Abstract
A lifted hydrogen/nitrogen turbulent jet flame issuing into a vitiated coflow is investigated using the conditional moment closure (CMC) supplemented by the presumed mapping function (PMF) approach for the modelling of conditional mixing and velocity statistics. Using a prescribed reference field, the PMF approach yields a presumed probability density function (PDF) for the mixture fraction, which is then used in closing the conditional scalar dissipation rate (CSDR) and conditional velocity in a fully consistent manner. These closures are applied to a lifted flame and the findings are compared to previous results obtained usingβ-PDF-based closures over a range of coflow temperatures (Tc). The PMF results are in line with those of theβ-PDF and compare well to measurements. The transport budgets in mixture fraction and physical spaces and the radical history ahead of the stabilisation height indicate that the stabilisation mechanism is susceptible toTc. As in the previousβ-PDF calculations, autoignition around the “most reactive” mixture fraction remains the controlling mechanism for sufficiently highTc. Departure from theβ-PDF predictions is observed whenTcis decreased as PMF predicts stabilisation by means of premixed flame propagation. This conclusion is based on the observation that lean mixtures are heated by downstream burning mixtures in a preheat zone developing ahead of the stabilization height. The spurious sources, which stem from inconsistent CSDR modelling, are further investigated. The findings reveal that their effect is small but nonnegligible, most notably within the flame zone.
Highlights
In a previous Conditional Moment Closure (CMC) study [1], the lifted H2/N2 turbulent jet flame of Cabra et al [2] was thoroughly investigated using several CMC submodels and chemical kinetic mechanisms over a narrow range of coflow temperatures (Tc)
The usage of the presumed mapping function (PMF) closures does not affect the radial location of stabilisation as CMC-PMF yields 1.47, which is exactly the same value predicted by CMC-βG and CMCβM
Compared to the results of CMC-PMF, those of CMC-βG and CMC-βM are in better agreement with the experiments at x/d = 10
Summary
In a previous Conditional Moment Closure (CMC) study [1], the lifted H2/N2 turbulent jet flame of Cabra et al [2] was thoroughly investigated using several CMC submodels and chemical kinetic mechanisms over a narrow range of coflow temperatures (Tc). As for the closure of the Conditional Scalar Dissipation Rate (CSDR), the models of Girimaji [7] and Mortensen [8] were considered. Both models are derived by doubly integrating the PDF transport equations and using the same set of boundary conditions. The former is based on the homogeneous form of the equation, while, in the latter, the inhomogeneous terms are retained and PDF gradient modelling is applied to close the CV fluctuations. Mortensen’s model provides a fully consistent CSDR closure and degenerates exactly to Girimaji’s when the inhomogeneous terms are discarded
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