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Derivation of an empirical frequency-dependent friction factor for transient response analysis of water trap seals in building drainage systems

Flows in building drainage systems (BDS) are inherently unsteady. The changing nature of these flows produce pressure transients that can be harmful to water trap seals, the last line of defence against sewer gas ingress into habitable spaces. Air pressure transients propagate throughout BDS until they are diminished by either a relief valve, an open termination or, under certain circumstances, produce their own ‘relief valve’ through a compromised water trap seal. The spread of the SARS virus through empty water traps in Hong Kong in 2003 highlighted the worst possible consequences of water trap seal compromise. These air pressure transients can be simulated and their effects predicted. Only one numerical model exists for modelling airflow and the associated air pressure regime in BDS—the method of characteristics-based AIRNET. The current water trap boundary condition within the AIRNET model consists of a steady laminar frictional flow relationship, which does not replicate the unsteady pressure regime in the building drainage system. An improvement on this frictional representation is due to Carsten—Zilke, a methodology that allows a moving frictional term for water to trap surface interaction. This research proposes an alternative, empirically derived friction factor, and represents a significant simplification of the calculation process, leading to a robust, dynamic prediction methodology for water trap seal response to applied air pressure waves. Practical application: The development of new empirically derived frictional expressions to predict the effects of air pressure transients on appliance trap seals within a method of characteristics model provides far superior prediction results to those currently available. These new expressions enhance the modelling capabilities of AIRNET and prove that high frequency air pressure waves do not contribute to water trap seal depletion. The non-destructive nature of short duration or high frequency air pressure wave oscillations has contributed to the development of a non-invasive methodology for detecting water trap seal defects in building drainage systems, and this research serves to prove conclusively that using low amplitude, short duration pulses or sinusoidal pressure waves with a frequency above 3 Hz is non-destructive to traditional water trap seals in building drainage systems.