Probability Density Function Method Research Articles

Transported PDF modeling of compressible turbulent reactive flows by using the Eulerian Monte Carlo fields method

Although the transported probability density function (PDF) method has been developed for decades, its application has been mainly focused on the low-Mach number flow problems. This work extends the transported PDF method to compressible flow problems. The Eulerian Monte Carlo fields (EMCF) solution method is employed to solve the transported PDF equation for compressible flow problems. A pseudo stagnation enthalpy is introduced and its stochastic partial differential equation is derived to ensure total energy conservation numerically. A new mixing model called interaction by partial exchange with mean (IPEM) is introduced to expand the available choices of mixing models for the EMCF method. The consistency of the EMCF method is examined for solving the transported PDF equation. Numerical implementation details are discussed, such as the density coupling between the compressible flow solver and the EMCF solver, discretization schemes for the mixing terms and the stochastic terms. The implemented compressible flow solver coupled with the EMCF solver is verified and validated in a series of test cases with increasing level of complexity, ranging from a statistically one-dimensional turbulent mixing layer to a self-excited resonance model rocket combustor. It is observed that in general with the increase of compressibility, there is an increase in the sensitivity of the modeling results to the different models and algorithms. This makes it necessary to develop a thorough understanding of the model sensitivity in order to develop a robust and accurate simulation solver for highly compressible turbulent reactive flows. The thermo-acoustic instability inside the model rocket combustor case is captured reasonably, which demonstrates the overall capability of the developed compressible turbulent combustion solver based on the transported PDF method.

Coupling of mixing models with manifold based simplified chemistry in PDF modeling of turbulent reacting flows

For general reacting flows the numerical simulation faces two main challenges. One is the high dimensionality and stiffness of the governing conservation equations due to detailed chemistry, which can be solved by using simplified chemical kinetics. The other one is the difficulty of modeling the coupling of turbulence with thermo-chemical source term. The probability density function (PDF) method allows to calculate turbulent reacting flows by solving the thermal-chemical source term in closed form. Usually, the PDF method for turbulent processes such as mixing processes and the reduction method for chemical kinetics are developed separately. However, coupling of both processes plays an important role for the numerical accuracy. To investigate the importance of coupling between turbulence and simplified chemistry, two different coupling strategies for mixing and reduced chemistry are discussed and tested for the well-known Sandia Flames E and F, in which there is a strong interaction between turbulence and chemical kinetics. The EMST mixing model is chosen for turbulent mixing, while the Reaction-Diffusion Manifolds (REDIMs) is used as simplified chemistry. However, the proposed strategies are also valid for other mixing models and manifold based simplified chemistry.

Fully coupled sectional modelling of soot particle dynamics in a turbulent diffusion flame

Soot particle dynamics, including particle size distributions (PSDs) and related statistics, are of increasing practical significance due to evolving regulatory demands. The combination of a mass and number density preserving sectional model with a transported joint probability density function (JPDF) method ensures a full coupling of the joint scalar space, e.g. soot and gas phase reactions and radiative heat losses, within a method that can represent ignition/extinction phenomena as well as the slow (low Damköhler number) soot inception and oxidation chemistry in turbulent flames. This approach is here applied to the sooting non-premixed Sandia ethylene jet flame via a 78-dimensional joint-scalar space, including enthalpy, gas phase species and 62 soot sections. Soot nucleation is treated as a global step from acetylene to pyrene with the rate fitted using comparisons with full detailed chemistry. Soot surface growth is treated via a PAH analogy and soot oxidation is considered via O, OH and O2 using a Hertz–Knudsen approach. Comparisons with measured temperature, gas phase species and the mean soot volume fraction show good agreement while the introduction of zero soot diffusivity leads to substantially improved predictions of the RMS of the soot volume fraction. The calculated PSDs at the burner centreline show a transition from one to two-peaks along the axial direction with the mode of the second peak increasing from 14 to 32 nm. Scatter plots, joint statistics of soot parameters and temperature, and the chemical source terms across soot sections suggest that surface growth is dominant when PSDs are unimodal and that the competition of oxidation, coagulation/aggregation and surface growth leads to a PSD shape transition. It is also shown that local extinction events lead to the presence of soot in cool fuel lean mixtures.

Large eddy simulation based multi-environment PDF modelling for mixing processes of transcritical and supercritical cryogenic nitrogen jets

Turbulent cryogenic nitrogen jets at transcritical and supercritical conditions are numerically investigated by LES-based multi-environment probability density function method together with the tabulated thermodynamic properties. To account for the non-ideal thermodynamic effects, the mixture properties are calculated by using Soave-Redlich-Kwong equation of state. The effect of sub-grid scale fluctuations of thermodynamic properties is modelled by the multi-environment PDF. Numerical results indicate that the present multi-environment PDF approach has the prediction capability to capture the essential features of cryogenic nitrogen jets under the supercritical pressure. Comparing with the supercritical jet, the transcritical jet features the longer and denser core which is relatively resilient to core destruction caused by turbulence. It is also found that the stronger pseudo-boiling strength and the larger density difference are directly tied with the longer cold-core length. In terms of the sub-grid scale scalar fluctuation, the transcritical jet shows the larger magnitude than the supercritical jet. In the transcritical nitrogen jet, it is identified that the strong sub-grid fluctuations of density and isobaric specific heat are closely tied with the pseudo boiling process. These numerical results suggest that the high-fidelity numerical modelling for transcritical flows must have the capability to realistically represent the combined effects of turbulence and thermodynamic nonlinearities, sub-grid scale fluctuations, and scalar conditional statistics.

Investigation of local correlations between particulate matter ([formula omitted]) and air temperature in the Caribbean basin using Ensemble Empirical Mode Decomposition

This study investigates the relationship between particulate matter that have an aerodynamic diameter less than 10 µm diameter (PM10) and air temperature (T) in the Caribbean basin. To conduct this analysis, eleven years of daily time series recorded in Guadeloupe archipelago were used. Firstly, the stationarity threshold of both time series is quantified using the infinite moving average. Then, statistical analyses were performed using the conditional mean and the joint probability density function method. Both methods used showed a dependence between PM10 and T particularly during the high dust season, i.e. from May to September. From a dynamical point of view, the coherence function highlighted a global correlation information between PM10 and T in the frequency domain. To capture possible localized correlation information, both time series are studied in a multiscale way using a new cross-correlation technique classically based on Empirical Mode Decomposition (EMD) termed the Time-Dependent Intrinsic Correlation (TDIC) analysis. After computing EMD and Ensemble Empirical Mode Decomposition (EEMD) methods, a mode-mixing problem is detected in EMD frame. Consequently, for the first time in air pollution field, a combination of EEMD and TDIC is performed. The achieved results show that the strength and nature of association between PM10 and T vary with time scales and time spells. We found that PM10 from African and marine aerosols are strongly correlated to T respectively for large and small periodicities. One also observed that extreme weather events such as heavy rainfall, hurricanes or drought induce a strong anti-correlation.

Time-variant reliability analysis via approximation of the first-crossing PDF

Time-variant reliability analysis can effectively estimate the safe state of structures under dynamic uncertainties during their lifecycle. However, one of its key challenging issues is computational efficiency. To improve the efficiency, this paper develops an approximation of the first-crossing probability density function (PDF) method, termed AFC-PDFM, based on the first-crossing theory. The response surface of the first-crossing time point (FCTP) about input variables is first estimated by using the moving least squares method (MLSM) and uniform design. Furthermore, an iterative algorithm is developed to compute the origin moments of the FCTP based on the MLSM response surface. Finally, the PDF of the FCTP is obtained by combining the origin moments and the maximum entropy method to avoid direct calculations of the first-crossing rate, which is often intractable, and then the time-variant reliability is estimated. Three examples are implemented to testify and validate the effectiveness of the proposed method and potential applications to engineering problems.

A general frame for uncertainty propagation under multimodally distributed random variables

Uncertainty propagation under multimodally distributed random variables, called multimodal distribution propagation for short, is a challenging problem due to the complicate probability density function of the random variables. In this paper, a general frame based on a new finite mixture model (λMM) constructed by derivative lambda probability density function and polynomial chaos expansion method is put forward to efficiently solve the multimodal distribution propagation problem. First, λMM with high accuracy and extensive applicability is proposed to represent the arbitrary unimodal distributions and multimodal distributions. Second, a pseudo EM method proved strictly is proposed to estimate the parameters of this λMM. Third, the statistical moments of the response by polynomial chaos expansion method is derived mathematically. Since the new mixture model can be decomposed into several unimodal probability distributions, the multimodal distribution propagation can be successfully converted into several unimodal distribution propagations, which further can be easily solved by polynomial chaos expansion method. Finally, the maximum entropy principle is adopted to evaluate the probability density function of the result of every unimodal distribution propagation, which is then superimposed into the final probability density function of the system response. The proposed frame only requires the first four statistical moments to evaluate the probability density function and avoid calculating the higher statistical moments, especially for the situation that the probability distribution of the system response is multimodal. Four examples are presented to verify the high accuracy and efficiency of the proposed general frame for uncertainty propagation.

Quantifying torque from the Milky Way bar using Gaia DR2

ABSTRACT We determine the mass of the Milky Way bar and the torque it causes, using Gaia DR2, by applying the orbital arc method. Based on this, we have found that the gravitational acceleration is not directed towards the centre of our Galaxy but a few degrees away from it. We propose that the tangential acceleration component is caused by the bar of the Galaxy. Calculations based on our model suggest that the torque experienced by the region around the Sun is $\approx 2400\, {\rm km^2\, s^{-2}}$ per solar mass. The mass estimate for the bar is $\sim 1.6\pm 0.3\times 10^{10}\, \mathrm{M_\odot }$. Using greatly improved data from Gaia DR2, we have computed the acceleration field to great accuracy by adapting the orbital Probability Density Function (oPDF) method (Han et al. 2016) locally and used the phase space coordinates of ∼4 × 105 stars within a distance of 0.5 kpc from the Sun. In the orbital arc method, the first step is to guess an acceleration field and then reconstruct the stellar orbits using this acceleration for all the stars within a specified region. Next, the stars are redistributed along orbits to check if the overall phase space distribution has changed. We repeat this process until we find an acceleration field that results in a new phase space distribution that is the same as the one that we started with; we have then recovered the true underlying acceleration.

Compressibility Effects on the Scalar Dissipation Rate

ABSTRACT Scalar dissipation rate plays an important role in combustion, especially for fast chemistry in non-premixed flames. Even for finite-rate chemistry, it is a parameter of major importance in models based on flamelets, probability density function methods, and conditional moment closures. Compressibility can influence the behavior of scalar dissipation but existing models do not consider them in the form of large dilatational effects, which are present in combustion in high-speed propulsion systems such as scramjets in hypersonic flight. This paper considers these effects on the scalar dissipation rate, in particular its mean value, spectral density, probability density function, as well the alignment of the scalar gradient with the strain field of the flow. The major result of this study is that the majority of the compressibility effects on inertial-type scales can be taken into account if the classical scaling laws of incompressible turbulence are rescaled by taking only the solenoidal contributions. However, additional effects of compressibility need to be considered at smaller scales.

A Zero-Dimensional Velocity-Composition-Frequency Probability Density Function Model for Compression-Ignition Engine Simulation

<div class="section abstract"><div class="htmlview paragraph">Numerical simulation of in-cylinder processes can significantly reduce the development and refinement costs of engines. While it can be argued that higher fidelity models improve accuracy of prediction, it comes at the expense of high computational cost. In this respect, a 3D analysis of in-cylinder processes may not be feasible for evaluating large number of design and operating conditions. The situation can be more foreboding for transient simulations. In the current work a phenomenological combustion modeling approach is explored that can be implemented in a lower fidelity modeling framework and can approach the accuracy of higher dimensional models with significant reduction in computational cost. The proposed model uses transported probability density function (tPDF) method within a 0D framework to provide a computationally efficient solution while capturing the essential physics of in-cylinder combustion. Scalar mixing is accounted for by a modified Euclidean Minimum Spanning Tree (EMST) mixing model. A new model has been formulated to calculate the mixing timescale using the velocity-composition-frequency (VCF) tPDF method. Numerical comparisons have been performed for two engines: one with a 3D-CFD simulated diesel engine to compare the in-cylinder composition and thermal stratification, and one with a diesel engine where measured data is available over a range of operating conditions encompassing a range of speed, load, and exhaust-gas recirculation (EGR). A 42-species chemical mechanism including thermal NO is used to represent the gas-phase chemistry. The proposed 0D-VCF model predicted pressure, heat-release-rate, equivalence-ratio vs temperature distribution, and NOx are compared to the 3D-CFD data, as well as to the experimentally measured data. The proposed model was able to capture the 3D-CFD trend of equivalence-ratio vs temperature distribution at different crank-angle degrees quite accurately. The 0D-VCF model computed pressure and heat-release-rate along with the NOx showed reasonable agreement with the experiment. In summary, the proposed 0D numerical model has the potential to provide a computationally less expensive alternative to a 3D numerical simulation for estimating engine performance and engine-out emission quantities when transient or large number of operating points are to be simulated.</div></div>

An investigation on the impact of small-scale models in gasoline direct injection sprays (ECN Spray G)

The work presents a numerical investigation of gasoline direct injection and the resulting early development of spray plumes from an eight-hole injector (Engine Combustion Network Spray G). The objective is to evaluate the impact on the droplet size distribution (DSD) statistics from the assumed model physics, particularly for the small scales. Two modelling approaches are compared: Eulerian–Lagrangian spray atomisation with adaptive mesh refinement and a stochastic fields transported probability density function method. The two models simulate the small scales and sub-grid droplet physics with different approaches, but based on the same concept of transport of liquid surface density. Both approaches predict similar liquid distributions in the near-field comparable to experimental measurements. The spray break-up patterns are very similar and both models reproduce quasi-log-normal droplet distributions, with same overall Sauter mean diameters. The Eulerian–Lagrangian spray atomisation with probability density function approach shows different break-up behaviour between droplets originating from the dilute region and those originating from the dense core region. The transition from Eulerian to Lagrangian can be observed in the Eulerian–Lagrangian spray atomisation with adaptive mesh refinement predicted distribution with an abrupt change in the DSD. Both methods are able to produce similar DSD below filter width/grid size resolution.

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

AbstractWhile current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build‐up to detonation, a new paradigm is put forth for modelling sub‐grid, reaction‐induced fluctuations (i. e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin‐type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i. e. deterministic) and diffusion (i. e. stochastic) coefficients. Additionally, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave‐like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no‐go estimation (e. g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i. e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Thus, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub‐grid stochastic behaviour of shocked heterogeneous solid explosives.

LES/TPDF investigation of the role of reaction and diffusion timescales in the stabilization of a jet-in-hot-coflow CH4/H2 flame

Moderate or Intense Low oxygen Dilution (MILD) combustion is a promising technology to meet the ever-stringent emission regulation while maintain high thermal efficiency. In this study, large eddy simulation (LES) in conjunction with transported probability density function (TPDF) method has been carried out for the first time to investigate the impact of reaction and diffusion timescales on the stabilization process of the jet-in-hot-coflow (JHC) CH4/H2 flame emulating MILD conditions. First it is demonstrated that the LES/TPDF simulations yield improved predictions of the species and temperature fields due to its capability in capturing finite-rate chemistry and resolving molecular transport at the filter scale. Then the impact of reaction and diffusion timescales on the stabilization process are investigated. It is found that the attenuation of chemical kinetics results in larger stabilization heights and unstable flame bases. More importantly the variation of stabilization height is found to be linearly proportional to that of auto-ignition delay time, illustrating the crucial importance of chemical kinetics during flame stabilization. The results show that the flame is initiated from the lean mixture away from the shear layer, which implies the importance of molecular transport during flame stabilization. Particle-level budget analysis further shows that the resolved molecular diffusion is important for flame base dynamics by contributing more than half of the overall conditional diffusion rate. Finally, a scaling rule for the characteristic flame stabilization time is proposed based on the auto-ignition delay time and characteristic time of diffusion, and it works reasonably well for all the cases considered. These findings shed light on the key physico-chemical mechanisms of the stabilization process for JHC flames under the MILD combustion mode. Moreover, the assessment on subgrid mixing and resolved molecular diffusion reveals that the simulation exhibits low sensitivity to the mixing model and mixing timescale while being highly sensitive to the resolved molecular diffusion, highlighting the key modelling aspects related to LES/TPDF simulation of this flame.

Transported PDF simulation of auto-ignition of a turbulent methane jet in a hot, vitiated coflow

In the current work, the auto-ignition of a turbulent round methane jet is studied numerically by means of a transported probability density function (PDF) method. The methane jet is issued into a hot, vitiated coflow, where it ignites to form a steady lifted flame. For this flame, experimental data of hydroxyl, temperature and mixture fraction are provided in the area where the fuel auto-ignites. To model this experiment, the transport equation for the thermochemical PDF is solved using a hybrid finite volume / Lagrangian Monte-Carlo method. Turbulence is modelled using the k-ϵ turbulence model including a jet-correction. Computational results are compared to experimental data in terms of mean quantities, variances and lift-off height. Moreover, the structure of the one-point, one-time marginal PDF of temperature is analysed and compared to experimental data which are provided in this work. It is found that the transported PDF method in conjunction with the k-ϵ model is capable of reproducing these statistical data very well. In particular the effect of ignition on the marginal PDF of temperature can be well reproduced with this approach. To further analyse the relevant processes in the evolution of the temperature PDF, a statistically homogeneous system is studied both numerically and analytically.

Experimental Study of the Two-Phase Flow Patterns of Air-Water Mixture at Vertical Bend Inlet and Outlet

Air-water two-phase flow in pipes introduces a noticeable challenge due to the complexity of the fluids. Thus, to estimate the best design and reasonable financing cost of the transportation pipelines where the bends are presenting a part of their accessories, the investigators should have been able to estimate the flow regime occurring at different directions. An experiment was carried out by using a 90o bend fixed with two pipes where the flow was upstream from a vertical to a horizontal pipe which were representing the bend inlet and outlet respectively. Two wire-mesh sensors were used for obtaining the data of the void fractions (α) at water superficial velocities (Usl) which changed from 0.052 to 0.419m/s, and air superficial velocities (Usg) from 0.05 to 4.7m/s. Furthermore, the characterization of flow regimes of the air-water flow at both bend inlet and outlet were competed accurately by using void fraction analysis of the time series, Power Spectral Density (PSD), tomographic images observed by the sensor program, and the Probability Density Function (PDF) method. The flow regimes of vertical flow lines at the bend inlet were observed as bubbly, cap-bubble, slug, and churn flow, whereas the flow regimes of the horizontal flow line at the bend outlet were characterized as having stratified, stratified wavy, bubbly, plug, slug, wavy annular, and semi-annular flow due to the gravity and bend effects.

A Fully Consistent Hybrid Les/Rans Conditional Transported Pdf Method for Non-premixed Reacting Flows

ABSTRACT A novel hybrid modeling approach that combines a finite-volume large eddy simulation (LES) with a Reynold-Averaged Navier-Stokes (RANS) conditional probability density function (PDF) method for turbulent non-premixed reacting flows is presented. The hybrid method incorporates the turbulent flow modeling of the LES with the chemistry–turbulence interaction modeling of the Lagrangian RANS-PDF. Specifically, the conditional composition RANS-PDF method is applied as the turbulence-chemistry closure for the LES. For a statistically steady-state case, the evolution of stochastic particles in a RANS framework reduces the computational effort, compared to the classical LES filtered density function (FDF), by performing the expensive chemical ODE integration at a lower spatial resolution. This approach is justified by the slow spatial variations of the reacting variables conditioned on the mixture fraction. Here, a consistent two-way coupling between the LES flow-field and the conditional composition RANS-PDF is formulated. The accuracy and the consistency of the method are established studying the Sandia flame series with detailed chemistry. Good predictions of the mean flow-fields and mean and conditional reactive scalars have been obtained, compared with the experimental data, with an overall decrease of the computational effort up to two orders of magnitude.

Atmospheric dispersion using a Lagrangian stochastic approach: Application to an idealized urban area under neutral and stable meteorological conditions

We present an adaptation of the Lagrangian stochastic dispersion model of the computational fluid dynamics (CFD) open source code Code_Saturne to simulate atmospheric dispersion of pollutants in complex urban geometries or around industrial plants. The wind is modeled within the same code with an Eulerian RANS (Reynolds-averaged Navier-Stokes equations) approach and thus involves the solution for the ensemble-mean velocity field and turbulent moments, using eddy viscosity or Reynolds stress turbulence models adapted to the atmosphere and complex geometries. The Lagrangian stochastic model used for the dispersion of the particles within this flow field is the simplified Langevin model, which pertains to the approaches referred to as PDF (Probability Density Function) methods. This formulation of model has not been widely used in atmospheric applications, despite interesting theoretical and computational benefits. Therefore, its usage must be validated on different atmospheric cases. In this paper, we present the validation of the model with a field experiment, considering atmospheric stratification and buildings: the MUST (Mock Urban Setting Test) campaign, conducted in Utah’s desert, USA.

Numerical investigation of flow and scalar fields of piloted, partially-premixed dimethyl ether/air jet flames using stochastic multiple mapping conditioning approach

Turbulent piloted partially-premixed jet flames of dimethyl ether/air have been investigated using the Reynolds-Averaged Navier-Stokes (RANS) based stochastic multiple mapping conditioning (MMC) approach. The MMC model combines the advantages of mapping closure concept, conditional moment closure, and probability density function (PDF) methods. In the present work, the evolution of the mapping function in the reference space is described using a single reference variable based on the mixture fraction. To achieve localness in the composition space, the turbulent mixing is conditioned on the reference space. In addition to localness, MMC preserves the various characteristics of a good mixing model, such as linearity, Gaussianity, independence, and boundedness. A skeletal chemical mechanism for dimethyl ether is used, which consists of 28 species and 24 reversible reactions. Modified Curl's mixing model is adapted to model the micro-mixing term, and standard two-equation k−ε turbulence model is used to model the Reynolds stress term with a modified set of constants. The computed conditional and unconditional statistics demonstrate an excellent agreement with the available experimental data even for flame displaying a large degree of local extinction and re-ignition. For these flames, radical species distribution conditioned on mixture fraction confirms the physical separation between the OH and CH2O species, which was earlier reported using simultaneous laser-induced fluorescence measurements of these radicals. Predicted unconditional scalar dissipation rate for DME-D and DME-F flames reaffirm that near the inlet an overlap between OH and CH2O radicals are observed where the scalar dissipation rate is fairly high. Subsequently, a distinct separation between these radicals becomes evident at downstream locations where the scalar dissipation rate decreases. For the flames investigated here, a strong correlation is noticed between the peak heat release rate and the reaction rate indicator, ROH based on the product of concentrations of OH and CH2O radicals.

Turbulent electric current in the marine convective atmospheric boundary layer

The atmospheric boundary layer considered a part of the planetary global electric circuit is known to exhibit a most dramatically changing in space and time atmospheric electrical variables. Extremely low specific electrical conductivity in the lower atmosphere is accompanied by the work of the electric generator associated with turbulent dynamo realizing itself through the space charge transport by boundary layer flows. The electromotive force of this generator acting in fair weather atmospheric regions provides a contribution to the global potential drop between the lower ionosphere and the earth's surface. In this study, the vertical electric current density produced by the turbulent transfer of space charge is investigated in the cases of the buoyancy-dominated and shear-dominated convective boundary layer (CBL) over the oceans based on second-order dissipation-conditioned Lagrangian stochastic model (LSM) applied near air-sea interface and conjugated with first-order LSM in the rest of the CBL. The total electric charge flux is treated in terms of mechanical transfer of atmospheric ions and charged aerosol particles by Lagrangian turbulence together with the drift of small ions in the self-consistent electric field. This approach based on a transported probability density function method offers persuasive advantages for quantitative estimates of local perturbations in the fair-weather electric field created by the atmospheric space charge carried by turbulent flows. It is found that the space charge density vertical profile only slightly depends on turbulence everywhere except for the wavy boundary layer about 10 m thick, a new parameterization of space charge vertical profile is proposed. Based on the simulation results, it can be predicted that in the buoyancy-dominated CBLs the electric field must be greater than in the sheared CBLs with other things being equal. Turbulent electromotive force and changes in total downward atmospheric electric current density are quantified. Simulated vertical profiles of electrical conductivity, space charge, electric field, and turbulent current density reasonably well reproduce previously reported observation results.

A combined PPAC-RCCE-ISAT methodology for efficient implementation of combustion chemistry

Probability density function (PDF) methods are now well established and can be used to accurately simulate flames with strong turbulence chemistry interactions. A pre-partitioned adaptive chemistry (PPAC) methodology (Liang et al., Combustion and Flame, 2015) has been proposed recently for the efficient implementation of combustion chemistry in particle PDF methods. PPAC generates a library of reduced kinetic models in an offline preprocessing stage. At runtime, PDF particles are dynamically assigned one reduced model and its corresponding reduced representation, leading to a significant decrease in both storage requirements and CPU time required for the integration of chemical source terms. In this work, we augment PPAC by combining it with storage retrieval and dimension reduction techniques. Specifically, this work combines PPAC with in-situ adaptive tabulation (ISAT) and rate-constrained chemical equilibrium (RCCE). Implementations for PPAC-ISAT, PPAC-RCCE, and PPAC-RCCE-ISAT are described and their performance is examined for a partially stirred reactor (PaSR) test case. The combined PPAC-RCCE-ISAT methodology shows a significant improvement over the stand-alone PPAC methodology by reducing the number of redundant direct integrations of similar compositions and reducing the number of variables that need to be retained at runtime.