DNS Database Research Articles

Closure modeling for the conditional Reynolds stresses in turbulent premixed combustion

Turbulence is significantly affected by combustion-induced dilatation in low Karlovitz number premixed flames. Conventional turbulence modeling approaches based on traditional unconditional averaging are limited in accurately capturing combustion heat release effects since they must capture both the direct influence of combustion heat release on turbulence and the flame dynamics. Solving momentum transport equations conditionally averaged with respect to a flame structure variable (progress variable for premixed combustion) could provide a superior framework for modeling combustion-affected turbulence since the flame dynamics are embedded into the flame structure variable conditioning. However, the conditional momentum equations contain numerous unclosed terms that evolve in both physical and phase spaces. Of the many unclosed terms, the conditional Reynolds stresses (conditional analog of the Reynolds stresses) represent the influence of turbulent transport on the conditional velocities. In this work, a new model consisting of two components for the conditional Reynolds stresses in turbulent premixed flames is developed to capture heat release effects on turbulence. The first component is the conditional analog of the Boussinesq model that characterizes turbulent shear effects in physical space. The second component depends on the conditional velocity gradient not in physical space but in phase space and captures the anisotropy in the conditional Reynolds stresses driven by thermal expansion effects that vary within the flame structure. The model is validated a priori using DNS databases of turbulent premixed jet flames at low and high Karlovitz numbers. At low Karlovitz number, the phase space term enables the model to capture direct heat release effects on all conditional Reynolds stress components, specifically the correct anisotropy of the normal components and the sign of the shear component. At high Karlovitz number where heat release effects on turbulence are insignificant, turbulent shear effects are dominant, and the phase space term has a nearly negligible effect.

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this work, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.

Resolvent modelling of near-wall coherent structures in turbulent channel flow

Turbulent channel flow was analysed using direct numerical simulations at friction Reynolds numbers Reτ=180 and 550. The databases were studied using spectral proper orthogonal decomposition (SPOD) to identify dominant near-wall coherent structures, most of which turn out to be streaks and streamwise vortices. Resolvent analysis was used as a theoretical approach to model such structures, as it allows the identification of the optimal forcing and most amplified flow response; the latter may be related to the observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were compared for several combinations of frequencies and wavenumbers. For both Reynolds numbers, the best agreement between SPOD and resolvent modes was observed for the cases where the lift-up mechanism from resolvent analysis is present, which are also the cases where the optimal resolvent gain is dominant. These results confirm the outcomes in our previous studies (Abreu et al., 2019; Abreu et al., 2020), where we used a DNS database of a pipe flow for the same Reynolds numbers.

Multi-observable reputation scoring system for flagging suspicious user sessions

Conventionally, network and cloud infrastructure security is handled by firewalls which monitor traffic and block malicious access by matching certain observables, e.g., IP, and DNS, to blacklisted entries in intelligence databases. Therefore, such an approach fails to deal with emerging threats that utilize unclassified observables, and to report suspicious activities of individual users. In this paper we propose MuSeR, a novel approach to assign reputation scores for observables, even when no prior information is available, and flag suspicious sessions by conducting inter-observable analysis of user requests. In essence, MuSeR opts to assist network and cloud administrators mitigate attacks while avoiding unwarranted blocking of benign access. MuSeR achieves such an objective by associating session reputation scores based on the trustworthiness of the user navigation pattern, and conducting dynamic analysis of individual observables involved within requests. Specifically, MuSeR employs a new machine learning model for classifying observables using features specifically chosen to factor in evidence provided by blacklists, and access patterns of known attacks. To determine a request score, MuSeR maps the classifier probabilities to adaptive subjective logic and then uses multinomial fusion to leverage evidence from the different observables. Given the request scores, MuSeR further promotes a novel session reputation scoring model that uses three-valued subjective logic to handle trust propagation and aggregation over user requests. The effectiveness ofMuSeR is validated using a large dataset obtained from popular databases such as WHOIS, CYMUS, and passive DNS databases.

The role of differential diffusion during early flame kernel development under engine conditions - part I: Analysis of the heat-release-rate response

Although experimental evidence for the correlation between early flame kernel development and cycle-to-cycle variations (CCV) in spark ignition (SI) engines was provided long ago, there is still a lack of fundamental understanding of early flame/turbulence interactions, and accurate models for full engine simulations do not exist. Since the flame kernel is initiated with small size, i.e. with large positive curvature, differential diffusion is expected to severely alter early flame growth in non-unity-Lewis-number (Le ≠ 1) mixtures as typically used in engines. In this work, a DNS database of developing iso-octane/air flame kernels and planar flames has been established with flame conditions representative for stoichiometric engine part-load operation. Differential diffusion effects on the global heat release rate are analyzed by relating the present findings to equivalent flames computed in the Le=1 limit. It is shown that in the early kernel development phase, the normal propagation velocity is significantly reduced with detrimental consequences on the global burning rate of the flame kernel. Besides this impact on the overall mass burning rate, the initial production of flame surface area by the normal propagation term in the flame area balance equation is noticeably reduced. By using the optimal estimator concept, it is shown that strong fluctuations in local heat release rate inherent to Le ≠ 1 flames in the thin reaction zones regime are mainly contained in the parameters local equivalence ratio, enthalpy, and H-radical mass fraction. Differential diffusion couples the evolution of these parameters to the unsteady flame geometry and structure, which is analyzed in Part II of the present study (Falkenstein et al., Combust. Flame, 2020).

A collaborative effort towards the accurate prediction of turbulent flow and heat transfer in low-Prandtl number fluids

This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various low-Prandtl flow configurations in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with low-Prandtl fluids, and a forced convection planar jet case with two different Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wall-bounded mixed convection flow at low-Prandtl number with varying Richardson number (Ri) values; a wall-bounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jet; a mixed-convection cold-hot–cold triple jet configuration corresponding to Ri = 0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis (SGDH) based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in low-Prandtl fluids.

The role of differential diffusion during early flame kernel development under engine conditions – part II: Effect of flame structure and geometry

From experimental spark ignition (SI) engine studies, it is known that the slow-down of early flame kernel development caused by the (Le > 1)-property of common transportation-fuel/air mixtures tends to increase cycle-to-cycle variations (CCV). To improve the fundamental understanding of the complex phenomena inside the flame structure of developing flame kernels, an engine-relevant DNS database is investigated in this work. Conclusive analyses are enabled by considering equivalent flame kernels and turbulent planar flames computed with Le > 1 and Le=1. In Part I of the present study (Falkenstein et al., Combust. Flame, 2020), a reduced representation of the local mixture state was proposed for the purpose of this analysis. Fluctuations in heat release rate attributed to differential diffusion were found to be governed by the parameters local enthalpy, local equivalence ratio, and H-radical mass fraction. Here, a coupling relation for the diffusion-controlled mixture parameter local enthalpy with local flame geometry and structure is derived, characterized by the key parameters κ and |∇c|/|∇c|lam. The analysis shows that the large positive global mean curvature intrinsic to the flame kernel configuration may detrimentally affect the local mixture state inside the reaction zone, particularly during the initial flame kernel development phase. External energy supply by spark ignition may effectively bridge over this critical stage, which causes the impact of global mean flame kernel curvature to be small under the present conditions compared to the overall effect of Le ≠ 1 observed in a statistically planar flame. Once ignition effects have decayed, the mixture state inside the reaction zone locally exhibits an identical dependence on |∇c| as in a strained laminar flame. This implies that differential diffusion effects at Karlovitz numbers representative for part-load conditions are not weakened by small-scale turbulent mixing, which is undesirable for the engine application, but can be favorable in terms of modeling.

Statistics of Two-phase Coupling in Turbulent Spherically Expanding Flames in Mono-sized Fuel-droplet Mists

ABSTRACT The statistics of flame–droplet interaction have been investigated for spherically expanding spray flames based on a three-dimensional DNS database. The source terms due to two-phase coupling arising from droplet evaporation in different governing equations for the gaseous carrier phase are considered to examine the effects of droplet diameter and overall (i.e. liquid+gaseous) equivalence ratio on the interaction between liquid and gaseous phases. Larger droplets are found to show higher probabilities of having greater values of slip velocity, and this behavior has been found to be unaffected by the overall equivalence ratio. Droplet diameter and number density have been found to significantly affect the interaction between liquid and gaseous phases since smaller droplets with overall fuel-lean equivalence ratio rarely interact with the flame in the reaction zone. Furthermore, source terms associated with the coupling between liquid and gaseous phases significantly contribute to mass, momentum, energy and mixture fraction transport equations. However, the contribution of droplet evaporation is relatively weak for the reaction progress variable transport equation.

Scaling of Second-Order Structure Functions in Turbulent Premixed Flames in the Flamelet Combustion Regime

The second-order velocity structure function statistics have been analysed using a DNS database of statistically planar turbulent premixed flames subjected to unburned gas forcing. The flames considered here represent combustion for moderate values of Karlovitz number from the wrinkled flamelets to the thin reaction zones regimes of turbulent premixed combustion. It has been found that the second-order structure functions exhibit the theoretical asymptotic scalings in the dissipative and (relatively short) inertial ranges. However, the constant of proportionality for the theoretical asymptotic variation for the inertial range changes from one case to another, and this value also changes with structure function orientation. The variation of the structure functions for small length scale separation remains proportional to the square of the separation distance. However, the constant of proportionality for the limiting behaviour according to the separation distance square remains significantly different from the theoretical value obtained in isotropic turbulence. The disagreement increases with increasing turbulence intensity. It has been found that turbulent velocity fluctuations within the flame brush remain anisotropic for all cases considered here and this tendency strengthens towards the trailing edge of the flame brush. It indicates that the turbulence models derived based on the assumptions of homogeneous isotropic turbulence may not be fully valid for turbulent premixed flames.

Propagation of premixed flames in the presence of Darrieus–Landau and thermal diffusive instabilities

We study the propagation of premixed flames, in the absence of external turbulence, under the effect of both hydrodynamic (Darrieus–Landau) and thermodiffusive instabilities. The Sivashinsky equation in a suitable parameter space is initially utilized to parametrically investigate the flame propagation speed under the potential action of both kinds of instability. An adequate variable transformation shows that the propagation speed can collapse on a universal scaling law as a function of a parameter related to the number of unstable wavelengths within the domain nc. To assess whether this picture can persist in realistic flames, a DNS database of large scale, two-dimensional flames is presented, embracing a range of nc values and subject to either purely hydrodynamic instability (DL) or both kinds of instability (TD). With the aid of similar DNS databases from the literature we observe that when adequately rescaled, propagation speeds follow two distinct scaling laws, depending on the presence of thermodiffusive instability or lack thereof. We verify the presence of secondary cutoff values for nc identifying (a) the insurgence of secondary wrinkling in purely hydrodynamically unstable flames and (b) the attainment of domain independence in thermodiffusively unstable flames. A possible flame surface density based model for the subgrid wrinkling is also proposed.

DNS study of the global heat release rate during early flame kernel development under engine conditions

Despite the high technical relevance of early flame kernel development for the reduction of cycle-to-cycle variations in spark ignition engines, there is still a need for a better fundamental understanding of the governing in-cylinder phenomena in order to enable resilient early flame growth. To isolate the effects of small- and large-scale turbulent flow motion on the young flame kernel, a three-dimensional DNS database has been designed to be representative for engine part load conditions. The analysis is focussed on flame displacement speed and flame area in order to investigate effects of flame structure and flame geometry on the global burning rate evolution. It is shown that despite a Karlovitz number of up to 13, which is at the upper range of conventional engine operation, thickening of the averaged flame structure by small-scale turbulent mixing is not observed. After ignition effects have decayed, the flame normal displacement speed recovers the behavior of a laminar unstretched premixed flame under the considered unity-Lewis-number conditions. Run-to-run variations in the global heat release rate are shown to be primarily caused by flame kernel area dynamics. The analysis of the flame area balance equation shows that turbulence causes stochastic flame kernel area growth by affecting the curvature evolution, rather than by inducing variations in total flame area production by strain. Further, it is shown that in local segments of a fully-developed planar flame with similar surface area as the investigated flame kernels, temporal variations in flame area rate-of-change occur. Contrasting to early flame kernels, these effects can be exclusively attributed to curvature variations in negatively curved flame regions.

Analysis of premixed flame kernel/turbulence interactions under engine conditions based on direct numerical simulation data

Although the evolution of premixed flames in turbulence has been frequently studied, it is not well understood how small flames interact with large-scale turbulent flow motion. Since this question is of practical importance for the occurrence of cycle-to-cycle variations in spark ignition engines, the objective of the present work is to fundamentally differentiate early flame kernel development from well-established turbulent flame configurations. For this purpose, a DNS database consisting of three flames propagating in homogeneous isotropic turbulence (Falkenstein et al., Combust. Flame, 2019) is considered. The flames feature different ratios of the initially laminar flame diameter to the integral length scale. To quantify flame kernel development, the time evolution of flame topology and flame front geometry are analysed in detail. It is shown that some realizations of the early flame kernel are substantially influenced by high compressive strain caused by large-scale turbulent flow motion with characteristic length scales greater than the flame kernel size. As a result, the initial spherical kernel topology may become highly distorted, which is reflected in the stochastic occurrence of excessive curvature variance. Two mechanisms of curvature production resulting from early flame kernel/turbulence interactions are identified by analysis of the mean curvature balance equation. Further, it is shown that the curvature distribution of small flame kernels becomes strongly skewed towards positive curvatures, which is contrary to developed turbulent flames. Hence, the transition of ignition kernels to self-sustaining turbulent flames is very different in nature compared with the development of a statistically planar flame brush.

Large Eddy Simulation of soot evolution in turbulent reacting flows: Presumed subfilter PDF model for soot–turbulence–chemistry interactions

In turbulent reacting flows, soot evolution is strongly influenced by small-scale soot–turbulence–chemistry interactions. Specifically, soot is formed during combustion of fuel-rich mixtures and, in non-smoking flames, is rapidly oxidized at slightly fuel-rich mixtures before being transported by turbulence into fuel-lean mixtures. Furthermore, different soot evolution mechanisms are dominant over distinct regions of mixture fraction. For these reasons, a new subfilter PDF is proposed to account for this distribution of soot in mixture fraction space. In this model, the sooting mode of a soot subfilter PDF is locally activated only at fuel-rich mixture fractions where surface growth is locally faster than oxidation. This model is first validated a priori against a recent DNS database of a turbulent nonpremixed jet flame. Compared to a subfilter PDF model without any mixture fraction dependence, a significant decrease in the oxidation source term is observed, while the surface growth source term remains hardly affected. This new model is implemented within a Large Eddy Simulation (LES) framework, applied to two laboratory-scale turbulent nonpremixed sooting jet flames, and validated via comparisons with experimental measurements of time-averaged centerline temperature and soot volume fraction. Both the new model and the previous model predict the temperature fairly well. However, compared to the previous model, the soot volume fraction predicted by the new model is significantly increased and in much better agreement with the experimental measurements. In addition, the sensitivity to the subfilter PDF is significantly greater than the sensitivity to grid resolution and is greater or at least comparable to the sensitivity to chemical mechanism.

A scanning particle tracking velocimetry technique for high-Reynolds number turbulent flows

We propose a novel robust 3D particle tracking technique based on a scanning laser setup. The method yields Lagrangian statistics in densely seeded turbulent flows with good spatial and temporal resolution, overcoming some of the inherent difficulty with line-of-sight-based volumetric methods. To do this, we have developed an effective triangulation method greatly reducing ghost particle reconstruction using images from two cameras. A laser sheet is rapidly traversed (‘scanned’) across a measurement volume illuminating only a thin slice of the flow at a time. Particle images are taken at closely spaced, overlapping nominal laser sheet locations giving multiple intensity recordings for each individual particle. The laser-sheet intensity varies as a Gaussian across its thickness, which is here exploited to deduce the particle’s probable location along the scan direction to sub-sheet number resolution by fitting a similar Gaussian profile to the particle’s multiple intensity recordings. The method is presently verified via numerical experiment using a DNS database. Following successful reconstruction of a time series of 3D particle fields, particle tracks are formed from which all components of Lagrangian velocity and acceleration are calculated.

Multi-dimensional and transient effects on flamelet modeling for turbulent pulverized coal combustion

The transport along mixture fraction iso-surfaces is generally denoted as multi-dimensional effect, which is not considered in the classical one-dimensional (1D) flamelet model. This work investigates multi-dimensional and transient effects on flamelet modeling for turbulent pulverized coal combustion. To this end, instantaneous flamelets are extracted from a fully resolved 3D DNS database generated for a turbulent pulverized coal flame with a 33 array of particles. At first, the importance of transport along the iso-mixture fraction surface is analyzed based on the flamelet regime diagram. By this means, the flamelet regime of the local combustion is clarified. Then, the relevance of transient effects is investigated using budget analyses for transient terms in both physical space and composition space. Particularly, the significance of the Eulerian and Lagrangian transient terms is quantified. It is found that compared to the other transient processes, the transient change in the inner flame structure, i.e., the Lagrangian transient process, is dominant. Interestingly, the budget analyses show that the Lagrangian transient term can be partially recovered by the steady flamelet model. The findings obtained from the flamelet regime diagram and the budget analyses are consistent with the flamelet solutions where the multi-dimensional and transient terms are included in/excluded from the flamelet equations. The generalized flamelet equations including both multi-dimensional and transient terms can effectively reproduce the instantaneous flamelets in the DNS. Finally, a priori analyses are conducted to evaluate the multi-dimensional and transient effects on the final performance of the flamelet model. Overall, the a priori results are consistent with findings obtained from the budget analyses.

Analysis of chemical pathways and flame structure for n-dodecane/air turbulent premixed flames

This paper analyzes turbulence-chemistry interactions of an n-dodecane-air flame, focusing on the degree to which flame structure and fuel oxidation pathways change in turbulent flames relative to their corresponding laminar flames. This work is based on a lean (ϕ = 0.7) n-dodecane-air flame DNS database from Aspden et al. (2017). The relative roles of dominant reactions that release heat and produce/consume radicals are examined at various turbulence intensities and compared with stretched flame calculations from counterflow flames and perfectly stirred reactors. These results show that spatially integrated chemical pathways are relatively insensitive to turbulence intensity and mimic the behavior of stretched flames. In other words, the contribution of a given reaction to heat release or radical production, integrated over the entire flame, is insensitive to turbulence. Localized analysis conditioned on topological feature of the flame and on temperature is also performed. The former analysis reveals that larger alteration of pathways occurs in the positively-curved regions of the flame. Most significantly, it shows that the thermal structure of the flame is altered, as peak reaction rates and heat release in the low temperature (i.e., below 1200 K) region shift towards higher temperatures with increases in Karlovitz number. This result is particularly interesting given that prior work with lighter fuels (e.g., hydrogen) showed the opposite behavior. Various stretched, laminar flame calculations with altered transport effects were performed for reference. These calculations, using mixture-averaged and Le = 1 transport model, can capture similar shifts towards higher temperatures in laminar flames with increasing stretch. However, the stretch rate and transport values must be tuned to match these shifts in thermal structure differently, depending upon reactions, species, and Ka value. This effect is particularly prominent for low temperature species. Thus, these results show that flames do not simply shift to a Le = 1 thermal structure with high turbulence intensity, as previously suggested, but there is interplay between altered scalar diffusivity and stretch effects.

Modelling of a planar impinging jet at unity, moderate and low Prandtl number: Assessment of advanced RANS closures

The numerical simulation of turbulent heat transfer in complex industrial flows represents a major challenge for RANS models. The impinging jet configuration is a popular test case for turbulence models, due to both the challenging nature of the flow field for the RANS approach and its widespread use in industrial applications. As a consequence, a large number of studies in the literature is dedicated to the assessment of a broad variety of turbulence models in this configuration. In particular, a significant effort has been put into the assessment of different closures for the turbulent momentum flux. In contrast, relatively little attention has been paid to the modelling of the turbulent heat flux term, and the classical Reynolds analogy is almost universally employed for this purpose despite its well-known limitations. Nevertheless, recently there has been a growing interest towards the development and assessment of more advanced closures for the turbulent heat flux. In this context, in the present work six turbulence models relying on different closures for both the turbulent momentum and heat fluxes have been used to simulate a planar impinging jet at unity, moderate and low Prandtl number and thoroughly assessed against a recently published reference DNS database. It is shown that the use of an advanced differential closure for the Reynolds stresses can result in an improvement in the prediction of the flow field. This, in turn, directly results in a more accurate prediction of the mean temperature at unity Prandtl number when the Reynolds analogy is employed for the closure of the turbulent heat flux. On the other hand, the inadequacy of the latter approach appears evident at low Prandtl values, and the necessity to account at least for the variability of the turbulent Prandtl number is demonstrated. It is then inferred that the most promising approach for such complex cases is represented by the combined use of anisotropic models for both the turbulent flow and the thermal fields.

Prediction of Reynolds stresses in high-Mach-number turbulent boundary layers using physics-informed machine learning

Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonical incompressible flows. However, its performance on high-Mach-number flows is still not clear. In this work we use the PIML approach to predict the discrepancies in RANS modeled Reynolds stresses in high-Mach-number flat-plate turbulent boundary layers by using an existing DNS database. Specifically, the discrepancy function is first constructed using a DNS training flow and then used to correct RANS-predicted Reynolds stresses under flow conditions different from the DNS. The machine-learning technique is shown to significantly improve RANS-modeled turbulent normal stresses, the turbulent kinetic energy, and the Reynolds-stress anisotropy. Improvements are consistently observed when different training datasets are used. Moreover, a high-dimensional visualization technique and distance metrics are used to provide a priori assessment of prediction confidence based only on RANS simulations. This study demonstrates that the PIML approach is a computationally affordable technique for improving the accuracy of RANS-modeled Reynolds stresses for high-Mach-number turbulent flows when there is a lack of experiments and high-fidelity simulations.

Direct Numerical Simulation Database for Supersonic and Hypersonic Turbulent Boundary Layers

This paper presents a direct numerical simulation database of high-speed zero-pressure-gradient turbulent boundary layers developing spatially over a flat plate with nominal freestream Mach number ranging from 2.5 to 14 and wall-to-recovery temperature ranging from 0.18 to 1.0. The flow conditions of the DNS are representative of the operational conditions of the Purdue Mach 6 quiet tunnel, the Sandia Hypersonic Wind Tunnel at Mach 8, and the AEDC Hypervelocity Tunnel No. 9 at Mach 14. The DNS database is used to gauge the performance of compressibility transformations, including the classical Morkovin’s scaling and strong Reynolds analogy as well as the newly proposed mean velocity and temperature scalings that explicitly account for wall heat flux. Several insights into the effect of direct compressibility are gained by inspecting the thermodynamic fluctuations and the Reynolds stress budget terms. Precomputed flow statistics, including Reynolds stresses and their budgets, will be available at the website of the NASA Langley Turbulence Modeling Resource, allowing other investigators to query any property of interest.

An a priori analysis of a DNS database of turbulent lean premixed methane flames for LES with finite-rate chemistry

Abstract An a priori analysis of a DNS database of turbulent lean premixed methane flames is presented considering the relative effects of turbulence and LES filtering, along with a potential modelling approach for LES with finite-rate chemistry. The leading-order effect was found to be due to the filter operation; flame response to turbulence was a secondary effect, and manifested primarily as an increase in standard deviations about conditional means. It was found that the radicals O, H and OH were less impacted by the filter than other high-temperature radicals, which were significantly reduced in magnitude by the filter. By considering reaction path diagrams, key reactions have been identified that are responsible for disparities between the desired filtered reaction rates and the reaction rates evaluated using quantities available in LES calculations (i.e. the filtered species and temperature). More specifically, the hydrogen abstraction reactions that take CH 4 to CH 3 (by O, H and OH) were found to have particularly enhanced reaction rates, and dominate the reaction path. Under the conditions presented, reaction paths were found to be independent of turbulence intensity. In general, the filtered reaction rates from the DNS were found to align more closely with the filtered laminar profile than the reaction rate of filtered species and temperature, (but disparities were found to decrease with increasing Karlovitz number). A simple model for scaling reaction rates is considered based on filtered laminar flame profiles, and the resulting reaction paths demonstrate proof-of-concept of a simple approach for formulating a reaction rate model for LES with finite-rate chemistry.