[Paper Review] Dynamics of unconfined spherical flames

Louis Leblanc, Maha Manoubi+4 more|arXiv (Cornell University)|Oct 31, 2012

Fluid Dynamics and Heat Transfer3 citations

TL;DR

This study investigates unconfined spherical hydrogen-air flames using the soap bubble technique to maintain constant pressure, revealing that buoyancy dominates flame dynamics in weak mixtures (low flame speed), causing flame balls to rise and transition into mushroom shapes. The experiments validate Zingale and Dursi's scaling laws, with a critical radius of 4 cm for 10% H₂-air mixtures where buoyancy overcomes flame propagation time scales.

ABSTRACT

Using the soap bubble technique, we visualize the dynamics of unconfined hydrogen-air flames using high speed schlieren video. We show that for sufficiently weak mixtures, i.e., low flame speeds, buoyancy effects become important. Flame balls of a critical dimension begin to rise. The experiments are found in very good agreement with the scaling laws proposed by Zingale and Dursi. We report the results in a fluid dynamics video.

Motivation & Objective

• To study flame dynamics under unconfined, constant-pressure conditions, which are difficult to replicate in standard lab settings.
• To investigate the role of buoyancy in weakly burning hydrogen-air mixtures with low laminar flame speeds.
• To validate theoretical scaling laws for flame rise and transition between buoyancy- and flame-speed-dominated regimes.
• To characterize the morphological transition from spherical to mushroom-shaped flames due to buoyant forces.
• To determine the critical flame radius at which buoyancy effects become dominant over flame propagation.

Proposed method

• The soap bubble technique is used to create a near-constant pressure environment, simulating unconfined deflagrations.
• High-speed schlieren visualization captures flame dynamics in real time, enabling observation of instabilities and shape transitions.
• Flame propagation time scale is derived from laminar flame speed S and density ratio ρb/ρu via t_burn = R/(S × ρb/ρu).
• Buoyant rise time scale is modeled using force balance between buoyancy and pressure drag, yielding V_rise = (2/3)√[Rg(1−ρb/ρu)], leading to t_rise = R/V_rise.
• A dimensionless ratio θ = t_burn / t_rise is used to distinguish regimes: θ ≫ 1 for weak mixtures (buoyancy-dominated), θ ≪ 1 for strong mixtures (flame-speed-dominated).
• The critical radius R_switch is calculated from θ = 1, using R_switch = (9/4)(S²/g)(ρb/ρu)⁻²(1−ρb/ρu)⁻¹ to predict transition point.

Experimental results

Research questions

• RQ1 At what flame radius does buoyancy begin to dominate over flame propagation in weak hydrogen-air mixtures?
• RQ2 How do flame morphology and dynamics change from spherical to mushroom-shaped as buoyancy effects increase?
• RQ3 To what extent do experimental observations of flame rise and shape evolution align with the theoretical scaling laws of Zingale and Dursi?
• RQ4 What is the critical flame radius for transition between buoyancy- and flame-speed-dominated regimes in low-flame-speed mixtures?
• RQ5 How do flame speed and density ratio influence the onset of buoyant rise in unconfined spherical flames?

Key findings

• For a 30% H₂-air mixture with a flame speed of 2.5 m/s and ρb/ρu = 0.14, the critical radius R_switch is calculated to be 85 m, far exceeding experimental scales, confirming negligible buoyancy effects.
• For a 10% H₂-air mixture with S = 0.1 m/s and ρb/ρu = 0.3, the critical radius R_switch is 4 cm, matching experimental observations of flame rise and detachment.
• Flame balls in weak mixtures begin to rise once their radius approaches the critical size, with visual evidence of detachment from the bottom wall at a few centimeters.
• The transition from spherical to mushroom-shaped flames is observed experimentally, with unburned fuel left behind, and a new flame kernel re-ignites and propagates through the residual mixture.
• The experimental data show excellent agreement with the theoretical scaling laws proposed by Zingale and Dursi, particularly in the prediction of the transition radius.
• High-speed schlieren video captures the full dynamics, including instabilities and buoyancy-driven rise, confirming the validity of the theoretical framework under unconfined conditions.