The Fundamentals of Building Internal Pressure Dynamics Induced Through a Dominant Opening

Abstract

A dominant opening created in a building during a windstorm may subject the building to significant internal pressure dynamics that can impact on the safety of the envelope and the structure as a whole. This paper reviews previous work in this area and considers a number of issues surrounding the dynamics of building internal pressure induced through a dominant opening to provide new insights into the problem. A rigorous derivation of the governing equation reveals that the formulation of Vickery is the correct one to use for a full scale building. However, it is more appropriate to characterise the building internal pressure dynamic system by non dimensionalising this equation using a time scale representing the system, such as the Helmholtz resonance period, instead of a time scale representing the onset turbulence used in the published literature. In this manner, the importance and physical significance of, as well as the ranges for, a number of dimensionless parameters, including the onset flow Mach number, the opening air slug inertia ratio, opening loss coefficient, and the opening inertia coefficient, are discussed. A frequency ratio that represents the location of the Helmholtz resonance frequency in the turbulence spectrum was also obtained. This revealed a length ratio, the ratio of turbulence integral length scale to the opening air slug length, as obtained by previous writers, as being another important non dimensional parameter. A typical range for this parameter is also established. It is shown that the opening loss and inertia coefficients in use in the literature can range widely and it is not always easy to determine this for a specific situation in a predictive manner. To compound this problem, determining these coefficients for the full scale building from model-scale tests in a wind tunnel is difficult, primarily due to the presence of linear damping that is not present at full scale. This is shown to be mitigated with the volume distortion approach to model scale testing. Furthermore, a re-consideration of the opening flow physics has revealed that since the flow velocity and thus the Reynolds number varies cyclically from zero to a maximum level, the loss coefficient can vary significantly within each flow oscillation cycle. A correlation available in the literature was utilised to demonstrate the influence of varying loss coefficient on internal pressure response; and of testing under non windstorm conditions. It was found that testing at low wind speeds, both at full scale and at model scale, can lead to overestimation of the internal pressure response; while at the same time giving an incorrect indication of a relatively high constant value of loss coefficient. Volume distortion at model scale however, accounting for the design full scale to model scale velocity ratio, leads to correct estimation of the internal pressure response. However the corresponding loss coefficient obtained can be large, and may not be used to simulate internal pressure response at full scale under windstorm conditions. This partially explains the reporting of high loss coefficient values in the published literature. Extreme care must therefore be exercised with internal pressure data obtained at non windstorm conditions, either at full or model scale.