The attached model shows a small example of how Simscape works in evaluating Across and Through variables, and specifically how the constant area orifice(same as fixed orifice) block works. In the attached model example.mdl, two orifices connect into a double-acting hydraulic cylinder whose mechanical piston is connected to a mass-damper-spring system. One end of the orifices have a pressure source that maintains the pressure constant (-4e6) at this end. Since pressure is an across variable, both the lower ports of orifices o1, and o2 have the same constant pressure kept by the pressure source.
At the other end of the orifices, the pressure is determined by the hydraulic cylinder, specifically the variable volume chambers within this cylinder. (To see this block, right click on the cylinder and select look under mask. Note that this has 2 variable volume chambers). The variable volume chamber's initial condition(such as initial piston position,etc) determine the initial pressure at this end of the orifices. Once the pressure difference is determined across the orifices, the flow rate is found out based on the pressure-flowrate equation of the orifices, as mentioned in the doc link:
<http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/hydro/ref/fixedorifice.html>
Once the current flow rate is obtained, the pressure of the orifices at the upper port at the next time is obtained from the current flow rate, and current pressure and the control signal input of the variable volume chamber, according to the flow rate-pressure equation shown in the below link:
<http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/simscape/ref/pistonchamber.html>
Thus, the pressure is internally determined, and the flow rate across the orifices obtained directly from the equation of the orifice.
To read more about how Simscape works, and how across and through variables are used to resolve the blocks internally, please visit the following links:
<http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/simscape/ug/bq89sba-1.html#bq89sba-2>
<http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/simscape/ug/bql2kkl-2.html>
To read more about the Double acting Hydraulic cylinder, visit here:
<http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/hydro/ref/doubleactinghydrauliccylinder.html>
A good debugging technique on a Simscape hydraulics model, is to use Ideal Pressure Sensors and Flow Rate Sensors at different points to measure the pressure and flow rates there. In the attached model, an ideal pressure sensor is used to measure the pressure at the lower ports of the orifices.(Please see the scope 'pressure at lower ports')
It might also be helpful to think of pressure-flowrate in the same terms as voltage-current, following kirchoffs laws.
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