Development of a Double Mantle Heat Exchanger Storage Model

The first step leading to a realistic thermosiphon simulation model is the implementation of a double mantle heat exchanger storage tank. This development was carried out based on a simple hot water storage model already available in CARNOT and a validated TRNSYS double mantle heat exchanger storage tank model developed at Malaga University, Spain [5].

Подпись:
In order to consider stratification effects within the hot water storage, it is necessary to divide it into n user settable vertical layers with either a uniform height or volume. Figure 1a shows one volume segment of height dh and the storage section it affects in terms of energetic calculations (dotted lines). The model is one-dimensional and, therefore, the storage is not divided into additional layers alongside its length. Hence every volume element of the model is calculated using the full length of the storage (Figure 1b).

Подпись: dUt dt Подпись: V dT Q Q c-P-V ■ = Qm - Qo dt Подпись: (1) Подпись: dT = Qtn - Qou dt c- p - V Подпись: (2)

The thermal behaviour of the model is described by mathematical-physical correlations within every node. For every element in the collector fluid and the tap water, the energy balance is drawn. Within this energy balance, the changes of the inner energy of every element have to be equal to the difference of the entering and leaving heat flow (1, 2).

The main advantage of the CARNOT model in comparison to the TRNSYS model can be found in the way the storage model is discretised.

The storage model in TRNSYS does not consider the heat conductivity of the mantle and storage as well as the transfer coefficients of all materials (including liquids) directly. In order to describe the heat flux within the TRNSYS model, the convective heat transmission on the surfaces and the heat conduction through the different layers, like e. g. steel or insulation materials, are combined resulting in an overall heat transfer coefficient. This coefficient has to be estimated and validated by measurement data. The advantage of this method is the reduced amount of variables, e. g. if there are unknown conditions, there is just one parameter to estimate.

The major advantage of the more complex model built for CARNOT is the possibility to use this model in optimization and development simulations, as almost every important parameter — like materials and geometric values — can be tuned. Figure 2 shows the calculated heat transfer mechanisms heat conduction and convection.

The TRNSYS model uses the same length for the inner and outer mantle of the storage. In the CARNOT model, these lengths can be varied. This has the advantage of adapting the length and fluid capacity of real double mantle storages, as shown in Figure 1. The model calculates the heat transfer from the heat exchanger to the tap water only according to the heat exchanger length lma„ae (Figure 1a). For the rest of the storage length the occurring heat loss from the hot water through the storage material, the insulation and the convective losses into the surrounding ambience is calculated.

Besides the thermal part of the storage, the calculation of the pressure drop is one of the most important variables in thermosiphon systems, as the circulation of the system is maintained by very small pressure differences, due to density decrease or temperature increase along the collector, in the range of 10 — 300 Pa (or 1 — 30mm water column) [6]. The model considers the pressure drop according to height differences in the storage between entering and returning pipes (Figure 1). The dynamic pressure drop resulting from differences in velocity between the piping and the heat exchanger is calculated using the flow rate and the geometrical parameters of entering pipes and storage tank. Bends and other obstacles at the connection between the piping and the storage’s heat exchanger mantle are described by additional friction coefficients. As the velocity of the heat

transfer fluid within the double mantle heat exchanger is nearly zero, there is no dynamic pressure drop calculated.