modelIsochoric

Information

Isochoric process (density rho_in = rho_out, specific volume v_in = v_out) mainly suitable for representing stationary-flow representations of isochoric periodic heat transfer in a closed cycle system (systemSpec==Cycle). Inlet amd Outlet refer to the initial and final state of the process. Alternatively it can be used to represent a pseudo stationary-flow isochoric process (systemSpec==Flow).

The following quantities can be specified either as parameters or as time-varying input signals:

• Temperature difference: dT = T_out - T_in
• Outlet temperature: T_out

Specifying the outlet specific enthalpy h_out, specific enthalpy difference dh, outlet specific internal energy u_out or specific internal energy difference du would create a system of nonlinear equations, as there is no function Medium.setState_dhX(state) or Medium.setState_duX(state) available. This feature is therefore currently not included.

The heat flow rate can optionally be an EnergyFlowInput or an EnergyFlowOutput; see UsersGuide.EnergyFlow for details. During simulation, the physical positive direction of the heat flow rate is visualized on the icon layer by a red arrow.

The model supports four possible operating modes:

1. If the outlet state is set and the heat flow rate is not an input, the model is balanced.
   In this case, the heat flow rate Q_flow is computed from the given specific internal energy difference du and mean mass flow rate m_flow: Q_flow = m_flow*du.
2. If the outlet state is set and the heat flow rate is an input, the model is locally overdetermined.
   This condition is indicated by a plus symbol on the icon layer. The mean mass flow rate is then computed from the given heat flow rate Q_flow and specific internal energy difference du: m_flow = Q_flow/du. To obtain an overall balanced system, a locally underdetermined component, such as Sink_free , must be connected.
3. If the outlet state is not set and the heat flow rate is an input, the model is balanced.
   In this case, the specific internal energy difference du is calculated from the given mass flow rate m_flow and heat flow rate Q_flow: du = Q_flow/m_flow. Determining the outlet state (p,h) from du introduces one implicit nonlinear equation. The parameter dp_start is used to initialize the nonlinear equation solver iteration.
4. If the outlet state is not set and the heat flow rate is not an input, the model is not permissible.
   In this case, both the heat flow rate Q_flow and the specific internal energy difference du are unknown, and the equation Q_flow = m_flow*du cannot be balanced. This condition is indicated by a prominent red lightning symbol.

Assumptions for the isochoric process (closed system, cyclic operation, systemSpec == Cycle):

• Cycle-averaged steady state: Over multiple consecutive cycles, the system satisfies dE_sys/dt = 0 and dm_sys/dt = 0.
• The mass flow rate m_flow represents the cycle-averaged mass throughput of the system.
• No net external forces on the system: The control volume is not subject to acceleration as a rigid body, i.e. \sum F_external = 0.
• No boundary work: w_exp = p*dv = 0.
• Negligible kinetic and potential energy changes: Differences between inlet and outlet are neglected, i.e. g*z_2 + 1/2*c_2^2 ≈ g*z_1 + 1/2*c_1^2.
• Constant composition: No change in species mass fractions across the control volume, i.e. X_in = X_out.

Assumptions for the isochoric process (open system, steady-flow, systemSpec == Flow):

• Steady-state conditions: dE_sys/dt = 0, dm_sys/dt = 0
• No net external forces on the system: The control volume is not subject to acceleration as a rigid body, i.e. \sum F_external = 0.
• Isochoric pressure work (pseudo shaft work): w_p = v*dp.
• Negligible kinetic and potential energy changes: Differences between inlet and outlet are neglected, i.e. g*z_2 + 1/2*c_2^2 ≈ g*z_1 + 1/2*c_1^2.
• Constant composition: No change in species mass fractions across the control volume, i.e. X_in = X_out.

Parameters

Connectors

Components

Revisions

• 2026-08, by Silvan Keim (silvan.keim@dlr.de):
  Improved icon.
• 2026, by Raphael Gebhart (raphael.gebhart@dlr.de):
  Initial version.