Due to the alternating batch process the operation of the two sorptive heat exchangers is characterized by their transient behaviour. Therefore, a dynamic model of the sorptive heat exchanger was developed applying the modelling language Modelica and using the simulation environment Dymola. The dynamic model of the sorptive heat exchanger is using the Modelica Standard Library (version

2.2.2. ) in combination with the Modelica_Fluid (Beta version) library which is the commonly used library for thermofluid modelling in Modelica at Fraunhofer ISE. For the description of the moist air properties the Modelica. Media. MoistAir model was applied.

The two-dimensional numerical model is based on the following assumptions and simplifications:

• Modelling of one pair of adsorption and cooling channels

• Lumped, constant heat and mass transfer coefficients for adsorption and evaporation processes • No heat transfer and thus no heat losses to the surrounding

The sorptive heat exchanger model may be discretized in a desired number of volume elements. Each element comprises an adsorption channel model, a cooling channel model as well as a model of the heat exchanger wall.

Adsorption channel model

Both the adsorption and cooling channel models are based on finite volume elements. Applying the Modelica_Fluid standardized connectors, volume elements may be connected by fluid ports in which the medium variables of state pressure and enthalpy, the medium mass flow rate and in case of multi­substance media such as moist air the component mass fraction are handed over.

The sorption material and therefore the physical description of the sorption process is included in the adsorption channel model. The driving force of the adsorption process is the pressure difference between the partial pressure of vapour in the air volume pv and the equilibrium pressure of the sorption material pequ. The sorption process is mathematically described by the following linear interrelation:

in which flsorp (in the order of 10-8 kg/Ns) is the global mass transfer coefficient describing the

kinetics of water uptake by the sorption material. In order to solve the equation the equilibrium pressure pequ must be determined from the sorption equilibria. To this purpose a generalized form of Dubinin’s theory of volume filling is applied and implemented in a sorption material package for the use in Modelica [2]. The interaction between the sorption material and the air volume is described by postulating the balance equations of mass and energy via a set of differential equations. In the adsorption channel model the heat of adsorption is released in the sorption material, raising its temperature. Cooling of the sorption material is then calculated by convective heat transfer to the process air bulk flow and via conduction through the separating heat exchanger wall. To this purpose, the heat exchanger wall and the adsorption model volume element are connected via a heat port in which the state variable temperature and the flow variable heat flow rate are handed over.

Heat exchanger wall model

The heat exchanger wall model is a predefined Modelica model including the thermal mass of the aluminium wall and the heat conduction through the wall. It is connected to the cooling channel and the adsorption channel models via heat ports.

Cooling channel model

The cooling channel model is structurally similar to the adsorption channel model. The evaporation model again follows a linear driving force approach:

The cooling channel wall is always covered by a thin water film from which water evaporates into the air flow. Water is introduced to the volume element at a constant temperature and assumed to instantaneously reach the surface temperature which is a valid assumption for a thin water film [3]. Knowing the evaporation rate determined by equation 2 and taking account of the convective heat transfer rate between the cooling channel air flow and the heat exchanger wall, the balance equations of heat and mass conservation are solved.