You need a battery. Alternators usually won't work or they won't be stable without a battery.
The battery negative goes to the frame of the alternator.
Battery +ve goes to B+
Between battery +ve and D+ you need a switch and a lamp in series, to simulate the ignition switch and the alternator warning lamp. I suggest a 2 - 6 W incandescent bulb. The lamp will glow when the switch is off and the alternator is not running. That is providing the field current to get the alternator running. Without that current, a lot of alternators won't start.
Alternators are designed to be run up to about 15000 rpm. You should run the alternator at 5000 rpm or more to get the maximum current from it.
A normal power supply will be quieter than an alternator.