Assumed PDF turbulence-chemistry closure with temperature-composition correlations

This paper presents an experimental and numerical study of the flow field and heat release (HRL) zone of a six-nozzle FLOX®-based combustor at atmospheric pressure. The combustor is suitable for the use in a micro gas turbine (MGT) based combined heat and power (CHP) system with an electrical power output of 3 kW. The velocity field was measured using stereoscopic particle image velocimetry (PIV). The heat release zone was visualized by OH*-chemiluminescence (OH* CL) and the flame front by OH planar laser-induced fluorescence (OH PLIF). The results are compared with CFD simulations to evaluate the quality of the applied numerical turbulence and combustion models. The simulations were performed using Reynolds-averaged Navier-Stokes equations in combination with the k-ω-SST-turbulence model. Since the FLOX®-based combustion is dominated by chemical kinetics, a reaction mechanism with detailed chemistry, including 22 species and 104 reactions (DRM22), has been chosen. To cover the turbulence-chemistry interaction, an assumed probability density function (PDF) approach for species and temperature was used. Except for minor discrapancies in the flow field, the results show that the applied models are suitable for the design process of the combustor. In terms of the location of the heat release zone, it is necessary to consider possible heat losses, especially at lean operating conditions with a distributed heat release zone.

Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities: A Probability Density Function Approach

LES/PDF based modeling of soot–turbulence interactions in turbulent flames

In this paper, a new "presumed" Probability Density Function (PDF) approach coupled with a Lagrangian tracking method is proposed for turbulent combustion modeling. The test and the investigation of the model are conducted by comparing the model results with DNS data for a premixed flame subjected in a decaying turbulent field. The newly constructed PDF, which incorporates the instantaneous chemical reaction term, demonstrates consistent improvement over conventional assumed PDF models. It has been found that the time evolution of the mean scalar, the variance and the mean reaction rate are strongly influenced by a parameter deduced by a Lagrangian equation which takes into account explicitly the local reaction rate. Tests have been performed for a moderate Damk?hler number, and it is expected the model may cover a broader range of Damk?hler number. The comparison with the DNS data demonstrates that the proposed model may be promising and affordable for implementation in a moment-equation solver.

LES-based Eulerian PDF approach for the simulation of scramjet combustors

Abstract. A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables and hydrometeor size distributions, as well as to probability distributions characterizing data uncertainties. The general formulation is presented based upon two well-known basic principles: the maximum-entropy principle and the Liouville equation. The maximum-entropy principle defines the most likely general distribution form if necessary constraints are specified. This paper proposes to specify these constraints as the output variables to be used in a host model. Once a general distribution form is defined, the problem of the temporal evolution of the distribution reduces to that of predicting a small number of parameters characterizing it. This paper derives prognostic equations for these parameters from the Liouville equation. The developed formulation, which is applicable to a wide range of atmospheric modeling problems, is specifically applied to the condensation growth of cloud droplets as a demonstration.

Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems: A Probability Density Function Approach

Comparison of transported scalar PDF and velocity-scalar PDF approaches to ‘Delft flame III’

Transported probability density function modelling of the vapour phase of an n-heptane jet at diesel engine conditions

Present work is concerned with the flow field analysis inside an annular gas turbine combustor both under non-reacting and reacting conditions. Three-dimensional gas turbine combustor of 20-degree sector has been modeled using the pre-processor GAMBIT. Flow through the combustor has been simulated using FLUENT code by solving the appropriate governing equations viz., conservation of mass, momentum and energy. RNG κ-ε turbulence model is used for physical modeling. Initially prediffuser optimization has been carried out with respect to angle, length and contours. Flow through holes is modeled using porous jump boundary condition as well as modeling real holes themselves to study the efficacy of real hole modeling. Total pressure loss has been calculated to evaluate the cold flow as well as hot flow losses. Combustion has been modeled using the Probability Density Function (PDF) approach. Temperature and species concentrations are predicted.

An investigation of a turbulent spray flame using Large Eddy Simulation with a stochastic breakup model

An examination of existing shoreline fumigation models and formulation of an improved model

This work presents a direct and transparent interpretation of two concepts for modelling turbulent combustion: generalised Multiple Mapping Conditioning (MMC) and sparse-Lagrangian Large Eddy Simulation (LES). The MMC approach is presented as a hybrid between the Probability Density Function (PDF) method and approaches based on conditioning (e.g. Conditional Moment Closure, flamelet, etc.). The sparse-Lagrangian approach, which allows for a dramatic reduction of computational cost, is viewed as an alternative interpretation of the Filtered Density Function (FDF) methods. This work presents simulations of several turbulent diffusion flame cases and discusses the universality of the localness parameter between these cases and the universality of sparse-Lagrangian FDF methods with MMC.

A numerical modeling of turbulent methanol-air nonpremixed jet flames with a five-step and a four-step reduced reaction mechanisms is presented. The model calculates the scalar properties by a joint pdf (probability density function) approach and a second-order moment closure for the turbulent velocity field. Although the flame is considered adiabatic, mixture enthalpy has been included as a passive scalar to properly account for the pilot flame which has a flame temperature higher than the adiabatic flame temperature of the stoichiometric mixture. A total of seven scalars, including two passive scalars and five reactive scalars, are used to describe the thermo-chemical states of the reactive mixtures. The evolution of the joint pdf of these seven scalars was simulated by the Monte Carlo technique. An extensive analysis of the predicted results in comparison with experimental data is presented. The predicted mass fractions of most reactive species are in good agreement with the experimental data, and the probability of local flame extinction is reasonably predicted as well. Carbon monoxide is the only species for which a substantial discrepancy exists between the predictions and the measurements. The noted discrepancy is similar to that observed in a previous numerical study of turbulent methane-air nonpremixed jet flames by Chen et al.(1989).Although several possible causes are investigated, no satisfactory reasons were found to explain the noted discrepancies.

In this paper, the average bit error rate (ABER) performance of binary coherent and non-coherent modulation is investigated over a new fading channel which is well known as Beaulieu-Xie fading channel. This fading model consists of multiple no. of line-of-sight (LOS) components with some diffuse power. Specifically, the closed-form expressions are derived for the exact ABER of binary phase-shift keying (BPSK) and differential phase-shift keying (DPSK) by using the probability density function (PDF) approach. The final exact expression for BPSK is obtained in the form of infinite series which needs a reasonable number of terms to converge and the final expression for DPSK is expressed in terms of elementary functions. It is observed that ABER decreases with increase in specular power and/or with decrease in fading severity. The obtained results are applied to general scenarios for various values of fading parameters by adjusting the specular power and fading severity. The numerical results plotted by using the derived expressions show a close agreement with the results obtained by Monte Carlo simulation.