A319 FLT CREW RPTS COMPRESSOR STALLS DURING CLB AT FL190. AFTER LEVELOFF AT FL200 WITH HIGH ENG VIBRATIONS; FLT CREW ELECTS TO DECLARE AN EMER AND RETURN TO ZZZ.

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CLBING OUT OF FL190 TO FL200; WE EXPERIENCED 3 LOUD EXPLOSIONS FROM THE #1 ENG. THE THRUST OSCILLATED WITH LARGE YAW MOVEMENTS IN THE ACFT. LEVEL AT FL200 THE ENG STABILIZED ITS THRUST BUT CONTINUED TO HAVE HIGH VIBRATION INDICATIONS. NO RED WARNING OR AMBER CAUTIONS WERE DISPLAYED BY THE EWC. THE FO AND I WENT THROUGH THE ECAM PAGES AND EXCLUDING THE HIGH VIBRATION INDICATIONS THE ENG PARAMETERS WERE NORMAL. ABOUT THAT TIME THE FLT ATTENDANT CALLED FROM THE BACK AND SAID THEY AND A FEW PAX SAW FLAMES FROM THE #1 ENG DURING THE EXPLOSIONS BUT WAS NOT ON FIRE. WE DECLARED AN EMER AND CHOSE TO RETURN TO ZZZ FOR THE LNDG. DURING THE DECLARATION OF THE EMER WE ASKED ATC TO NOTIFY THE COMPANY OF THE EMER AND THAT WE WERE RETURNING TO ZZZ. ATC GAVE US VECTORS BACK AND WE BEGAN A SLOW DSCNT TO THE FIELD. IN THE DSCNT; WITH THE THRUST REDUCED; THE VIBRATION WAS NOT AS PREVALENT. FO MAINTAINED THE FLT CTLS WHILE I CHANGED DEST AND LNDG RWY INFO IN THE MCDU. WHEN I HAD FINISHED THE SET-UP TO LAND; WE ACCOMPLISHED THE DSCNT AND APCH CHKLIST. WE ENTERED THE BASE LEG FOR THE RWY AND THE FO AND I DISCUSSED THE LAST MIN THAT COULD BE DONE BEFORE LNDG AND ALSO THE POSSIBILITIES THAT COULD OCCUR DURING THE TOUCHDOWN. WE ADVISED TWR THAT OUR INTENTIONS WERE TO LAND ON RWY XX AND TURN OFF AND STOP FOR AN EXTERNAL INSPECTION OF THE ACFT FOR FIRE OR VISUAL DAMAGE THAT MIGHT AFFECT US CONTINUING TO THE GATE. THE LNDG WENT NORMAL AND AS PLANNED. THE CFR CLRED THE ACFT OF VISUAL ABNORMALITIES AND WE TAXIED TO THE GATE.