That pump is similar to the variable speed pump in our Power-Tracs. In our case, it is used in a closed loop situation. The fluid is just recirculated through the pump and wheel motor system, and the charge pump keeps the system full. The case drains in my wheel motors leak fluid , and this fluid goes back to the pump, and the pump case fluid which is about 10 to 20 % of the pump flow will flow out to a hyd radiator and back to tank. . My pump also has a 10 micron filter in the suction circuit for the charge pump.
What exactly are you trying to do.
Are you trying to use it as a general type of hyd pump?
It is designed to provide a variable flow to say wheel motors, and is like an automatic transmission. When you move the squash plate lever, the pump will pump more fluid at high pressure, and when in neutral, very little fluid is flowing. The charge pump will still try and keep the pump full, and flush out the case drain for the pump.
The valve that controls all this is called a squash plate.
Since the picture showed it being used in a mower, there would probably be two of these in a ZTR, and only 1 in a hyd tractor lawn mower.
So in general, it is used to send a variable flow of hyd fluid to a hyd motor, and that motor can be controlled from 0 speed to max speed. The squash plate, if turned one direction, the motor may turn fwd, and if turned the other way will turn in rev.
When using this pump, the terms used are open loop, or closed loop. Has nothing to do with open and closed center.
If you try and over work this kind of pump, the relief valves in the pump will activate.