When it comes to rejecting or denying someone entry, there are numerous phrases that can be used interchangeably with "turn someone away". First, we have "refuse admission", which implies denying someone's entry to a place or event. Additionally, "reject" suggests dismissing or declining someone's request or application. Another synonym is "rebuff", highlighting the act of refusing someone firmly or bluntly. Similarly, "repel" signifies driving someone away or warding off their attempts to gain entry. "Disqualify" implies denying eligibility or disqualifying someone from participating. Lastly, "debar" signifies excluding or barring someone from entry or participation. These synonyms effectively convey the act of turning someone away in various contexts.