B190 CREW LNDG CLE TOLD TO EXPECT RWY 6R BUT LINED UP ON RWY 6L AND SENT AROUND.

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WE LEFT ERIE INTL ARPT (ERI) FOR CLEVELAND HOPKINS. UPON OBTAINING THE ATIS IN CLEVELAND; THEY WERE ADVERTISING LNDG ON RWY 6L AND DEPARTING RWY 6R. WE THEN PUT IN FREQS AND SET UP FOR THE RWY 6L ILS. UPON CONTACT WITH CLEVELAND APCH; WE WERE TOLD TO EXPECT RWY 6R FOR LNDG. THE FO AND I HEARD RWY 6L. WE CONTINUED FOR RWY 6L. APCH THEN PUT US ON A DOWNWIND AND HAD US CALL TWR. UPON CONTACT WITH TWR WE WERE CLRED TO LAND RWY 6R. ALTHOUGH WE STILL THOUGHT THEY SAID WE WERE CLR TO LAND RWY 6L. WE TURNED ONTO A 4-5 MI FINAL FOR RWY 6L AND STARTED CONFIGURING FOR LNDG ON RWY 6L. ON ABOUT A 2-3 MI FINAL TWR TOLD US TO GO AROUND. ON THE GAR THEY TOLD US THAT WE WERE CLRED TO LAND ON RWY 6R. WE THEN WERE PUT ON A DOWNWIND FOR RWY 6L AND LANDED RWY 6L. AFTER TAXIING CLR OF ALL RWYS; WE WERE TOLD TO CALL THE TWR AFTER WE GOT TO THE GATE. AT THAT TIME I SPOKE WITH A WOMAN CTLR WHO SAID THE SUPVR WAS REVIEWING THE TAPES. AFTER REVIEWING THE TAPES; THE CTLRS CONFIRMED WE WERE CLRED FOR THE VISUAL APCH AND LNDG ON RWY 6R. THE CTLR ADVISED ME TO PAY CLOSER ATTN TO WHICH RWY WE WERE BEING CLRED FOR BECAUSE DURING A HIGHER TFC TIME; THE CTLRS MAY NOT HAVE NOTICED US LINED UP ON THE WRONG RWY. THE HUMAN FACTORS THAT I BELIEVE ARE RELATED TO THIS ISSUE ARE REST PROBS. I HAD BEEN FLYING STAND UP OVERNIGHTS SINCE SUNDAY NIGHT. THE TRIP STARTS AT XA35 AT NIGHT AND WE REMAIN ON DUTY UNTIL XB05 THE FOLLOWING MORNING. WE HAVE REST DURING THE DAY AND START AGAIN AT XC35 THAT NIGHT. I HAD DONE THIS FOR 5 CONTINUOUS DAYS AND MY FO HAD DONE THIS FOR 2 CONTINUOUS DAYS. ANOTHER FACTOR AFFECTING THIS WAS THAT THE ATIS WAS ADVERTISING LNDG ON RWY 6L AND THEN APCH SAID WE WERE CLRED FOR RWY 6R. WE NEVER PICKED UP ON THE FACT THAT APCH CLRED US FOR RWY 6R. IN RETROSPECT; WE SHOULD HAVE CONFIRMED THE RWY THAT WE WERE CLRED TO LAND ON; BUT WE HAD NEVER QUESTIONED WHICH RWY BECAUSE WE ALWAYS THOUGHT WE WERE CLRED FOR RWY 6L. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID CTLRS AT CLE ARE CONSTANTLY MAKING CHANGES AND NOT KEEPING THE ATIS UP TO DATE. RPTR SAID THE TWR TAPES SHOWED THAT THEY WERE CORRECTLY READING BACK THE CLRNCS BUT STILL LINED UP WITH THE WRONG RWY.