For the construction of the detailed RealFuel3 model and reduced models a five-step procedure is followed:
- Combustion property target measurement of target fuel
- Surrogate fuel formulation
- Chemical kinetic model
- Chemical kinetic model reduction
- Chemical kinetic model calculation
Combustion property target measurement of target fuel
We have previously elaborated and tested a Combustion Property Target (CPT) methodology to identify and regulate the gas phase combustion behaviors of complex multi component mixtures that are real liquid transportation fuels. The motivations and assumptions describing its appropriateness are outlined in [1,2]. In brief summary, this approach is based on matching select physical and chemical properties of a targeted aviation fuel to be used as constraining parameters of fundamental significance, such that the reactivity of one fuel may be constrained to that of another. These studies have utilized the Derived Cetane Number (DCN), molar hydrogen to carbon (H/C) ratio, average molecular weight (MW), and the Threshold Sooting Index (TSI) as fundamental metrics to define properties of aviation fuels that are important for a large variety of combustion phenomena.
Surrogate fuel formulation
The 2nd Generation combustion property target surrogate formulator reported previously , considers n-dodecane, iso-octane, n-propyl benzene and 1,3,5, trimethyl benzene as surrogate fuel components.
Chemical kinetic model
A single municipal detailed chemical kinetic model comprising the surrogate components of both the 1st generation and 2nd generation Jet-A POSF 4658 surrogate fuel components has been assembled and reported previously . Here, the surrogate fuel chemistry is described by using the recent aromatic chemistry sets of Metcalfe et al. , Won et al.  and Diévart et al.  for toluene, n-propyl benzene and 1,3,5-trimethyl benzene respectively. These assemblies are extensions of one another, entirely self-consistent in construction. Thus, the performance demonstrated in each supporting work is expected to be implicitly valid in the surrogate model performance.
The higher n-alkane chemistry of Westbrook et al.  has been adopted for n-alkanes from n-pentane up to and inclusive of n-dodecane. The iso-alkane chemistry of Mehl and co-workers  is adopted to describe the oxidation of iso-octane and related iso-alkenyl species of carbon numbers greater than four. So called cross-reactions involving the interaction of high molecular weight fuel radicals or intermediates from the different generic functional classes are not considered in the kinetic model, which only allows fuel components to interact through their respective influence on the small species population (C4-C5 chemistry level).
Following careful considerations of the observations discussed above in composing surrogate fuels for typical synthetic paraffinic alternative fuels, this model has been expanded for the capacity of larger normal alkanes up to n-hexadecane through further adoption of the work of Westbrook et al.  and also to describe iso-cetane low and high temperature chemistry through adoption of the iso-cetane submodel proposed by Oehlschlaeger et al. . In the case where there has been a conflict or duplication of nomenclature, chemistry or thermodynamic parameters between the individual component sub-models, chemical reaction, rate constant and thermodynamic parameters have been chosen in the following order of preference; Metcalfe et al. (Won et al., Dievart et al.) > Mehl et al.> Westbrook et al. > Oehlschlaeger et al. Careful attention has been taken to ensure that each submodel is properly compatible at the interface C4-C5 chemistry level. A Lennard-Jones model is utilized to estimate binary diffusion coefficients. Wherever possible the input parameters are retained from the parent models. Otherwise collisional diameter and energy well depth parameters have been estimated largely based on those recommended in a review conducted by Mourits et al. , and correlated to molecular weight in a similar manner to Wang and Frenklach  by Dooley et al. . The detailed model construction is composed of 3147 species and more than 10,000 reactions.
Chemical kinetic model reduction
Even for the idealized one dimensional flame geometries considered for parametric kinetic model testing, as here, a certain level of model reduction from the highly detailed parent model is a prerequisite. Model reduction techniques are essential, not just to reduce computational costs but also to reduce the numerical stiffness associated with such a large number of conservation equations for broad classes of independent fuel chemistries and reaction pathways. When performing model reduction to ascertain detailed model performance, great care has been taken to ensure that the reduced model computations retain fidelity to those of the detailed parent model.
The Path Flux Analysis (PFA) kinetic model reduction scheme  has been utilized in this study. The procedure to produce reduced models first involves obtaining a numerical database of time dependent detailed chemical species profiles computed by the detailed model under homogenous constant volume ignition delay conditions (as described below). Subsequently, a second speciation database is constructed under steady-state perfectly stirred reactor conditions.
For the objective of ascertaining the performance of the detailed model under flame conditions for surrogate fuel components, after inspection of the target datasets, both databases are populated by considering conditions of: fuel/air mixtures of equivalence ratio of 0.6, 1.0 and 1.5, at 1 atm and temperatures of 1000 K, 1200 K, 1500 K, and 1800 K. It is important to note that the choice of target conditions that define the reduction process, is a decision (an assumption) made by the user. Thus it should be regarded as a source of uncertainty in the reduced model. The limitations of these approaches in terms of how smaller reduced models can be produced without losing the “true” fidelity of the parent model has not been fully addressed. In order to discuss this issue, as before, a range of reduced models for each fuel component have been generated by exercising the PFA “fidelity threshold” value incrementally from 0.05 to 0.35.
This procedure is followed specifying each “fuel” individually (n-hexadecane, iso-cetane, and each of the multicomponent mixtures suggested as surrogate fuels) to produce a range of reduced models. By testing the entire range of reduced models for each individual surrogate fuel component, the minimum model size to deviate in performance is identified, thus indicating an invalid reduction.
Chemical kinetic model simulations
All modelling simulations are conducted with a modified CHEMKIN II solver. Shock tube simulations are zero-dimensional and begin at the onset of the reflected shock period. Constant volume and homogeneous adiabatic conditions are assumed behind the reflected shock wave, consistent with the experimentally observed pressure profiles in e.g. [9,14]. The reflected shock pressure and temperature are input as the initial pressure and temperature respectively. The simulated ignition delay time is defined consistent with the diagnostic utilised in each particular set of experiments.
Laminar burning velocities are calculated by simulating freely propagating flames using the PREMIX module with the mixture averaged transport model. Simulations were performed over a constant domain size. The use of at least 900-1300 grid points for each computation of each model assured that increments of at least 0.04 for both CURV and GRAD are met and that the reported solutions are sufficiently resolved to be practically independent of grid size. In addition, the computation of a valid solution is verified by confirming that the computed peak flame temperature is equivalent to the adiabatic flame temperature of each respective flame. For the pure component reduced models presented below, peak flame temperatures are always within at most +/- 14 K of the adiabatic flame temperature at constant pressure. The laminar burning velocity computations reported are estimated to be within +/- 0.5 cm/s of the true (grid independent) solution.
At the outset of this study it is recognized that numerical calculations of the combustion process in practical combustor geometries under flowing conditions requires significant large memory allocations. Considering this intended application, a mixture averaged transport model is more desirable than the alternative multicomponent description as it is computationally much less expensive. Thus we have chosen to evaluate model performance against experiment with this transport description even though it is less fundamentally accurate than alternatives. It is also recognised that calculations with a multicomponent transport approach and treatment of thermal diffusive effects will result in burning velocities generally 1-2 cm/s lower than those reported here.
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