for the Space Shuttle RCS can be found in this report: SSRCS
Pressure fed engines of PSLV's fourth stage (PS4) are hypergolic (MON/MMH) and their combustion chamber is regeneratively cooled with their Columbium alloy nozzle being cooled radiatively. They are modified versions of PSLV first stage (PS1) Roll Control Thrusters.
Here is a good view of cooling channels machined on combustion chamber walls.