Turbulent natural convection in isothermally heated open-ended building shafts: Numerical analysis of ventilation performance

We investigate buoyancy-driven ventilation in open-ended building shafts whose walls are isothermally heated, aiming to quantify passive removal of warm, polluted air from pedestrian-level urban canyons. Three-dimensional RANS CFD simulations (SST k − ω ) are carried out for a 36 m building containing a central shaft of height H = 32 m with square cross-sections b = 2 , 3, and 4 m and wall–ambient temperature differences Δ T = 10 , 20 , 3 0 ∘ C , corresponding to R a ≈ 2 . 9 × 1 0 13 − 7 . 6 × 1 0 13 (turbulent regime). A sensitivity study comparing far-field boundaries modeled as stationary walls versus zero gauge pressure outlets shows that the resulting mass flow rates differ by less than 10 %. The flow remains developing along the shaft and exhibits inlet separation with a delayed reattachment in wider shafts; three zones are identified: recirculation, core-flow, and boundary-dominated. Predicted mass flow rates span 3.76 − − 16 . 63 kg/s , with ventilation effectiveness (mass flow per unit heat input) 0.179–0.645 kg/kJ; increasing b improves effectiveness, whereas increasing Δ T enhances heat transfer faster than mass flow, reducing effectiveness. Partial validation against Churchill–Chu correlations for an isothermal vertical plate shows average Nusselt numbers within ≤ 15 % over most of the plate length. Two simplified models (a stack model with losses and a 1-D model) capture trends but underpredict 3-D effects tied to corner dynamics and entry recirculation; accuracy improves when the stack model uses a friction factor inferred from wall shear. From the CFD data, we propose building-scale correlations for the average Nusselt number, effective friction factor, and entry length as functions of Rayleigh number and aspect ratio b / H , to guide preliminary design of passively ventilated shafts in urban settings.