The Washington Opera will open its next season with a new production of Bizet's "Carmen" under the National Symphony's principal guest conductor, Rafael Fru hbeck de Burgos. It will be Fru hbeck's American operatic debut.

The "Carmen," which is to be staged by Broadway director Michael Kahn, was announced yesterday along with six other productions to be performed at the Kennedy Center Opera House and the Terrace Theater between Oct. 30, 1982, and Jan. 30, 1983. It will mark the company's second successive extended repertory season, with performances almost nightly over a period of three months.

Joining "Carmen" in the Opera House will be Puccini's "Tosca" and Verdi's "Falstaff." In the Terrace Theater the company will mount a new version of Rossini's "La Cenerentola" directed by Gian Carlo Menotti; new productions of Mozart's "The Abduction From the Seraglio" and Britten's "The Turn of the Screw"; and a double bill of Gilbert and Sullivan's "Trial by Jury" and Offenbach's "Monsieur Choufleuri."

The season will be expanded to 63 performances from last year's 57. According to general director Martin Feinstein, that will make the Washington Opera season "the fourth longest in the United States after the regular seasons of the Metropolitan Opera, the New York City Opera and San Francisco."

Fru hbeck's "Carmen" will star Argentinian mezzo Alicia Nafe' in the title role. It will be her United States debut. Other singers include Dennis Bailey as Don Jose, J. Patrick Raftery as Escamillo and Elizabeth Knighton as Micaela. John Conklin will do the sets and Jane Greenwood the costumes. "Carmen" will be paid for by the Gramma Fisher Foundation.

"Tosca" will star Shirley Verrett in the title role and Carlo Bergonzi as Cavaradossi. Charles Long will sing Scarpia, Franc,ois Loup will be the Sacristan and John Mauceri will conduct. Feinstein said that two existing productions of "Tosca" are under consideration and that one will be chosen soon.

The "Falstaff" will be a production designed for the Canadian Opera by Wolfgang Skalicki. Thomas Stewart will star in the title role. Other principals will include Patricia Wells, Michael Devlin, Karen Hunt, Neil Rosenshein and Nucci Condo. Peter Mark Schifter, who did the G&S/Offenbach double bill, will direct and Cal Stewart Kellogg is the conductor.

Zack Brown will design Menotti's the "Cenerentola" production, as he did Menotti's "La Bohe me" this past season. Kellogg will conduct and the cast will include Gary Bennett, Alan Glassman, Loup and Claudette Peterson.

Britten's "The Turn of the Screw," a setting of the Henry James novel, will alternate with "Cenerentola." It will be a production designed for the Grand Theatre of Geneva by Jean-Claude Maret and will be directed by Franc,ois Rochaix. Mauceri is the conductor and the cast will include Susan Peterson, Elizabeth Knighton, Barbara Hocher and Bailey.

Gerard Schwarz, conductor of the Los Angeles Chamber Orchestra and a conductor of the Mostly Mozart series, will make his operatic debut in Mozart's "Abduction." The production will be in English and will be directed by Donald Saddler, who did "Wiener Blut." Zack Brown will design it and the cast includes Karen Hunt, David Gordon, Kathryn Gamberoni and Ronald Hedlund.

The double bill will be repeated with last season's participants.