Modeling the Air Change Rate in a Naturally Ventilated Historical Church: Multiplelinear Regression Analysis (Civil Project)

In this study the air infiltration through the envelope of a naturally ventilated stone church located in Bergby (Gävle, Sweden) is studied. The project is focused on Multiple Linear Regression (MLR) modeling the air change rate (ACH) inside the church hall and studying the factors (stack effect and wind effect) that influence the air infiltration.

The weather parameters outside the building were recorded in a weather station and the properties of the air inside the church was analyzed with different methods. Infrared thermography techniques and thermistors were used to measure the temperature inside, the tracer gas method to measure the ACH and the blower door technique to measure the tightness of the building envelope. In order to know the pressure coefficients on the church envelope a physical model of the building was studied in a wind tunnel.

Firstly, only the values obtained from the weather station were used to calculate the predictors of ACH and see which parameter influence more on its variation:  temperature difference (∆T) indicating the stack effect; and wind speed (WS), the component of wind speed perpendicular to the long-side facades of the church (WS90) and their square values (WS2 and WS902) indicating the wind effect.

The data obtained in the wind tunnel were later used to do the MLR study with new predictors for indicating wind effect (∆Cp∙WS, ∆Cp∙WS2, ∆CpOUT-IN·A∙WS, ∆CpOUT-IN·A∙WS2, ∆CpC-H∙WS, ∆CpC-H∙WS2).

Better prediction of ACH was obtained with the square of the wind speed (WS2) instead of the magnitude itself (WS). However, the latter (WS) provided better results than the regression with the magnitude of the perpendicular component of the wind (WS90). Although wind speed influences in ACH, it alone seems to be a very poor predictor of ACH since has a negative correlation with ΔT when the data under study include both day and night.

However when high wind speed are detected it has quite strong influence. The most significant predictions of ACR were attained with the combined predictors ∆T & WS and ∆T & ∆CpOUT-IN·A∙WS2. The main conclusion taken from the MLR analysis is that the stack effect is the most significant factor influencing the ACH inside the church hall.

This leads to suggest that an effective way of reducing ACH could be sealing the floor and ceiling of the church because from those areas the air infiltration has big influence on the ACH inside the church hall, and more in this case that have been noted that the floor is very leaky.

Although different assumptions have been done during the analyses that contribute to make the predictions deviate from reality, at the end it would be possible to asses that MLR can be a useful tool for analyzing the relative importance of the driving forces for ACR in churches and similar buildings, as long as the included predictors not are too mutually correlated, and that attained models that are statistically significant also are physically realistic.
Source: University of Gävle
Author: Goicoechea, Saioa | López, Patricia

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