Probability Density Function Method Research Articles

Evaluation and Validation of CryoSat-2-Derived Water Levels Using In Situ Lake Data from China

CryoSat-2 altimetry has become a valuable tool for monitoring the water level of lakes. In this study, a concentrated probability density function (PDF) method was proposed for preprocessing CryoSat-2 Geophysical Data Record (GDR) data. CryoSat-2 altimetry water levels were preprocessed and evaluated by in situ gauge data from 12 lakes in China. Results showed that the accuracy of the raw GDR data was limited due to outliers in most of the along-track segments. The outliers were generally significantly lower than the in situ values by several meters, and some by more than 30 m. Outlier detection, therefore, improves upon the accuracy of CryoSat-2 measurements. The concentrated PDF method was able to greatly improve the accuracy of CryoSat-2 measurements. The preprocessed CryoSat-2 measurements were able to observe lake levels with a high accuracy at nine of the twelve lakes, with an absolute mean difference of 0.09 m, an absolute standard deviation difference of 0.04 m, a mean root mean square error of 0.27 m, and a mean correlation coefficient of 0.84. Overall, the accuracy of CryoSat-2-derived lake levels was validated in China. In addition, the accuracy of Database for Hydrological Time Series of Inland Waters (DAHITI) and HYDROWEB water level products was also validated by in situ gauge data.

Assessment of Presumed/Transported Probability Density Function Methods for Rocket Combustion Simulations

Combustion models of different fidelity are applied to a seven-element gaseous methane/oxygen subscale rocket combustion chamber. The covered region of thermo-chemical states is analyzed for two non-adiabatic flamelet-based methods, from which one is well established and the other one has just recently been proposed for hydrogen/oxygen combustion. Of particular interest is their applicability in situations with strong heat losses. Consequently, the tabulated combustion models are linked with a presumed probability density function approach, and the results are assessed using a transported probability density function method. An analytically reduced chemical reaction mechanism with 13 species and 73 reactions is used for all models in order to allow for direct comparison of turbulence–chemistry interaction. The results are evaluated with respect to temperature, gas composition, and wall heat transfer and they are brought in context with their respective computational costs. Finally, the results are compared to available experimental data in terms of wall heat flux and pressure measurements. Locally and temporally resolved results provide additional insights to the experiment.

Aggregating risk matrices under a normative framework

Risk matrices have been proven as useful risk management tools, especially in the cases where data are not sufficient. Current usage of risk matrices in both literature and practice is related to single risk assessment. However, sometimes the decision makers care more about the overall risk consisting of several of single risks, which is in the scope of the aggregation of single risks measured by risk matrices. Unfortunately, two notions, namely, incomparability of different qualitative risk ratings and incomparability of different risk types, hinder the aggregation of risk matrices. Therefore, few literature studied on this issue and even ISO have not given a solution. In this paper, a general framework for risk matrix aggregation is proposed. The basic idea is to transform the risk matrices into other equivalents to operate the aggregation process. Based on this framework, three methods, namely, the fuzzy set method, the interval number, and the probability density function methods, are introduced. The three methods are applied to an illustrative example to show the feasibility of the general framework. Then these methods are compared from three different aspects, i.e., comprehensibility, complexity, and degree of explanation of risk matrix. In practice, when these methods are employed to aggregate risk matrices, the findings of this paper show that the interval number method is the least robust; though the probability density function method has a lower degree of explanation of risk matrix, it could be taken as a substitution as the fuzzy set method, thanks to its simplicity.

Consistency and convergence of Eulerian Monte Carlo field method for solving transported probability density function equation in turbulence modeling

The transported probability density function (PDF) method is an attractive model for the closure of turbulent mixing and turbulent reactive flows. The transported PDF method suffers from the curse of dimensionality and an efficient numerical implementation of the method has always been a research topic of great importance. The Eulerian Monte Carlo field (EMCF) method (also termed as the stochastic field method) has been proposed as an efficient solution approach for solving the PDF transport equation for two decades. In this work, we revisit the EMCF method and examine its mathematical consistency analytically and numerically. It is found that the EMCF method is not mathematically consistent with the PDF transport equation that the method intends to solve. This creates a serious inconsistency issue and causes uncertainties in the yielded numerical solutions by EMCF. It is imperative to examine the effect of the inconsistency. We evaluate the effect of the inconsistency in a simplified turbulent mixing layer test case. Corrections to remedy the mathematical inconsistency are proposed and examined. The effectiveness of the corrections is demonstrated numerically through convergence testing. The effect of the Reynolds number on the inconsistency is explored. The impact of the inconsistency is also investigated in a thermal wake behind a line source in grid turbulence to assess the importance of the issue in real turbulence problems.

An Efficient Population Density Method for Modeling Neural Networks with Synaptic Dynamics Manifesting Finite Relaxation Time and Short-Term Plasticity.

When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity (STP). The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire (EIF) neurons, show good agreement between the results of csPDM and Monte Carlo simulations (MCSs). Compared to the original full-dimensional PDM (fdPDM), the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.

Micromixing Models for PDF Simulations of Turbulent Premixed Flames

ABSTRACTTransported probability density function (TPDF) methods are attractive for modeling turbulent flames as the highly nonlinear chemical reactions appear in closed form. The ability of the TPDF methods to capture complex phenomena such as extinction and re-ignition has been well demonstrated for turbulent non-premixed flames. However challenges remain when applying the TPDF methods to turbulent premixed flames, for which modeling molecular diffusion is difficult because the local species gradients may be strongly influenced by chemical reactions. The specification of a constant mechanical-to-scalar timescale ratio to relate the scalar mixing timescale to the turbulence timescale is questionable for premixed flames in the flamelet regime. In this paper, recent progress on scalar mixing is reviewed with particular focus on the analysis and modeling of the scalar mixing timescales in turbulent premixed flames using direct numerical simulation (DNS) datasets. The scalar dissipation rate of the progress variable from temporally evolving turbulent lean premixed H2-air flames in the thin reaction zone regime is analyzed using the chemical explosive mode analysis to understand its dependence on combustion modes and transient flame features. Moreover, models for the mixing timescale of the progress variable are discussed, with a focus on a recently developed hybrid mixing timescale model. This work concludes with a discussion on modeling differential diffusion in turbulent premixed flames.

Numerical study of a large-scale pulverized coal-fired boiler operation using CFD modeling based on the probability density function method

The paper presents results of numerical modeling of pulverized coal combustion process in the front wall coal-fired boiler. The developed numerical model of the coal combustion process included particle heating, devolatilization, char combustion, as well as turbulent flow and radiative heat transfer. In gas phase combustion process modeling, the mixture fraction approach with PDF was used. Presented modeling results were carried out using the Open Source CFD code – Code_Saturne, and were used to study the pulverized coal combustion in a 225 MWe power plant unit. The input data and boundary conditions were defined based on the collected data about boiler operating conditions and Rosin-Rammler law was used to calculate coal particle distribution. The behavior of pulverized coal and air flow through the burners, as well as the three-dimensional flue gas path through the combustion chamber, was analyzed. Results in form of velocity, temperature, unburned coal and combustion products distribution were presented to show places inside the boiler with high erosion hazard and place where intensive particle deposition may occur, as well as to show the impact of coal particle diameters on Unburned Carbon (UBC) content. Calculation results confirm proper locations of Over-Fire Air (OFA) nozzles and allowing continuing of combustion process at the furnace outlet using only OFA II and OFA III nozzles set. Based on the obtained results is possible to increase the understanding and conduction detailed investigation of boiler operation. The results have been validated with data collected from the power station measurement system and were analyzed in order to find an answer for operational questions regarding optimization of combustion characteristics.

The effects of flue-wall design modifications on combustion and flow characteristics of an aluminum anode baking furnace-CFD modeling

A modern aluminum smelter has a capacity of 1–2 million tons of aluminum per annum which requires more than 0.5–1.0 million tons of heat treated (baked) carbon anodes per year. The anode baking process is very energy intensive, approximately requires 2 GJ of energy per ton of carbon anodes which will be approximately 1–2 million GJ of energy per year. Since the plant testing is very expensive, anode baking furnace modeling is imperative to investigate the effects of different operational and geometrical parameters on the furnace energy consumption.In the numerical modeling of turbulent reactive flows, the accuracy of the model highly depends on the description of turbulence-chemistry interaction, and the robustness of the radiative transfer equation solver. Hence, the present study tested different turbulence-chemistry interaction frameworks and radiative transfer equation solvers for confined turbulent diffusion flames and results are compared with the experimental data. It was observed that the k-ε realizable turbulence model combined with the presumed probability density function method as turbulence-chemistry interaction, and discrete ordinates method as radiative transfer equation solver illustrate excellent agreement with the experimental data.Anode baking homogeneity is an important consideration in the design of the anode baking furnace, which requires appropriate flow distribution in the flue-wall cavity. Hence, the developed numerical framework was employed to investigate the effects of flue-wall design modifications on combustion and heat transfer characteristics of anode baking furnace energy consumption. It was observed that the modified design results in a higher thermal efficiency (lower energy consumption), and more homogenous temperature and flow fields which result in the baking of anodes more uniformly which consequently result in the evolution of more homogenous material properties. Consequently, the energy consumption in the aluminum reduction cell will also be significantly reduced. The present study also investigated the effect of flue-wall flow blockage due to packing coke infiltration on baking energy consumption for the aged anode baking furnaces and introduced three modified flue-wall designs.

Transported probability density function based modelling of soot particle size distributions in non-premixed turbulent jet flames

The need to establish actual particle size distributions (PSDs) of soot emissions from the nanoscale upwards, along with the current global indicators based on soot mass, stems from increasingly strict regulatory demands. In the current work, a mass and number density preserving sectional model is coupled with a transported probability density function (PDF) method to study the evolution of soot PSDs in two non-premixed turbulent jet flames at Reynolds numbers of 10,000 and 20,000. The transported PDF approach is closed at joint-scalar level and includes mass fractions of gas phase species, soot sections, as well as enthalpy, leading to a fully coupled 78-dimensional joint-scalar space, treating interactions between turbulence and gas phase/soot chemistry as well as radiation without further approximation. The gas phase chemistry features 144 reactions, 15 solved and 14 steady-state species and an acetylene-based soot inception model is calibrated using comprehensive detailed chemistry up to pyrene and applied to a well-stirred/plug flow reactor configuration. The derived nucleation rate is subsequently applied in the turbulent flame calculations. Soot surface growth is treated via a PAH analogy and oxidation via O, OH and O2 is accounted for. The sectional model features 62 sections covering particle sizes in the range 0.38 nm ≤ dp ≤ 4.4 µm and includes a model for the collision efficiency of small particles ( ≤ 10 nm) based on the Lennard–Jones potential. The computed results reproduce the evolution of the PSDs with encouraging accuracy. It is also shown that the distribution of soot in mixture fraction space is affected by local extinction events.

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.

A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damköhler numbers (Da) are considered. The low Da case (Da-) features extinction followed by reignition while extinction in the high Da case (Da+) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da- and Da+ cases. The EMST model captures well the trend for extinction and reignition for the Da- case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da+ case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.

Numerical Study of a Cyclonic Combustor under Moderate or Intense Low-Oxygen Dilution Conditions Using Non-adiabatic Tabulated Chemistry

A cyclonic burner operating under moderate or intense low-oxygen dilution (MILD) conditions is simulated using a perfectly stirred reactor (PSR) incorporated within a tabulated chemistry approach. A presumed joint probability density function method is used with appropriate submodels for the turbulence–chemistry interaction. Non-adiabatic effects are included in the PSR calculation to take into account the effects of non-negligible wall heat loss in the burner. Five different operating conditions are investigated, and the computed mean temperatures agree well with measurements. A substantial improvement is observed when the non-adiabatic PSR is used, highlighting the importance of heat transfer effects for burner configurations involving internal exhaust gas recirculation. Furthermore, enhanced reaction homogeneity is observed in this cyclonic configuration for the globally lean case, leading to a more spatially uniform temperature variation with MILD combustion.

Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations

A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.

Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows

A mean shift (MS) particle model has been developed before to account for molecular diffusion in the transported probability density function (PDF) methods for turbulent reactive flows (McDermott and Pope, Journal of Computational Physics, 2007, 226, 947–993). The MS model is superior over the traditional random walk model for its capabilities to incorporate differential molecular diffusion and to yield a consistent DNS limit of scalar variance production/dissipation. The MS model, however, yields inconsistent transport of the scalar variance because of the missing molecular diffusion in the resultant variance transport equation. To yield fully consistent transport of scalar mean and variance, a variance consistent mean shift (VCMS) model is developed in this work. The VCMS model formulations are developed for both a single-scalar system and a multi-scalar system. Boundedness violation of particle scalars exists in both the MS and VCMS models and causes a realizability issue of the models. A correction algorithm (called MP correction by McDermott and Pope) has been developed before to correct the boundedness violation in the MS model. The MP correction is found to produce overcorrection to the particles, resulting in an underprediction of the scalar variance. In addition, it is only applicable to the IEM mixing model. In this work, three new boundedness correction algorithms are developed based on the strategies of a least-decay factor (LDF), clipping at scalar bounds (CSB), and clipping with paired mixing (CPM). The accuracy and consistency of the VCMS models are examined and validated thoroughly in a turbulent mixing layer problem. The effectiveness and accuracy of the different boundedness correction algorithms are also examined and assessed in the mixing layer problem. The applicability of the CPM correction to other mixing models (MCurl and EMST) is also demonstrated.

Nonlocal PDF methods for Langevin equations with colored noise

Langevin equations describe systems driven by internally generated or externally imposed random excitations. If these excitations correspond to Gaussian white noise, it is relatively straightforward to derive a closed form equation for the joint probability density function (PDF) of state variables. Many natural phenomena present however correlated (colored) excitations. For such problems, a full probabilistic characterization through the resolution of a PDF equation can be obtained through two levels of approximations: first, mixed ensemble moments have to be approximated to lead to a closed system of equations and, second, the resulting nonlocal equations should be at least partially localized to ensure computational efficiency. We propose a new semi-local formulation based on a modified large-eddy diffusivity (LED) approach; the formulation retains most of the accuracy of a fully nonlocal approach while presenting the same order of algorithmic complexity as the standard LED approach. The accuracy of the approach is successfully tested against Monte Carlo simulations.

Application of the Eulerian subgrid Probability Density Function method in the Large Eddy Simulation of a partially premixed swirl flame

ABSTRACTA gas turbine model combustor is studied using Large Eddy Simulation with a transported Probability Density Function approach solved by the Eulerian stochastic field method. The chemistry is represented by a reduced methane mechanism containing 15 steps and 19 species while the subgrid scale stresses and scalar fluxes are modelled, respectively, via a dynamic Smagorinsky model and a gradient diffusion approximation. The test case comprises a partially premixed swirl flame in a complex geometry. Four stochastic fields are utilised in the simulations, which are performed for two different combustor operating conditions involving a stable and an unstable flame. Good agreement between the simulation and measurement data is shown in a comparison of mean velocity, temperature and species mass fraction profiles, as well as scatter plots of the instantaneous thermochemical properties. In conclusion, the predictive capabilities of the employed Large Eddy Simulation method are successfully demonstrated in this work.

A method to assess randomness of functional connectivity matrices

BackgroundFunctional magnetic resonance imaging (fMRI) allows for the measurement of functional connectivity of the brain. In this context, graph theory has revealed distinctive non-random connectivity patterns. However, the application of graph theory to fMRI often utilizes non-linear transformations (absolute value) to extract edge representations. New methodIn contrast, this work proposes a mathematical framework for the analysis of randomness directly from functional connectivity assessments. The framework applies random matrix theory to the analysis of functional connectivity matrices (FCMs). The developed randomness measure includes its probability density function and statistical testing method. ResultsThe utilized data comes from a previous study including 603 healthy individuals. Results demonstrate the application of the proposed method, confirming that whole brain FCMs are not random matrices. On the other hand, several FCM submatrices did not significantly test out of randomness. Comparison with existing methodsThe proposed method does not replace graph theory measures; instead, it assesses a different aspect of functional connectivity. Features not included in graph theory are small numbers of nodes, testing submatrices of an FCM and handling negative as well as positive edge values. ConclusionThe random test not only determines randomness, but also serves as an indicator of smaller non-random patterns within a non-random FCM. Outcomes suggest that a lower order model may be sufficient as a broad description of the data, but it also indicates a loss of information. The developed randomness measure assesses a different aspect of randomness from that of graph theory.

The path to CAM6: coupled simulations with CAM5.4 and CAM5.5

Abstract. This paper documents coupled simulations of two developmental versions of the Community Atmosphere Model (CAM) towards CAM6. The configuration called CAM5.4 introduces new microphysics, aerosol, and ice nucleation changes, among others to CAM. The CAM5.5 configuration represents a more radical departure, as it uses an assumed probability density function (PDF)-based unified cloud parameterization to replace the turbulence, shallow convection, and warm cloud macrophysics in CAM. This assumed PDF method has been widely used in the last decade in atmosphere-only climate simulations but has never been documented in coupled mode. Here, we compare the simulated coupled climates of CAM5.4 and CAM5.5 and compare them to the control coupled simulation produced by CAM5.3. We find that CAM5.5 has lower cloud forcing biases when compared to the control simulations. Improvements are also seen in the simulated amplitude of the Niño-3.4 index, an improved representation of the diurnal cycle of precipitation, subtropical surface wind stresses, and double Intertropical Convergence Zone biases. Degradations are seen in Amazon precipitation as well as slightly colder sea surface temperatures and thinner Arctic sea ice. Simulation of the 20th century results in a credible simulation that ends slightly colder than the control coupled simulation. The authors find this is due to aerosol indirect effects that are slightly stronger in the new version of the model and propose a solution to ameliorate this. Overall, in these early coupled simulations, CAM5.5 produces a credible climate that is appropriate for science applications and is ready for integration into the National Center for Atmospheric Research's (NCAR's) next-generation climate model.

Soot and spectral radiation modeling for high-pressure turbulent spray flames

A transported probability density function (PDF) method and a photon Monte Carlo/line-by-line (PMC/LBL) spectral model are exercised to generate physical insight into soot processes and spectral radiation characteristics in transient high-pressure turbulent n-dodecane spray flames, under conditions that are relevant for compression-ignition piston engines. PDF model results are compared with experimental measurements and with results from a locally well-stirred reactor (WSR) model that neglects unresolved turbulent fluctuations in composition and temperature. Computed total soot mass and soot spatial distributions are highly sensitive to the modeling of unresolved turbulent fluctuations. To achieve reasonable agreement between model and experiment and to capture the highly intermittent nature of soot in the turbulent flame, it is necessary to accurately represent mixing and the low diffusivity of soot particles. This is accomplished in the PDF framework using a mixing model that enforces locality in the gas-phase composition space, while not mixing the transported soot variables. The results suggest that mixing is at least as important as kinetics in controlling soot formation and evolution in high-pressure turbulent flames. Regarding radiation, radiant fractions and global influences of radiation in these flames are relatively small. Nevertheless, an examination of spectral radiative heat transfer provides valuable insight into the nature and modeling of radiation in high-pressure turbulent combustion systems. There are complex spectral interactions that are revealed using PMC/LBL. CO2 dominates the total radiative emission and reabsorption, but most of the emitted CO2 radiation is reabsorbed before reaching the walls. On the other hand, most of the emitted soot radiation reaches the walls, but soot radiation is a small contribution overall; H2O dominates the radiation that reaches the walls. Global turbulence–radiation interactions (TRI) effects are small, but radiative emission from soot increases by approximately a factor two when TRI are considered. Radiative transfer contributes both to energy redistribution in the vessel and to wall heat losses. The results suggest that a simple model that considers soot radiation and the principal CO2 and H2O spectral bands might be sufficient to capture the key influences of radiation in engine CFD. It is expected that these findings will contribute to the development of truly predictive CFD models for engines and other high-pressure turbulent combustion systems.

A hybrid CFD RANS/Lagrangian approach to model atmospheric dispersion of pollutants in complex urban geometries

Lagrangian atmospheric dispersion models consist of tracking the trajectories of particles of pollutant emitted into the atmosphere. In this paper, the objective is to compare the Lagrangian and Eulerian dispersion models in the same computational fluid dynamics code (Code Saturne), therefore using the same wind and turbulence fields for both. The Lagrangian stochastic model used in this work is the simplified Langevin model (SLM) of Pope (1985, 2000) and pertains to the approaches referred to as probability density function methods. This model has been extensively used in turbulent combustion or multiphase flows, but to our knowledge, it has not been used in atmospheric dispersion applications. First, we show that the SLM respects the well-mixed criterion. Then, we validate the model in the case of a continuous point release with uniform mean wind speed and turbulent diffusivity. Finally, we validate the model with an experimental campaign involving a stably stratified surface layer.