A dimensionless modeling framework for scaling flameless combustion furnaces: Integrating energy–exergy and flow-similarity analyses for predictive, low-emission, and scalable industrial design

Flameless combustion offers ultra-low emissions and high thermal uniformity, but scaling such systems from laboratory to industrial applications remains challenging due to complex interactions between flow, heat transfer, and chemical kinetics. Conventional scale-up methods rely on empirical modifications that often disrupt the distributed combustion regime. This study presents a dimensionless scaling methodology, grounded in the π–Buckingham theorem, for preserving regime stability during the transition from a 10 kW laboratory furnace to a 300 kW semi-industrial prototype. Four alternative scaling strategies—differing in geometric similarity and treatment of thermal conductivity—were assessed using three-dimensional CFD simulations validated against experimental data. The evaluation encompassed thermal fields, pollutant formation, flue gas recirculation (FGR), turbulent Reynolds and Damköhler numbers, and energy–exergy efficiencies. All configurations maintained flameless operation, but the approach combining temperature-dependent conductivity with a variable aspect ratio delivered the most favorable balance of performance indicators. It achieved an average temperature of 1689 K (close to 1754 K in the laboratory case), reduced the reactive zone thickness by 36 %, and raised the FGR peak to approximately 450 % above laboratory levels. Turbulent Reynolds and Damköhler numbers remained within ranges typical of stable flameless regimes. NO and CO emissions were minimized to 6 mg/kJ and 22.2 ppm, respectively, fully meeting EPA standards. Energy and exergy efficiencies were preserved at 39 % and 68 %, closely matching laboratory performance. The proposed framework provides a transferable and physics-based pathway for designing large-scale, low-emission flameless combustion systems without post hoc empirical adjustments, facilitating reliable industrial deployment.