Corrigendum to “Modeling of the optimum tilt of a solar chimney for maximum air flow”

Abstract

There is an error in Eqs. (45) and (46) describing the average gas velocity in a solar chimney. These equations are used to describe the air velocity as a function of the chimney geometry and of the average density and, therefore, temperature of the air inside the chimney. In these equations sin(s) (s: slope of the chimney with respect to the horizontal), should not be raised to the second power. The term sin(s) originates from transforming the vertical chimney equations to the inclined case. In doing this, one should either keep the vertical Cartesian axes system and so replace the length of the chimney, L, with the product L∗ sin(s), or rotate the axes by s and then replace the acceleration of gravity by g∗ sin(s). Apparently, it is naive to do both.

This error affected the estimated average gas velocity presented in Figs. 7a, 8a, 9a, 12a and 13. The CFD predictions shown in the same plots are irrelevant to our code, i.e., are not affected by the error. Inspection of the written numerical code indicates that the error also did not affect the predictions of the Air temperature, Glazing temperature and Absorber temperature shown in the figures.

The authors give below a short account of the significance of this error to the main conclusions of the article. Regarding Figs. 8 and 9, the correct optimum tilt for maximum air flow is ∼50–60o (∼65–70o in the paper) which is again in fair agreement with the CFD prediction of ∼60o. Fig. 12a displays optimum tilt of the chimney and maximum air velocity values versus the months of a year. The correct values of the optimum tilt are lower by ∼5–15o than those presented in the paper and the maximum air velocity values are higher by at most ∼10% (for summer months) than those presented in the paper. However, the qualitative trend of both the maximum air velocity and optimum tilt versus the months of a year remains the same. Fig. 13 discusses whether it is worth it to incline a chimney to its maximum air velocity tilt compared to its operation at a vertical position (tilt = 90o). The highest deviation in air velocity between the two cases is expected to occur in summer time where the new calculations indicate a deviation of ∼18% instead of the mentioned in the paper ∼10%. For winter time, the deviation between the inclined and vertical cases is expected to be insignificant. All in all, the closing statements of the article that for winter time the gain is not so large “against concerns about the stability of the construction” and for summer time “decisions must be made more carefully” are still valid.