The traditional method of collecting large quantities of data by holding each factor constant, in turn until all possibilities, is an approach that quickly becomes impossible due to the number of factors increases (full factorial) as in this case of seven-factor test with about 3 levels in each factor. It i

solved by choosing a set of test points that allow to estimate the model with the maximum confidence using just a fraction of the number of test runs; for this case only 100 optimally-chosen (space-filling) runs is enough to fit the model.

The chosen operating conditions are those typical for an air conditioning (Tev = 10°C, TCon = 30°C): condensation pressure of 250 hPa, evaporation pressure of 40 hPa and ambient temperature of 25°C. The simulation factors were summarized in Table 1 with the correspondent range of variation. As material of the fins were tested the aluminium, the cooper and the stainless steel AISI 316L. The input data relevant to implicit numerical aspects are: 6 s of time step, 12 nodes for axial and radial direction.

Table 1 — Simulation factors and the respectively range of variation

Hot water temperature, Tae Hot water mass flow, ma Cycle period, t Number of tubes, nt Number of fins, nc Thickness of the fins Fin and tube material

The designed test plan was simulated and the results were tested by a variety of radial basis functions (Gaussian, Thin-Plate Spline, Logistic, Wendland, Multiquadrics, Reciprocal Multiquadrics) and Quadratic to find out the function that has the lowest root mean square error (RMSE); it was chosen Quadratic for coefficient of performance (COP) and specific cooling power (SCP) with the following RMSE of 0.012056 and 2.7091, respectively.

4. Results

The statistical model results are extensive and spread; for this reason a base-case, taken as reference, was chosen by the great COP with the relatively higher SCP, considering that the maximum of both occurs in different operating conditions. It was found: a hot water temperature of 100 °C with 0.8 kg/s, the cycle period of 40 minutes, 56 tubes and 100 cooper fins of 0.5 mm.

To evaluate the influence of the simulation factors, the results are showed in the surrounding of the base-case. Fig. 4 reports the effects on the COP of: (a) cycle period for some number of fins; (b) hot water temperature for some cycle periods; (c) number of fins, switching the material; (d) hot water mass flow, switching the material; (e) number of tubes, switching the material; (f) number of fins for a given thickness. Analyzing these graphics it was concluded that the coefficient of performance (COP) increases with:

• the number of fins, however for long cycles (40 min.) fewer fins is more efficient;

• the cycle period;

• the hot water temperature; for levels greater than 105 °C, it does not change the COP;

• the number of fins; the maximum happens in 135 fins independently of the material;

• the material, in this case, aluminium is the best;

In the same way, the Fig. 5 depicts the effects on the SCP of: (a) hot water mass flow, switching the material; (b) cycle period for some number of fins; (c) number of tubes, switching the hot water mass

flow; (d) number of tubes, switching the material; (e) number of fins, switching the material; (f) hot water temperature for some number of tubes. The main conclusions that can be taking is that the specific cooling power (SCP) increases with:

• the material; in this case, cooper is the best;

• the number of fins.

(c) (d) n. n t c (e) (f) Fig. 4 — Influence of the simulation factors on the COP.

(b)

t

(d)

c

(e) (f)

Fig. 5 — Influence of the simulation factors on the SCP.

5. Concluding remarks

The present study investigated statistically the results of an adsorber mathematical model in order to optimize its design, founding the best operation point and the influence of each of the seven design factors (hot water temperature and mass flow, cycle period, number of tubes, number of fins, thickness of the fins and material of the fins).

The results showed that all the factors are statistically significant and interdependent. In other words, a change in one factor affects directly the others. It shows the importance of the statistical model for analyzing the main design parameters. As main results, it was found that the system performance (COP) is strongly dependent on the number of fins, the material and the cycle period. For the specific cooling power (SCP), the more relevant factors are the number of fins, the number of tubes and the hot water temperature.

The optimized adsorber parameters were the following: the hot water temperature of 100 °C with 0.8 kg/s, the cycle period of 40 minutes, 56 tubes and 100 cooper fins of 0.5 mm. It results on a COP of 0.52 and SCP of 51 W/kg.

6. Acknowledgements

The authors gratefully acknowledge the CNPq for the financial support provided to this work through

Research Project Grant No. 504229/2004-4 and the CAPES for the scholarship given for the first

author (DBR) of this paper.

References

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