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Turbulence-Chemistry Interaction (TCI) impact
What is turbulent combustion?
What is turbulent combustion?
Turbulent combustion is the process of burning a fuel–air mixture under turbulent flow conditions. In other words, when a flame develops in a flow where velocity fluctuations, eddies, and vortices exist, the turbulence strongly interacts with the chemical reactions. This complex physics brings the following important features: (1) multi-scale nature, (2) enhanced mixing, and (3) complex regimes of flame structure as detailed below:
Multiscale nature – Turbulence involves a cascade of eddies ranging from large to very small. These interact with chemical reaction zones, which may be extremely thin.
Enhanced mixing – Turbulence brings fresh reactants to the flame and removes products quickly, accelerating combustion.
Complex regimes – Depending on turbulence intensity and flame thickness, you can have wrinkled flamelets (flame is thin, turbulence just wrinkles it), and distributed reaction zones (high turbulence disrupts flame structure).
How can we model the turbulent combustion?
How can we model the turbulent combustion?
Major challenge in modeling the turbulent combustion phenomenon is identified by the turbulence chemistry interaction (TCI) problem, which acts as a essential role in determining highly energetic and random motion of the turbulent flame. The turbulent flame is in general featured by observing its intrinsic non-linear natures and multiscale physics. To accomodate this highly demanding feature in the numerical modeling platform, it is important to understand various strategies of TCI modeling in engineering level CFD framework.
A general mathematical framework for engine combustion modeling is largely based on mass-weighted averaged (called Favre average) Navier-Stokes (NS) equations. Using this averaging technique, the resulting balance equations may include several unclosed terms due to turbulent transport, which is mathematically formulated by non-linear and high order of moments of fluctuating scalars. Especially, mean reaction rate source for individual chemical species introduces numerous high order unclosed moments, which is numerically impossible to be integrated in CFD framework.
Modeling of Non-Premixed Combustion
Modeling of Non-Premixed Combustion
A specialty of turbulent non-premixed combustion modeling lies in the needs to define mixture fraction, z, which locally measures the fuel/oxidizer ratio and defines boundaries conditions in non-premixed flame problems. It should also be noted that the mixture fraction is considered a passive scalar; by definition it is neither consumed nor produced by chemical reactions, thus it is transported only due to fluid dynamics transport phenomena. Due to this nature, the mean quantities of mixture fraction and its variance can also be resolved by implementing a relevant set of transport equations.
Unsteady Flametlet Model: Representative Interaction Flamelet (RIF) model
Unsteady Flametlet Model: Representative Interaction Flamelet (RIF) model
In a general effort to achieve computationally efficient TCI modeling, the primitive variable method is often preferred because the turbulent mean scalar variables can be resolved from reduced-order manifold of TCI solution libraries rather than integrating numerically stiff ODE problems.
The representative interactive flamelets (RIF) model executes the flamelet solver (i.e., RIF solver) dynamically and allows the flamelet solution to be interacted with the CFD mixture field solutions.
The RIF model utilizes a dynamically computed flamelet library and turbulent mean scalars are calculated by weighting the laminar flamelet solutions with a relevant choice of statistics, described by a presumed probability density function (PDF). The basic principle of the RIF model is identical with this approach except that it incorporates the unsteady history of flamelets that would otherwise be unable to follow the rapid change of mixing field, especially in the high-pressure diesel spray problem. The internal structure of the flamelet solver working with CFD solver is illustrated in the figure (left).
Eulerian Particle Flamelet Model (EPFM)
Eulerian Particle Flamelet Model (EPFM)
The RIF model with a single flamelet solution may not properly capture the relevant dynamics of unstable and unsteady spray flame. To circumvent this limitation, Eulerian Particle Flamelet Model (EPFM) allows to use dynamically changing flamelet history by tracking the fuel-air mixture element in space and time.
In this model, a mass-weighted fraction of Eulerian particles is tracked as a marker solution of injected mixtures that correspond to each flamelet history and the model allows multiple Eulerian particles that are sequentially initiated from the injector exit as simulated in the figure (right). Each solution of the multiple Eulerian marker is paired with their flamelet solution library, and allows to account for spatially changing chemically reactive scalars. It should also be noted that different Eulerian marker solutions may overlap together due to turbulent mixing; therefore, each of flamelet solutions is weight-averaged to determine resulting turbulent ‘mean’ value.
The mixing intensity can be resolved by domain-averaging the scalar dissipation rate and then provided to the each flamelet solution to account for the stretched flamelet effect. This is very important because this allows transient ignition and quenching impact to be addressed in the 1-D flamelet solution.
Implementation of RIF + EPFM framework in OpenFOAM
Implementation of RIF + EPFM framework in OpenFOAM
This is first-of-its-kind approach to implementing the dynamic flamelet solver with the EPFM approach in OpenFOAM platform. This implementation was tested in the GTFOAM (Generic Thermo-Fluids OpenFOAM Library), which was one-of-kind task in my dissertation. The GTFOAM+RIF model setup was verified against the conventional combustion model (Well-Stirred Reactor: WSR) and also compared with the commerically available CFD software, CONVERGE in resolving the spray flame structure under a diesel-like test condition. Figures shown below present the comparisons in predicting ignition delay and flame lift-off length for ECN Spray A configuration with RIF vs. WSR model frameworks. Overall, the general tendency was properly captured by the GTFOAM+RIF modeling framework and presents superior prediction accuracy compared to the CONVERGE simulations.
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