modelPolytropicPerfectGas

Information

Polytropic process (p*v^n = const.) of a perfect gas (p*v = R*T, cp = const.) suitable for modeling compressors, blowers, fans, and turbines. The model can be used for a steady-flow open process or for a periodic closed cycle process.

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

• Pressure difference: dp = p_out - p_in
• Pressure ratio: pRatio = p_out / p_in
• Outlet pressure: p_out
• Outlet temperature: T_out
• Compression ratio: rhoRatio = rho_out / rho_in
• Outlet density: rho_out
• Outlet specific volume: v_out

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

• Polytropic efficiency: eta_pol
• Polytropic exponent: n
• Isentropic efficiency: eta_is
• Outlet pressure: p_out
• Outlet temperature: T_out

Relevant specific works for a steady-flow open process are:

• shaft: w_s (+ q) = dh = cp*dT
• pressure: w_p + w_r = w_s, w_p = n/(n-1)*R*dT
• friction: w_f

Relevant specific works for a periodic closed cycle process are:

• internal: w_i (+ q) = du = cv*dT
• expansion: w_exp + w_r = w_i, w_exp = 1/(n-1)*R*dT
• ambient pressure: w_amb = - p_inf*dv
• net expansion: w_exp_net = w_exp - w_amb
• friction: w_f

Note:

• Defining the outlet temperature T_out twice yields an unbalanced model
• Defining the outlet pressure p_out twice yields an unbalanced model
• Defining the outlet temperature T_out, power P and mass flow rate m_flow yields an unbalanced model

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

The model supports four possible operating modes:

1. If the outlet state is set and the power is not an input, the model is balanced.
   In this case, the power P of a steady-flow open process is computed from the given specific enthalpy difference dh and mass flow rate m_flow: P = m_flow*dh. For a periodic closed process the power is computed from the given specific internal energy difference du and mean mass flow rate m_flow: P = m_flow*du,
2. If the outlet state is set and the power is an input, the model is locally overdetermined.
   This condition is indicated by a plus symbol on the icon layer. The mass flow rate is then computed from the given power P and specific enthalpy difference dh or specific internal energy difference du: m_flow = P/dh or m_flow = P/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 power is an input, the model is balanced.
   In this case, the specific enthalpy difference dh or specific internal energy difference du is calculated from the given mass flow rate m_flow and power P: dh = P/m_flow or du = P/m_flow.
4. If the outlet state is not set and the power is not an input, the model is not permissible.
   In this case, both the power P and the specific enthalpy difference dh (or the specific internal energy difference du) are unknown, and the equations P = m_flow*dh or P = m_flow*du cannot be balanced. This condition is indicated by a prominent red lightning symbol.

Further assumptions for the polytropic process:

• Steady-state conditions: dE_sys/dt = 0, dm_sys/dt = 0
• No heat transfer: Q_flow = 0
• Losses accounted for via polytropic efficiency eta_pol, polytropic exponent n or isentropic efficiency eta_is
• 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.
• Rigid boundary, no expansion work: w_exp = 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.

The heat flow rate can be accounted for as P → P + Q_flow, w_s → w_s + q, w_i → w_i + q, w_r → w_r + q.

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.