Systems and methods for controlling backpressure in a heat engine system having hydrostaic bearings

A method for controlling flow of a bearing fluid to a hydrostatic bearing of a turbopump assembly, comprising:

• providing a pump having:
• at least one hydrostatic bearing;
• a bearing fluid supply source fluidly coupled to the at least one hydrostatic bearing and configured to supply a bearing fluid thereto, the supplied bearing fluid including a working fluid in a supercritical state;
• a bearing fluid drain;
• a bearing fluid discharge line fluidly coupled to the at least one hydrostatic bearing, the bearing fluid drain, a backpressure regulation valve and a to pressure sensor;
• wherein:
• the backpressure regulation valve is configured to be throttled between an opened position and a closed position, and the pressure sensor is configured to generate pressure data indicative of bearing fluid pressure in the bearing fluid discharge line;
• controlling flow of the bearing fluid to the hydrostatic bearing by:
• controlling a bearing fluid supply system to provide the bearing fluid from the bearing fluid supply source to the hydrostatic bearing;
• receiving pressure data from the pressure sensor;
• determining a thermodynamic state of the bearing fluid in the bearing fluid discharge line, based at least in part on the received pressure data;
• and
• throttling the backpressure regulation valve between the respective opened and closed positions to regulate a backpressure of the bearing fluid in the bearing fluid discharge line, in order to maintain therein the thermodynamic state of the working fluid that is in a supercritical state.