Principles and motivation

Hydraulic Discrete Partitioning is a technique that can lead to large reductions in run times for certain types of hydraulic systems. The principle is to divide a big hydraulic system into smaller sub-systems and run the simulation as a sort of co-simulation. Co-simulation has deservedly gained a bad reputation for often giving poor accuracy and not always giving any speedup. This technique depends on the following concept: there is a master system and one or more slave systems. A master system requests a slave to do some work and the slave delivers the work to the master when it is finished. The problem with co-simulation is that the intermittent (or discrete) nature of the communication is normally non-physical and hence it introduces large errors.

However, if the intermittent communication is physical then in theory, the co- simulation can deliver precisely the same results as a conventional simulation but in a shorter time. A well-known example of this is discrete control of a physical system. The discrete controller is the master and the physical system is the slave. Communication between master and slave is based on the sample/update times. Hydraulic discrete partitioning also uses a genuine physical discrete communication to produce a model that is natural for co-simulation and has no loss of accuracy due to the co-simulation. Discrete Partitioning takes advantage of the physics of wave propagation in hydraulic lines. These waves travel at a finite speed.

Not all line submodels model the line using finite wave propagation. The ones in Simcenter Amesim that do are based on the Lax-Wendroff concepts, they are:

• HLLW0

• HLLW1

• HLLW2

They contain a vector of pressure values and a vector of flow rate values. These are discrete internal variables. At the ends there are explicit state variables which enable the line to communicate with other Simcenter Amesim submodels without causing algebraic loops. It is possible to achieve exactly the same results as these line submodels by connecting three component submodels thus:

Figure 1: Connected submodels

The center section is always HLLWPIPE0 and the two ends are either HLLWCNXFLOW0 or HLLWCNXEFFORT0. If we plot graphs of variables over a short period of time, we can see their discrete nature.

Figure 2: HLLW1 - 1 pressure at internal nodes [bar]

Not all hydraulic systems benefit from this modeling technique. The sort of systems that can do so have the following characteristics:

• They are "busy" systems which are never in steady state equilibrium.

• There are rapid transients.

• It is vitally important to take into account wave effects in pipes.

• The systems are composed of several subsystems separated by lines.

Such systems are likely to include the Lax-Wendroff lines HLLW0, HLLW1, HLLW2 or the distributive/lumped alternatives: HL004x. Examples of applications that benefit from hydraulic discrete partitioning are:

• Fuel injection systems.

• ABS braking systems.