Christos E. Frouzakis

Entropic lattice Boltzmann method for microflows

A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar–Gross–Krook (ELBGK) is studied in detail in order to quantify its relevance for microflow simulations. ELBGK is equipped with boundary conditions which are derived from molecular models (diffusive wall). A map of three-dimensional kinetic equations onto two-dimensional models is established which enables two-dimensional simulations of quasi-two-dimensional flows. The ELBGK model is studied extensively in the simulation of the two-dimensional Poiseuille channel flow. Results are compared to known analytical and numerical studies of this flow in the setting of the Bhatnagar–Gross–Krook model. The ELBGK is in quantitative agreement with analytical results in the domain of weak rarefaction (characterized by Knudsen number Kn, the ratio of mean free path to the hydrodynamic scale), up to Kn∼0.01, which is the domain of many practical microflows. Moreover, the results qualitatively agree throughout the entire Knudsen number range, demonstrating Knudsens minimum for the mass flow rate at moderate values of Kn, as well as the logarithmic scaling at large Kn. The present results indicate that ELBM can complement or even replace computationally expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number hydrodynamics pertinent to microflows.

Three-dimensional simulations of premixed hydrogen/air flames in microtubes

The dynamics of fuel-lean (equivalence ratio φ=0.5) premixed hydrogen/air atmospheric pressure flames are investigated in open cylindrical tubes with diameters of d=1.0 and 1.5 mm using three-dimensional numerical simulations with detailed chemistry and transport. In both cases, the inflow velocity is varied over the range where the flames can be stabilized inside the computational domain. Three axisymmetric combustion modes are observed in the narrow tube: steady mild combustion, oscillatory ignition/extinction and steady flames as the inflow velocity is varied in the range 0.5≤ U IN ≤ 500 cm s -1 . In the wider tube, richer flame dynamics are observed in the form of steady mild combustion, oscillatory ignition/extinction, steady closed and open axisymmetric flames, steady non-axisymmetric flames and azimuthally spinning flames (0.5 ≤ U IN ≤ 600 cm s -1 ). Coexistence of the spinning and the axisymmetric modes is obtained over relatively wide ranges of U IN . Axisymmetric simulations are also performed in order to better understand the nature of the observed transitions in the wider tube. Fourier analysis during the transitions from the steady axisymmetric to the three-dimensional spinning mode and to the steady non-axisymmetric modes reveals that the m = 1 azimuthal mode plays a dominant role in the transitions.

Two-dimensional direct numerical simulation of opposed-jet hydrogen-air diffusion flame

Opposed-jet diffusion flame experiments are routinely analyzed with one-dimensional models obtained by assuming a specific form for the velocity field. In this study, two-dimensional simulations of the hydrogen-air laminar opposed-jet counterflow diffusion flame using detailed chemical kinetics and realistic transport were performed for parabolic and uniform inflow velocity profiles at the exits of the nozzles. Two-dimensional simulations allow for the detailed examination of the hydrodynamics and the assessment of the validity of the assumptions made in the traditional one-dimensional simulations. Using typical nozzle size and separation distance employed in experiments, we analyzed the effects of nozzle outflow boundary conditions, finite size, and finite separation distance on the structure of the strained laminar diffusion flame. We also analyzed the variations of the divergence of the velocity field (compressibility due to chemical reaction) and that of the hydrodynamic pressure. The two-dimensional simulation results show that the cost-effective one-dimensional model provides an accurate description of the flame structure even for low-strain hydrogen-air flame provided that the velocity profiles at the nozzle exits are uniform. Although in the one-dimensional model, the nozzle size to separation ratio is assumed to be large, our two-dimensional results show that a ratio of 1 is adequate. Finally, we observed that the velocity gradient (the axial derivative of the axial velocity component along the axis of symmetry) measured in experiments at a point just before the flame region is inadequate in describing the characteristic strain rate “seen” by the flame.

Lattice Boltzmann method for direct numerical simulation of turbulent flows

We present three-dimensional direct numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann (LB) model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible-flow spectral element solver are reported. It is demonstrated that the LB method is a promising alternative for DNS as it quantitatively captures all the computed statistics of fluid turbulence.

Direct numerical simulation of multiple cycles in a valve/piston assembly

The dynamics and multiple-cycle evolution of the incompressible flow induced by a moving piston through the open valve of a motored piston-cylinder assembly was investigated using direct numerical simulation. A spectral element solver, adapted for moving geometries using an Arbitrary Lagrange/Eulerian formulation, was employed. Eight cycles were simulated and the ensemble- and azimuthally-averaged data were found to be in good agreement with experimentally determined means and fluctuations at all measured points and times. During the first half of the intake stroke the flow field is dominated by the dynamics of the incoming jet and the vortex rings it creates. With decreasing piston speed a large central ring becomes the dominant flow feature until the top dead center. The flow field at the end of the previous cycle is found to have a dominant effect on the jet breakup and the vortex ring dynamics below the valve and on the observed significant cyclic variations. Based on statistical averaging, the evolut...

ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re~O(10) to Re≤1000 was predicted by a single simulation algorithm.1–5

Analysis and Reduction of the CH4-Air Mechanism at Lean Conditions

Abstract A palette of computational techniques are employed for the analysis and reduction of a detailed 53-species methane-air mechanism including nitrogen chemistry in a perfectly stirred reactor (PSR). The analysis of the mechanism for a PSR operating at an equivalence ratio φ = 0.5, inlet temperature Tin = 400°C and pressure p = 1 bar, enables a first reduction to a 26-species skeletal mechanism. Computational singular perturbation is then applied to find the species at quasi-steady state. The resulting 11-species reduced mechanism is tested at different operating conditions in the PSR, as well as in a reactor network of a PSR followed by a plug flow reactor (PSR), showing good aggreement with the full mechanism over a range of equivalence ratios up to stoichiometric.

Chaotic dynamics in premixed hydrogen/air channel flow combustion

The complex oscillatory behaviour observed in fuel-lean premixed hydrogen/air atmospheric pressure flames in an open planar channel with prescribed wall temperature is investigated by means of direct numerical simulations, employing detailed chemistry descriptions and species transport, and nonlinear dynamics analysis. As the inflow velocity is varied, the sequence of transitions includes harmonic single frequency oscillations, intermittency, mixed mode oscillations, and finally a period-doubling cascade leading to chaotic dynamics. The observed modes are described and characterised by means of phase-space portraits and next amplitude maps. It is shown that the interplay of chemistry, transport, and wall-bounded developing flow leads to considerably richer dynamics compared to fuel-lean hydrogen/air continuously stirred tank reactor studies.

Remeshed smoothed particle hydrodynamics for the simulation of laminar chemically reactive flows

We present an extension of the remeshed smooth particle hydrodynamics (RSPH) method for the simulation of chemically reactive flows. The governing conservation equations are solved in a Lagrangian fashion, while particle locations, which are distorted by the flow, are periodically re-initialized (remeshed) on a grid. The RSPH implementation is employed for the simulation of a hydrogen/air opposed-jet burner with detailed chemistry and transport. The effect of particle number (resolution), compressibility (Mach number) and outflow boundary condition (length of the domain) on the solution are considered. The RSPH computational results are compared with numerical results obtained by a spectral element implicit scheme and by a one-dimensional code. It is shown that RSPH provides a flexible and accurate alternative for the numerical simulation of chemically reacting flows.

Numerical study of opposed-jet H2/Air diffusion flame : Vortex interactions

Abstract We consider the interaction of vortices of different size and strength (vorticity) and a diffusion flame of N2-diluted H2 and air stabilized on an opposed-jet burner. In our direct numerical simulations, which take into account the effects of detailed chemistry and transport, we demonstrate the effects of flame curvature of opposite orientations by placing a vortex on either the air or the fuel side of the diffusion flame. When the flame curvature is convex towards the fuel stream, the flame burns more intensely even at a scalar dissipation rate, X, close to the critical (extinction) value, X c of the flat one-dimensional diffusion flame (for the same composition of the reactant streams). On the other hand, if the flame curvature is convex towards the air stream, the flame weakens and in some cases extinguishes even when the local X is significantly lower than X c. Depending on the curvature orientation, the extinction scalar dissipation rate can vary considerably. This observation raises questions on the common use of a single extinction scalar dissipation rate in many turbulent diffusion flame simulations. Our results indicate that the role of curvature in the transient flame-vortex interaction is similar to what was observed in previous studies of steady curved flames. We also observe that the reignition process following local extinction is two-dimensional. The reignition process observed in our simulations may not be described well by flamelet models (steady or transient) that are based on one-dimensional formulations.