Probability Density Function Approach Research Articles

Comparative study of combustion processes generated by the use of different fuels: energy and exergy analysis

Through energy and exergy analysis, the present work revisits the combustion processes generated using different fuels (CH4, C3H8, H2, LPG, Natural gas and Biogas) under the same operating conditions. First, numerical computations, in which the turbulent dynamic k-ϵ model coupled with a probability density function (PDF) approach together with different sub-models that ensure the reliability of the results, are used. Then, the First and Second Laws of thermodynamics are applied to all fuel combustion cases considered previously to predict the energy loss, exergy destruction and their corresponding efficiencies. Next, variations in the air factor, the air inlet temperature and the fuel inlet temperatures are considered to analyse the response of combustion system performance as well as energy and exergy losses for the different fuels under investigation. The results show an amelioration of combustion parameters for the mixture of fuel and air using values of λ greater than 1. Also, the preheating of the inlet air temperature has a positive effect on energetic parameters. However, preheating the inlet fuel does not take a considerable role in the efficiency amelioration and loss reduction of the combustion system. It further turns out that biogas features higher energy efficiency compared to other fuels, at approximately 89.64%, while hydrogen fuel exhibits higher exergy efficiency at around 78.70% followed by biogas with 74.96%.

Advanced numerical simulation of hydrogen/air turbulent non-premixed flame on model burner

A numerical investigation of hydrogen (H2)/air turbulent non-premixed flame on the model burner was conducted. A large eddy simulation of reacting flow with partial and detailed chemical kinetic mechanisms was employed to obtain a high-resolution and accurate prediction of thermochemical states inside the combustion chamber, including pollutant NO, which have not been adequately predicted until now. This study employed temperature and species mass fraction data from two combustion cases of fully developed turbulent and transition regimes with a fuel composition of 50 % H2 and 50 % N2, experimentally measured by the German Aerospace Center (DLR) and TU Darmstadt. A reactor-based partially-stirred reactor (PaSR) model was used to handle the turbulence chemistry interaction. The employed chemical mechanisms included GRI-Mech 3.0 and partial Mevel mechanism. The effects of chemical mechanism and inlet jet velocity on simulation accuracy were discussed. The more elaborative nitrogen reactions in GRI-Mech 3.0 result in a better NO prediction compared to the partial Mevel mechanism. The implementation of finite rate chemistry in a PaSR model yields a significantly improved prediction of NO from the flamelet probability density function approach with less than 1 % root mean square deviation from experimental data. The performed simulation successfully captured the thermochemical profile of a fully developed turbulent flame; however, further improvement on boundary condition modeling is still required for a flame undergoing a transition from laminar to turbulent regimes. Finally, using the partial Mevel mechanism leads to a computational cost reduction of 32.66 % compared to the GRI-Mech 3.0 mechanism, which confirms the proportional relation between the size of the mechanism and computational cost.

Stability and uncertainty assessment of geoelectrical resistivity model parameters: a new hybrid metaheuristic algorithm and posterior probability density function approach

Abstract. Estimating a reliable subsurface resistivity structure using conventional techniques is challenging due to the nonlinear nature of the inverse problems. The performance of the inversion techniques can be pretty ambiguous based on the optimal error, although traditional methods have proven to be quite effective. In this work, the impacts of the constraints accessible from a borehole are examined for further assessment and to enhance algorithm effectivity. The vPSOGWO strategy is a new approach that is based on a model search space without any prior information, and it describes the hybridization of particle swarm optimization (PSO) with the Grey Wolf Optimizer (GWO). To understand the efficiency and novelty of the algorithm, it has been validated on two different kinds of synthetic resistivity data with various sets of noise and, subsequently, applied to three field datasets of different geological terrains. The analyzed results suggest that the subsurface resistivity model shows considerable uncertainty. Thus, it is superior to examine the histograms and posterior probability density functions (PDFs) of such solutions to exemplify the global solution. A PDF with a 68.27 % confidence interval (CI) selects a region with a higher probability. Therefore, the inverted models are used to estimate the mean global solution and the most negligible uncertainties, where the mean global solution represents the best solution. Our vPSOGWO-inverted outcomes have been proven to be more accurate than classic PSO, GWO, and state-of-the-art variants of classic approaches. As a result, this novel method plays a vital role in vertical electrical sounding (VES) data inversion.

N-Euler mathematical modelling and numerical simulation of liquid–gas–solid flows

Three phase flows are omnipresent in industrial as well as natural configurations. Understanding the behaviour of solid particles interacting with liquid–air flows can be of great interest for both topics. In this paper we present a new liquid–gas–solid modelling technique based on the hybrid method combining liquid–gas two-fluid phase-average approach and probability density function (PDF) methods for solid dispersed phases. The PDF approach is based on single particle dynamic equation taking into account its interaction with more than one fluid and separate stochastic Lagrangian equations for each fluid phase velocity seen by the particles. This method does not assume the carrier phases typology. The solid particles can interact with bubbles, droplets, pockets and stratified flow through drag only (other interaction forces are supposed to be negligible for our cases). In this work, it is assumed that the total drag applied to the particle is a linear combination of the drags computed if the particles were interacting separately with each fluid phases. Finding the linear combination coefficient represent the main modelling step. Particle collisions and particle turbulent dispersion are taken into account in the model. Dispersed bubbles can undergo coalescence and fragmentation. The effect of all these sub-models is studied in the comparison with experimental data.The fluid and particle equations are first derived before introducing the appropriate coupling terms. Then, the closure terms for turbulence and multiphase drag are introduced. The model is implemented in neptune_cfd, a finite volume solver developed by EDF, CEA, IRSN and Framatome which allows for the numerical resolution of separate Eulerian equations (mass, momentum and energy) for n phases coupled by interfacial transfer terms. The model is then compared against experimental data obtained in a bubble column charged with particles. The results obtained with it are satisfactory and enable us to study more in details its hypothesis and to confirm comments made in the first section. Eventually, the model is tested on an industrial case which shows its efficiency.

Longitudinal and azimuthal thermo-acoustic instabilities in an industrial gas turbine combustor operating at elevated pressure

This work numerically investigates longitudinal and azimuthal thermo-acoustic instabilities in the swirl-stabilised can-type industrial SGT-100 gas turbine combustor operated at elevated pressures of 3 and 6 bar. Previous experiments have shown that the combustor is susceptible to self-excited flame oscillations sustained by a thermo-acoustic feedback loop at specific operating conditions. In order to gain a better understanding of this feedback loop, a fully compressible large eddy simulation method is applied. The unknown sub-grid scale turbulence-chemistry interactions are modelled via a transported probability density function approach solved by the Eulerian stochastic fields method. First, the reaction zones and global flame topology at both operating pressures are analysed and compared to experimental images providing good qualitative agreement. Radial profiles of time-averaged and root-mean-square quantities furthermore demonstrate good quantitative agreement with the available measurement data. The applied simulation approach is capable of successfully reproducing self-excited thermo-acoustic instabilities in the longitudinal direction. The fundamental frequency of the predicted limit-cycle oscillation matches the experimentally measured frequency with high accuracy. Similar to the experimental observations, the fluctuation amplitudes of the pressure and global heat release rate increase significantly upon increasing the mean operating pressure from 3 to 6 bar. In addition to the dominant longitudinal mode, a high-frequency, low-amplitude azimuthal mode is also identified at both pressures. This azimuthal mode is periodically amplified and attenuated by the superposed longitudinal mode and induces small asymmetric (around the burner circumference) fluctuations of the local fuel and total mixture mass flow rates entering the flame region.

Profile constraint in toroidal plasmas and methodologies to break leading to transport barrier

Internal transport barriers (ITBs) observed in magnetically confined toroidal plasmas are promising for achieving high-performance burning plasmas, which are established from low-confinement L-mode plasmas dominated by anomalous transport exhibiting strong profile constraints. We studied the origin causing such L-mode plasmas using flux-driven gyro-kinetic based global toroidal simulations covering from core to edge. The simulations are incorporated with real space based statistical probability density function (PDF) approach, which directly measures the heat flux eddy distribution across the entire torus to identify the non-diffusive nature of turbulent transport with different spatio-temporal scales, such as micro-scale avalanches, macro-scale bursts, meso-scale E × B shear layers, etc., as the origin causing the constraints. Based on studies of such L-mode plasmas, we present a methodology to overcome such constraints and demonstrate ITB formations by the control of quasi-stationary global radial E × B shear through the toroidal plasma rotation driven by either externally using momentum injection and intrinsically using both ions and electron simultaneous heating.

Effects of Hydrogen Enrichment on Thermoacoustic and Helical Instabilities in Swirl Stabilised Partially Premixed Flames

The effects of hydrogen enrichment on flame and flow dynamics of a swirl-stabilised partially premixed methane-air flame are studied using large eddy simulation. The sub-grid reaction rate is modelled using unstrained premixed flamelets and a presumed joint probability density function approach. Two cases undergoing thermoacoustic oscillations at ambient conditions are studied. The addition of hydrogen modifies both thermoacoustic and fluid dynamical characteristics. The amplitude of the fundamental thermoacoustic mode increases with the addition of 20% hydrogen by volume. A second pressure mode associated with the chamber mode is also excited with the hydrogen addition. Intermittent single, double and triple helical instabilities are observed in the pure methane case, but are suppressed substantially with hydrogen addition. The results are analysed in detail to shed light on these observations. The feedback loop responsible for the thermoacoustic instability is driven by mixture fraction perturbations resulting from the unequal impedances of the fuel and air channels. It is shown that hydrogen addition increases the flame’s sensitivity to these perturbations, resulting in an increase in amplitude. This higher amplitude thermoacoustic oscillation, along with a higher local heat release rate in the presence of hydrogen, is shown to considerably modify the flow structures, leading to a suppression of the helical instabilities.

Short-term wind power forecasting by bidirectional attention mechanism LSTM and its probability interval prediction by sliding-window KDE

Deterministic point wind power forecasting (DP-WPF) and its probability interval prediction (PIP) are indispensable to short-term peak alleviation and frequency regulation in power systems with large-scale wind power injection. To improve short-term DP-WPF by long short-term memory (LSTM), a horizontal/vertical bidirectional feature attention (BFA) based LSTM model is proposed. More specifically, the BFA-LSTM model has three parts: first, multivariate time series are fed into LSTM to extract long-short-term temporal features; second, the LSTM outputs are processed horizontally as well as vertically for retrieving step-wise/multistep-wise temporal features, respectively, namely, in the bidirectional attention sense; third, both the horizontal and vertical attention weights are adaptively adjusted according to the feature importance in DP-WPF. Cases comparison shows that the suggested modeling is stably superior to most common counterparts. To address PIP by kernel density estimation (KDE), sliding-window KDE is leveraged for probability analysis. More precisely, probability density functions (PDF) and probability intervals are estimated with sliding-window samples, which are non-parametric operations and involve finitely many local samples. Superior performances of PIP by sliding-window KDE at different confidence levels indicate that the sliding-window PDF approach is highly effective in contrast to those with all samples.

Application of a two-progress variable model for carbon monoxide emissions from turbulent premixed and partially premixed enclosed flames

A large eddy simulation study is undertaken with the objective of improving carbon monoxide (CO) estimations compared to measurements of enclosed turbulent flames in laboratory scale burners. The sub-grid combustion is modelled using a presumed joint probability density function approach with tabulated chemistry based on unstrained flamelets. The thermochemical conditions are mapped using the mixture fraction and reaction progress variable. A second progress variable is used to represent the post-flame oxidation of CO. The CO mass fraction is transported, and the CO production and consumption rates are stored in separate look-up tables using each progress variable. The two-progress variable model is assessed using enclosed flames that are stabilised behind a bluff body and in a gas turbine model combustor with swirling flows. The performance of the two-progress variable model is assessed by using standard practice approaches to compute the CO mass fraction with a single progress variable, which include obtaining the CO mass fraction from a look-up table or from its transport equation. Transporting the CO mass fraction with a single progress variable gives significant overestimations in the burnt regions of the bluff body stabilised flame. The two-progress variable model gives significant improvements in the burnt regions, since the disparate time scales of CO production and consumption are captured by this model. The look-up approach also significantly overestimates the CO mass fraction in the flame stabilisation region in both configurations, where convection and diffusion processes are dominant. Therefore, the CO mass fraction needs to be transported with two progress variables to capture the intricate convection-diffusion-reaction balance in the flame stabilisation region and within the flame brush. Furthermore, the two-progress variable model gives improvements in the post-flame oxidation regions towards the chamber exit in the gas turbine model combustor, whereas the look-up approach gives significant overestimates.

A super-grid approach for LES combustion closure using the Linear Eddy Model

LES–LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level ‘super-grid’ comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection–reaction–diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed ‘super-grid LEM’ or ‘SG-LEM’. The paper describes LEM reaction–diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES–LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES–LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.

A pressure-coupled Representative Interactive Linear Eddy Model (RILEM) for engine simulations

The Representative Linear Eddy Model (RILEM) was introduced by Lackmann et al. (2018) as an alternative modeling approach to simulate turbulent non-premixed combustion in engines. The model utilizes a RANS approach for turbulence and the Linear Eddy Model (LEM) with a presumed probability density function (PDF) approach for combustion closure. A distinct feature of RILEM is its potential to handle arbitrary combustion regimes and the consideration of complex physical phenomena such as differential diffusion effects. The original version of RILEM implemented a volume-based coupling between LEM and the flow solver. This work presents a new variant of RILEM, i.e., Multiple Representative Interactive Linear Eddy Model (MRILEM) based on a pressure-based coupling, to overcome some deficiencies of the original RILEM, namely statistical fidelity. Due to the introduced pressure coupling, the effects of heat losses (wall heat fluxes, latent heat of evaporation) on combustion are intrinsically included via the pressure trace. Furthermore, we introduce a new step function PDF for the progress variable defined by its mean value only. Issues with an incomplete solution space for mixture fraction and progress variable due to the stochastic nature of LEM are remedied with a PDF scaling technique, aided by a novel parameterization of the progress-variable PDF The new variant of RILEM is evaluated using part- and full-load cases of a heavy-duty metal engine. The impact of utilizing multiple LEM lines on the completeness of the solution space and its influence on the distribution of scalar values in the CFD domain was demonstrated. Results for pressure trace, flame structure, and CO emissions are analyzed and compared with simulations using the Multi-Zone Well-Mixed Model (MZWM) model and experiments. While pressure traces agree well among the different models and experiments, noteworthy differences are observed between the models regarding CO emissions and temperature. Effects of turbulence chemistry interaction were noticed when comparing MRILEM to the results of the MZWM simulation, namely flame brush and species mass fraction distribution.

A Priori Direct Numerical Simulation Assessment of MILD Combustion Modelling in the Context of Reynolds Averaged Navier–Stokes Simulations

A priori Direct Numerical Simulation (DNS) assessment of mean reaction rate closures for reaction progress variable in the context of Reynolds Averaged Navier–Stokes (RANS) simulations has been conducted for MILD combustion of homogeneous (i.e., constant equivalence ratio), methane-air mixtures. The reaction rate predictions according to statistical (e.g., presumed probability density function), phenomenological (e.g., eddy-break up (EBU), eddy dissipation concept (EDC) and the scalar dissipation rate (SDR) based approaches), and flame surface description (e.g., Flame Surface Density) based closures are compared. The performance of the various reaction rate closures has been assessed by comparing the models’ predictions to the corresponding quantities extracted from DNS data. It has been found that the usual presumed probability density function (PDF) approach using the beta-function predicts the PDF of the reaction progress variable in homogenous mixture MILD combustion throughout the flame brush for all cases considered here provided that the scalar variance is accurately predicted. The accurate estimation of scalar variance requires the solution of a modelled transport equation, which depends on the closure of Favre-averaged SDR. A linear relaxation based algebraic closure for the Favre-averaged SDR has been found to capture the behaviour of the Favre-averaged SDR in the current homogenous mixture MILD combustion setup. It has been found that the EBU, SDR and FSD-based mean reaction rate closures do not adequately predict the mean reaction rate of the reaction progress variable for the parameter range considered here. However, a variant of the EDC closure, with model coefficients expressed as functions of micro-scale Damköhler and turbulent Reynolds numbers, has been found to be more successful in predicting the mean reaction rate of reaction progress variable compared to other modelling methodologies for the range of turbulence intensities and dilution levels considered here.

A stochastic model of edge-localized modes in magnetically confined plasmas.

Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated with instabilities in the low-to-high confinement transition and the H-mode. Specifically, we present a stochastic Langevin model of edge-localized modes (ELMs) by including stochastic noise terms in a previous ODE ELM model. We calculate exact time-dependent PDFs by numerically solving the Fokker-Planck equation and characterize time-varying statistical properties of ELMs for different energy fluxes and noise amplitudes. The stochastic noise is shown to introduce phase-mixing and plays a significant role in mitigating extreme bursts of large ELMs. Furthermore, based on time-dependent PDFs, we provide a path-dependent information geometric theory of the ELM dynamics and demonstrate its utility in capturing self-regulatory relaxation oscillations, bursts and a sudden change in the system. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Large eddy simulation of multi-regime combustion with a two-progress variable approach for carbon monoxide

Simulations of two cases in a novel multi-regime burner configuration are undertaken using a presumed joint probability density function (PDF) approach with tabulated chemistry. The flame conditions are varied by changing the central jet equivalence ratio, which produces different multi-regime combustion modes in the non-premixed inner flame. An outer premixed flame and recirculation zone behind a bluff body are present to supply heat and combustion products to stabilise the inner flame. A two-progress variable approach is tested to improve predictions of carbon monoxide (CO) in the post-flame regions, where CO oxidation occurs. The large eddy simulation set-up and sub-grid combustion model are assessed through comparisons with time-averaged measurements for radial profiles at different streamwise locations. The jet break-up length, the shear layers and the mixture fraction distribution are well captured in both cases. The temperature distribution is well captured for the inner flame in each case but the temperature and mixture fraction are over predicted in the downstream regions of the outer premixed flame, which is due to increased dilatation that suppresses air entrainment. Improved predictions of the CO mass fraction are obtained for the outer premixed flames with the two-progress variable approach. Over predictions are seen in the upstream regions of the inner flame when the CO mass fraction is obtained from a look-up table, suggesting that the CO mass fraction should be transported to include the convection/diffusion balance in regions where there is no flame. Furthermore, transporting the CO mass fraction with a one-progress variable approach produces over predictions in the burnt regions, suggesting a two-progress variable model is needed to capture the consumption region of CO. The multi-regime combustion characteristics are observed to be stronger in flame MRB26b, where non-premixed and rich premixed combustion is present. For flame MRB18b, the non-premixed contribution is smaller and weak stratified combustion is observed.

A feasibility study on the use of low-dimensional simulations for database generation in adaptive chemistry approaches

Large eddy simulation (LES)/ Probability Density Function (PDF) approaches are now well established and can be used for simulating challenging turbulent combustion configurations with strong turbulence chemistry interactions. Transported PDF methods are known to be computationally expensive compared to flamelet-like turbulent combustion models. The pre-partitioned adaptive chemistry (PPAC) methodology was developed to address this cost differential. PPAC entails an offline preprocessing stage, where a set of reduced models are generated starting from an initial database of representative compositions. At runtime, this set of reduced models are dynamically utilised during the reaction fractional step leading to computational savings. We have recently combined PPAC with in-situ adaptive tabulation (ISAT) to further reduce the computational cost. We have shown that the combined method reduced the average wall-clock time per time step of large-scale LES/particle PDF simulations of turbulent combustion by 39%. A key assumption in PPAC is that the initial database used in the offline stage is representative of the compositions encountered at runtime. In our previous study this assumption was trivially satisfied as the initial database consisted of compositions extracted from the turbulent combustion simulation itself. Consequently, a key open question remains as to whether such databases can be generated without having access to the turbulent combustion simulation. Towards answering this question, in the current work, we explore whether the compositions for forming such a database can be extracted from computationally-efficient low-dimensional simulations such as 1D counterflow flames and partially stirred reactors. We show that a database generated using compositions extracted from a partially stirred reactor configuration leads to performance comparable to the optimal case, wherein the database is comprised of compositions extracted directly from the LES/PDF simulation itself.

Error analysis of SISO and dual-branch communications with generalized Gaussian noise over FTR fading channels

In this paper, we present error probability analysis for single-input single-output (SISO) and asymmetric dual-branch networks with additive white generalized Gaussian noise (AWGGN) over millimeter-wave (mmW) fluctuating two-ray (FTR) fading channels. Then, we examine the error probability evaluation of a SISO system with imperfect phase errors over mmW FTR fading channels. The probability density function (PDF) approach is employed for the error probability performance evaluation and the novel PDF of the asymmetric dual-branch system over Nakagami-m/mmW FTR fading channels is obtained. Specifically, closed-form expressions are derived for the error probability of the SISO and asymmetric dual-branch networks. The derived error expressions facilitate in effectively evaluating the performance of considered networks in the presence of AWGGN and imperfect phase noise with optimal fading parameters and modulation type. The theoretical derivations are extensively confirmed through exact simulations.

Large Eddy Simulation of a Reacting Kerosene Spray in Hot Vitiated Cross-Flow

The evaporation and combustion characteristics of a kerosene spray injected perpendicularly into a cross-flow of high-temperature vitiated air is investigated. This fundamental flow configuration has wider implications for the future development of ultra-low emission aeronautical combustors, particularly with respect to technologies involving MILD combustion. Large eddy simulations with a Eulerian–Lagrangian framework are performed to investigate the spray evolution and the characteristics of the reaction zone for a range of conditions. For the closure of turbulence-chemistry interactions at the sub-grid scales, a transported probability density function approach solved by the Eulerian stochastic fields method is applied. A configuration based on the use of airblast atomisation is assessed first and compared with experimental observations. The effect of the atomiser air-to-liquid mass flow ratio is studied in greater detail, both in terms of the resulting gas-phase properties and the droplet evaporation process. Then, the effect of ambient pressure on the global spray flame behaviour is examined. For this part of the study, no atomising air is included in the simulation to separate the effects of ambient pressure on the spray from the interaction with the air jet. Analysis of the flame and spray properties at cross-flow operating pressures of 1 atm, 2 bar and 4 bar highlights the strong coupling between the reacting flow and droplet evaporation characteristics, which are highly affected by the penetration of the spray into a flow field characterised by relatively large gradients of temperature. The results reported in this work provide fundamental understanding for the development of novel low-emission combustion technologies and demonstrate the feasibility of applying large eddy simulation with detailed chemistry for the investigation of reacting aviation fuel sprays in hot vitiated cross-flow.

Analysis of GFDM in generalized [formula omitted] fading channel: A simple probability density function approach for beyond 5G wireless applications

Generalized frequency division multiplexing (GFDM) is a flexible radio waveform which offers high degree of freedom in varying the number of time slots, number of subcarriers, and pulse shaping filters. In addition to this, it also covers orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE) as corner cases. A well-known fact is that the performance of a wireless communication system is predominately effected by the characteristics of the fading environment. In this paper, symbol error rate (SER) closed-form expression of GFDM system under the generalized η−μ fading channel is derived. The proposed derivation includes Rayleigh, Nakagami-m, and Nakagami-q fading channels as special cases. A Mote-Carlo simulation test-bed is carried out using MATLAB to compare with analytical results and to validate the derived expressions based on the probability density function (PDF) approach. Further, this paper investigates the performance of the GFDM system by varying various parameters such as fading values, pulse shaping filters, roll-off factor, and modulation order. The detailed analysis suggests that the probability of SER is highly dependent on the above parameters. The results obtained are more useful in evaluating the performance of GFDM based communication system in a generalized manner.

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated.

Numerical study on pressure oscillations amplitude distribution induced by water flow into pipe filled with steam

The direct contact condensation (DCC) between subcooled water and steam is an important thermo-hydraulic phenomenon experienced in industrial sectors especially in nuclear industry. The pressure oscillations are inevitable events during steam-water DCC involving high pressure peaks, responsible for the possible failure of mechanical equipment and systems. This computational fluid dynamics study explores the underlying physics of condensation pressure oscillations by injecting subcooled water into steam section. Based on the probability density function (PDF) approach, the effects of different parameters such as velocity and temperature of injected water, water-steam differential pressure and degree of superheated steam on the amplitude of pressure oscillations distribution have been studied. Moreover, the first and second dominant frequencies of pressure oscillations have also been obtained from fast Fourier transform. It has been found that the PDF of the pressure oscillations is strongly related to injecting water velocity, water temperature and steam-water differential pressure while weakly dependent on steam superheating.