Direct Numerical Simulation Cases Research Articles

Direct numerical simulation of ammonia/n-heptane dual-fuel combustion under high pressure conditions

Ammonia (NH3) combustion has received increasing attention for its carbon-free nature. However, the utilization of ammonia in engines is constrained by its relatively low reactivity. To overcome this shortcoming, ammonia blending with high-reactivity fuels has been used. In the present work, direct numerical simulation (DNS) of ammonia/n-heptane dual-fuel combustion was performed to understand the effects of ammonia addition on the combustion behavior of n-heptane sprays. Three DNS cases with NH3 energy ratios of 0%, 20%, and 40% were considered. Two-stage combustion was observed in all cases. It was found that both the first-stage and second-stage ignition delay times increase with increasing NH3 energy ratio, and the peak of mean heat release rate (HRR) reduces with increasing NH3 energy ratio. For low-temperature combustion, ignition kernels were observed in the case with pure n-heptane while ignition occurs almost volumetrically in the cases with NH3 addition. The reaction zone of the cases with NH3 addition is thicker compared to that of the case with pure n-heptane. The reactions of NH3 involve radicals, such as OH, which affects the low-temperature combustion of n-heptane. In the stage of high-temperature combustion, individual ignition kernels with significant heat release rate were observed in the cases with NH3 addition, where the reaction zones are thin. In contrast, for the case with pure n-heptane, large heat release rate occurs simultaneously over the entire domain with thick reaction zones. Ignition occurs in regions characterized by low scalar dissipation rate for both low-temperature and high-temperature combustion in all cases. It was found that, though the contributions of NH3-related reactions to the total HRR are noticeable, the contributions of important elementary reactions to the total HRR in pure n-heptane combustion still prevail in the cases with NH3 addition, which indicates that n-heptane chemistry dominates that of NH3 in this work.

Design of a Direct numerical Simulation of flow and heat transfer in a T-junction

Several investigations have been undertaken to study the velocity and temperature fields associated with the thermal mixing between fluids, and resulting thermal striping in a T-junction. However, the available experimental databases are not sufficient to describe the involved physics in adequate detail, and, due to experimental limitations, accurate data on velocity and temperature fluctuations in regions close to the wall are not available. Computational Fluid Dynamics (CFD) can play an important role in predicting such complex flow features. However, predicting complex thermal fatigue phenomena is a challenge for the available momentum and heat flux turbulence models. Furthermore, such models need to be extensively validated.The aim of the present work is to design a reference numerical experiment for Direct Numerical Simulation (DNS) of a thermal fatigue scenario using Reynolds-Averaged Navier-Stokes (RANS) simulations. First, the feasibility of scaling down the Reynolds number from experimental cases to a computationally-feasible range is investigated. The junction corner shape is also modified to a slightly rounded corner, ensuring that the underlying fundamental physical phenomena of turbulence and thermal mixing flow features are preserved. Finally, the pipe lengths of the model were calibrated to ensure there would be no interference of the upstream developing region and the outlet boundary conditions on the thermal mixing at the junction. A sample under-resolved DNS case, with unity and low-Prandtl number passive temperature scalars, with iso-temperature, iso-flux and mixed (Robin) wall boundary conditions, are presented. This proof-of-concept simulation contributes to the finalization of the set-up for fully-resolved DNS with respect to the computational grid size selection and transient characteristics.

Investigation of the derivation and consistency of the quasi-two-dimensional flamelet models for non-premixed flames

Three non-premixed quasi-two-dimensional flamelet (Q2DF) models can be derived via integrating one-dimensional flamelet libraries, which are generated by premixing the third stream with the fuel stream or (and) the oxidizer stream as the premix fraction (η) varied from zero to unity. These models are attractive and considered effective substitutes for two-dimensional flamelet (2DF) formulations; however, the connections between these Q2DF models and 2DF equations have not been clearly illustrated formerly. In this work, the 2DF formulations are converted from the space defined by two mixture fractions (Z1×Z2) to that used for each Q2DF model (ξ×η) in which ξ designates a newly defined mixture fraction. For moderate Reynolds number conditions, it is considered that the Q2DF models and the 2DF formulations are equivalents as the one-dimensional (1D) flamelet elemental libraries are integrated upon sufficient grids of η. To confirm this, the two-dimensional (2D) direct numerical simulations (DNS) and three-dimensional (3D) large-eddy simulation (LES) are performed to provide reference data since it is readily to associate the 2DF formulations with variable transports in physical space. The 2D DNS cases present various three-feed systems characterized by different third streams and ensure a well-mixed mixture in moderate η, while the 3D LES case is performed with a large flux of pure CO2 as the third stream. Three Q2DF models are compared by using the same tracking parameters obtained from, respectively, the DNSs and LES. The comparisons based on the DNS cases demonstrate that the Q2DF models can reproduce the DNS data with quite satisfying accuracy, and it is confirmed that the accuracy has nothing to do with the type of the third stream. Through the LES results and the related comparisons, it can be concluded that the Q2DF models are reliable to predict the experimental measurements, and on the condition of a sufficient η resolution, the three Q2DF models can give the same prediction in the whole range of η.

High-resolution reconstruction and a-priori modeling of turbulent flames in the context of large eddy simulation using the convolutional neural network

In large eddy simulation (LES) of turbulent combustion, accurate modeling of the unresolved scalar flux and filtered reaction source terms is challenging. In the present work, a convolutional neutral network (CNN) was developed for the high-resolution reconstruction of the unfiltered progress variable, velocity and reaction rate based on the filtered quantities that are available from LES or by filtering the direct numerical simulation (DNS) data. The unclosed terms in the filtered progress variable transport equation were then modeled using the reconstructed quantities from the proposed CNN model and the approximate deconvolution method (ADM). Two DNS cases, i.e., case A and case B, with different Karlovitz numbers (Ka) were performed to assess the performance of the models a−priori. The unfiltered and filtered DNS results were first presented. It was found that the small-scale wrinkling structures of the flames and turbulence are largely filtered out, and the reaction zone is broadened by filtering. Then, the progress variable, velocity and reaction rate were reconstructed from the filtered DNS data. The results of reconstruction by ADM and the CNN model were compared with those from the DNS. It was found that the distributions of various quantities predicted by the CNN model agree well with those of the DNS. Finally, the unresolved scalar flux and reaction source terms in the filtered progress variable transport equation were modeled. The statistics of the modeled results were analyzed and it was shown that the CNN model performs better than ADM. Overall, the CNN model is promising for the data reconstruction and model development of turbulent combustion.

SGS Reaction rate modelling for MILD combustion based on machine-learning combustion mode classification: Development and a priori study

A neural network (NN) aided model is proposed for the filtered reaction rate in moderate or intense low-oxygen dilution (MILD) combustion. The framework of the present model is based on the partially stirred reactor (PaSR) approach, and the fraction of the reactive structure appearing in the PaSR is predicted using different NN’s, to consider both premixed and non-premixed conditions while allowing the use of imbalanced training data between premixed and non-premixed combustion direct numerical simulation (DNS) data. The key ingredient in the present model is the use of local combustion mode prediction performed by using another NN, which is developed in a previous study. The trained model was then assessed by using two unknown combustion DNS cases, which yields much higher dilution level (more intense MILD condition) and higher Karlovitz number than the DNS cases used as training data. The model performance assessment has been carried out by means of the Pearson’s correlation coefficient and mean squared error. For both the present model and zeroth-order approximated reaction rate, the correlation coefficient with the target values shows relatively high values, suggesting that the trend of predicted field, by the present model and zeroth-order approximation, is well correlated with the actual reaction rate field. This suggests that the use of PaSR equation is promising if the fraction of the reactive structure is appropriately predicted, which is the objective in the present study. On the other hand, substantially lower mean squared error is observed for a range of filter sizes for the present model than that for the zeroth-order approximation. This suggests that the present filtered reaction rate model can account for the SGS contribution reasonably well.

A Priori Direct Numerical Simulation Analysis of the Closure of Cross-Scalar Dissipation Rate of Reaction Progress Variable and Mixture Fraction in Turbulent Stratified Flames

The cross-scalar dissipation rate of reaction progress variable and mixture fraction widetilde{{varepsilon_{cxi } }} plays an important role in the modelling of stratified combustion. The evolution and statistical behaviour of widetilde{{varepsilon_{cxi } }} have been analysed using a direct numerical simulation (DNS) database of statistically planar turbulent stratified flames with a globally stochiometric mixture. A parametric analysis has been conducted by considering a number of DNS cases with a varying initial root-mean-square velocity fluctuation u^{prime } and initial scalar integral length scale ell_{phi }. The explicitly Reynolds averaged DNS data suggests that the linear relaxation model for widetilde{{varepsilon_{cxi } }} is inadequate for most cases, but its performance appears to improve with increasing initial ell_{phi } and u^{prime } values. An exact transport equation for widetilde{{varepsilon_{cxi } }} has been derived from the first principle, and the budget of the unclosed terms of the widetilde{{varepsilon_{cxi } }} transport equation has been analysed in detail. It has been found that the terms arising from the density variation, scalar-turbulence interaction, chemical reaction rate and molecular dissipation rate play leading order roles in the widetilde{{varepsilon_{cxi } }} transport. These observations have been justified by a scaling analysis, which has been utilised to identify the dominant components of the leading order terms to aid model development for the unclosed terms of the widetilde{{varepsilon_{cxi } }} transport equation. The performances of newly proposed models for the unclosed terms have been assessed with respect to the corresponding terms extracted from DNS data, and the newly proposed closures yield satisfactory predictions of the unclosed terms in the widetilde{{varepsilon_{cxi } }} transport equation.

Effect of flame–flame interaction on scalar PDF in turbulent premixed flames

Direct numerical simulation (DNS) results are analysed to investigate the effect of flame–flame interaction on the scalar distribution in a large eddy simulation context. The DNS data consist of turbulent premixed planar flame, V-flame and swirl flame cases with different turbulence and equivalence ratio, and relatively large Damköhler number conditions are considered for the three DNS cases. The volumetric fraction of non-flamelet type reaction zones Φ¯, which are caused by flame–flame interaction (FFI), is identified by the trained neural network. The quantification of scalar PDF mode is carried out by means of the bimodality coefficient. Various scalar PDFs are constructed with different sample volumes of the filter size. The PDFs with high bimodality coefficient samples show clear bimodal distributions, whereas low bimodality coefficient samples show unimodal or plateau distributions. The conditional PDF and conditional average of the bimodality coefficient conditioned based on Φ¯ clearly show negative correlation between these two quantities. These results suggest that the presence of FFI events leads to bimodality loss of the scalar field, even when the Damköhler number is large. Reaction zones with non-bimodal scalar distribution are also found to have very small scalar gradient. Thus, the reaction rate of such reaction zones could be underestimated in flamelet-type modelling. However, such deficit may be straightforwardly complemented additively, for example, by considering a zero-dimensional canonical reactor with the fraction Φ¯.

A priori assessment of convolutional neural network and algebraic models for flame surface density of high Karlovitz premixed flames

Accurate modeling of the unresolved flame surface area is critical for the closure of reaction source terms in the flame surface density (FSD) method. Some algebraic models have been proposed for the unresolved flame surface area for premixed flames in the flamelet or thin reaction zones (TRZ) regimes where the Karlovitz number (Ka) is less than 100. However, in many lean combustion applications, Ka is large (Ka > 100) due to the strong interactions of small-scale turbulence and flames. In the present work, a direct numerical simulation (DNS) database was used to evaluate the performance of algebraic FSD models in high Ka premixed flames in the context of large eddy simulations. Three DNS cases, i.e., case L, case M and case H, were performed, where case L is located in the TRZ regime with Ka < 100 and case M and case H are located in the broken reaction zones regime with Ka > 100. A convolutional neural network (CNN) model was also developed to predict the generalized FSD, which was trained with samples of case H and a small filter size, and was tested in various cases with different Ka and filter sizes. It was found that the fraction of resolved FSD increases with increasing filtered progress variable c̃ and decreasing subgrid turbulent velocity fluctuation u′Δ. The performance of CNN and algebraic models was assessed using the DNS database. Overall, the results of algebraic models are promising in case L and case M for a small filter size; the CNN model performs generally better than the algebraic models in high Ka flames and the correlation coefficient between the modeled and actual generalized FSD is greater than 0.91 in all cases. The effects of c̃ and u′Δ on the performance of different models for various cases were explored. The algebraic models perform well with large values of c̃ and small values of u′Δ in high Ka cases, which indicates that they can be applied to high Ka flames in certain conditions. The performance of the CNN model is better than the algebraic models for a large filter size in high Ka cases.

2-D and 3-D measurements of flame stretch and turbulence–flame interactions in turbulent premixed flames using DNS

Abstract

Application of machine learning for filtered density function closure in MILD combustion

Abstract A machine learning algorithm, the deep neural network (DNN) 1 , is trained using a comprehensive direct numerical simulation (DNS) dataset to predict joint filtered density functions (FDFs) of mixture fraction and reaction progress variable in Moderate or Intense Low-oxygen Dilution (MILD) combustion. The important features of the DNS cases include mixture fraction variations, turbulent mixing lengths, exhaust gas recirculation (EGR) dilution levels, etc., posing a great challenge for data-driven modelling. The DNN architecture is built and optimised with extreme care to achieve high robustness and accuracy, resorting to dimensionality reduction techniques such as principal component analysis (PCA) to identify and remove the outliers in the training data. To better interpret the predictive ability of the DNN, two analytical joint FDF models respectively using two independent β and copula distributions, are also employed for a detailed comparison with the DNS data. The FDFs in MILD combustion behave differently compared to those in conventional flames because the reaction zones are more distributed. They generally exhibit non-regular (neither Gaussian nor bi-modal) distributions and strong cross correlations, which cannot be captured adequately by the analytical models. However, the DNN is well suited for this physico-chemically complex problem and its predictions are in excellent agreement with the DNS data for a broad range of mixture conditions and filter sizes. Furthermore, a priori assessment is conducted for filtered reaction rate closure. It is found that the DNN model significantly outperforms the analytical models for all cases showing very good predictions for the filtered reaction rate for a range of filter sizes. The DNN prediction improves as the filter size becomes larger than the characteristic reaction zone thickness while the analytical models works relatively better for smaller filter sizes. This is a clear advantage for the DNN to be used in practical LES applications.

Reduced chemical reaction mechanisms for simulating sodium emissions by solid-fuel combustion

Starting from a reference and comprehensive chemical mechanism for alkali metal emissions (Glarborg and Marshall, 2005), combined with an hydrocarbon oxidation described with a skeleton mechanism (Kazakov and Frenklach, 1994), reduced and optimized chemical kinetics are derived. The objective is to provide a set of chemical schemes useful for three-dimensional (3D) numerical simulations of alkali metal emissions by pulverized solid-fuel combustion systems. An automated procedure relying on one-dimensional (1D) premixed flames is applied to obtain a combined reduced mechanism, whose performance is then evaluated in one-dimensional strained diffusion flames, micro-mixing based canonical problems and three-dimensional carrier-phase direct numerical simulation (DNS) of coal combustion. Predictions of the reduced mechanism on major sodium species, i.e., Na, NaOH, NaCl and Na2SO4 agree well with that of the detail reference scheme under all the considered conditions. A parametric study with 14 two-dimensional (2D) DNS cases is then performed to better understand the reactive flow properties and estimate the prediction capabilities of the reduced mechanism for various Na/Cl/S ratio in the volatiles. After pursuing the chemistry reduction, a global sodium mechanism with only 9 species and 8 reaction-steps is also discussed. The systematic comparison between the 3D DNS results obtained with the reference chemical scheme against those with the reduced ones confirm the validity of the reduction strategy. A reduction of up to 84% in computational cost is reached with the optimized global scheme, thus allowing for addressing real pulverized-coal combustion systems.

Law of the wall for a temporally evolving vertical natural convection boundary layer

Abstract

Development of reduced and optimized reaction mechanism for potassium emissions during biomass combustion based on genetic algorithms

A reduced mechanism for potassium chemistry under combustion conditions is derived from a detailed chemical mechanism for alkali metal emissions (Glarborg and Marshall, 2005), which could be useful for three-dimensional (3D) numerical simulations of potassium emissions by biomass combustion furnaces. An automated chemistry reduction and optimization approach relying on canonical micro-mixing problem is applied to develop the reduced mechanism, whose performance is then evaluated in two-dimensional (2D) carrier-phase direct numerical simulation (DNS) of pulverized-biomass combustion. Good agreement is achieved between predictions of the reduced and the detailed mechanisms on the four major potassium species, i.e., K, KOH, KCl and K2SO4. The prediction capabilities of the reduced mechanism for various K/Cl/S ratios in the volatiles are further investigated by a parametric study with 14 two-dimensional DNS cases. The potassium chemistry under those various conditions are well predicted by the reduced potassium mechanism with a CPU cost reduction reaching up to 71.3% compared to the detailed reference mechanism.

Trailing-edge broadband noise prediction of an airfoil with boundary-layer tripping

Hybrid methods for trailing edge noise prediction are applied to a NACA 6512-63 airfoil at zero angle of attack embedded in the actual narrow stream of the Siegen open-jet anechoic wind-tunnel. Incompressible large-eddy simulations (LES) of the airfoil trailing-edge flow yield the noise sources, and different analytical acoustic analogies then predict the acoustic far-field pressure. The chord-based Reynolds number of 1.9 × 105 triggers long laminar flow regions along the airfoil, leading to instability waves with an associated broadband noise radiation. To avoid this laminar-instability noise, the airfoil boundary layer is experimentally tripped on both sides. The actual serration tripping is included in the numerical grid as well as a simplified stair-step trip. Aerodynamic and acoustic results of the performed LES are compared with measurements and compressible direct numerical simulation (DNS) results. No noticeable influence of the trip geometry is found whereas the numerical schemes play a more important role. LES predictions with boundary layer trip compare well with experimental measurements and DNS cases. If the boundary-layer trip is not sufficiently thick in the numerical model, or not present at all, the far-field acoustic pressure is overpredicted and resembles more closely the sound radiation from the untripped airfoil with laminar instability noise.

DNS-driven analysis of the Flamelet/Progress Variable model assumptions on soot inception, growth, and oxidation in turbulent flames

Modeling suites for Large-Eddy Simulations of soot evolution in turbulent flames include a number of submodels describing the chemistry of soot precursors, particle dynamics, heterogeneous soot chemistry, turbulent mixing, and combustion. To understand the reasons for model failure and to enhance the overall model performance, it is necessary to identify and subsequently improve model components with a leading order effect on the overall error. In this work, errors in soot predictions associated with flamelet-based combustion models are isolated and quantified in a combined a-priori and partial a-posteriori analysis using large-scale Direct Numerical Simulation (DNS) data of a sooting turbulent jet diffusion flame. Gas-phase quantities entering the calculation of the soot source terms and hence coupling the combustion model to the soot model are analyzed in the DNS first. The performance of a Flamelet/Progress Variable model with respect to these quantities is then analyzed a-priori for two DNS cases employing a mixture-averaged transport model and unity Lewis numbers. Then, the soot evolution along Lagrangian trajectories extracted from the DNS is re-computed using rate coefficients directly taken from the DNS and from the flamelet table. In the context of this partial a-posteriori analysis, flamelet-induced errors are also compared to errors induced by the chemical soot model. The soot surface growth and oxidation rate coefficients are reasonably well predicted by the flamelet library. Considerably larger errors in the model-predicted soot mass originate from the tabulated quantities entering the calculation of PAH-based soot growth rates. However, these errors can be reduced to a few percent if the rate is appropriately scaled with the mass fraction of polycyclic aromatic hydrocarbons (PAH). However, this requires the solution of a transport equation for the PAH mass fraction, and modeling the source term in this equation is shown to be challenging. Overall, the largest uncertainties can be attributed to the chemical mechanism for PAH formation and the model for the PAH source term.

DNS analysis of the effects of combustion on turbulence in a supersonic H2/air jet flow

In this paper, the effects of combustion on turbulence features are investigated by direct numerical simulation (DNS) of supersonic round turbulent hydrogen jet flows. Two DNS cases are conducted: the one is combustion hydrogen/air jet and the other is non-combustion jet with the same components as a comparison case. In the DNS, the supersonic jet consists of 85% hydrogen and 15% nitrogen in volume with temperature of 305 K and jet velocity of 900 m/s. The ambient air velocity is 20 m/s and temperature is 1150 K. The Reynolds numbers based the jet exit diameter and hydrogen jet velocity both are 22000 and the jet Mach numbers both are 1.2. The DNS results show that occurrence of combustion significantly delays the transition of the jet flow, and results in a 38% decrease in the peak of turbulent kinetic energy, compared with the non-combustion jet flow. The decreasing of the Reynolds number due to the heat release is considered as the main reason. Compared with the non-combustion jet flow, the combustion jet flow has more complete coherent vortex rings in the early stage. In addition, the positive and minus energy fluxes of combustion jet flow are always larger than that of non-combustion jet flow.

The Effects of Combustion on Turbulent Statistics in a Supersonic Turbulent Jet

The effects of combustion on turbulent statistics in a supersonic turbulent jet are investigated by using direct numerical simulation (DNS). To study the combustion effects, two DNS cases (reacting case and non-reacting case) are conducted and the comparison of turbulent statistics are used to study the combustion effects. The medium of jet is 85% hydrogen with temperature 305K and the co-flow is hot air with temperature 1150K. The Reynolds numbers based on the jet diameters are 22000 and the jet Mach numbers are 1.2. The DNS results show that combustion case has both larger decay rate constant of centerline streamwise mean velocity and larger spreading rate of half-velocity jet width than the non-reacting case. It also shows that the combustion case achieves the self-similarity slower. For reacting jet, the vortex structures are more smooth in the near field and vortex filament structures are larger in the far field. Combustion causes the turbulent zone to be delayed downstream and increases the probability of strong velocity pulsation.

Clustering of rapidly settling, low-inertia particle pairs in isotropic turbulence. Part 2. Comparison of theory and DNS

Part 1 (Rani et al. J. Fluid Mech., vol. 871, 2019, pp. 450–476) of this study presented a stochastic theory for the clustering of monodisperse, rapidly settling, low-Stokes-number particle pairs in homogeneous isotropic turbulence. The theory involved the development of closure approximations for the drift and diffusion fluxes in the probability density function (p.d.f.) equation for the pair relative positions $\boldsymbol{r}$. In this part 2 paper, the theory is quantitatively analysed by comparing its predictions of particle clustering with data from direct numerical simulations (DNS) of isotropic turbulence containing particles settling under gravity. The simulations were performed at a Taylor micro-scale Reynolds number $Re_{\unicode[STIX]{x1D706}}=77.76$ for three Froude numbers $Fr=\infty ,0.052,0.006$, where $Fr$ is the ratio of the Kolmogorov scale of acceleration and the magnitude of gravitational acceleration. Thus, $Fr=\infty$ corresponds to zero gravity, and $Fr=0.006$ to the highest magnitude of gravity among the three DNS cases. For each $Fr$, particles of Stokes numbers in the range $0.01\leqslant St_{\unicode[STIX]{x1D702}}\leqslant 0.2$ were tracked in the DNS, and particle clustering quantified both as a function of separation and the spherical polar angle. We compared the DNS and theory values for the exponent $\unicode[STIX]{x1D6FD}$ characterizing the power-law dependence of clustering on separation. The $\unicode[STIX]{x1D6FD}$ from the $Fr=0.006$ DNS case are in reasonable agreement with the theoretical predictions obtained using the second drift closure (referred to as DF2). To quantify the anisotropy in clustering, we calculated the leading–order coefficient in the spherical harmonics expansion of the p.d.f. of pair relative positions. The coefficients predicted by the theory (DF2) again show reasonable agreement with those calculated from the DNS clustering data for $Fr=0.006$. However, we note that in spite of the high magnitude of gravity, the clustering is only marginally anisotropic both in DNS and theory. The theory predicts that the spherical harmonic coefficient scales with $\unicode[STIX]{x1D6FD}(=\unicode[STIX]{x1D6FD}_{2}St_{\unicode[STIX]{x1D702}}^{2})$, where $\unicode[STIX]{x1D6FD}_{2}$ is the ratio of the drift and diffusion flux coefficients. Since the drift flux, and thereby $\unicode[STIX]{x1D6FD}_{2}$, is seen to decrease with gravity for $St_{\unicode[STIX]{x1D702}}<1$, the anisotropy is also correspondingly diminished.

Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

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.