A mathematical model for heat detector activation time under ship fire in a long-narrow space

The prediction of fire detector activation time is essential to ship fire safety design. In this study, a model was developed to predict heat detector activation time under ship fires in a long-narrow space. Firstly, smoke transport time of fires in a long-narrow space was determined by the time of smoke spreading from fire resource to the target location (i.e. the location of heat detector in this study) on the ceiling. Theoretical calculation method concerning smoke transport time under steady fires was then proposed based on the correlations of temperature and velocity developed in previous studies. Series of experiments were conducted in a reduced-scale test rig for validation. Using the proposed method, a dimensionless model of transport time under steady fires was theoretically derived. Secondly, following the temperature rise equation of heat detector and considering the influence of smoke transport time lag, analytic solution was obtained by integrating for steady or quasi-steady fires. And a time-varying spreadsheet template combining with Improved Euler's Method was proposed to predict the activation time for unsteady fires. Case study results showed the proposed model is applicable for long-narrow spaces, which breaks its usage limits of DETACT-T2.