Hyrdaulic Systems Simulation Tool |
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Hydraulic Lines
Into the hydraulic lines block there are 12 blocks relevant to hydraulic lines, hydraulic inertance, hydraulic resistance and the hydraulic compliance.
For the hydraulic lines there are three blocks: the first represents the lines upstream the valves, both supply and return lines, the second represents both the controlled lines downstream the 4 way valves, while the last represents the single controlled line downstream the 3 way valves. In case of very long pipes, to increase the simulation accuracy, it is possible to utilise more than one line block, connected in series. The hydraulic lines blocks represent the fluid inertia, the resistance and the compliance of a pipe; in the library the blocks representing inertance (plus resistance), resistance and compliance are also available and can be used to simulate a pipe network. In this case each pipe can be represented by one inertance block or by a resistance block, while the compliance will be used to represent the connection point; the compliance value shall take into account the total volume of the pipe and the input flow shall be the sum of the flow of each input pipe. Also for the hydraulic inertance, resistance and compliance there are blocks relevant to the double lines and to the single line; the single line blocks, at their turn, are relevant to supply and to return line. The difference between supply and return line is only due to sign convention: for supply line if the input pressure is higher then the output pressure the flow is positive, while for return lines if the output pressure is higher then the input pressure the flow is positive.
The line between the power supply and a valve can be represented utilising a block ‘Double Hydraulic Line Upstream Valve’ but can also modelled utilising inertance and compliance blocks, as shown in the following figure. It can be noted that the Pressure signal of the Hydraulic Supply is divided into two signals: the first is the supply pressure, input to the supply line, and the second is the return pressure, input to the return line. The two line output pressure signals are both connected through a mux to the valve input pressures. Based on this configuration, as stated above, the input Pressure of the return Inertance is the system return pressure and the output pressure of the line is the valve return pressure. The return flow is considered positive when the direction of flow is from valve to system return and consequently the return line ‘In_Pressure’ (system return) shall be less then the return line ‘Out_Pressure’ (Valve return). The same is for the flows. The inertance block take into account both the fluid inertance and the line resistance, so the flow is a function of the pressure at the to line ends. The two outputs (Out_Flow and In_flow) are effectively the same signal duplicated only to simplify the connections and for uniformity with the other line blocks that have each two inputs and to outputs. Similarly the compliance pressure is a function of the input and output flows and the two pressures are the same signal.
The Inertance blocks can be substituted by Resistance blocks. The Inertance take into account both the inertance and the resistance but in same case can be convenient consider only the resistance, to increase the simulation speed. The inductance shall be considered only for pipes very long or having large section. In any case, when a pipe is modelled, the computation time can increase so it is advisable to use a numerical integration methods suitable for stiff problems like ‘ode23tb’. In some cases, it can be also useful to use a fixed step method with a small time step (e.g. 0,00001 seconds or less). Based on the above, it is strongly recommended to simulate an hydraulic line only when the resistance, the inductance or the compliance are not negligible, e.g. in case of long lines. Otherwise the introduction of these blocks can reduce the simulation speed or can lead to mathematical instability without improve the simulation accuracy.
The ‘Double Hydraulic Line upstream valve’ blocks has the following inputs and output:
the lines upstream pressures (is a two elements vector)
the lines output flows (is a two elements vector)
the lines input flows (is a two elements vector)
the lines downstream pressures (is a two elements vector)
The ‘Double Hydraulic Line downstream 4 way valve’ blocks has the following inputs and output:
the lines downstream pressures (is a two elements vector)
the lines input flows (is a two elements vector)
the lines output flows (is a two elements vector)
the lines upstream pressures (is a two elements vector)
The ‘Single Hydraulic Line downstream 3 way valve’ has the following inputs and output:
the lines downstream pressure
the lines input flow
the lines output flow
the lines upstream pressure
The ‘Double Hydraulic Inertance’ or ‘Resistance’ block has the following inputs and output:
the lines input pressures (is a two elements vector)
the lines output pressures (is a two elements vector)
the lines input flows (is a two elements vector)
the lines output flows (is a two elements vector)
The ‘Single Hydraulic Inertance’ or ‘Resistance’ has the same input and output but the signals are not two element vectors.
The ‘Double Hydraulic Compliance’ block has the following inputs and output:
the lines input flows (is a two elements vector)
the lines output flows (is a two elements vector)
the lines input pressures (is a two elements vector)
the lines output pressures (is a two elements vector)
The ‘Single Hydraulic Compliance’ has the same input and output but the signals are not two element vectors.
The following figure shows how to connect the blocks to represent the lines upstream and downstream of the valve.