Results analysis and numerical model correction

The analysis of monitoring results for the different parameters under study in the ASD prototype, allowed the identification of two main differences between monitoring and simulation results:

• volumetric airflow within the ASD was lower than the predicted;

• air flow velocities over brine surface were much lower than expected average values.

Such differences where evaluated under two different and complementary approaches:

• air flow differences seemed to imply much larger head losses in the prototype than those assumed for the numerical model calculations;

• lower airflow velocities over brine surface really mean a certain velocity profile between the brine surface and the evaporation channel cover, which must be taken properly into account.

Results for air average velocity in the solar chimney from ASD prototype monitoring and numerical simulation, for the first 12 day monitoring period, are presented in Fig.4.1:

From the graphic in Fig.4.1 it is possible to see that the observed and simulated results for air flow average velocity are in phase, validating the comment above about the numerical model underestimation of head losses in the ASD prototype (instead of an error in the calculation of air flow motion driving force) according to [2].

A correction of the head loss calculation was made after analysis of ASD monitoring results of average air flow velocity in the Solar Chimney section for different driving force conditions (the driving force was calculated after numerical model presented in [2], for the observed climate conditions), after Fig.4.2, with all the data collected over an extended 30 days period:

Given that ASD inner air flow velocity is such that head loss equals available driving force, correction in the numerical model of the average air flow velocity calculation (in the chimney section and, consequently, in the evaporation section), was made with the equation below representing the solid line in Fig.4.2:

Uchim =V 0.05 + 0.3DF (1)

where DF stands for driving force, in [Pa], in line with the quadratic evolution of head loss with velocity.

Results for the observed air flow velocity over the brine surface (30 cm above it) and average airflow velocity in the same evaporation channel section (corrected from the average air flow velocity in the chimney section) were previously presented in Fig.3.4. Those results clearly show that, instead of a uniform velocity profile with convection occurring at an average airflow velocity, as assumed in the original numerical model, a more complex velocity profile occurs over the brine surface, with lower velocities around the interface region brine/airflow.

In order to include such airflow dynamics in the calculation of the evaporation rate, a general expression for boundary layer was included, after an estimated evolution throughout the evaporation channel, according to Fig.4.3 (the behaviour considered results also from some qualitative observations made with the injection of smoke):

The average velocity profile is described according to the following expression:

where Uo stands for undisturbed air velocity, y stands for height above brine surface and CH for total channel height. For the average air flow velocity in the evaporator section:

Air flow velocity to convection mass transfer calculation is, then, calculated as a function of the distance from brine surface and average air flow velocity, after (2) and (3):

(4)

Average velocity profiles in the evaporation section, calculated after (4) for different average air flow velocities, are presented In Fig.4.4:

Simulation results for the observed monitoring period, after implementation of these corrections to the model, can be seen in Fig.4.5, for two different representative heights from the brine surface to velocity profile calculations, 40 mm and 50 mm:

This shows that indeed the model, corrected as described, reproduces nicely the observed results. Air flow velocity calculation, for convection mass transfer, at 40 mm above the brine surface seems to fit better the observed evaporation results.

All of this will be further confirmed with more data, coming from the next measuring period It should be noted that this paper is being written according to the deadline of April 1st for its submission. More data is being recorded and, in particular, corresponding to sunnier spring and summer conditions, and will be presented at the Congress in June.