Modified Tank Model for TRNSYS Simulations

Annual system simulations were carried out with the simulation tool TRNSYS (Klein,

1998). A multi-node storage model was used (DrQck, 2000), with N = 100 equidistant nodes to describe the thermal stratification in the tank in one dimension. The model takes into account storage losses, heat transfer through heat exchangers, forced convection through the store, as well as an effective conductivity between the nodes to describe additional heat transfer caused by convection and conductivity. Furthermore, heat transport within the tank is modeled due to ‘numerical diffusion’. If the number of nodes, i. e. the discrimination of the model, is changed, the modeled heat transport is changed as well.

If a temperature inversion occurs, that is, if a colder temperature layer is placed above a warm temperature layer, the mean value of both layers is calculated in the next simulation time step. This corresponds to complete mixing of the two layers. The height in which the cold water enters the tank in the simulation is therefore decisive for the thermal stratification. Thus, the virtual inlet height hin can be used as a variable to model the mixing behaviour for different inlet devices.

The 2P-Model: Identification of 2 parameters

In recent studies (Jordan and Furbo 2003-1) the virtual inlet height into the tank hin was described as a function of boundary conditions (flow rate and temperatures) as well as two parameters to take into account different inlet device designs with the following energy

balance: [pTin “ jpstore(h)dh]-g • hin = 1 PTin • [7]eff2 (е4и — !)

veff is the effective upward velocity. It can be described as a function of the flow rate divided by an effective cross sectional area Ac:

The two model parameters reff and hoffset need to be identified with experiments for each inlet design. The 2P-model is used for comparison with a more general model in the simulations described in following sections.

The Ring model

The ring model is a further development of the 2P-model, to describe the variable hta as a function of solely the given buffer plate geometry and reference conditions.

The effective cross sectional area Ac is described by a ring around the buffer plate, with

the plate radius veff = — = m 2 (equ. 4)

Plm ‘ Ac, ring PTiii ‘n ‘ (r _rplate)

with the outer ring radius r as the sum of the plate radius and the ring width lw:

r _ rplate ^ lw •

With Ac = Ac, ring the virtual inlet height hin can be calculated with (equ. 1) and (equ. 2):

[PTin _ jPstore (h)dh ] ‘ g ‘ hin _ 2 p

The ring width lw was found to be approximately constant for the investigated inlet devices.

Comparison of measured and simulated temperature distributions

To compare measured and calculated thermal stratifications in the tank, the measured values of the initial storage temperatures, inlet temperatures and flow rates were used as input values for the simulation. 33 measurements (with 3 different initial tank temperatures, 4 flow rates and the three buffer plates) were used for model validation.

The comparison of measured and calculated values with the least square method yield to the value of lw = 10 mm for the ring width for all three inlets.

Figure 7b shows the simulated temperature distribution with the ring model corresponding to the measurement shown in figure 7a. The simulated and measured temperatures throughout the measurements cannot directly be compared, due to the fact that the thermocouples are placed in the corner of the tank. This causes a time delay between measured and simulated results of the mean values in the temperature nodes. For example, after two minutes, the temperature difference at h = 14 cm is higher than 16 K. Furthermore, in the simulation, the bottom part (up to h = 60 mm) of the store is more stratified than in the experiments.

Nevertheless, the measured temperatures in the tank are fairly well modelled. The mean square deviation sq of the thermal stratification directly at the end of the draw-off yields to

°.3 K with sq = N(Tmeas, n "Tcalc, n)2 .

Instantaneous temperature inversions can be noticed in the simulations, these layers are mixed in the next time step.

Since the temperature at the bottom of the tank decreases during the draw-off, hin rises continuously (figure 7c). The high values of hin at the very beginning of the simulations are due to the high inlet temperature caused by warm water in the pipes that remained there from the heating of the tank. The inlet heights determined for the times at which the PIV — vector maps were captured are hin=55mm(At = 10s), 45mm(1min), 110mm(2min) and 150mm (3min). Thus, hin corresponds to a height in the upper part of the vortex in the vector maps (figure 6a-d).

In figure 9 measured and calculated temperature distributions in the tank are shown, in figures a) and b) for the small, in c) for the medium size and in d) for the large buffer plate.

a) Small inlet, 2P-model.

c) Medium inlet, ring model. d) Large inlet, ring model.

Fig. 9 a)-d): Comparison of simulated (grey curves) and measured (black curves) temperature distributions.

As shown in c) and d) the temperatures can be very well predicted with the ring model, with lw = 10 mm. However, the deviation between measured and simulated values using the ring model increases significantly for the smallest buffer plate (9b). For large flow rates and small temperature differences between storage water and entering water, the model overestimates the mixing in the tank. The predicted temperatures at the bottom of the tank turn out too high. This can be explained by the flow patterns, which differ strongly for the small inlet compared to the larger ones as shown in figure 3. Therefore, the 2P-model needs to be applied in order to model the small inlet with a sufficient accuracy (Fig. 9a).

Annual System Simulations

A typical Danish small solar domestic hot water system was modelled with the simulation tool TRNSYS. A scheme of the system is shown in figure 10. It consists of a small storage tank with coil heat exchangers inside, a burner, pipes, and a pump. Parameters and assumptions for the calculations are listed in Table 1.

Two different domestic hot water load profiles were used, generated with the program DHWcalc (Jordan and Vajen, 2004). The flow rates of the first profile were chosen according to the Danish norm DS 439 (2000), with distributions around 6, 9, and 12 l/min and an average daily draw-off volume of 30, 30, and 40 litres, respectively. For the second profile, flow rate distributions around 3 and 8 l/min (mean daily draw-off volume 50 l each) were taken into account.

Annual system simulation results of the net utilized solar energy Qsol, net and the performance reduction rate rp are shown in figures 11 and 12. The net utilized solar energy is defined as the difference of the domestic hot water consumption energy QDhw and the

auxiliary energy supplied Qaux: Qsolnet = QDhw — Qaux

The performance reduction rate rp defines the relative additional auxiliary energy supply for a tank with a buffer plate diameter d compared to a tank with an ideal buffer plate:

rP

with d„: maximum diameter, which corresponds to an ideal inlet device.

Thus, rp characterizes the impact of the additional mixing caused by a non-ideal buffer plate in a solar storage tank. For an ideal inlet device cold water enters the tank in the lowest layer.

As shown in figure 11 for DHW-profile A with fairly high flow rates, the solar fraction is increased by 5 % for the investigated solar heating system with the large buffer plate (ring model) compared to one with the small buffer plate (2p model). The performance reduction rate (of the real buffer plates compared to ideal ones) drops from about 8 to 3% for the large and the small buffer plate, respectively (figure 12). The ring model under­predicts the net utilized solar energy for the smallest inlet by about 2%.

When the DHW profile with more moderate flow rates (profile B) is taken into account, the net utilized solar energy is increased by 3 % for the large compared to the small buffer plate. This corresponds to a decrease of rp from about 5 to 2% (large plate to small plate).

Conclusions

The flow fields around inlet devices can be visualized with an optical method called Particle Image Velocimetry (PIV). Velocity vector fields show vortex structures, which refer to the heights reached by the entering cold water into the store. It was found that the flow of the entering water was first directed to the tank bottom, if the tested buffer plate diameter is sufficiently larger than the diameter of the inlet pipe. In contrary, when using the same buffer plate diameter as the tube diameter, for most reference conditions, large vertical velocity components can be measured close to the inlet gap. Only when small flow rates and large buoyancy forces are applied, the flow is deflected downwards with a small buffer plate.

A mathematical model was developed to describe the impact of the buffer plate diameter on the mixing in the tank, while taking into account the operating conditions (temperatures and flow rate). The model contains one unknown parameter, i. e. the width of a ring around the buffer plate lw that determines the effective cross section for the upward flow in the tank. This width was found to be the same value for all three tested buffer plates. Thus, the constant was assumed to be generally valid within a certain range of diameters for the given tank geometry. However, whereas the thermal stratification can be described well for sufficiently large buffer plate diameters, the inaccuracy between measured and calculated temperatures increase rapidly for buffer plate diameters similar to the inlet pipe diameter. For these small buffer plates an additional, empirical parameter needs to be taken into account.

Annual system simulations of a typical small Danish solar domestic hot water system were carried out with two different domestic hot water profiles. The simulation results showed that the net utilized solar energy were increased by 3 to 5 % when the largest investigated buffer plate was used compared to the results for the smallest (marketed) buffer plate.

Future investigations should be focused on the impact of the tank geometry on the model constant lw. Furthermore, a more general function should be developed to describe the mixing effects for small buffer plates and for inlets through the tank side.