Conditional scalar dissipation statistics in a turbulent counterflow

1998 ◽  
Vol 361 ◽  
pp. 1-24 ◽  
Author(s):  
KATERINA SARDI ◽  
A. M. K. P. TAYLOR ◽  
J. H. WHITELAW
Keyword(s):  
Diffusion Flames ◽  
Probability Distributions ◽  
Mixture Fraction ◽  
Mixing Layer ◽  
Scalar Dissipation ◽  
Jet Flows ◽  
Residence Times ◽  
Scalar Turbulence ◽  
The Mean ◽  
Log Normal

Cold-wire measurements of a scalar, temperature, its fluctuations and the axial and radial components of the scalar dissipation between two opposed turbulent jet flows, where one jet was slightly heated, show that the residence times of the scalar in the mixing layer were short, that the scalar fluctuations and their dissipation were strongly correlated and that the probability distributions of the conditional scalar dissipation components were log-normal at values of the dissipation larger than the mean. The first finding is consistent with the fact that the scalar turbulence was ‘young’, in the sense that residence times were shorter than the large-eddy turn-over time, so that the results are likely to be representative of scalar turbulence when scalar mixing first takes place between two streams, for example close to the stabilization region of turbulent diffusion flames. The second implies that the mean scalar dissipation, conditional on the stoichiometric mixture fraction, is larger than the unconditional mean by up to an order of magnitude. Dependence of the distributions of the mean and r.m.s. conditional scalar dissipation on the shape of the scalar p.d.f. was demonstrated by relating the largest conditional dissipation values to the rarest scalar fluctuations and it was found that this dependence was also valid in other flows where scalar dissipation has been measured. The third finding implies that the use of a log-normal distribution to describe the p.d.f. of the conditional scalar dissipation, in the context of flame extinction modelling, will be in error by only 15% provided that the mean and the r.m.s. conditional scalar dissipation are accurately known.

A Skewed PDF Combustion Model for Jet Diffusion Flames

1990 ◽  
Vol 112 (4) ◽  
pp. 1002-1007 ◽  
Author(s):  
M. M. M. Abou-Ellail ◽  
H. Salem
Keyword(s):  
Diffusion Flames ◽  
Mixture Fraction ◽  
Beta Function ◽  
Delta Function ◽  
Turbulent Jet ◽  
Combustion Model ◽  
Jet Diffusion Flames ◽  
Numerical Predictions ◽  
Methane Flame ◽  
The Mean

A combustion model based on restricted chemical equilibrium is described. A transport equation for the skewness of the mixture fraction is derived. It contains two adjustable constants. The computed values of the mean mixture fraction (f) and its variance and skewness (g and s) for a jet diffusion methane flame are used to obtain the shape of a skewed pdf. The skewed pdf is split into a turbulent part (beta function) and a nonturbulent part (delta function) at f = 0. The contribution of each part is directly related to the values of f, g, and s. The inclusion of intermittency in the skewed pdf appreciably improves the numerical predictions obtained for a turbulent jet diffusion methane flame for which experimental data are available.

Implementation and Validation of a New Soot Model and Application to Aeroengine Combustors

2000 ◽  
Author(s):  
M. Balthasar ◽  
F. Mauss ◽  
M. Pfitzner ◽  
A. Mack
Keyword(s):  
Transport Equation ◽  
Gas Phase ◽  
Dissipation Rate ◽  
Soot Formation ◽  
Mixture Fraction ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Gas Phase Reactions ◽  
The Mean ◽  
Soot Model

The modelling of soot formation and oxidation under industrially relevant conditions has made significant progress in recent years. Simplified models introducing a small number of transport equations into a CFD code have been used with some success in research configurations simulating a reciprocating diesel engine. Soot formation and oxidation in the turbulent flow is calculated on the basis of a laminar flamelet library model. The gas phase reactions are modelled with a detailed mechanism for the combustion of heptane containing 89 species and 855 reactions developed by Frenklach and Warnatz and revised by Mauss. The soot model is divided into gas phase reactions, the growth of polycyclic aromatic hydrocarbons (PAH) and the processes of particle inception, heterogeneous surface growth, oxidation and condensation. The first two are modelled within the laminar flamelet chemistry, while the soot model deals with the soot particle processes. The time scales of soot formation are assumed to be much larger than the turbulent time scales. Therefore rates of soot formation are tabulated in the flamelet libraries rather than the soot volume fraction itself. The different rates of soot formation, e.g. particle inception, surface growth, fragmentation and oxidation, computed on the basis of a detailed soot model, are calculated in the mixture fraction / scalar dissipation rate space and further simplified by fitting them to simple analytical functions. A transport equation for the mean soot mass fraction is solved in the CFD-code. The mean rate in this transport equation is closed with the help of presumed probability density functions for the mixture fraction and the scalar dissipation rate. Heat loss due to radiation can be taken into account by including a heat loss parameter in the flamelet calculations describing the change of enthalpy due to radiation, but was not used for the results reported here. The soot model was integrated into an existing commercial CFD code as a post-processing module to existing combustion CFD flow fields and is very robust with high convergence rates. The model is validated with laboratory flame data and using a realistic 3-D BMW Rolls-Royce combustor configuration, where test data at high pressure are available. Good agreement between experiment and simulation is achieved for laboratory flames, whereas soot is overpredicted for the aeroengine combustor configuration by 1–2 orders of magnitude.

Implementation and Validation of a New Soot Model and Application to Aeroengine Combustors

2000 ◽  
Vol 124 (1) ◽  
pp. 66-74 ◽  
Author(s):  
M. Balthasar ◽  
F. Mauss ◽  
M. Pfitzner ◽  
A. Mack
Keyword(s):  
Transport Equation ◽  
Gas Phase ◽  
Dissipation Rate ◽  
Soot Formation ◽  
Mixture Fraction ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Gas Phase Reactions ◽  
The Mean ◽  
Soot Model

The modeling of soot formation and oxidation under industrially relevant conditions has made significant progress in recent years. Simplified models introducing a small number of transport equations into a CFD code have been used with some success in research configurations simulating a reciprocating diesel engine. Soot formation and oxidation in the turbulent flow is calculated on the basis of a laminar flamelet library model. The gas phase reactions are modeled with a detailed mechanism for the combustion of heptane containing 89 species and 855 reactions developed by Frenklach and Warnatz and revised by Mauss. The soot model is divided into gas phase reactions, the growth of polycyclic aromatic hydrocarbons (PAH) and the processes of particle inception, heterogeneous surface growth, oxidation, and condensation. The first two are modeled within the laminar flamelet chemistry, while the soot model deals with the soot particle processes. The time scales of soot formation are assumed to be much larger than the turbulent time scales. Therefore rates of soot formation are tabulated in the flamelet libraries rather than the soot volume fraction itself. The different rates of soot formation, e.g., particle inception, surface growth, fragmentation, and oxidation, computed on the basis of a detailed soot model, are calculated in the mixture fraction/scalar dissipation rate space and further simplified by fitting them to simple analytical functions. A transport equation for the mean soot mass fraction is solved in the CFD code. The mean rate in this transport equation is closed with the help of presumed probability density functions for the mixture fraction and the scalar dissipation rate. Heat loss due to radiation can be taken into account by including a heat loss parameter in the flamelet calculations describing the change of enthalpy due to radiation, but was not used for the results reported here. The soot model was integrated into an existing commercial CFD code as a post-processing module to existing combustion CFD flow fields and is very robust with high convergence rates. The model is validated with laboratory flame data and using a realistic three-dimensional BMW Rolls-Royce combustor configuration, where test data at high pressure are available. Good agreement between experiment and simulation is achieved for laboratory flames, whereas soot is overpredicted for the aeroengine combustor configuration by 1–2 orders of magnitude.

A Skewed Two-Dimensional Probability Density Function for Methane-Air Turbulent Diffusion Flames

2010 ◽  
Author(s):  
Mohsen Abou-Ellail ◽  
Ryo S. Amano ◽  
Samer Elhaw ◽  
Karam Beshay ◽  
Hatem Kayed
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Diffusion Flames ◽  
Mixture Fraction ◽  
Two Dimensional ◽  
Flamelet Model ◽  
The Mean

The present paper describes a mathematical model for turbulent methane-air jet diffusion flames. The mathematical model solves density-weighted governing equations for momentum, mass continuity, turbulent kinetic energy and its dissipation rate. The combustion model solves density-weighted transport equations for the mixture fraction “f”, its variance “g” and its skewness “s”. These variables are used to compute one part of the probability density function (PDF) in mixture fraction domain. The second part of the PDF is computed from the numerical solutions of the mixture fraction dissipation rate “χ” and its variance χ˜″2. The resulting two-dimensional PDF is defined in the mixture-fraction-scalar-dissipation-rate 2D space. The flamelet combustion sub-model is used to compute the mean flame temperature, density and species mass fractions. The flamelet model provides instantaneous state relationships for the stretched flamelets up to the extinction limit. The mean flame properties are computed through the integration of the stretched flamelet state relationships over the two-dimensional PDF. The present 2D probability density function model can predict rim-attached flames as well as unstable lifted flames. This is because the flamelet model provides information on the flame instability arising from the stretching effects of highspeed flowing gases. The new two-dimensional probability density function is used to predict the flame properties of a free jet methane-air flame for which experimental data exists.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals Subcritical Transmission in the Early Stage of COVID-19 in Korea

2021 ◽  
Vol 18 (3) ◽  
pp. 1265
Author(s):  
Yong Sul Won ◽  
Jong-Hoon Kim ◽  
Chi Young Ahn ◽  
Hyojung Lee
Keyword(s):  
Incubation Period ◽  
Early Stage ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Contact Tracing ◽  
Statistical Characterization ◽  
Serial Interval ◽  
Imported Cases ◽  
The Mean ◽  
Reporting Delays

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

Large-scale structure and entrainment in the supersonic mixing layer

1995 ◽  
Vol 284 ◽  
pp. 171-216 ◽  
Author(s):  
N. T. Clemens ◽  
M. G. Mungal
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Layer ◽  
Mie Scattering ◽  
Planar Laser ◽  
The Cross ◽  
Convective Mach Number ◽  
Stream Direction

Experiments were conducted in a two-stream planar mixing layer at convective Mach numbers,Mc, of 0.28, 0.42, 0.50, 0.62 and 0.79. Planar laser Mie scattering (PLMS) from a condensed alcohol fog and planar laser-induced fluorescence (PLIF) of nitric oxide were used for flow visualization in the side, plan and end views. The PLIF signals were also used to characterize the turbulent mixture fraction fluctuations.Visualizations using PLMS indicate a transition in the turbulent structure from quasi-two-dimensionality at low convective Mach number, to more random three-dimensionality for$M_c\geqslant 0.62$. A transition is also observed in the core and braid regions of the spanwise rollers as the convective Mach number increases from 0.28 to 0.62. A change in the entrainment mechanism with increasing compressibility is also indicated by signal intensity profiles and perspective views of the PLMS and PLIF images. These show that atMc= 0.28 the instantaneous mixture fraction field typically exhibits a gradient in the streamwise direction, but is more uniform in the cross-stream direction. AtMc= 0.62 and 0.79, however, the mixture fraction field is more streamwise uniform and with a gradient in the cross-stream direction. This change in the composition of the structures is indicative of different entrainment motions at the different compressibility conditions. The statistical results are consistent with the qualitative observations and suggest that compressibility acts to reduce the magnitude of the mixture fraction fluctuations, particularly on the high-speed edge of the layer.

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