Falcon 2000 flight crew reported engine vibration and fluctuating RPM's from the number 2 engine. The crew shut the engine down and diverted to the nearest suitable airport.
Synopsis
Falcon 2000 flight crew reported engine vibration and fluctuating RPM's from the number 2 engine. The crew shut the engine down and diverted to the nearest suitable airport.
Narrative
I was Pilot Flying. Climbing through 38000 ft. the First Officer brought to my attention the ignition light flashing on Engine number 2; I turned on the number 2 ignition. While monitoring the engine parameters; we noticed the #2 N1; and fuel flow started fluctuating. A small vibration developed and climbing through 40200 ft. I asked First Officer too tell ATC we needed to level out at 40000 ft. Shortly after leveling the engine fluctuations and vibrations started getting worse. I asked for the precautionary shutdown and secure checklist and took the communications. I told ATC we needed to start coming down. At first; they wouldn't let us due to traffic below; so I [requested priority handling] and turned left to start our descent. As Pilot Monitoring was running the Checklist the #2 engine ended up shutting itself down; so he finished the engine secure checklist inflight. We elected not to try restarting due to the vibrations. We choose ZZZ as our diversion airport due to its location and weather. The First Officer contacted the FBO and had them advise Operations of our diversion. Ran the associated engine out approach and landing checklists and landed at ZZZ Runway XXR without further issue. Tower had us hold on the Runway briefly then we continued to the FBO. My initial though were icing but there was no visible damage to the N1 blades; so I'm unsure. I don't know what caused this; so it's hard to provide recommendations.
Second reporter narrative
We were operating a Part 135 flight with 2 passengers; from ZZZ1 to ZZZ2. During climb out at about 38;000 ft. I noticed the right engine 'IGN' on the synoptic; then it went out. I mentioned this to the other pilot; and we both watched to see what might be happening. There was then about a 5% N2 RPM split between engines; with the number 2 engine being lower; then the 'IGN' alert came back on. Captain selected the #2 Ignition and we continued to monitor. The number two engine continued to fluctuate from the number 1 engine RPM to finally about 10% below. There was also a slight N2 engine vibration indication that did not match the #1 engine (no vibration). We did not note any N1 vibe indication on either engine. That is; both engine N1 vibration readings were near zero. When we saw the increasing vibration and RPM fluctuations; at about 40;200 ft. we told ATC we wanted to level off at 40000 ft. for a possible engine problem and to please standby. Shortly after that; the engine shut down or flamed out. We [requested priority handling] performed the appropriate procedures; and decided to divert to ZZZ. All ATC facilities gave us priority handling and we landed on Runway XXR without incident. The Tower told us to stop 'on the numbers' at the end of our Runway; so another plane could land on a Runway that intersected our Runway. This may have caused some concern from an outside observer; but we only remained on the Runway due to the Tower's request. I believe they stopped other aircraft from landing until we were safely on deck. After that we taxied to the FBO without incident. Unknown but possible internal engine damage. Since I cannot say I know the cause I have no recommendation. I will say that all the ATC facilities gave support.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.