Ashraf N. Al-Khateeb

Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

The interplay between chemistry and transport is addressed by exploring the coupling between the spatial and temporal scales of one-dimensional laminar premixed combustion in reactive mixtures described by detailed chemical kinetics and multicomponent transport. System dynamics are investigated in the neighbourhood of the equilibrium state; in so doing, the time scales associated with modes of varying wavelength for the complete unsteady, spatially inhomogeneous system are obtained. The results reveal that short wavelength modes are dominated by diffusion-based time scales, and long wavelength modes are dominated by reaction-based time scales. The analysis further identifies critical wavelengths where the effects of reaction and diffusion are balanced, and it is seen that the critical wavelengths are well estimated by classical diffusion theory.

Phenomenology of Electrostatically Manipulated Laminar Counterflow Non-Premixed Methane Flames

AbstractThe effect of electrostatic fields on the dilute plasma of chemi-ions generated by a non-premixed, N2-diluted, methane-oxygen flame was studied in an experimental burner whereby a counterflow flame was positioned between the parallel plates of a large-scale capacitor. It was shown that flame morphology and location could be controlled solely through electrostatics. The location of the flame could be controlled through applied voltage, virtually independently of overall mixture composition and strain rate applied on the flame. In fact, through electrostatic actuation, it was possible to push the flame without extinction literally at the fuel nozzle, where there is very little oxidizer. Also, a computational framework for the study of these flames was developed in a computer program and verified with previous computations of the same flame. In future work, this framework will be used in tandem with the electrostatics computations that the computer program enables in order to probe the underlying phy...

On Numerical Resolution Requirements in Combustion Modeling

We discuss one-dimensional steady laminar premixed flames in a mixture of calorically imperfect ideal gases described by detailed kinetics and multi-component transport. The required spatial discretization to capture all detailed continuum physics in the reaction zone is determined through use of a robust method developed to rigorously calculate the finest length scale a posteriori. This is accomplished by reformulating the governing equations as a nonlinear system of differential algebraic equations. Then, the solution of the steady reaction zone structure is obtained, and the generalized eigenvalues of the locally linearized system are calculated at each point in the reaction zone. Their reciprocals provide all local length scales. Application of the method to laminar flames reveals that the finest length scale is on the order of 10−4 cm. Independent estimates from grid convergence studies on the continuum equations as well as from the underlying molecular collision theory verify the result. This finest length scale is orders of magnitude smaller than common engineering geometric scales, the discretization scales employed in nearly all multi-dimensional and/or unsteady laminar premixed flame simulations in the literature, and the flame thickness.Copyright

Veried Computations of Laminar Premixed Flames

The required spatial discretization to capture all detailed continuum physics in the reaction zone for one-dimensional steady laminar premixed hydrogen-air ames described by detailed kinetics and multi-component transport is accurately estimated a priori by a simple mean free path calculation. To verify this, a robust method has been developed to rigorously calculate the nest length scale a posteriori. The method reveals that the nest length scale is at the micron-level. This result is consistent with an estimate from the underlying molecular collision theory, and orders of magnitude smaller than the discretization scales employed in nearly all multi-dimensional and/or unsteady laminar premixed ame simulations in the literature. It is well understood that in any mathematically based scientic theory, associated computations should have delit y with the underlying mathematics, and the underlying mathematical model has to represent the observed physics. The rst issue is demonstrated by comparing computational results with another known solution and/or performing a formal grid convergence study, while the second issue is demonstrated by comparing the computational predictions with experimental data. Addressing these two issues, in this order, is a necessity in any computational study to build condence in both the simulation strategy and the underlying mathematical model. The exercise of demonstrating the harmony of the discrete solution with the foundational mathematics is known as verication. 1 For multi-scale problems, verication is dicult due to the range of the spatiotemporal scales, which may span many orders of magnitude. In this kind of problem, usually modeled by highly nonlinear equations, signican t coupling across the scales can occur, so that errors at small scales can rapidly cascade to the large scales. Moreover, the strength of the coupling across the scales is not known a priori. So, all the physical scales of the mathematical model, temporal and spatial, have to be captured in order to have full condence that predictions are repeatable, grid-independent, and thus veriable. Subsequently, in the validation step one can choose what physical phenomena and to what accuracy one wants to reproduce experiments. The main aim of this paper is to rigorously determine the required spatial resolution to capture all physical scales in a standard multi-scale problem: the steady one-dimensional laminar premixed ame propagating freely at atmospheric pressure in a stoichiometric mixture of hydrogen-air described by detailed kinetics and multi-component transport. Here, the robust method to calculate the length scales employed in Powers and Paolucci 2,3 for gas phase detonation is implemented with modication for deagration. The method is robust in that it has little dependence on the details of the underlying numerical method used to calculate the laminar ame. It simply requires a local determination of the state of the system, which is followed by a Jacobian formulation, and a generalized eigenvalue analysis. As such, it is able to estimate with great accuracy the length scales on a fundamental mathematical, non-numerical, basis. The minimum length scale which must be resolved in order for the mathematical model to be veried is thus determined. In the rst section, the governing partial dieren tial equations (PDEs) for unsteady reactive o w are presented. This is followed by a reduction of the PDEs into a system of dieren tial algebraic equations (DAEs) which describes the spatial evolution of the state variables. Following a short description of the generalized

Laminar Non-Premixed Counterflow Flames Manipulation through the Application of External Direct Current Fields

AbstractElectrostatically manipulated, laminar, non-premixed, counterflow methane flames were studied experimentally and computationally. It was established experimentally that the flame position c...

Slow attractive canonical invariant manifolds for reactive systems

We analyze the efficacy of a standard manifold-based reduction method used to simplify reaction dynamics and find conditions under which the reduction can succeed and fail. In the standard reduction, a heteroclinic trajectory linking saddle and sink equilibria is taken as a candidate reduced manifold which we call a Canonical Invariant Manifold (CIM). We develop and exercise analytic tools for studying the local behavior of trajectories near the CIM. In so doing, we find conditions under which nearby trajectories are attracted to the CIM (ACIM) as well as conditions for which the dynamics on the ACIM are slow (SACIM). The method is demonstrated on a (1) simple model problem, (2) Zel’dovich mechanism for nitric oxide production, and (3) hydrogen–air system. For systems that evolve in a three-dimensional composition space, we find that normal stretching away from the CIM in a volume-shrinking vector field is admitted and that depending on the magnitude of the local rotation rate, may or may not render the CIM to be attractive. The success and failure of the candidate CIM as a SACIM is displayed for the model system. Results for the Zel’dovich mechanism and hydrogen–air systems are less definitive, though for specific conditions a SACIM is identified for both systems.

Analysis of the Reaction-Advection-Diffusion Spectrum Oflaminar Premixed Flames

The dynamics of one-dimensional laminar premixed combustion in reactive mixtures described by a 1) simple one-species model, 2) simple two-species model, and 3) detailed chemical kinetics model with multicomponent transport in hydrogen–air is investigated. For each model 1) spatially homogeneous results are first obtained, followed by 2) timeindependent, spatially inhomogeneous results, and ended by 3) a generalized eigenvalue analysis to calculate the spatially discretized systems’ time scale spectrum. The results reveal that for spatially resolved structures, the systems’ short wavelength modes are dominated by diffusion-based time scales, coarse wavelength modes are dominated by reactionbased time scales, and modes near a cross-over wavelength have time scales dictated by a combination of reaction and diffusion effects.

Calculation of Slow Invariant Manifolds for Reactive Systems

One-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady, isothermal, isochoric, spatially homogeneous, closed reactive systems are calculated. The technique is based on global analysis of the composition space of the reactive system. The identification of all the system’s finite and infinite critical points plays a major role in calculating the system’s slow invariant manifold. The slow invariant manifolds are constructed by calculating heteroclinic orbits which connect appropriate critical points to the critical point which corresponds to the unique stable physical critical point of chemical equilibrium. The technique is applied to small and large detailed kinetics mechanisms for hydrogen combustion.