A distribution valve comprises: a housing, and a spool in the housing, the spool mounted in a valve chamber so as to be rotatable along an axial axis, and the spool comprising a sidewall comprising a first spheroidal segment and a second spheroidal segment, a spool first port in the first spheroidal segment, and a spool second port in the second spheroidal segment; and an intermediate member mounted between the housing and the spool and fixed relative to the housing and in sliding contact with the sidewall of the spool in a sealed manner, wherein a first valve port is defined when the spool first port and an intermediate first port overlap, and a second valve port is defined when the spool second port and an intermediate second port overlap, wherein a degree of opening of the valve ports changes as the spool rotates relative to the housing.