Can air to air refuelling can be done with rocket engines as is done with conventional aircraft jet engines? If no then what are the possible hazards or conditions preventing this?
It depends if you are asking about rocket ships or rocket planes. On any note, its unlikely in the lower atmosphere, but in orbit, quite possibly.
There are a few issues you may encounter,
- Some rockets use solid fuel which cant be pumped from one tank to the next so you would not be able to refuel on the go.
- As @TomMcW mentions in the comments most rocket engines also carry oxidizer which you would need to pass over as well, doubling the volume you normally need to pass
- Most rockets use liquid oxygen which is stored at very high pressures, you would need to not only have another craft carrying a specialized tank but a way to transfer the oxygen in the proper state.
- You would need to transfer the fuel with out causing a pressure issue that lead to cavitation in the engine. During the design of the Saturn V Engines pressure variances in fuel flow caused serious cavitation issues and even lead to the loss of a test bed engine. While this problem was inevitably solved, the solution (as far as I know) does not account for pumping into the tank during operation.
- Rockets move fairly fast and also roll on takeoff so some sort of connection mechanism would need be quite complex. Matching speeds is less of an issue than having something revolve around another object that is rotating on an axis.
- Most rocket planes operate above the celling of practical refueling aircraft.
Frankly there is little practical reason as most rocket planes don't really need to refuel. Historically rocket planes like the Bell X-1 or the X-15 were built as test beds to push speed and altitude limits they carried the fuel they needed, burned it, broke the record, and glided home using histories oldest engine, gravity.
Refueling spacecraft has not proved to be a need yet as we have been able to successfully escape earth orbit on a single tank of gas. Building a rocket in space and sending it off has been theorized but there no examples of that yet and in that case you could ferry fuel up in small loads and deal with the docking in orbit.
Once in orbit docking two craft is fairly straight forward, then just connect the fuel lines and pump (presumably with out the engines running)...
Refueling is done a few times per year on the ISS. A visiting spacecraft arrives, docks and transfers some of its fuel to tanks on the ISS for its engines.
Refueling while in orbit is relatively simple: docking is a solved problem, and there is no turbulence etc. to make things difficult.
Refueling while a rocket engine is running is more difficult. You could consider the Shuttle an example: its main engines are fed from the external tank, so fuel has to be transferred from the tank to the orbiter. This is doable because the tank is already attached before liftoff.
Flying two rockets in close formation in flight (while still in the atmosphere) and transferring fuel between them is very difficult - the shockwaves coming off each rocket will interfere with the other one, I'd expect there to be lots of turbulence making it difficult for two rockets to fly in close formation and reliably hook up for the fuel transfer.
Both aircraft (tanker & tankee) need to be really close, and their relative velocity needs to be zero. Both could be achieved by rockets, as the wing loading is very high, and thus the interference by air movement/density changes is really low.
The problem is the third requirement: You need to be able to pass a hose between the two. Rockets typically are supersonic, and i see no way of doing that at those speeds.
Also: Rockets are 90% fuel at launch, so the action of giving / receiving fuel will alter their mass relatively more than the refuelling of a plane.
If your question was just about rocket- driven planes: Those usually have no fine regulation of their rocket drives, instead using surfaces for control, so i doubt those would be able to pace themselves beside a tanker.
Another factor to consider: the extreme speed and altitude of anything rocket propelled.
Rockets, which carry both fuel and oxidizer, tend to operate well in excess of Mach 1, typically at altitudes in excess of 100,000 feet. Any lower, and they could use air and dispense with carrying oxidizer.
True that the ISS is refueled and reprovisioned regularly, but it is a very stable platform with a high level of mass that orbits in microgravity, as does a resupply vessel.
Lower down, the rocket is still fighting off gravity, where even a minor problem can result in a rapid change of direction. Getting two ships linked up at Mach 4 would be extremely risky... just one little deviation, and it's kaboom for both of them... wouldn't be enough time to react.
And, there is the expense involved versus the benefits. If you're thinking of a hyper speed transport going halfway around the world at Mach 5 or 6 at over 150,000 feet, the tanker needs not only the fuel and oxidizer to match the transport's speed, but the fuel to transfer as well, plus enough fuel to account for the extra weight of the transfer fuel and oxidizer. It would be a hideously expensive proposition.
The same holds true for a launch to orbit ship. A refueling rocket would need to be quite a bit larger than the launch rocket, and two rocket launches would have to be coordinated, so why not just dispense with the idea of refueling and make the launch vehicle larger?
In addition to the comments above, note that it takes several minutes of skilled aviating to rendezvous an aerial tanker with the vehicle to be refueled. Since the initial boost phase of a typical launch is only of order ~minutes long, by the time the rendezvous is accomplished, it's time to jettison the first stage...