Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate

In this paper, the steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of an incompressible, viscous and electrically conducting fluid over a stretching vertical flat plate is theoretically investigated with Hall effects taken into account. The governing equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the magnetic parameter, the Hall parameter and the buoyancy parameter on the velocity profiles, the cross flow velocity profiles and the temperature profiles are presented graphically and discussed. Investigated results indicate that the Hall effect on the temperature is small, and the magnetic field and Hall currents produce opposite effects on the shear stress and the heat transfer at the stretching surface

Two-dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first-order and second-order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth-order RungeKutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two-dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side-by-side. Results of these simulations were extensively compared with the previous numerical data. Copyright (C) 2011 John Wiley & Sons, Ltd

Autoignition in a non-premixed medium: DNS studies on the effects of three-dimensional turbulence

Direct numerical simulation (DNS) results of autoignition in anon-premixed medium under an isotropic, homogeneous, and decaying turbulence are presented. The initial mixture consists of segregated fuel parcels randomly distributed within warm air, and the entire medium is subjected to a three-dimensional turbulence. Chemical kinetics is modeled by a four-step reduced reaction mechanism for autoignition of n-heptane/air mixture. Thus, this work overcomes the principal limitations of a previous contribution of the authors on two-dimensional DNS of autoignition with a one-step reaction model. Specific attention is focused on the differences in the effects of two- and three-dimensional turbulence on autoignition characteristics. The three-dimensional results show that ignition spots are most likely to originate at locations jointly corresponding to the most reactive mixture fraction and low scalar dissipation rate. Further, these ignition spots are found to originate at locations corresponding to the core of local vortical structures, and after ignition, the burning gases move toward the vortex periphery Such a movement is explained as caused by the cyclostrophic imbalance developed when the local gas density is variable. These results lead to the conclusion that the local ignition-zone structure does not conform to the classical stretched flamelet description. Parametric studies show that the ignition delay time decreases with an increase in turbulence intensity. Hence, these three-dimensional simulation results resolve the discrepancy between trends in experimental data and predictions from DNSs of two-dimensional turbulence. This qualitative difference between DNS results from three- and two-dimensional simulations is discussed and attributed to the effect of vortex stretching that is present in the former, but not in the latter

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term <w\eta>, based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling <w\eta> is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate <N\eta> is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms <YiYj\eta> to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures

Direct numerical simulation of autoignition in a non-premixed, turbulent medium

In this paper, direct numerical simulation of autoignition in an initially non-premixed medium under isotropic, homogeneous, and decaying turbulence is presented. The pressure-based method developed herein is a spectral implementation of the sequential steps followed in the predictor-corrector type of algorithms; it includes the effects of density fluctuations caused by spatial inhomogeneities ill temperature and species. The velocity and pressure field are solved in the spectral space while the scalars and density field are solved in the physical space. The presented results reveal that the autoignition spots originate and evolve at locations where (1) the composition corresponds to a small range around a specific mixture fraction, and (2) the conditional scaler dissipation rate is low. A careful examination of the data obtained indicates that the autoignition spots originate in the vortex cores, and the hot gases travel outward as combustion progresses. Hence, the applicability of the transient laminar flamelet model for this problem is questioned. The dependence of autoignition characteristics on parameters such as (1) die initial eddy-turnover time and (2) the initial ratio of length scale of scalars to that of velocities are investigated. Certain implications of new results on the conditional moment closure modeling are discussed

Dynamic combustion of solid propellants: effects of unsteady condensed phase degradation layer

A numerical model is developed for pressure- and/or radiation-driven dynamic combustion of solid propellants. The model relaxes the two key assumptions invoked in the classical, quasisteady, homogeneous, one-dimensional flame (QSHOD) model, namely, the quasisteady gas-phase (QSG) and quasisteady condensed phase degradation layer (QSC). First, the proposed non-QSC model is validated with respect to previous results of radiation-driven burning. The model is further validated for steady burning results by comparing with experimental data. Then, the effects of relaxing the QSC assumption on dynamic burning predictions are investigated under conditions of 1) an oscillating and 2) an exponentially decreasing pressure. It is confirmed that relaxing the assumptions of both QSC and QSG are equally important for computing the unsteady burning characteristics of solid propellants. For pressure-driven burning relaxing the QSC assumption results in a destabilizing effect on the frequency response function. The predicted response function magnitude is quantitatively compared with experimental data for double base propellants. The comparison seems to be better with a value of condensed phase activation energy higher than that suggested by A. A. Zenin ("Thermophysics of Stable Combustion Waves of Solid Propellants," Nonsteady Burning and Combustion Stability of Solid Propellants, edited by L. De Luca, E. W. Price, and M. Summerfield, Vol. 143, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, pp. 197–231). Results of unsteady simulations of burning under a rapid depressurization transient exhibit salient features of combustion recovery and extinction observed in experiments. The predicted critical depressurization rate is found tomarkedly decrease (by a factor of four in the particular case simulated) when the QSC assumption is relaxed

Autoignition of turbulent hydrogen jet in a coflow of heated air

Autoignition of hydrogen, leading to flame development under turbulent flow conditions is numerically investigated including a detailed chemical mechanism. The chosen configuration consists of a turbulent jet of hydrogen diluted with nitrogen which is issued into a coflow of heated air. Numerical simulations are performed with the Conditional Moment Closure model, to capture the transient evolution of the flow. Turbulence closure is achieved using the kappa-epsilon model. Simulations revealed that the injected hydrogen mixes with coflowing air autoignites and a stable diffusion flame is established Sometimes flashback,., of the ignited mixture is observed, whereby the flame travels upstream and stabilizes. It is found that the constants assumed in various modeling terms can severely influence the degree of mixing. Hence, certain modifications to these constants are suggested, and improved predictions are obtained. The sensitivity of autoignition length to the coflow temperature is investigated. The predicted autoignition lengths show a reasonable agreement with the experimental data and LES results. (c) 2008 International Association for Hydrogen Energ

Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate