Two-dimensional Direct Numerical Simulations Research Articles

Combustion mechanism of liquid fuel spray in a gaseous flame

Two-dimensional direct numerical simulation is applied to spray flames stabilized in a laminar counterflow, and the detailed behavior is studied in terms of the droplet group combustion. The stretch ratio of the laminar counterflow is 40 l/s. n-decane (C10H22) is used as a liquid spray fuel, and a one-step global reaction is employed for the combustion reaction model. The results show that with increasing the issued liquid fuel mass fraction, two types of spray combustion appear in front of and inside the high gaseous temperature region, i.e., “premixed-like combustion” and “diffusion-like combustion,” respectively. A droplet group combustion behavior is observed in the diffusion-like combustion region. This diffusion-like combustion, however, disappears when the issued droplet size becomes small, because the droplets complete their evaporation before entering into the high gaseous temperature region. The droplet group combustion tends to reduce the gaseous temperature. This is caused mainly by the suppression of combustion reaction due to the lack of oxygen and partially by the energy exchange through the convective heat transfer between droplets and gaseous phase. The gaseous temperature reduction is promoted by the latent heat of vaporization of the droplets. The use of the parcel approach has a risk of causing a delay of combustion reaction, since the partial fuel vapor pressure increases at limited locations, which suppresses the global droplet evaporation rate.

Averaging approach for microchannel heat sinks subject to the uniform wall temperature condition

The present paper is devoted to modeling methods for thermal analysis of microchannel heat sinks. The averaging approach presented in earlier works for the case of constant surface heat flux is extended to the problems subject to the uniform wall temperature condition. The solutions for velocity and temperature distributions are obtained by solving one-dimensional averaged governing equations without resorting to a two-dimensional direct numerical simulation. General solutions for both high-aspect-ratio and low-aspect-ratio microchannel heat sinks are presented. Asymptotic solutions in high-aspect-ratio and low-aspect-ratio limits are also given in explicit form. The solutions presented in the paper are validated by comparing them with the results of direct numerical simulation. The friction factors, Nusselt numbers and thermal resistances for microchannel heat sinks with a uniform base temperature are obtained from the presented solutions. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Finally, characteristics of the thermal resistance of the microchannel heat sink are discussed.

DNS of a premixed turbulent V flame and LES of a ducted flame using a FSD-PDF subgrid scale closure with FPI-tabulated chemistry

Two complementary simulations of premixed turbulent flames are discussed. Low Reynolds number two-dimensional direct numerical simulation of a premixed turbulent V flame is first performed, to further analyze the behavior of various flame quantities and to study key ingredients of premixed turbulent combustion modeling. Flame surface density, subgrid-scale variance of progress variables, and unresolved turbulent fluxes are analyzed. These simulations include fully detailed chemistry from a flame-generated tabulation (FPI) and the analysis focuses on the dynamics of the thin flame front. Then, a novel subgrid scale closure for large eddy simulation of premixed turbulent combustion (FSD-PDF) is proposed. It combines the flame surface density (FSD) approach with a presumed probability density function (PDF) of the progress variable that is used in FPI chemistry tabulation. The FSD is useful for introducing in the presumed PDF the influence of the spatially filtered thin reaction zone evolving within the subgrid. This is achieved via the exact relation between the PDF and the FSD. This relation involves the conditional filtered average of the magnitude of the gradient of the progress variable. In the modeling, this conditional filtered mean is approximated from the filtered gradient of the progress variable of the FPI laminar flame. Balance equations providing mean and variance of the progress variable together with the measure of the filtered gradient are used to presume the PDF. A three-dimensional larger Reynolds number flow configuration (ORACLES experiment) is then computed with FSD-PDF and the results are compared with measurements.

Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime

The influence of differential diffusion on the statistical behavior of the local displacement speed (Sd) in relation to flame curvature is studied based on three-dimensional compressible direct numerical simulations (DNS) of statistically planar flames with single-step Arrhenius-type chemistry. Three different Lewis number cases (Le=0.8, 1.0, and 1.2) are considered. In order to study the influence of differential diffusion on curvature effects in flame propagation, temperature statistics are presented in terms of standard probability density functions (pdfs) and also joint pdfs with curvature for the nonunity Lewis number cases. Temperature statistics are found to be consistent with previous incompressible combustion DNS studies. It is found that both dilatation and tangential strain rate are negatively correlated with curvature. The relative strength of these two correlations determines the nature of the correlation between surface density function (SDF) (∣∇c∣) and curvature. It is also found that the variations of temperature and SDF on an isosurface of reaction progress variable (c) have significant influence on local displacement speed behavior. Displacement speed statistics are presented in terms of standard pdfs as well as joint pdfs with curvature for the three Lewis number cases. The curvature response of the displacement speed and its different components is found to be nonlinear which is consistent with previous two-dimensional DNS with detailed chemistry. The observed nonlinear behavior in the present study in the absence of a detailed chemical mechanism is explained through the influence of differential diffusion.

Theoretical and Experimental Characterization of the Ultrafast Aircraft Thermometer: Reduction of Aerodynamic Disturbances and Signal Processing

Abstract The ultrafast aircraft thermometer, built for measuring temperature in clouds at flight speeds up to 100 m s−1, employs a 2.5-μm-thick platinum-coated tungsten wire as a sensing element. When temperature increases, the wire resistance increases. The changes are amplified by an electronic system. Temperature measurements made in a wind tunnel and during flights show noise that is related to the von Kármán vortex street generated behind the shield that protects the sensing element against the impact of cloud droplets. To reduce both the level of turbulence and the amount of water collected on the shield, suction is applied through the slits in its sides. The effect of suction on the flow field is twofold. First, at the Reynolds numbers that the thermometer is operated suction eliminates aerodynamic disturbances. Second, suction diverts the inner part of the boundary layer into the slit. This inner part is a region of strong shear and, therefore, a region where intensive viscous heating takes place. When the suction is on much of the air that is heated in the boundary layer in the front part of the shield is removed through the slits and never reaches the sensor. To study the role of the shield with suction and confirm its chosen shape, two-dimensional (2D) direct numerical simulations (DNSs) are performed of the airflow and of the trajectories of droplets of various sizes and initial positions. The influence on the temperature distribution of the irreversible dissipation of energy due to air viscosity is also examined. This is found to have a small but measurable effect. The effects associated with sampling and processing of the analog signal obtained from the sensing wire are discussed. The results herein quantitatively explain the nature of the measured aerodynamic noise.

Vortex-induced vibrations at subcritical Re

Flow past a stationary cylinder becomes unstable at Re. Flow-induced vibrations of an elastically mounted cylinder, of low non-dimensional mass, is investigated at subcritical Reynolds numbers. A stabilized finite-element formulation is used to solve the incompressible flow equations and the cylinder motion in two dimensions. The cylinder is free to vibrate in both the transverse and in-line directions. It is found that, for certain natural frequencies of the spring–mass system, vortex shedding and self-excited vibrations of the cylinder are possible for Re as low as 20. Lock-in is observed in all cases. However, the mass of the oscillator plays a major role in determining the proximity of the vortex-shedding frequency to the natural frequency of the oscillator. A global linear stability analysis (LSA) for the combined flow and oscillator is carried out. The results from the LSA are in good agreement with the two-dimensional direct numerical simulations.

A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids

In order to examine the influence of initial bubble conditions on bubble rise motion, two-dimensional direct numerical simulations of the motion of a gas bubble rising in viscous liquids were carried out by a coupled level set/volume-of-fluid (CLSVOF) method. For dimensionless groups predicting a “spherical-cap bubble shape” (high Eötvös and low Morton numbers), we have found computationally that solutions depend on initial bubble conditions. Specifically, for spherical-cap bubble areas, we could obtain computational results of toroidal bubbles or spherical-cap bubbles depending on initial bubble conditions. On the other hand, we showed for low Eo and high M conditions that initial bubble conditions did not affect the final state of bubble rise motion.

Noise Radiated by Flow Impingement on a Flat Plate Using DNS with a Virtual Boundary Method

Uniform flow impinging on the rectangular leading edge of a flat plate is simulated using an incompressible, two-dimensional direct numerical simulation with uniform grid, the solid surface being modelled by the virtual boundary method previously developed by Goldstein et al. Access is given to the hydrodynamic field at a Reynolds number of 500, which shows the separation at the edge, the development of a double recirculating bubble, a periodic vortex-shedding, and the generation of a boundary layer profile after the re-attachment point. Curle's analogy is then applied to evaluate the sound emission in the far field. Results are given in terms of far field pressure levels directivity and pressure spectra associated with surfacic or volumic sources. The emission from the surfacic sources reaches its maximum value in the direction perpendicular to the plate and acoustic frequencies tend to follow the main wall pressure frequencies of the flow, while the emission from the volumic sources exhibits a shear noise behaviour and acoustic frequencies seem to be the double of the main velocity frequencies.

Effects of mixing on ammonia oxidation in combustion environments at intermediate temperatures

Ammonia often occurs in combustion gases as a product of fuel-nitrogen. Since either NO or N 2 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.

Effects of imperfect premixing coupled with hydrodynamic instability on flame propagation

The problem of flame propagation in imperfectly premixed mixtures—mixtures of reactants with variable composition—is considered in this numerical study. We carry out two-dimensional direct numerical simulations of a flame propagating in a globally lean fuel-oxidizer mixture with imposed velocity and composition fluctuations of various intensities. The configuration adopted is that of a flame front interacting with spatially evolving fluctuations, and the characteristic scales of the domain and of the fluctuations imposed are significantly larger than the characteristic thickness of the flame, to account for important flame dynamics such as the hydrodynamic instability. One-step chemistry and Fick’s diffusion law are considered, along with unity Lewis number assumption for all the species. It is observed, in agreement with previous results, that relatively weak fluctuations in composition alone may lead to a large increase in flame length and burning rate. The hydrodynamic instability caused by gas expansion, catalyzed by the composition fluctuations interacting with the flame, is found to be responsible for the flame length enhancement. It is observed as well that the relative importance of this effect diminishes as the velocity fluctuations present become more intense, and that composition fluctuations have a small impact on flame length for these cases. It is additionally found that, with increasing intensity of composition fluctuations, there is eventually a reduction of burning rate per unit length of flame which leads, consequently, to a weak reduction of overall burning rate for the largest velocity fluctuation intensities covered by this study.

반응 및 비반응 제트 유동장에서 단일 와동의 전개 및 구조에 대한 수치모사

반응 및 비반응 유동장에서 단일와동의 전개 및 와(渦) 구조 검토를 위해 2 차원 직접 수치모사를 수행하였다. 수치기법으로는 낮은 마하수 근사법이 적용된 예측-교정자법이 적용되었으며, 연소모텔로는 2단계 총괄 반응식이 사용되었다. 반응 및 비반응 유동장에서 단일와동의 거동 비교를 통해, 와동의 전개특성 및 구조는 화학반응으로부터 생성된 열 뿐만 아니라 부력에 의해 생성된 외부 와동에 크게 영향을 받음을 확인하였다. 또한 반응장의 경우에 부피 팽창항, Baroclinic torque항 및 부력항에 의해 와동의 구조가 크게 변화될 수 있음을 알았다. A two-dimensional direct numerical simulation was performed to investigate the evolution and vortical structure of a single vortex in reacting and non-reacting jet flow fields. A predictor-corrector-type numerical scheme with a low Mach number approximation was used, and a two-step global reaction mechanism was adopted as the combustion model. Through the comparisons of single vortex behaviors in reacting and non-reacting jet flow fields, it was found that the evolution characteristics and vortical structure of the single vortex were significantly influenced by a outer vortex that was generated from the buoyance effect as well as the chemical heat release. Furthermore, it was also identified that the differences of the vortical structure in reacting and non-reacting jet flow fields were mainly attributed to the thermal expansion, Baroclinic torque and buoyance effect.

와동에 의해 교란된 대향류 비예혼합화염의 화학종 전달기구 및 화염구조

A two-dimensional direct numerical simulation was performed to investigate the flame structure of CH₄/N₂-Air counterflow nonpremixed flame interacting with a single vortex The detailed transport properties and a modified 16-step augmented reduced mechanism based on Miller and Bowman's detailed chemistry were adopted in this computation The results showed that an initially flat stagnation plane, on which an axial velocity was zero, was deformed into a complex-shaped plane, and an mitral stagnation point was moved far away from a vortex head when the counterflow field was perturbed by the vortex It was noted that the movement of stagnation point could alter the species transport mechanism to the flame surface It was also identified that the altered species transport mechanism affected the distributions of the mixture fraction and the scalar dissipation rate.

04/02259 Investigation on degradation of polyethylene to oils in supercritical water: Su, X. et al. Fuel Processing Technology, 2004, 85, (8–10), 1249–1258

Two-dimensional direct numerical simulations (DNSs) of ignition of lean primary reference fuel (PRF)/air mixtures at high pressure and intermediate temperature near the negative temperature coefficient (NTC) regime were performed with a 116 species-reduced mechanism to elucidate the effects of fuel composition, thermal stratification, and turbulence on PRF homogeneous charge compression-ignition (HCCI) combustion. In the DNSs, temperature and velocity fluctuations are superimposed on the initial scalar fields with different PRF compositions. In general, it was found that the mean heat release rate increases slowly and the overall combustion occurs rapidly with increasing thermal stratification regardless of the fuel composition. In addition, the effect of the fuel composition on the ignition characteristics of PRF/air mixtures was found to be significantly reduced with increasing thermal stratification. Chemical explosive mode (CEM) and displacement speed analyses verified that nascent ignition kernels induced by hot spots due to a high degree of thermal stratification usually develop into deflagration waves rather than spontaneous auto-ignition at reaction fronts and as such, the mean heat release rate becomes more distributed over time. These analyses also revealed that the fuel composition effect vanishes as the degree of thermal stratification is increased because the deflagration mode of combustion, of which propagation characteristics are nearly identical for different PRF/air mixtures, becomes more prevailing with increasing degree of thermal stratification. Ignition Damköhler number was proposed to quantify the successful development of deflagration waves from nascent ignition kernels; for cases with large ignition Damköhler number, turbulence with high intensity and short timescale can advance the overall combustion by increasing the overall turbulent flame area instead of homogenizing initial mixture inhomogeneities.

Two-dimensional numerical investigations of small-amplitude disturbances in a boundary layer at Ma=4.8: Compression corner versus impinging shock wave

Two-dimensional direct numerical simulations and linear stability theory investigations have been carried out for a compression ramp at Ma=4.8 and compared to earlier results of a laminar boundary layer with impinging shock wave. The inflow parameters in both flows were identical; the ramp angle of the compression corner was chosen to cause a separation bubble, which has exactly the same length compared to the case with impinging shock. It turned out, that the two cases are almost identical for the base flow properties. This is in accordance with similarity assumptions, e.g., free interaction theory, which for smaller Reynolds numbers states, that the boundary layer should be independent of the sort of shock-boundary layer interaction. However, linear stability theory results differ near the corner and the impinging shock, respectively. Direct numerical simulations of small-amplitude disturbances, which were introduced into the laminar boundary layer, also behave in a very similar way. Amplitude distributions exhibit the same characteristics. The according distributions of the ramp flow have slightly larger amplitudes than the case with impinging shock.

Direct Numerical Simulations of Type Ia Supernovae Flames. I. The Landau‐Darrieus Instability

Planar flames are intrinsically unstable in open domains because of thermal expansion across the burning front, i.e., the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus instability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multimode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small-scale cutoff to the growth of the instability, and look for the proposed breakdown of the nonlinear stabilization at low densities. The effects of curvature on the flame are quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.

Unsteady effects of strain rate and curvature on turbulent premixed flames in an inflow–outflow configuration

Three-dimensional direct numerical simulation (DNS) studies of premixed turbulent flames have been carried out using an inflow–outflow configuration at moderate Reynolds number ( Re) and with single-step Arrhenius chemistry in the thin reaction zones regime. The compressible Navier–Stokes equations are solved together with a transport equation for a reaction progress variable ( c). Results are obtained for several quantities of interest, including the gradient magnitude of the progress variable (|∇ c|) and the displacement speed ( S d) of each progress variable isosurface. The probability density function (pdf) of displacement speed and the implications of the pdf shape are discussed in terms of the relative magnitude of reaction rate and molecular diffusion effects. The pdf of S d itself, as well as the pdfs of its different components S r, S n, and S t, in the present three-dimensional simulations is found to be consistent with previous results based on two-dimensional DNS with detailed chemistry. The validity of the assumption (ρS d ) s ≈ρ 0S L is assessed on averaging ρS d over the isosurfaces of c across the flame brush. The unsteady effects of tangential strain rate ( a T) and curvature ( κ m) on flame propagation are also considered. Curvature and displacement speed are found to be negatively correlated, while the conditional pdf of tangential strain rate and displacement speed at zero curvature locations also shows a negative correlation, again consistent with previous two-dimensional detailed-chemistry DNS.

Numerical simulations of dense clouds on steep slopes: application to powder-snow avalanches

AbstractIn this paper, two-dimensional direct numerical simulations (DNS) of dense clouds moving down steep slopes are presented for the first time. The results obtained are in good agreement with the overall characteristics, i.e. the spatial growth rate and velocity variations, of clouds studied in the laboratory. In addition to the overall flow structure, DNS provide local density and velocity variations inside the cloud, not easily accessible in experiments. The validity of two-dimensional simulations as a first approach is confirmed by the dynamics of the flow and by comparison with experimental results. The interest of the results for powder-snow avalanches is discussed; it is concluded that two-dimensionality is acceptable and that large density differences need to be taken into account in future simulations.

差分格子ボルツマン法によるエッジ音の直接計算(J13-3 空力音III,J13 流体関連の騒音と振動)

Two-dimensional direct numerical simulation of the edge-tones by the finite difference lattice Boltzmann method (FDLBM)is reported. We use anew lattice BGK compressible fluid model that has an additional term and allow larger time increment comparing the conventional FDLBM, and also use a boundary fitted coordinates. We have succeeded in capturing very small pressure fluctuations result from periodically oscillation of jet around the edge. That pressure fluctuations propagate with the sound speed. It is clarified that the sound wave generated in rather wide region and. individual vortices do not affect the sound wave propagation. We showed that the frequency of edge-tones depend on the jet flow speed.

와동과 상호작용하는 대향류 비예혼합화염의 소염특성

A two-dimensional direct numerical simulation was performed to investigate the flame structure of CH₄/N₂-air counterflow nonpremixed flame interacting with a single vortex. The detailed transport properties and a modified 16-step augmented reduced mechanism based on Miller and Bowman's detailed chemistry were adopted in this simulation. The characteristic vortex and chemical time scales were introduced to quantify and investigate the extinction phenomenon during a flame-vortex interaction. The results showed that fuel- and air-side vortex cause an unsteady extinction. In this case, the flame interacting with a vortex was extinguished at much larger scalar dissipation rate than steady flame. It was also found that the air-side vortex extinguished a flame more rapidly than the fuel-side vortex. Furthermore, it was noted that the degree of unsteady effect experienced by a flame can be investigated by comparing the above two characteristic time scales, and this analysis could give an appropriate reason for the results of the previously reported experiment.

Inverse-Imaging Method for Detection of a Vortex in a Channel

A simple vortex-imaging algorithm using a least-square method is considered. The position and the circulation of a vortex convected in a channel are identie ed from the time history of pressure at a limited number of points on the wall. The capabilities of the algorithm are demonstrated using two-dimensional direct numerical simulations. A few observer points on one side of the wall are sufe cient to detect the position and the circulation of a compact vortex to a reasonable degree of accuracy. An advanced algorithm can even detect two nearby vortices to the same degree of accuracy. Because the algorithm assumes a point vortex solution, the accuracy of the detection deteriorates as the vorticity distribution spreads.