Flame Dynamics and Reignition modeling

Turbulent diffusion flames experience velocity gradients (strain rate) that vary in space and time, increasing in magnitude with increasing Reynolds number. Since the combustion conversion rate is limited by the fixed chemical time scales of the elementary reactions that describe the combustion of each fuel-oxidizer mixture, eventually combustion is unable to adjust to fast flow time scales and the reaction is partially and locally quenched. The quenching or extinction process starts at those locations where the rate of heat release, which sustains the high temperature of the combustion, is unable to balance the rate at which the flow extracts heat from the reaction zone. The flame ceases to exist once the temperature drops sufficiently bellow the extinction temperature of the flame (all remnant temperature and chemical products diffuse quickly away and radicals recombine into stable, practically inert, species). If the Reynolds number keeps increasing, for example by increasing the velocity in a jet flame, extinction will propagate and quench the flame globally (not just locally or transitorily). The process by which high strain rates quench the flame is called extinction while the healing of a quenched zone, by advection or heating to more favorable regions is termed reignition. These locally quenched regions of a flame are called here “flame holes”; although the extinction zones can have arbitrary shapes even resembling strips or islands. After the development of the flame hole, the quenched region grows, shrinks, merges, splits, and changes shape depending on the evolution of the flame rim. The figure below shows a jet flame with extinguished flame holes.

DNS of Jet Diffusion Flame with Reduced Chemistry

In this project we study how flame holes behave in realistic three-dimensional flows using reduced mechanisms for methane-air combustion. These simplified mechanisms are used to reduce the amount of computation but keeping the chemistry model realistic. We show bellow movies of a diffusion jet flame at different stages.

Postprocesing of a large database requires collaborations among disciplines. This was accomplished by utilizing fast algorithms from computer graphics that were applied to the database.

The Collapse of a Diffusion Flame Hole

In this project we studied analytically the dynamics of the collapse of a diffusion flame hole in a counterflow using the edge-flame model of Buckmaster. We discovered that the rate of collapse of a hole is dictated by the balance of the temporal rate of change and diffusion in the transport equations for the temperature and species. Moreover, the temporal evolution of the hole radius is given by a half-power of time.

Flame reignition

When an active flame gets close to quenched mixture, it can initiate reignition of the gas faster than otherwise possible. We investigate the details of the dynamics of this process, which turns out to be the result of balancing of diffusion and reaction in an uncommon manner.

Flame hole dynamics

Computationally modeling all these flow/chemistry interactions at high Reynolds numbers is prohibitively expensive using first-principle methods, i.e. resolving all fields. The transport and reaction of each chemical species needs to be computed and the number of species is large, ranging from tens to hundreds of species in reduced and full chemical mechanisms, respectively. More importantly, in turbulent reacting flows of interest for flame hole dynamics, the reaction zone thickness is typically many times smaller than that required to resolve the turbulence. In the absence of extinction, one well-established modeling approach is to represent the mixture as an ensemble of thin reaction zones called flamelets. The reaction takes place near the stoichiometric surface, where fuel and oxidizer meet in stoichiometric proportions. Flamelets are based on an asymptotic analysis technique (not based on ad-hoc modeling concepts). Modeling turbulent diffusion flames that are partially quenched using flamelets needs to incorporate the structure of the boundary that separates a flame from a quenched region. It is found that the flame hole boundary propagates at its own speed and it has a rather complex multidimensional structure (at least nominally two dimensional). The flame boundary structure is a proper type of flame called an edge flame and it has mixed propagation properties that is strain-rate dependent. The generalization of the flamelet modeling concept to broken flamelets is called flame hole dynamics. It is a physically-based enhancement to flamelets that incorporates the physics of the flame boundary using edge flame physics to model broken flamelets. This modeling approach removes the need for detailed calculation of the advection-diffusion-reaction problem that is tightly coupled in the edge flame. The only information required in this modeling approach is the edge flame velocity as well as the orientation of the flame boundary curve, since the edge flame is supposed to propagate normal to the flame rim. Time-dependent effects, such as unstationary response of the edge flame to time variations of mixture composition, strain rate, etc, are not incorporated at this level of closure, but they could be included in future, extended models, if deemed necessary. In the end, one needs to solve an evolution equation for a flame state field on the moving stoichiometric surface, and here is where the Cartesian embedding methods play a crucial role. The movie below shows a fully integrated flamelet/flame-hole dynamic simulation of a lifted jet flame.