A CARJ HAS YAWING EVENTS ON 2 TKOFS. THEY HAD ABORTED THE TKOF ON THE FIRST INCIDENT. AFTER AN INSPECTION AND SUBSEQUENT TKOF TWR RPTED LOUD NOISES AND FLAME FROM THEIR R ENG AT ZZZ.

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DURING TKOF ROLL ON RWY 9L IN ZZZ WE EXPERIENCED A STRAIGHT R YAW AT ABOUT 60 KIAS WHICH WE THOUGHT WAS DUE TO TIRE/BRAKE PROBS OR PERHAPS AN ANIMAL THAT WE MAY HAVE RAN OVER. AT 80 KIAS; A SECOND MORE PRONOUNCED YAW MADE BOTH MYSELF AND THE CAPT CALL FOR AN ABORT. THE CAPT PERFORMED THE ABORT WHILE I NOTIFIED THE TWR. WE DID NOT REQUEST ASSISTANCE. WE ABORTED PRIOR TO V1; AS THE AIRPLANE WAS NEARING 105 KIAS. AS WE TAXIED TO THE RAMP; I CALLED TO INFORM THE FLT ATTENDANTS; OUR PAX; AND OPS. MAINT MET THE ACFT AND PERFORMED A HIGH ENERGY ABORT INSPECTION; ALSO LOOKING THE ACFT OVER; PAYING CLOSE ATTN TO THE GEAR; BUT COULD NOT FIND ANY PROS. A PAX SITTING IN THE EMER EXIT ROW (ACR X FO) COMMENTED THAT HE HEARD LOUD NOISES UNDERNEATH HIS SEAT DURING TKOF. AFTER MAINT RELEASED US; WE ATTEMPTED ANOTHER DEP TO JAX. WHILE ROLLING FOR TKOF; ABOUT THE TIME THE CAPT CALLED V1; A SERIOUS YAW TO THE R OCCURRED. THE CAPT SAID TO CONTINUE; THUS I FOCUSED ON MAINTAINING HDG DURING ROTATION. ANOTHER LARGE YAWING MOMENT ASSOCIATED WITH A SINKING FEELING OCCURRED AS THE GEAR CAME UP. TWR IMMEDIATELY CALLED US WITH RPT OF VERY LOUD NOISES COMING FROM OUR ACFT WITH LARGE FLAMES SHOOTING FROM ONE OF OUR ENGS. QUICKLY GLANCING TOWARD THE EICAS I DID NOT SEE ANY FLUCTUATIONS; NOR WAS THERE ANY OTHER INDICATION WITH THE EXCEPTION OF THE L ENG 'APR' ICON. THE R ENG INDICATED FULL PWR. WE ACCELERATED QUICKLY WHILE EVERY 2-3 SECONDS WE'D GET A SIGNIFICANT YAWING MOMENT TO THE R. ATC ASSIGNED US 3000 FT AND ASKED IF WE NEEDED ANY ASSISTANCE. THE CAPT INFORMED ATC THAT WE DESIRED TO RETURN FOR LNDG. THE CAPT PERFORMED THE IMMEDIATE ACTION ITEMS; AND AS THE R THRUST LEVER WAS BROUGHT BACK THE YAW FLUCTUATIONS STOPPED. THE CAPT ASSESSED THAT THIS WAS PROBABLY A COMPRESSOR STALL AND CHOSE TO LEAVE THE R THRUST LEVER AT IDLE. WE REACHED 3000 FT; SWITCHED TO DEP AND RECEIVED A L BASE TURN FOR LNDG AT ZZZ. ATC ASKED IF WE COULD SEE THE FIELD; BUT WE WERE UNABLE DUE TO IMC CONDITIONS. WE WERE THEN ASSIGNED 2500 FT IN ORDER TO TRY AND GET VMC; BUT TO NO AVAIL. THE CAPT MADE A SHORT PAX ANNOUNCEMENT; AND UPON COMPLETING THE AFTER TKOF CHKLIST DECIDED TO TAKE THE CTLS AND ASKED ME TO INFORM OPS OF OUR SIT AND RETURN. I INCORRECTLY TOLD OPS THAT WE SHUT DOWN OUR ENG (IT WAS AT IDLE). WHEN I SWITCHED TO TWR; I DECLARED AN EMER PER CAPT'S REQUEST. I NEXT SET UP THE ILS RWY 8L AND COMPLETED THE APCH TO LNDG CHKLIST. ONCE OFF THE RWY; THE FIRE TRUCKS INSPECTED OUR ENGS AND FOLLOWED US TO THE GATE. I CALLED TO CHK WITH THE FLT ATTENDANTS AND TO UPDATE THEM ON THE SIT. THE CAPT MADE A PA AT THE GATE PRIOR TO DEPLANING. MOST OF THE PAX WERE VERY GLAD TO BE SAFELY ON THE GND. HOWEVER; AN OLDER GENTLEMAN PULLED ME TO THE SIDE AND RUDELY TOLD ME HOW VERY DISAPPOINTED HE WAS OF OUR DECISION TO ATTEMPT A SECOND DEP TO JAX AFTER OUR FIRST ABORT; AND WAS GOING TO RPT THIS TO THE ACR. I INFORMED HIM THAT WE TRIED TO DO OUR BEST TO KEEP HIM SAFE; BUT HE TURNED AND WALKED AWAY IN DISAPPOINTMENT. MAINT CHKED THE COMPUTER INDICATION OF THIS INCIDENT THERE WERE NO EXCEEDENCES RECORDED WITH THE R ENG. THE COMPUTER ONLY SHOWED THAT THE L ENG WENT TO 'APR' PWR AND THERE WAS AN UNUSUALLY HIGH FAN VIBRATION ON THE R ENG. MAINT PERSONNEL COMMENTED THAT THE ENTIRE ARPT WAS SHAKEN BY THE LOUD NOISES FROM OUR ENG; AND MANY ON THE GND WERE ABLE TO SEE A VARIETY OF LARGE FLAMES COMING FROM OUR R ENG DURING TKOF. ALL THE INDICATIONS WE RECEIVED IN THE COCKPIT WERE THE YAWING MOMENTS; L ENG 'APR' ICON; AND AN OCCASIONAL SINKING FEELING. WE COULD NOT HEAR THE LOUD BANGS AND THERE WERE NO CAUTIONS NOR WARNINGS ASSOCIATED WITH THIS EMER. BESIDES THE SURPRISE ASSOCIATED WITH THIS SIT; THE CREW STAYED CALM AND FOCUSED WELL TO SAFELY RETURN THE ACFT ON THE GND.