The OP stated it is a delta wound primary and a wye secondary.
In reality the transformer is either a 3-winding delta-wye (typical for >15kVA) or it is a 2-winding T connection (typical for transformer <15kVA). In either case there is no neutral provision on the primary side, so it can only be wired with 2 or 3 phase conductors.
For all piratical purposes (ignoring additive vs subtractive connections and with generous rounding):
If only 2 phase conductors are brought to the primary the results are;
For a delta winding - one winding will be energized at full voltage and two windings will be energized at 50% voltage (they are connected in series) The resultant output should be 3 individual single phase 2-wire circuits of 120V L-N, 60V L-N and 60V L-N.
For a T connected windings - one winding will be energized at full voltage and the other winding at 0V. The resultant output will be single phase outputs of about 104V L-N, 104V L-N and 1 at 0V. Or one winding will be energized at 87% and half of one winding will be at 37%, the outputs could be about 75.6V, 44.4V and 0V (it depends on which primary winding is energized).
If 3 phase conductors are brought to the transformer, the output will be as designed even with one output phase conductor left 'open circuited'.
If the OP had a special transformer design of either an open-delta primary or an open wye primary, the effect of connecting only 2 phase conductors to the primary would be equivalent to having 2 single-phase transformers connected in series, the windings of an open-delta would about 50% voltage and those of the open-wye about 87%