Two-dimensional Direct Numerical Simulations Research Articles

Exhaust jet mixing and condensation effects in the near field of aircraft wakes

In order to investigate the process of contrail formation, an integral model and a two-dimensional direct numerical simulation have been used to analyse the mixing and entrainment processes of the engine exhaust through their interaction with the vortex wake of various aircraft. The objective of this study is to evaluate the partial vapour pressure of water and temperature in the near field of subsonic and supersonic aircraft. Results are presented involving the saturation calculation by post-processing solution fields which provide a qualitative indicator of the condensation process. After testing the numerical algorithm with some success, this study was performed for three transport subsonic aircraft: A-330, B-737 and DC-9; for the twin-engine ATTAS of DLR and for the Anglo-French supersonic Concorde. For subsonic aircraft, in the early wake, the distance where saturation is reached depends only upon the engine jet characteristics. The engine jet location with respect to the vortex axis has an important influence on the mixing rate and on the saturation evolution. For the supersonic aircraft, a low saturation ratio has been shown along the plume centreline. The wing-tip vortices contribute largely to increase the mixing and dispersion of the exhaust plume. Consequently, the water saturation profiles are clearly changed by the vortical structure. Effects of the aerodynamic parameters are analysed and discussed.

Analysis of the contribution of curvature to premixed flame propagation

Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.

Bluff-body propulsion produced by combined rotary and translational oscillation

Flows produced by combined oscillatory translation and rotation of a circular cylinder in quiescent fluid have been studied using a two-dimensional direct numerical simulation technique. Results are presented for one set of the five dimensionless groups which characterize these flows, for which it is found that a streaming flow normal to the axis of translation is generated. The consequent reaction force is then used to propel the cylinder in the direction opposite to the jet, thus demonstrating a novel propulsion mechanism for bluff bodies.

Pocket formation and the flame surface density equation

The occurrence and properties of singularities in the equation for the surface density function σ≡|∇| are analyzed analytically and numerically using data from two-dimensional direct numerical simulation (DNS) of pocket formation in a premixed methane-air flame. The various stages and the relevant time scales associated with pocket formation were determined in a previous study. It was found that isolated pockets form if and only if a nondegenerate critical point of a saddle point type appears. The appearance of a singularity in the isoline representing the flame front may have implications to modeling of the terms in the surface density function (SDF) approach during such transient events as pocket formation. The sink and source terms in SDF are evaluated in the neighborhood of a critical point using DNS data during pocket formation and an analytic representation of a scalar in the vicinity of the critical point that allows for the computation of all kinematic properties. The analytic and computational results show that the normal restoration and dissipation terms in the SDF become singular at the critical point when the pocket emerges. Furthermore, the analytic results show that the singularities exactly cancel, and therefore, the main conclusion is that it is unnecessary to model the singular behavior of these terms at critical points. However, closure of their sum is recommended.

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.

97/04902 Secondary effects in sampling ammonia during measurements in a circulating fluidised-bed combustor: Kassman, H. et al. J. Institute of Energy, September 1997, 70, 95–101

Ammonia often occurs in combustion gases as a product of fuel-nitrogen. Since either NO or N2 may predominate as the product of ammonia oxidation, there is considerable interest in understanding the factors responsible for selecting the final products. In flames, the selectivity is known to depend on whether the reaction zones are premixed or nonpremixed. This paper reports on a combined experimental and modeling investigation of ammonia chemistry in a hot combustion environment that is below flame temperatures, such as in post-combustion gases. Experiments that mix highly diluted ammonia–methane and oxygen–water streams are interpreted in terms of a plug-flow model, a simplified mixing reactor model, and a two-dimensional direct numerical simulation. The study finds that the final products of ammonia oxidation remain sensitive to mixing even at temperatures below those of self-sustaining flames. At low temperatures, ammonia oxidation occurs in a premixed reaction zone, but at sufficiently high temperatures a nonpremixed reaction zone may develop that produces significantly less NO than the equivalent premixed system. A direct numerical simulation is required to predict the behavior over the full range of conditions investigated experimentally, while a simplified mixing reactor model captures the essential features as long as the radial gradients are not too steep.

On the symmetry breaking instability leading to vortex shedding

It is well known that at early stages an impulsively started flow past a circular cylinder consists of twin vortices which are images of one another by reflection through the mid-plane. While the twin vortices are stable for Reynolds numbers below the critical Reynolds number value (Rec≃48), they become unstable above the critical Reynolds number. At Re>Rec, the flow keeps its symmetric recirculating bubble structure for a short time, undergoes a symmetry-breaking instability, and develops into a Karman vortex street. Föppl’s vortex model is studied here as a low-dimensional model for the symmetric bubble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable one. In this paper, we show by two-dimensional direct numerical simulations (DNS) of the impulsively started flow past a circular cylinder how the instability properties of the model qualitatively mimic those of the real flow.

UNSTEADY FLOW PAST ELLIPTIC CYLINDERS

Flow past elliptic cylinders is investigated for different Reynolds numbers and angles of attack by numerically solving the two-dimensional, unsteady incompressible Navier-Stokes equation. Results are obtained by using various numerical methods for consistency checks and also compared with available experimental results at Re=3000. The Navier-Stokes equation is solved in stream-function-vor ticity formulation using a finite difference method with third- and fifth-order upwinding for the convection terms. The pressure field is obtained by solving a Poisson equation and surface pressure values and vorticity information is integrated to obtain the sectional loads and pitching moment. Specific results are provided for Re=3000 and 10 000 for different parameter combinations for the early stages of flow development. The effects of Reynolds number, angles of attack (α)and thickness to chord ratios (t/c) are discussed through this two-dimensional direct numerical simulation (DNS).

Numerical simulations of autoignition in turbulent mixing flows

Two-dimensional direct numerical simulations have been performed of the autoignition of (i) laminar and turbulent shearless mixing layers between fuel and hotter air, (ii) thin slabs of fuel exposed to air from both sides, and (iii) homogeneous stagnant adiabatic mixtures. It has been found that the time for the first appearance of an ignition site is almost independent of the turbulence time scale, varies little in individual realisations of the same flow, decreases with partial premixing, is shorter in turbulent than in laminar flows, and decreases with decreasing width of the fuel stream. The autoignition time in the turbulent flows in longer than the ignition delay time of stagnant homogeneous mixtures and this implies that the heat losses due to mixture fraction gradients associated with mixture inhomogeneities increase the autoignition time. It has also been found that ignition always occurs at a well-defined mixture fraction f MR, which is accurately predicted by previous laminar flow analyses to depend only on the fuel and oxidant temperatures and the activation energy. As a measure of the heat losses of the heat-producing regions that eventually autoignite, the time evolution of the scalar dissipation rate, conditional on the most reactive mixture fraction, is examined and used to explain successfully all the observed trends of autoignition time with turbulent time scale, flow length scale, and partial premixing. The implications of these findings for modelling and for the interpretation of experimental data are discussed.

Two-dimensional weak shock-vortex interaction in a mixing zone

The interaction between a vortex or a pair of vortices and a shock is studied by using two-dimensional direct numerical simulation. The deformation of the shock structure is analyzed and the mechanisms leading to the formation of triple points are underscored. It is shown that they are related to the appearance of pressure gradients in the direction parallel to the shock resulting from the shock-vortex interaction. A distribution of an inert chemical species, i.e., mixture fraction, is prescribed within the vortex. From its time evolution, one analyzes the coupling between the response of the shock to the disturbance and the change in mixing rate. Modifications of the maximum of the scalar gradient are observed in the direction perpendicular to the shock and also, to a smaller extent, in the direction parallel to the shock. Nomenclature A(s) = stretching function of the mesh a,b,c,d = coefficients of the FADE scheme D = diffusion coefficient of the inert chemical species L = reference length of the problem M = Mach number N = total number of grid points in streamwise direction P = pressure Pr = Prandtl number q, qr = mesh stretching ratio and stretching rate R = radius of the vortex Re = acoustic Reynolds number (r, ft) = polar coordinates s = position on the uniform mesh

Spectral analysis of a simulated premixed flame surface in two dimensions

This paper presents two-dimensional direct numerical simulations of a passive flame surface passing through homogeneous isotropic turbulence. The flame was represented by a field variable, G(x, t), whose isocontours constitute flame surfaces. One well known complication in analyzing premixed combustion in a homogeneous environment is decoupling the effect of the decaying turbulent velocity field from the dynamics of the flame surface. To overcome this, the velocity field was made stationary by introducing a random forcing term into the Navier Stokes equations. Forcing was done over two different ranges of wavenumbers ( k f = 10−14, and k f = 80−84) thus creating turbulence with different length scales and inertial range power laws. By comparing the response of the flame to the two types of turbulence it was possible to determine the effect the spectral distribution energy has on the surface topology and mean rate of propagation. Indeed, the flames were found to be remarkably sensitive to the spectral distribution of the turbulent energy, and not just its magnitude. Furthermore, a k − 5 3 inertial range was shown to produce a flame surface that was preferentially wrinkled at intermediate to small scales for purely geometric reasons. By defining a surface area spectrum it was possible to rationalize this result by recognizing that flame surface area is closely related to the dissipation spectrum of the scalar field. Collectively the results suggest that knowledge of the energy spectrum at a minimum is required to predict a turbulent flame speed under general circumstances.

Applications of direct numerical simulation to premixed turbulent combustion

This paper describes recent progress in the field of Direct Numerical Simulations (DNS) for premixed turbulent combustion. A classification of Computational Fluid Dynamics techniques used in reacting flows is first proposed. Numerical methods and problems specific to DNS of combustion like grid resolution or boundary conditions treatment are discussed. The presentation of DNS results is done in the framework of flamelet modeling. The domain of validity of the flamelet assumptions is studied with simulations of flame vortex interactions. The local structure of flamelets in premixed turbulent combustion is investigated using two and three-dimensional DNS with simple chemistry models. Effects of complex chemistry are considered through recent two-dimensional DNS performed with realistic chemical schemes. Flame surface densities, flame strain and curvature statistics obtained from various three dimensional simulations are given and implications for modeling are presented. DNS is also exploited to deal with some specific problems like turbulent flame ignition or flame-wall interactions. This review is concluded with a discussion of current limitations and a list of future challenges.

Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity

A two-dimensional direct numerical simulation of the natural convection flow of air in a differentially heated square cavity was performed for a Rayleigh number of 10 10 . The simulation was commenced from isothermal and quiescent conditions and was allowed to proceed to a statistical steady state. Two-dimensional turbulence resulted without the introduction of random forcing. Good agreement of mean quantities of the statistically steady flow is obtained with available experimental results. In addition, the previously proposed (George & Capp 1979) − $\frac{1}{3}$ and $+\frac{1}{3}$ temperature and velocity variations in the buoyant sublayer are confirmed. Other statistics of the flow are consistent with available experimental data. Selected frames from a movie generated from the computational results show very clearly turbulence production via the sequence from initial instability, proceeding through transition, and eventually reaching statistical steady state. Prominent large-scale structures are seen to persist at steady state.

Studies on Turbulent flames: A. Flame Propagation Across velocity gradients B. turbulence Measurement in flames

This work focuses on sidewall quenching (SWQ) for premixed methane/air flames that are forced by a periodic oscillatory inflow with excitation frequency f = 100 Hz. The effects of steady-state and transient flame stretch on the near-wall flame dynamics are evaluated using two-dimensional direct numerical simulation (2D-DNS) and the GRI 3.0 reaction mechanism. The velocity fluctuations lead to significant changes in flame speed and flame stretch, as well as the associated Markstein numbers. The phenomenon of SWQ is analyzed using flame quenching distance, wall heat flux and heat release rate. For steady-state conditions, there is a strong correlation between the maximum wall heat flux WHFmax and the flame quenching Peclet Number (Peq), as well as between the flame speed and the flame stretch; for transient conditions, the flame quenching distance (dq) increases continuously from phase angles of 1/4f−1 to 3/4f−1 in one cycle as time progresses, and the fluctuation of the quenching distance (Δdq) decreases gradually with increasing equivalence ratio (∅). The flame stretch changes from negative to positive in the process from 1/4f−1 to 3/4f−1, while the heat release rate and fuel reaction rate near the wall gradually decrease. Furthermore, the FWI region is dominated by negative flame stretch while positive flame stretch is present at the base of the flame. Moreover, the methane/air flame has a nearly twofold increase in the consumption speed during the oscillation from phase angle 3/4f−1 to the next cycle at 1/4f−1 at ∅ = 0.5 and ∅ = 1.0. These results show that flow field perturbations are not negligible in elucidating the effects of flame-wall interactions.