Similarity-based modeling of forward volume-flow-weighted temperature in naturally ventilated tunnel fires

Temperature and longitudinal velocity are strongly non-uniform across a naturally ventilated tunnel-fire section, so local peak temperature alone does not represent bulk downstream smoke transport. We define the forward domain by ux > 0 and introduce the forward volume-flow-weighted temperature Tin,v and its dimensionless coefficient Wv*. An exact decomposition separates thermal-core fullness from velocity–temperature covariance. For the reported horizontal-tunnel configuration, a conditional rational relation between Wv* and plume similarity distance ξ was calibrated with 3, 5, and 7 MW simulations, giving R 2 = 0.9939 for the algebraic variable s and Wv* RMSE = 0.0035. Within 3.5 ≤ ξ ≤ 21 and L/H ≥ 2, held-out 1 and 9 MW cases gave Wv* RMSE values of 0.0058 and 0.0045. In the five-grid 3 MW assessment, the 0.20 m result differed from the 0.10 m result by a mean of 0.47% and a maximum of 1.42% in Wv*. A matched 100/200 m, 5 MW domain-length test gave a mean relative absolute Wv* difference of 0.768% over L = 7–35 m. In 1:5 Froude-scaled tests, three mass-loss calibrations deviated from target HRR by at most 3.81%; the mean experimental-to-numerical temperature-rise ratio across 21 pairs was 0.9831, and six 2 and 8 MW Wv* points gave MAPE = 1.56% against the fixed correlation. Within these bounds, the descriptor provides a configuration-conditioned measure of forward convective transport.