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Hydraulic Networks

Hydraulic networks are made of a concatenation of fluid elements (see section 4.1.17) filled with an incompressible medium. A fluid element consists of three nodes: in the end nodes the temperature and pressure are the unknowns, in the middle node the mass flow is unknown. The end nodes play the role of crossing points in the network, whereas the middle nodes represent the flow within one element. To determine these unknowns, three types of equations are available: conservation of mass and conservation of energy in the end nodes and conservation of momentum in the middle node. Right now, only stationary flow is considered.

The stationary form of the conservation of mass for incompressible fluids is expressed by:

| (83)

where is the density and the velocity vector. Integration over all elements connected to an end node yields:

| (84)

where is the mass flow from node i to node j or vice versa. In the above equation is always positive.

The conservation of momentum reduces to the Bernoulli equation. It is obtained by projecting the general momentum equation on a flow line within an element with end nodes i and j and reads:

| (85)

Here, is the height of the node, the pressure, the density, the gravity acceleration, the cross section in the node and is the head loss across the element. The head loss is positive if the flow runs from i to j, else it is negative (or has to be written on the other side of the equation). The head losses for different types of fluid sections are described in Section 4.3.

Notice that the height of the node is important, therefore, for hydraulic networks the gravity vector must be defined for each element using a *DLOAD card.

The conservation of energy in stationary form requires ([13]):

| (86)

where is the external heat flux, is the body flux per unit of mass, is the specific heat at constant pressure (which, for a fluid, is also the specific heat at constant specific volume, i.e. [16]) and is the absolute temperature (in Kelvin). Integration of the energy equation over all elements belonging to end node yields:

| (87)

where is the convection coefficient with the walls. If one assumes that all flow entering a node must also leave it and taking for both the value corresponding to the mean temperature value of the entering flow, one arrives at:

| (88)

where .

The calculation of hydraulic networks is triggered by the *HEAT TRANSFER keyword card. Indeed, such a network frequently produces convective boundary conditions for solid mechanics heat transfer calculations. However, network calculations can also be performed on their own, i.e. it is allowed to do *HEAT TRANSFER calculations without any solid elements.

To determine appropriate boundary conditions for a hydraulic network the same rules apply as for aerodynamic networks.

Next: Convergence criteria Up: Types of analysis Previous: Aerodynamic Networks Contents