Physics

This section describes the physical model solved by OMOTES.SIMULATOR_CORE for thermal networks. The solver computes hydraulic and thermal state variables at asset connection points and network nodes for each simulation step.

The primary unknowns are:

  1. Pressure \(p\) [Pa]

  2. Specific internal energy \(u\) [J/kg] (IE)

  3. Mass flow rate \(\dot{m}\) [kg/s]

Specific internal energy is used as the thermal state variable. Temperature is obtained through fluid-property relations \(u(T)\) and \(T(u)\).

Basic governing relations

The network equations are built from mass, energy, and pressure relations.

Mass conservation at a node

At each node, incoming and outgoing mass flows balance:

\[\sum_i \dot{m}_i = 0\]

Energy conservation at a node

At each node, convective energy transport balances with local heat input or extraction:

\[\sum_i \dot{m}_i u_i + Q_{node} = 0\]

where \(Q_{node}\) is net heat exchange associated with the node equation.

Pressure relation across an asset

Across each asset, pressure difference is related to driving and loss terms:

\[p_{out} - p_{in} + \Delta p_{asset} = 0\]

where \(\Delta p_{asset}\) depends on the asset model (for example pipe friction, minor losses, or prescribed boundary pressure).

Energy relation across an asset

Across each asset, transported thermal energy changes according to supplied or extracted heat:

\[\dot{m} (u_{out} - u_{in}) = Q_{asset}\]

where \(Q_{asset}\) is positive for net heat addition to the fluid and negative for net heat extraction.

These relations are combined with asset-specific constitutive equations in the pages below.

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