Canonical Configuration Research Articles

Cylinders and jets in crossflow: Wake formations as a result of varying geometric proximities

The combined flow physics of several canonical flow configurations is experimentally studied. Here, we analyze an array of jets issuing into a crossflow, then immediately navigating past an array of cylinders. This is achieved with a 2 × 3 triangular pattern of jets and symmetric cylinders at three jets to crossflow velocity ratios, enabling near-complete optical access of each jet, with velocities measured by time-resolved particle image velocimetry. Jet trajectories reveal that each configuration adheres to a power-law trend and that greater penetration is achieved by the downstream and confined jets compared to the more conventional upstream one. Recirculation regions of the upstream and downstream jets are nearly independent, with the confined jet encompassing regions of overlap with both. Turbulent statistics reveal the influence of geometric placement and velocity ratio on the time-averaged velocity, anisotropy, and Reynolds stresses incurred by each jet. Galilean decomposition utilizes a supplemental crossflow-only velocity field to delineate the influence of each jet's low- and high-pressure regions on the otherwise uniform stream. Proper orthogonal decomposition suggests that increased jet penetration decreases the number of modes required for truncation in the investigated spanwise plane. Vortex identification algorithms are applied to the reconstructed flow fields, reaffirming that with increasing velocity ratio, the jets generate vortices of their own in similar statistical formations as the cylinders. This investigation provides a foundation to aid future modeling efforts toward characterizing flow physics of importance in designing and passively controlling transverse jets with varying blockage proximities in a crossflow.

Canonical representations of fingers and dots trigger an automatic activation of number semantics: an EEG study on 10-year-old children

Over the course of development, children must learn to map a non-symbolic representation of magnitude to a more precise symbolic system. There is solid evidence that finger and dot representations can facilitate or even predict the acquisition of this mapping skill. While several behavioral studies demonstrated that canonical representations of fingers and dots automatically activate number semantics, no study so far has investigated their cerebral basis. To examine these questions, 10-year-old children were presented a behavioral naming task and a Fast Periodic Visual Stimulation EEG paradigm. In the behavioral task, children had to name as fast and as accurately as possible the numbers of dots and fingers presented in canonical and non-canonical configurations. In the EEG experiment, one category of stimuli (e.g., canonical representation of fingers or dots) was periodically inserted (1/5) in streams of another category (e.g., non-canonical representation of fingers or dots) presented at a fast rate (4 Hz). Results demonstrated an automatic access to number semantics and bilateral categorical responses at 4 Hz/5 for canonical representations of fingers and dots. Some differences between finger and dot configuration's processing were nevertheless observed and are discussed in light of an effortful-automatic continuum hypothesis.

Signal Reconstruction of Two-Color Pyrometry Technique Using CFD and a Detailed Spectral Radiation Model in a Marine Diesel Engine Setup

<div class="section abstract"><div class="htmlview paragraph">Optical soot pyrometry is a mature experimental technique that has been applied to a broad range of combustion systems for measuring soot temperature and concentration. Even though the method is widely used and well documented, the line of sight nature of the technique makes the interpretation of its results challenging. Notably, gradients in temperature and soot concentration along the line of sight or across the field of view can introduce significant levels of uncertainty in the results. This paper presents a numerical study where the signal from the experimental two-color pyrometry technique in a marine diesel engine reference experiment is reconstructed employing computational fluid dynamics (CFD) and a detailed Line-by-Line (LBL) spectral radiation model. The analysis is aimed at qualitatively supporting interpretability of experimental observations. Further, the role of soot and temperature gradients along and normal to the line of sight are assessed in two canonical configurations in which the signals are reconstructed numerically. In addition, the impact of different optical thicknesses is analyzed parametrically. The results obtained with the numerical pyrometry showed that gradients in temperature along the line of sight significantly affect the pyrometry temperature, leading to an overestimation of the effective soot averaged temperature in the range of 50 K to 250 K (i.e. 2-12%), depending on the soot concentration. Further, a saturation effect in the pyrometry KL-factor along the line of sight was observed at higher soot concentrations, resulting in an underestimation of the average soot volume by a factor of four to six in the canonical configurations. Gradients across the field of view were found to have a lower impact on the pyrometry results and to introduce much smaller biases than gradients along the line of sight.</div></div>

The effect of Dean, Reynolds and Womersley numbers on the flow in a spherical cavity on a curved round pipe. Part 2. The haemodynamics of intracranial aneurysms treated with flow-diverting stents.

The flow in a spherical cavity on a curved round pipe is a canonical flow that describes well the flow inside a sidewall aneurysm on an intracranial artery. Intracranial aneurysms are often treated with a flow-diverting stent (FDS), a low-porosity metal mesh that covers the entrance to the cavity, to reduce blood flow into the aneurysm sac and exclude it from mechanical stresses imposed by the blood flow. Successful treatment is highly dependent on the degree of reduction of flow inside the cavity, and the resulting altered fluid mechanics inside the aneurysm following treatment. Using stereoscopic particle image velocimetry, we characterize the fluid mechanics in a canonical configuration representative of an intracranial aneurysm treated with a FDS: a spherical cavity on the side of a curved round pipe covered with a metal mesh formed by an actual medical FDS. This porous mesh coverage is the focus of Part 2 of the paper, characterizing the effects of parent vessel Re, De and pulsatility, Wo, on the fluid dynamics, compared with the canonical configuration with no impediments to flow into the cavity that is described in Part 1 (Chassagne et al., J. Fluid Mech., vol. 915, 2021, A123). Coverage with a FDS markedly reduces the flow Re in the aneurysmal cavity, creating a viscous-dominated flow environment despite the parent vessel Re > 100. Under steady flow conditions, the topology that forms inside the cavity is shown to be a function of the parent vessel De. At low values of De, flow enters the cavity at the leading edge and remains attached to the wall before exiting at the trailing edge, a novel behaviour that was not found under any conditions of the high-Re, unimpeded cavity flow described in Part 1. Under these conditions, flow in the cavity co-rotates with the direction of the free-stream flow, similar to Stokes flow in a cavity. As De increases, the flow along the leading edge begins to separate, and the recirculation zone grows with increasing De, until, above De ≈ 180, the flow inside the cavity is fully recirculating, counter-rotating with respect to the free-stream flow. Under pulsatile flow conditions, the vortex inside the cavity progresses through the same cycle - switching from attached and co-rotating with the free-stream flow at the beginning of the cycle (low velocity and positive acceleration) to separated and counter-rotating as De reaches a critical value. The location of separation within the harmonic cycle is shown to be a function of both De and Wo. The values of aneurysmal cavity Re based on both the average velocity and the circulation inside the cavity are shown to increase with increasing values of De, while Wo is shown to have little influence on the time-averaged metrics. As De increases, the strength of the secondary flow in the parent vessel grows, due to the inertial instability in the curved pipe, and the flow rate entering the cavity increases. Thus, the effectiveness of FDS treatment to exclude the aneurysmal cavity from the haemodynamic stresses is compromised for aneurysms located on high-curvature arteries, i.e. vessels with high De, and this can be a fluid mechanics criterion to guide treatment selection.

A Novel One- and Zero-Dimensional Model for Turbulent Jet Ignition

Turbulent jet ignition (TJI) is a promising combustion technology for burning highly diluted air-fuel mixtures. Computationally efficient models to assess the effect of the operating conditions and design parameters on the ignition propensity and timing are of paramount importance for the development of combustion systems employing TJI. To this end, a one-dimensional (1-D) jet model, which is based on the solution of the section integrated mass and momentum conservation equations, is derived in the present study. The model is extended with two additional transport equations for the turbulence intensity and the ignition precursor/tracer, that marks the ignition event. One-dimensional transient flamelet calculations are performed to generate tables for the ignition precursor source term that account for the turbulence and chemistry interaction. Further simplification of the model is carried out to obtain a novel penetration correlation and a computationally inexpensive Lagrangian ignition model. The extended jet model is hierarchically validated using available literature data for non-reactive and reactive jets, as well as experiments conducted in a state-of-the-art optically accessible prechamber. The derived model is able to reproduce both flow-related quantities (velocity and turbulence profiles, jet penetration) and the ignition delay time under different variations. This study also illustrates how numerical simulations in canonical configurations (one-dimensional flamelet) can be used in practical applications of TJI.

A generalised spray-flamelet formulation by means of a monotonic variable

The external structure of the spray-flamelet can be described using the Schvab–Zel'dovich–Liñan formulation. The gaseous mixture-fraction variable as function of the physical space, , typically employed for the description of gaseous diffusion flames leads to non-monotonicity behaviour for spray flames due to the extra fuel supplied by vaporisation of droplets distributed into the flow. As a result, the overall properties of spray flames depend not only on Z and the scalar dissipation rate, χ, but also on the spray source term, . We propose a new general coordinate variable which takes into account the spatial information about the entire mixture fraction due to the gaseous phase and droplet vaporisation. This coordinate variable is based on the cumulative value of the gaseous mixture fraction and is shown to be monotonic. For pure gaseous flow, the new cumulative function, , yields the well-established flamelet structure in Z-space. In the present manuscript, the spray-flamelet structure and the new equations for temperature and mass fractions in terms of are derived and then applied to the canonical counterflow configuration with potential flow. Numerical results are obtained for ethanol and methanol sprays, and the effect of Lewis and Stokes numbers on the spray-flamelet structure is analysed. The proposed formulation agrees well when mapping the structure back to physical space thereby confirming our integration methodology.

Specific heat effects in two-dimensional shock refractions

Compressible mixtures in supersonic flows are subject to significant temperature changes via shock waves and expansions, which affect several properties of the flow. Besides the widely studied variable transport effects such as temperature-dependent viscosity and conductivity, vibrational and rotational molecular energy storage is also modified through the variation of the heat capacity \(c_p\) and heat capacity ratio \(\gamma \), especially in hypersonic flows. Changes in the composition of the mixture may also modify its value through the species mass fraction \(Y_\alpha \), thereby affecting the compression capacity of the flow. Canonical configurations are studied here to explore their sharply conditioned mechanical equilibrium under variations of these thermal models. In particular, effects of \(c_p(T,Y_\alpha )\) and \(\gamma (T,Y_\alpha )\) on the stability of shock-impinged supersonic shear and mixing layers are addressed, on condition that a shock wave is refracted. It is found that the limits defining regular structures are affected (usually broadened out) by the dependence of heat capacities with temperature. Theoretical and high-fidelity numerical simulations exhibit a good agreement in the prediction of regular shock reflections and their post-shock aerothermal properties.

The impact of a foehn wind on PM10 concentrations and the urban boundary layer in complex terrain: a case study from Kraków, Poland

Kraków, Poland, is a city with poor air quality, located in the large Wisła (Vistula) valley, and affected by a foehn wind from the Tatra Mountains. We analyzed 14 long episodes of the foehn from the periods Sep 2017 - Apr 2018 and Sep 2018 - Apr 2019. Data used included measurements of PM10 (i.e. particulate matter with an aerodynamic diameter up to 10 µm) concentrations) concentrations, air temperature and relative humidity, wind speed and direction from ground stations and mast measurements up to 100 m a.g.l., along with model analysis results. A non-operational configuration of the AROME CMC (the Application of Research to Operations at Mesoscale canonical model configuration) 1 km x 1 km was applied. A conceptual model concerning the impact of a foehn on urban air pollution was developed. The occurrence of a particular effect of a foehn on the PM10 spatial-temporal pattern depends on its mode of transfer through the city: a. a foehn flows above the valley where a strong cold air pool and a return flow can be found; b. a foehn enters the valley from the eastern, wider part or from the valley top and destroys the cold air pool; c. gravity waves generated by a foehn are strong enough to enter the western narrower part of the valley and cause large spatial differences in turbulence parameters within the city. The first transfer mode worsens air pollution dispersion conditions throughout the city and leads to large increases in PM10 levels (from below 50 to 150-200 µg⋅m−3), the second mode improves dispersion and leads to large decreases in PM10 levels (from 150-200 to below 50 µg⋅m−3) throughout the city, and the third generates large spatial differences in PM10 levels (50-70 µg⋅m−3) within the city. There is no single effect of a foehn on air pollution dispersion conditions.

Configuration characteristics of the Chinese First Quasi-axisymmetric Stellarator

The Chinese First Quasi-axisymmetric Stellarator (CFQS) will be the first operational quasi-axially symmetric stellarator in the world. The physical and engineering complexities led to the cancellation of two famous quasi-axisymmetric stellarators, CHS-qa and NCSX. Therefore, the major mission of the CFQS is to experimentally achieve the canonical quasi-axisymmetric configuration. The CFQS has been designed to possess a number of advanced features in fixed and free-boundary equilibria. It is a compact stellarator with an aspect ratio R/a ∼4.0. The neoclassical diffusion coefficient is similar to that of tokamaks in the collisionless regime. The MHD equilibrium of the CFQS configuration is stable up to volume-averaged normalized pressure β ∼1.1%. A region of the second ballooning stability exists in this facility with a large region of plasma, becoming second stable for β ∼2.7% in free-boundary equilibria. The gap between the first and second stability boundaries is very narrow, which is greatly beneficial for the CFQS operation in the second stable regime with high β plasma. A modular coil system with 16 coils is designed which robustly reproduces the standard quasi-axisymmetric magnetic field.

Magnetohydrodynamic Fast Sausage Waves in the Solar Corona

Characterized by cyclic axisymmetric perturbations to both the magnetic and fluid parameters, magnetohydrodynamic fast sausage modes (FSMs) have proven useful for solar coronal seismology given their strong dispersion. This review starts by summarizing the dispersive properties of the FSMs in the canonical configuration where the equilibrium quantities are transversely structured in a step fashion. With this preparation we then review the recent theoretical studies on coronal FSMs, showing that the canonical dispersion features have been better understood physically, and further exploited seismologically. In addition, we show that departures from the canonical equilibrium configuration have led to qualitatively different dispersion features, thereby substantially broadening the range of observations that FSMs can be invoked to account for. We also summarize the advances in forward modeling studies, emphasizing the intricacies in interpreting observed oscillatory signals in terms of FSMs. All these advances notwithstanding, we offer a list of aspects that remain to be better addressed, with the physical connection of coronal FSMs to the quasi-periodic pulsations in solar flares particularly noteworthy.

HARMONIE-AROME single-column tools and experiments

Abstract. The single-column version of the shared ALADIN-HIRLAM numerical weather prediction system, called MUSC, was developed by Météo-France in the 2000s and has a growing user-base in both HIRLAM and ALADIN countries. Tools to derive the required input, to run the experiments and to handle outputs of experiments carried out using MUSC have been developed within the HARMONIE-AROME canonical model configuration of the ALADIN-HIRLAM system are described within and constitute a large portion of this paper. The paper also illustrates the usefulness of the single-column approach for testing and developing HARMONIE-AROME physical parametrizations related to cloud microphysics and radiative transfer. Study cases concerning these physical parametrizations have been included for illustration purposes.

Processing of numerical representation of fingers depends on their location in space.

Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into accounttheir location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.

The effects of mixture preburning on detonation wave propagation

Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non-premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. This parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.

Deflagration to detonation transition in fast flames and tracking with chemical explosive mode analysis

In the context of vapour cloud explosion, the flame acceleration process can lead to conditions promoting deflagration to detonation transition (DDT), potentially leading to increased damages in accidental scenarios. This study focuses on this phenomenon by performing simulations of detonation reinitiation for fast flames in the Chapman–Jouguet deflagration regime. It is obtained experimentally by the attenuation of an incident detonation by an array of obstacles. A primary objective of the paper is to demonstrate the ability of the numerical model to reproduce the major experimental trends, namely the variation of the reinitiation propensity for different initial pressures and blockage ratios (BRs). Chemical explosive mode analysis (CEMA) is also adapted to the context of this study, in order to identify locally the propagation regime and to provide insights on the reinitiation mechanism. An a priori validation of the CEMA methodology is first performed on relevant canonical one-dimensional configurations. Subsequently, ensembles of five realizations are computed at different initial pressures and BRs and compared to experimental data. They are shown to reproduce the major observed trends in terms of detonation reinitiation length with respect to the operating conditions, with significant variability from one realization to another. In addition, the reinitiation mechanism is also found to be consistent with experimental observations and a previous numerical study of the same configuration. The CEMA methodology adapted to this context is able to identify locally the different propagation regimes, and to track the highly reactive zones that coherently couple with transverse pressure perturbations, leading to the formation of a strongly reacting kernel which eventually triggers the detonation reinitiation.

Displacement speed statistics in an open turbulent jet spray flame

In this study, a three-dimensional Direct Numerical Simulation of an open turbulent jet spray flame has been used to investigate the statistical behaviour of displacement speed Sd and its components to provide physical explanations for the observed behaviours at different axial locations downstream of the jet exit. The open turbulent jet spray flame exhibits fuel-lean conditions close to the jet exit but fuel-rich conditions have been observed further downstream due to the evaporation of fuel droplets. For the axial locations considered, combustion takes place under low Damköhler number conditions. The displacement speed of reaction progress variable isosurfaces shows qualitatively similar behaviour for all axial locations considered – predominantly positive across the major part of the flame but with small, potentially negative, values towards the burned-gas-side. The components of displacement speed arising from chemical reaction rate and flame normal molecular diffusion remain leading order contributors and the competition between these determines the mean behaviour of displacement speed. These observations are consistent with studies of turbulent spray flames in canonical configurations and low Damköhler number turbulent premixed and stratified flames. This suggests that flow geometry in the absence of mean curvature might not be important in determining the mean behaviour of displacement speed and its components. Therefore, the modelling methodologies employed for turbulent stratified flames can potentially be extended for turbulent spray flames. However, the modelling methodologies, which implicitly assume equality between the surface-weighted values of density-weighted displacement speed and local laminar burning velocity, might be rendered invalid for turbulent spray flames.

Effects of highly pulsatile inflow frequency on surface-mounted bluff body wakes

Abstract

Premixed flames for arbitrary combinations of strain and curvature

Many modeling strategies for combustion rely on laminar flamelet concepts to determine structure and properties of multi-dimensional and turbulent flames. Using flamelet tabulation strategies, the user anticipates certain aspects of the combustion process prior to the simulation and selects a flamelet model which mimics local flame conditions in the more complex configuration. Flame stretch, which can be decomposed into contributions from strain and curvature, is one of the conditions influencing a flame’s properties, structure, and stability. The objective of this work is to study premixed flame structures in the strain-curvature space using a recently published composition space model (CSM) and three physical space models for canonical flame configurations (stagnation flame, spherical expanding flame and inwardly propagating flame). Flames with effective Lewis numbers both smaller and larger than unity are considered. For canonical laminar flames, the stretch components are inherently determined through boundary conditions and their specific flame configuration. Therefore, canonical flames can only represent a certain sub-set of stretch effects experienced by multi-dimensional and turbulent flames. On the contrary, the CSM allows arbitrary combinations of strain and curvature to be prescribed for premixed flames exceeding the conditions attainable with the canonical flame setups. Thereby, also influences of negative strain effects and large curvatures can be studied. A parameter variation with the CSM shows that flame structures still significantly change outside the region of the canonical flame configurations. Furthermore, limits in the strain-curvature space are discussed. The present paper highlights advantages of composition space modeling which is achieved by detaching the representation of the flame structure from a specific canonical flame configuration in physical space.

Sensitivity Analysis of Bluff-Body Stabilized Premixed Flame Large-Eddy Simulations

Bluff-body stabilized turbulent premixed flames represent a challenging canonical configuration for computational simulation and validation. Past simulation results from many research groups on the same bluff-body flame test case demonstrate significant variation that is neither fully understood nor quantified. To identify potential sources of this variation, three categories of sensitivities are assessed for a stable combustion bluff-body flame test case: exit boundary conditions, turbulent combustion closure models, and grid resolution. Comparisons with experimental data are presented, and an analysis of the causes of the discrepancies is informed by the sensitivity analysis. Specifically, low grid sensitivities at the finest resolution indicate that notable discrepancies with the experiment are likely due to model or boundary condition errors. All three categories of sensitivities are identified as significant, and the dominant source of variation in the results depends on the resolution and flow variable of interest. In spite of a lack of thermoacoustic oscillations, exit boundary condition effects are shown to be substantial, and errors in velocity statistics are minimized by extending the computational domain into the exhaust region.

Computation of the mean hydrodynamic structure of gaseous detonations with losses

In this paper, computations of gaseous detonations in several configurations are performed and discussed. The objective is to investigate the detonation characteristics, specially the influence of losses, through a quantitative analysis of the mean hydrodynamic structure. The results are divided into two parts: The first one relates to the propagation of ideal detonations without losses and to their characterization for a specific set of thermodynamic parameters, and the second part investigates the influence of losses on the averaged hydrodynamic structure of detonations. This is achieved by means of a specific and canonical configuration, in which a detonation wave propagates in a reactive layer bounded by an inert gas. This topology is investigated through a comparison of the instantaneous flow-field, cellular structure, and averaged quantities such as the mean curvature and the hydrodynamic thickness. This configuration may be regarded as non-ideal, as the detonation experiences losses due to the expansion of the detonation products toward the inert layer. The prediction of the detonation characteristics, as well as the conditions at which quenching occurs, remains a challenge when losses are involved. The main objective is to assess to what extent the hydrodynamic thickness can be used as a relevant length scale in the analysis of the resulting database. The results also highlight the key features of this configuration, which isolates a specific issue related to the rotating detonation engines. The temperature of the inert layer strongly affects the structure of the detonation–shock combined wave. For a high-temperature inert gas confinement, a detached shock appears in the upper layer and a jet of fresh mixture develops downstream of the front. For this condition, we observed a reduction in the critical dimensions by a factor of two. The degree of regularity of the detonation structure, from weakly unstable to mildly unstable cases, through the variation of the reduced activation energy, was investigated. The hydrodynamic thickness appears to be a useful characteristic length scale for the detonation, as it allows a better analysis of the results and a scaling of data. Moreover, the detonation velocity deficit can be globally expressed as a function of the ratio of the hydrodynamic thickness to the mean radius of curvature at the bottom of the wall.

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. These observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.