Heat Exchanger - Constant Efficiency Model

Model description

This document describes a counterflow heat exchanger model that uses a constant effectiveness approach. The user provides the heat exchanger effectiveness, denoted \(\varepsilon\) (epsilon), as a model parameter.

The heat transfer rate is computed as:

\[\dot{Q} = \varepsilon \cdot \dot{Q}_{\max}\]

where \(\dot{Q}\) is the actual heat transfer rate and \(\dot{Q}_{\max}\) is the maximum possible heat transfer rate (based on the inlet conditions and an ideal exchanger).

The maximum possible heat transfer rate is the smaller of the maximum energy that the hot stream can give up and the maximum energy that the cold stream can accept:

\[\dot{Q}_{\max} = \min \left( \dot{m}_H \cdot (h_{su,H} - h_{ex,id,H}), \; \dot{m}_C \cdot (h_{ex,id,C} - h_{su,C}) \right)\]

Definitions:

  • \(\dot{m}_H\), \(\dot{m}_C\) Mass flow rates of the hot and cold streams, respectively (kg/s).

  • \(h_{su,H}\), \(h_{su,C}\) Specific enthalpies at the inlets of the hot and cold streams (J/kg).

  • \(h_{ex,id,H}\), \(h_{ex,id,C}\) Specific enthalpies at the outlets of the hot and cold streams in an ideal heat exchanger (i.e., infinite area / infinite NTU).

Procedure to compute heat transfer rate:

  1. Compute or obtain the inlet temperatures and specific enthalpies \(h_{su,H}\) and \(h_{su,C}\).

  2. Determine the ideal outlet temperatures for a perfect counterflow exchanger:

    • The ideal cold-stream outlet temperature equals the hot-stream inlet temperature.

    • The ideal hot-stream outlet temperature equals the cold-stream inlet temperature.

    Convert these ideal temperatures to enthalpies: \(h_{ex,id,C}\) and \(h_{ex,id,H}\).

  3. Compute the two candidate maximum heat transfer rates:

    • Hot-limited: \(\dot{Q}_{H,\max} = \dot{m}_H \cdot (h_{su,H} - h_{ex,id,H})\)

    • Cold-limited: \(\dot{Q}_{C,\max} = \dot{m}_C \cdot (h_{ex,id,C} - h_{su,C})\)

  4. Compute:

    \[\dot{Q}_{\max} = \min(\dot{Q}_{H,\max}, \dot{Q}_{C,\max})\]

  5. The actual heat transfer rate is then:

    \[\dot{Q} = \varepsilon \cdot \dot{Q}_{\max}\]

Outlet enthalpies are computed as:

\[h_{out,H} = h_{su,H} - \frac{\dot{Q}}{\dot{m}_H}\]
\[h_{out,C} = h_{su,C} + \frac{\dot{Q}}{\dot{m}_C}\]

Assumptions:

  • Counterflow geometry.

  • User-specified constant effectiveness \(\varepsilon\), with \(0 < \varepsilon \le 1\).

  • Ideal outlet enthalpies computed using the ideal counterflow limit.

  • No heat losses to the environment.

  • No pressure drop inside the heat exchanger.

Class description

class component.heat_exchanger.hex_csteff.HexCstEff[source]

Component: Counterflow Heat Exchanger with Constant Effectiveness (HXEffCst)

Model: Simplified Heat Exchanger Model with Constant Effectiveness

Description:

This model simulates a counterflow heat exchanger with a fixed effectiveness (η). It estimates the maximum possible heat transfer based on inlet conditions and applies the given effectiveness to compute the actual heat transfer rate. The model assumes a simplified configuration without discretization or detailed internal states. It is suitable for quick, steady-state evaluations in system-level models.

Assumptions:

  • Steady-state operation.

  • Constant effectiveness (η) is applied across the entire heat exchanger.

  • No phase change or pressure drop effects are modeled.

  • Uniform flow distribution on both hot and cold sides.

  • Fluid properties are retrieved from CoolProp.

Connectors:

su_C (MassConnector): Mass connector for the cold-side supply.

su_H (MassConnector): Mass connector for the hot-side supply.

ex_C (MassConnector): Mass connector for the cold-side exhaust.

ex_H (MassConnector): Mass connector for the hot-side exhaust.

Q (HeatConnector): Heat transfer connector representing the total exchanged heat.

Parameters:

eta (float): Effectiveness of the heat exchanger [-].

Inputs:

fluid_H (str): Hot-side fluid.

h_su_H (float): Hot-side inlet specific enthalpy [J/kg].

P_su_H (float): Hot-side inlet pressure [Pa].

m_dot_H (float): Hot-side mass flow rate [kg/s].

fluid_C (str): Cold-side fluid.

h_su_C (float): Cold-side inlet specific enthalpy [J/kg].

P_su_C (float): Cold-side inlet pressure [Pa].

m_dot_C (float): Cold-side mass flow rate [kg/s].

Outputs:

h_ex_C: Cold-Side Exhaust specific enthalpy at outlet [J/kg].

P_ex_C: Cold-Side Exhaust pressure at outlet [Pa].

h_ex_H: Hot-Side specific enthalpy at outlet [J/kg].

P_ex_H: Hot-Side pressure at outlet [Pa].

Q_dot: Total heat transfer rate across the exchanger [W].

Example of use

from labothappy.component.heat_exchanger.hex_csteff import HexCstEff

"Simple test - Model for recuperators in simple thermodynamic studies "

HTX = HexCstEff()

# Set input conditions
HTX.set_inputs(
    fluid_C='Water',
    T_su_C=273.15 + 60,
    m_dot_C=1,
    P_su_C=3e5,

    fluid_H='Water',
    T_su_H=273.15 + 110,
    m_dot_H=0.3,
    P_su_H=10e5,
)

# Set heat exchanger parameters
HTX.set_parameters(**{
    'eta': 0.95,
})

# Solve the model
HTX.solve()

# Output results
HTX.print_results()
HTX.print_states_connectors()

References

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