Why is flux in field winding constant in DC shunt motor, but not series motor?
A shunt motor's field winding is connected directly across the motor terminals hence, if you apply X volts to the motor you apply X volts to the armature and X volts to the field winding. If X is constant then the field current remains constant.
In a series connected motor, the field winding is in series with the armature hence, the current through the field is dependent on the current into the armature and that is dependent on the applied motor voltage and the mechanical load on the motor.