Evaporation From Confined Porous Media Due to Controlled IR Heating From Above

We report an experimental study of evaporation due to controlled infrared (IR) heating from above from an initially saturated confined porous medium consisting of nearly ‘mono-disperse’ particles which has been rarely used earlier. We have used three diagnostic tools simultaneously, evaporation rate measurements using a precision weighing balance, surface temperature measurements using IR imaging, and fluorescein dye mixed with water to visualize the drying front and the evaporation sites. IR images show that the first stage, so-called constant rate period (CRP), was maintained due to films of water reaching the top surface from the saturated region below. Gradually reducing evaporation rate in stage 1 is shown to be related to ‘shrinking evaporating patches’ on the top surface, clearly revealed as lower-temperature regions in the IR images. End of CRP coincides with disappearance of the low-temperature patches. We give end of CRP in terms of the average depth (L_cap) of the liquid level from the top surface at that time. L_cap and duration of CRP are strong functions of the porous medium bead size, transition to stage 2 happening earlier for coarser spheres. The obtained L_cap values deviated from the predictions of Lehmann et al. (Phys Rev E 77(5):056309, 2008) which we show is due to a small range of pore sizes in the current experiments. For both water and highly volatile n-pentane, we show that L_cap normalized by a length scale derived from gravity-surface tension force balance goes like Bo^0.20, for Bo varying from 2.0E ? 04 to 1.0E ? 01; Bo is the Bond number. Fluorescein dye imaging shows a different view of the evaporation stages. During CRP, highly concentrated deposits of the fluorescein dye particles, orange in colour, are seen in the top few bead layers. These orange deposits represent the sites on the beads surfaces where the evaporation has taken place. Even with external heating, evaporation from such a porous medium is limited to a finite depth from the evaporating end, similar to the observation by Lehmann et al. (2008) for isothermal evaporation in Hele-Shaw cell.     

Experimental and Numerical Simulations of Spray Impingement and Combustion Characteristics in Gasoline Direct Injection Engines under Variable Driving Conditions

Gasoline direct injection (GDI) increases engine power output and reduces emissions. In GDI engines, increasing injection pressure improves atomization, which increases thermal efficiency at the cost of wall wetting. When wall wetting occurs, both soot emissions and fuel consumption increase. Wall wetting in GDI engines under cold driving conditions has rarely been considered. In this study, experimental data characterizing droplet splashing/spreading phenomena were collected to inform numerical simulations of combustion characteristics and wall wetting subject to variable driving conditions and excess air ratio, λ. Fully 3D and unsteady numerical simulations were carried out to predict flow-field, combustion, and spray-impingement characteristics. To simulate a GDI engine, a spray-impingement model was developed using both experimental data and previous modeling efforts. The excess air ratio and driving-condition temperature were the variable parameters considered in this study. When decreasing λ from 1.0 to 0.7 by increasing the fuel-injection rate (fuel rich), the cylinder pressure increases to 61 % of the pressure when λ=1.0. Because of increasing the fuel-injection rate, the increased momentum in the fuel spray increases both wall wetting and soot generation. At low driving-condition temperatures, the cylinder pressure was up to 63 % less than that under warm conditions, but with increased soot generation. Simulations revealed a correlation between wall wetting and the soot emissions. Soot generation was most sensitive to changes in wall wetting.     

Experimental and Theoretical Sensitivity Analysis of Turbulent Flow Past a Square Cylinder

The Siemens SGT-800 3^rd generation DLE burner fitted to an atmospheric combustion rig has been numerically investigated. Pure methane and methane enriched by 80 vol% hydrogen flames have been considered. A URANS (Unsteady Reynolds Averaged Navier-Stokes) approach was used in this study along with the k ? ω SST and the k ? ω SST-SAS models for the turbulence transport. The chemistry is coupled to the turbulent flow simulations by the use of a laminar flamelet library combined with a presumed PDF. The effect of the mesh density in the mixing and the flame region and the effect of the turbulence model and reaction rate model constant are first investigated for the methane/air flame case. The results from the k ? ω SST-SAS along with flamelet libraries are shown to be in excellent agreement with experimental data, whereas the k ? ω SST model is too dissipative and cannot capture the unsteady motion of the flame. The k ? ω SST-SAS model is used for simulation of the 80 vol% hydrogen enriched flame case without further adjusting the model constants. The global features of the hydrogen enrichment are very well captured in the simulations using the SST-SAS model. With the hydrogen enrichment the time averaged flame front location moves upstream towards the burner exit nozzle. The results are consistent with the experimental observations. The model captures the three dominant low frequency unsteady motion observed in the experiments, indicating that the URANS/LES hybrid model indeed is capable of capturing complex, time dependent, features such as an interaction between a PVC and the flame front.     

Effects of Spray and Turbulence Modelling on the Mixing and Combustion Characteristics of an n-heptane Spray Flame Simulated with Dynamic Adaptive Chemistry

Accurate modelling of spray combustion process is essential for efficiency improvement and emissions reduction in practical combustion engines. In this work, both unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and large eddy simulations (LES) are performed to investigate the effects of spray and turbulence modelling on the mixing and combustion characteristics of an n-heptane spray flame in a constant volume chamber at realistic conditions. The non-reacting spray process is first simulated with URANS to investigate the effects of entrainment gas-jet model on the penetration characteristics and fuel vapor distributions. It is found that the droplet motion near the nozzle has significant influence on the fuel vapor distribution, while the liquid penetration length is controlled by the evaporation process and insensitive to gas-jet model. For the case considered, both URANS with the gas-jet model and large eddy simulations can properly predict the vapor penetration. For the combustion characteristics, it is found that LES yields better predictions in the global combustion characteristics. The URANS with gas jet model yields a comparable flame length and lift-off-length (LOL) to LES, but results in a larger ignition delay time compared to the experimental data. Another focus of this work is to qualify the convergence characteristics of the dynamic adaptive chemistry (DAC) method in these transient combustion simulations, where DAC is applied to reduce the mechanism locally and on-the-fly to accelerate chemistry calculations. The instantaneous flame structures and global combustion characteristics such as ignition delay time, flame lift-off length and emissions are compared between simulations with and without DAC. For URANS, good agreements are observed both on instantaneous flame structures and global characteristics. For LES, it is shown that the errors incurred by DAC are small for scatter distributions in composition space and global combustion characteristics, while they may significantly affect instantaneous flame structures in physical space. The study reveals that for DAC application in transient simulations, global or statistic information should be used to assess the accuracy, such as manifolds in composition space, conditional quantities and global combustion characteristics. For the cases investigated, a speed-up factor of more than two is achieved by DAC with a 92-species skeletal mechanism with less than 0.2 % and 3.0 % discrepancy in ignition delay and LOL, respectively.     

A Simple Approach for Specifying Velocity Inflow Boundary Conditions in Simulations of Turbulent Opposed-Jet Flows

A new methodology is developed to specify inflow boundary conditions for the velocity field at the nozzle exit planes in turbulent counterflow simulations. The turbulent counterflow configuration consists of two coaxial opposed nozzles which emit highly-turbulent streams of varying species compositions depending on the mode considered. The specification of velocity inflow boundary conditions at the nozzle exits in the counterflow configuration is non-trivial because of the unique turbulence field generated by the turbulence generating plates (TGPs) upstream of the nozzle exits. In the method presented here, a single large-eddy simulation (LES) is performed in a large domain that spans the region between the TGPs of the nozzles, and the time series of the velocity fields at the nozzle exit planes are recorded. To provide inflow boundary conditions at the nozzle exit planes for simulations under other conditions (e.g., different stream compositions, bulk velocity, TGP location), transformations are performed on the recorded time series: the mean and r.m.s. (root-mean-square) quantities of velocity, as well as the longitudinal integral length scale on the centerline, at the nozzle exits in simulations are matched to those observed in experiments, thereby matching the turbulent Reynolds number R e _t . The method is assessed by implementing it in coupled large-eddy simulation/probability density function (LES/PDF) simulations on a small cylindrical domain between the nozzle exit planes for three different modes of the counterflow configuration: N ₂ vs. N ₂; N ₂ vs. hot combustion products; and C H ₄/N ₂ vs. O ₂. The inflow method is found to be successful as the first and second moments of velocity from the LES/PDF simulations agree well with the experimental data on the centerline for all three modes. This simple yet effective inflow strategy can be applied to eliminate the computational cost required to simulate the flow field upstream of the nozzle exits. It is also emphasized that, in addition to the predicted time series data, the availability of experimental data close to the nozzle exit planes plays a key role in the success of this method.     

Effect of the mode of gas-surface interaction on intensive monatomic gas evaporation

The direct Monte Carlo simulation method is used for investigating the effect of the thermal accommodation coefficient α _E on the relations on the Knudsen layer boundary in the presence of intensive evaporation. The model of mirror reflection of molecules from the surface is considered. It is shown that diffuse reflection with α _E = 0 leads to almost the same relations on the Knudsen layer boundary as mirror reflection. The accuracy of the moment method is estimated in application to the problems of intensive evaporation with diffuse and mirror reflection from the surface.     

Spray-Flame Dynamics in a Rich Droplet Array

We numerically study spray-flame dynamics. The initial state of the spray is schematized by alkane droplets located at the nodes of a face-centered 2D-lattice. The droplets are surrounded by a gaseous mixture of alkane and air. The lattice spacing s reduced by the combustion length scale is large enough to consider that the chemical reaction occurs in a heterogeneous medium. The overall spray equivalence ratio is denoted by ?_T, with ?_T = ?_L + ?_G, where ?_G corresponds to the equivalence ratio of the gaseous surrounding mixture at the initial saturated partial pressure, while ?_L is the so-called liquid loading. To model such a heterogenous combustion, the retained chemical scheme is a global irreversible one-step reaction governed by an Arrhenius law, with a modified heat of reaction depending on the local equivalence ratio. ?_T is chosen in the range 0.9 ≤ ?_T ≤ 2. Three geometries (s = 3, s = 6, s = 12) and four liquid loadings, ?_L = 0.3, ?_L = 0.5, ?_L = 0.7, ?_L = 0.85 are studied. In the rich sprays, our model qualitatively retrieves the recent experimental measurements: the rich spray-flames can propagate faster than the single-phase flames with the same overall equivalence ratio. To analyse the conditions for this enhancement, we introduce the concept of “spray Peclet number”, which compares the droplet vaporization time with the combustion propagation time of the single-phase flame spreading in the fresh surrounding mixture.     

Integral boundary layer relations in the theory of wave flows for capillary liquid films

A generalized method of deriving the model equations is considered for wave flow regimes in falling liquid films. The viscous liquid equations are used on the basis of integral boundary layer relations with weight functions. A family of systems of evolution differential equations is proposed. The integer parameter n of these systems specifies the number of a weight function. The case n = 0 corresponds to the classical IBL (Integral Boundary Layer) model. The case n ≥ 1 corresponds to its modifications called the WIBL (Weighted Integral Boundary Layer) models. The numerical results obtained in the linear and nonlinear approximations for n = 0, 1, 2 are discussed. The numerical solutions to the original hydrodynamic differential equations are compared with experimental data. This comparison leads us to the following conclusions: as a rule, the most accurate solutions are obtained for n = 0 in the case of film flows on vertical and inclined solid surfaces and the accuracy of solutions decreases with increasing n. Hence, the classical IBL model has an advantage over the WIBL models.     

Numerical Simulation of Two Phase Turbulent Flow of Nanofluids in Confined Slot Impinging Jet

In this article, a numerical investigation is performed on flow and heat transfer of confined impinging slot jet, with a mixture of water and Al₂O₃ nanoparticles as the working fluid. Two-dimensional turbulent flow is considered and a constant temperature is applied on the impingement surface. The k ? ω turbulence model is used for the turbulence computations. Two-phase mixture model is implemented to study such a flow field. The governing equations are solved using the finite volume method. In order to consider the effect of obstacle angle on temperature fields in the channel, the numerical simulations were performed for different obstacle angles of 0° ? 60°. Also different geometrical parameters, volume fractions and Reynolds numbers have been considered to study the behavior of the system in terms of stagnation point, average and local Nusselt number and stream function contours. The results showed that the intensity and size of the vortex structures depend on jet- impingement surface distance ratio (H/W) and volume fraction. The maximum Nusselt number occurs at the stagnation point with the highest values at about H/W = 1. Increasing obstacle angle, from 15° to 60°, enhances the heat transfer rate. It was also revealed that the minimum value of average Nusselt number occurs in higher H/W ratios with decreasing the channel length.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Turbulent Mixing Layers

The influences of fuel Lewis number Le _F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le _F  = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u′ values. For all Le _F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le _F during the period of external energy addition. Moreover, Le _F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude \(\vert \nabla \xi \vert \) are negatively correlated at the most reactive region for all values of Le _F explored. The probability of finding high values of \(\vert \nabla \xi \vert \) increases with increasing Le _F . For a given value of u′, the extent of burning decreases with increasing Le _F . A moderate increase in u′ gives rise to an increase in the extent of burning for Le _F  = 0.8 and 1.0, which starts to decrease with further increases in u′. For Le _F  = 1.2, the extent of burning decreases monotonically with increasing u′. The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ _st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u′ and Le _F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le _F  = 1.2.     

Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10⁵) was simulated using the Navier-Stokes equations and the γ-Re_θ transition model coupled with the SST k ? ω turbulence model (hereinafter abbreviated as γ-Re_θ model). Considering the effect of free-stream turbulence intensity decay, the SST k ? ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k ? ω turbulence model is coupled with the γ-Re_θ transition model (hereinafter abbreviated as γ-Re_θ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Re_θ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Re_θ-SR model, and the three flow states were analyzed. It was found that compared with the SST k ? ω turbulence model, the γ-Re_θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Re_θ model, for relatively high inlet turbulence intensities, the γ-Re_θ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Re_θ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.     

Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics(MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations(PDEs)subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations(ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles,Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x-and z-directions are boosted with maximizing the values of nanoparticle solid volume fraction ? and rotation λ. Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.     

Effect of vibration on the creep of tensile-test specimens of the aluminum alloy Al−Mg−Si (PA-4)

In this work are presented the results of research on vibrational creep at normal temperature of an aluminum alloy containing magnesium and silicon (designated PA-4). A uni-directional positive load is applied to a tensile-test specimen, such that the stress intensity in the specimen is of the type\(\sigma (t) = \sigma _m (1 + Asin\omega t)\) whereσ _m is the mean (static) stress intensity andA =σ _a /σ _m is the ratio of the vibratory-stress intensity to the mean intensity. The results are given in the form of families of curves of plastic (i.e., permanent) deformation for various values ofA, namely,A=0.0000, 0.0065, 0.05500, 0.1000 and 0.2000. Taking the creep limit for plastic strain as ε _p = 1.8 percent, equations for this creep limit were deduced from experimental data. The following conclusions are drawn from these investigations:

1. 1.
   Vibrations of small-stress-amplitude ratioA encourage creep, particularly with more lengthy tests.     
   
   

Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number Le_F on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with Le_F ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ?^′= 0.2, 0.4 and 0.6) and the Taylor micro-scale l_? of equivalence ratio ? variation (i.e. l_?/l_f= 2.1, 5.5 and 8.3 with l_f being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u^′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ?^′ and l_?/l_f for global mean equivalence ratio 〈?〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing Le_F during the period of external energy deposition. The initial values of Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u^′/S_b(?=1), the extent of burning decreases with increasing Le_F. An increase in u^′ leads to a monotonic reduction in the burned gas mass for all values of Le_F in all stratified mixture cases but an opposite trend is observed for the Le_F=0.8 homogeneous mixture. It has been found that an increase in ?^′ has adverse effects on the burned gas mass, whereas the effects of l_?/l_f on the extent of burning are non-monotonic and dependent on ?^′ and Le_F. Detailed physical explanations have been provided for the observed Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f dependences.     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.     

Effect of tube diameter and capillary number on platelet margination and near-wall dynamics

I investigate the effect of tube diameter D and red blood cell capillary number Ca (i.e. the ratio of viscous to elastic forces) on platelet margination in blood flow at ≈37 % tube haematocrit. The system is modelled as three-dimensional suspension of deformable red blood cells and nearly rigid platelets using a combination of the lattice-Boltzmann, immersed boundary and finite element methods. Results of simulations during the dynamics before the steady state has been reached show that a non-diffusive radial platelet transport facilitates margination. This non-diffusive effect is important near the edge of the cell-free layer, but only for Ca > 0.2, when red blood cells are tank-treading. I also show that platelet trapping in the cell-free layer is reversible for Ca ≤ 0.2. Margination is essentially independent of Ca only for the smallest investigated tube diameter (D = 10 μm). Once platelets have reached the cell-free layer, they tend to slide rather than tumble. The tumbling rate is essentially independent of Ca but increases with D. Strong confinement suppresses tumbling due to the relatively small cell-free layer thickness at ≈ 37 % tube haematocrit.     

Mechanical Properties of Hard W-C Coating on Steel Substrate Deduced from Nanoindentation and Finite Element Modeling

Mechanical properties of a hard and stiff W-C coating on steel substrate have been investigated using nanoindentation combined with finite element modeling (FEM) and extended FEM (XFEM). The significant pile-up observed around the indents in steel substrate caused an overestimation of hardness and indentation modulus. A simple geometrical model, considering the additional contact surfaces due to pile-up, has been proposed to reduce this overestimation. The presence of W-C coating suppressed the pile-up in the steel substrate and a transition to sink-in behavior occurred. The FEM simulations adequately reproduced the surface topography of the indents in the substrate and coating/substrate systems as well. The maximum principal stresses of the indented W-C/steel coated system were tensile; they were always located in the coating and evolved in 3 stages. Cohesive cracking occurred during loading in the sink-in zone (stage III) when the ultimate tensile strength (σ _max ) of the coating was reached. The obtained hardness (H _c ), indentation modulus (E _c ), yield stress (Y) and strength (σ _max ) of the W-C coating were H _c ? =?20 GPa, E _c ? =?250 GPa, Y?=?9.0 GPa and σ _max ? =?9.35 GPa, respectively. XFEM resulted in fracture energy of the W-C coating of G?=?38.1 J?·?m^-2 and fracture toughness of K _IC ? =?3.5 MPa?·?m^0.5.     

Statistical Analysis of Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Study

Turbulent combustion of mono-disperse droplet-mist has been analysed based on three-dimensional Direct Numerical Simulations (DNS) in canonical configuration under decaying turbulence for a range of different values of droplet equivalence ratio (?_d), droplet diameter (a_d) and root-mean-square value of turbulent velocity (u^′). The fuel is supplied in liquid phase and the evaporation of droplets gives rise to gaseous fuel for the flame propagation into the droplet-mist. It has been found that initial droplet diameter, turbulence intensity and droplet equivalence ratio can have significant influences on the volume-integrated burning rate, flame surface area and burning rate per unit area. The droplets are found to evaporate predominantly in the preheat zone, but some droplets penetrate the flame front, reaching the burned gas side where they evaporate and some of the resulting fuel vapour diffuses back towards the flame front. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for ?_d > 1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets and this predominantly fuel-lean mode of combustion exhibits the attributes of low Damköhler number combustion and gives rise to thickening of flame with increasing droplet diameter. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion and the relative contribution of non-premixed combustion to overall heat release increases with increasing droplet size. The statistical behaviours of the flame propagation and mode of combustion have been analysed in detail and detailed physical explanations have been provided for the observed behaviour.     

Does Density Ratio Significantly Affect Turbulent Flame Speed?

In order to experimentally study whether or not the density ratio σ substantially affects flame displacement speed at low and moderate turbulent intensities, two stoichiometric methane/oxygen/nitrogen mixtures characterized by the same laminar flame speed S _L = 0.36 m/s, but substantially different σ were designed using (i) preheating from T _u = 298 to 423 K in order to increase S _L , but to decrease σ, and (ii) dilution with nitrogen in order to further decrease σ and to reduce S _L back to the initial value. As a result, the density ratio was reduced from 7.52 to 4.95. In both reference and preheated/diluted cases, direct images of statistically spherical laminar and turbulent flames that expanded after spark ignition in the center of a large 3D cruciform burner were recorded and processed in order to evaluate the mean flame radius \(\bar {R}_{f}\left (t \right )\) and flame displacement speed \(S_{t}=\sigma ^{-1}{d\bar {R}_{f}} \left / \right . {dt}\) with respect to unburned gas. The use of two counter-rotating fans and perforated plates for near-isotropic turbulence generation allowed us to vary the rms turbulent velocity \(u^{\prime }\) by changing the fan frequency. In this study, \(u^{\prime }\) was varied from 0.14 to 1.39 m/s. For each set of initial conditions (two different mixture compositions, two different temperatures T _u , and six different \(u^{\prime })\), five (respectively, three) statistically equivalent runs were performed in turbulent (respectively, laminar) environment. The obtained experimental data do not show any significant effect of the density ratio on S _t . Moreover, the flame displacement speeds measured at u′/S _L = 0.4 are close to the laminar flame speeds in all investigated cases. These results imply, in particular, a minor effect of the density ratio on flame displacement speed in spark ignition engines and support simulations of the engine combustion using models that (i) do not allow for effects of the density ratio on S _t and (ii) have been validated against experimental data obtained under the room conditions, i.e. at higher σ.     

A Conditional Moment Closure Study of Chemical Reaction Source Terms in SCCI Combustion

The objective of this study is to evaluate conditional moment closure (CMC) approaches to model chemical reaction rates in compositionally stratified, autoigniting mixtures, in thermochemical conditions relevant to stratified charge compression ignition (SCCI) engines. First-order closure, second-order closure and double conditioning are evaluated and contrasted as options in comparison to a series of direct numerical simulations (DNSs). The two-dimensional (2D) DNS cases simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane/air mixtures in a constant volume. The cases feature two different levels of stratification with three mean temperatures in the negative-temperature coefficient (NTC) regime of ignition delay times. The first-order closure approach for reaction rates is first assessed using hybrid DNS-CMC a posteriori tests when implemented in an open source computational fluid dynamics (CFD) package known as OpenFOAM\(^{{\circledR }}\). The hybrid DNS-CMC a posteriori tests are not a full CMC but a DNS-CMC hybrid in that they compute the scalar and velocity fields at the DNS resolution, thus isolating the first-order reaction rate closure model as the main source of modelling error (as opposed to turbulence model, scalar probability density function model, and scalar dissipation rate model). The hybrid DNS-CMC a posteriori test reveals an excellent agreement between the model and DNS for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. The a priori analysis reveals that the reason for disagreement is failure of the first-order closure hypothesis in the model due to the high level of conditional fluctuations. Second-order and double conditioning approaches are then evaluated in a priori tests to determine the most promising path forwards in addressing higher levels of stratification. The a priori tests use the DNS data to compute the model terms, thus directly evaluating the model assumptions. It is shown that in the cases with a high level of stratification, even the second-order estimation of the reaction rate source term cannot provide a reasonably accurate closure. Double conditioning using mixture-fraction and sensible enthalpy, however, provides an accurate first-order closure to the reaction rate source term.