Deviation of water mass fractions in StaticTwoPortHeatMassExchange

[BartgeierXC]

Basic description

@Laszlo1968 and me are modeling a moisture exchanger for a fuel cell system. For this we are using the Buildings library, as described in the following:

The model mainly consists of two linked submodels of the library:
Buildings.Fluid.Interfaces.StaticTwoPortHeatMassExchange.

As depicted below, the humidifier StaticTwoPortHeatMassExchange part of this model adds moisture to the dry air coming from the environment or out of a compressor in the amount which is specified by a certain defined efficiency.

The dehumidifier StaticTwoPortHeatMassExchange submodel takes the water/steam out of the moist air coming from the FC-Stack.
A certain amount of water is then given to the humidifier part of the model depending on an exchange effectiveness.

The mass flow rate of the exchanged water is given by the variable mWat_flow.

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Water exchange effectiveness

Calculating the effectiveness in terms of water exchange is done as follows:

Equation:

m_Wat,flow = m_flow,a1 · ϵ_L − m_flow,a2

The water mass flow rate of the hot moist air stream entering port_a1 is calculated by multiplying the signals of two sensors:

• massFracH2O_a1
• senMasFlo_a1

The effectiveness of water exchange is defined as a function of the air volume flow rate at port_a2 (in standard liters per minute).

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Energy balance

The energy balance consists mainly of two parts: sensible heat (Q_Sensible) and latent heat (Q_Latent).
Together with thermal losses to the environment, these form the total transferred heat Q_Trans.

The thermodynamic states and mass flow rates of the entering streams determine the maximum sensible heat that can be exchanged:

C_1,flow = max(port_a1.m_flow · Medium.specificHeatCapacityCp(dehumidifier.sta_a), 1.0e−6)
C_2,flow = max(port_a2.m_flow · Medium.specificHeatCapacityCp(humidifier.sta_a), 1.0e−6)

Then:

Q_Max,flow = C_Min,flow · (senTem_a2.T − senTem_a1.T)

where
C_Min,flow = min(C_1,flow, C_2,flow)

Sensors:

• senTem_a1.T → moist stream (port_a1)
• senTem_a2.T → dry stream (port_a2)

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Sensible heat effectiveness

If the temperature conditions for some operating points are given, the effectiveness of the sensible part is expressed as:

Q_Sens = ϵ_S · Q_Max,flow
T_Sens1 = (Q_Sens / C_Min,flow + senTem_a1.T) − 273.15
T_Sens2 = (senTem_a2.T − Q_Sens / C_Min,flow) − 273.15

The two calculated temperatures, T_Sens1 and T_Sens2, represent the values at the outgoing ports (port_b1 and port_b2). An empirical function gives a value for ϵ_S.

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Total transferred heat

The total amount of transferred heat and corresponding water mass flow is considered as:

Q_VapT0 + Q_Sens

with

Q_VapT0 = h_VapT0 · dehumidifier.m_Wat,flow

where h_VapT0 denotes the specific evaporation enthalpy of water at standard reference conditions.

The final transferred heat is adjusted using an offset PI-controller:

Q_Trans = firstOrderQflow.y
dehumidifier.Q_flow = Q_Trans
humidifier.Q_flow = −Q_Trans

Feedback condition:

senTem_b2.T − T_Sens2 = 0

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Mass fraction calculation

Using the sensor signals after the humidifier and dehumidifier does not yield proper results, since sensor-based outgoing mass fractions (_OM) deviate from the calculated values (_CV).

To obtain correct water mass fractions, the following calculations are applied:

X_w,dehumOut = (massFracH2O_a1.Xi · senMasFlo_a1.m_flow − m_Wat,flow) / senMasFlo_b1.m_flow
X_w,humOut = (massFracH2O_a2.Xi · senMasFlo_a2.m_flow + m_Wat,flow) / senMasFlo_b2.m_flow

Deviations in the sensor-based signals influence the energy balance due to incorrect water content,
which also affects the specific enthalpy. The deviations can also be observed directily when comparing the calculated with the measured mass fractions:

Does anybody have an idea where the deviation stems from or how to determine it? Maybe somebody had similar experiences working with MoistAir massfractions or the StaticTwoPortHeatMassExchange?

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The corresponding Modelica code for this model description can be found attached here:
FCSHumidifier.txt