Analysis of Algebraic Closures of the Mean Scalar Dissipation Rate of the Progress Variable Applied to Stagnating Turbulent Flames

2012 ◽  
Vol 90 (2) ◽  
pp. 301-323 ◽  
Author(s):  
Huy Quang Dong ◽  
Vincent Robin ◽  
Arnaud Mura ◽  
Michel Champion
Keyword(s):  
Dissipation Rate ◽  
Turbulent Flames ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Progress Variable ◽  
The Mean

scholarly journals A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

2020 ◽  
Author(s):  
M. P. Sitte ◽  
C. Turquand d’Auzay ◽  
A. Giusti ◽  
E. Mastorakos ◽  
N. Chakraborty
Keyword(s):  
Dissipation Rate ◽  
A Priori ◽  
Turbulent Flames ◽  
Large Eddy Simulations ◽  
Moment Closure ◽  
Scalar Dissipation ◽  
Combustion Model ◽  
Scalar Dissipation Rate ◽  
Jet Flame ◽  
Large Eddy

Abstract The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.

Relationship between the heat transfer law and the scalar dissipation function in a turbulent channel flow

2017 ◽  
Vol 830 ◽  
pp. 300-325 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Dependence

Integration across a fully developed turbulent channel flow of the transport equations for the mean and turbulent parts of the scalar dissipation rate yields relatively simple relations for the bulk mean scalar and wall heat transfer coefficient. These relations are tested using direct numerical simulation datasets obtained with two isothermal boundary conditions (constant heat flux and constant heating source) and a molecular Prandtl number Pr of 0.71. A logarithmic dependence on the Kármán number $h^{+}$ is established for the integrated mean scalar in the range $h^{+}\geqslant 400$ where the mean part of the total scalar dissipation exhibits near constancy, whilst the integral of the turbulent scalar dissipation rate $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$ increases logarithmically with $h^{+}$. This logarithmic dependence is similar to that established in a previous paper (Abe & Antonia, J. Fluid Mech., vol. 798, 2016, pp. 140–164) for the bulk mean velocity. However, the slope (2.18) for the integrated mean scalar is smaller than that (2.54) for the bulk mean velocity. The ratio of these two slopes is 0.85, which can be identified with the value of the turbulent Prandtl number in the overlap region. It is shown that the logarithmic $h^{+}$ increase of the integrated mean scalar is intrinsically associated with the overlap region of $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$, established for $h^{+}$ (${\geqslant}400$). The resulting heat transfer law also holds at a smaller $h^{+}$ (${\geqslant}200$) than that derived by assuming a log law for the mean temperature.

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.

scholarly journals Implementation of the Scalar Dissipation Rate in the REDIM Concept and its Validation for the Piloted Non-Premixed Turbulent Jet Flames

2021 ◽  
Vol 23 (3) ◽  
pp. 169
Author(s):  
C. Yu ◽  
U. Maas
Keyword(s):  
Dissipation Rate ◽  
Transport Model ◽  
Turbulent Flames ◽  
Turbulent Jet ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Jet Flames ◽  
Reduced Chemistry ◽  
The Impact ◽  
Turbulent Jet Flames

In order to address the impact of the concentration gradients on the chemistry – turbulence interaction in turbulent flames, the REDIM reduced chemistry is constructed incorporating the scalar dissipation rate, which is a key quantity describing the turbulent mixing process. This is achieved by providing a variable gradient estimate in the REDIM evolution equation. In such case, the REDIM reduced chemistry is tabulated as a function of the reduced coordinates and the scalar dissipation rate as an additional progress variable. The constructed REDIM is based on a detailed transport model including the differential diffusion, and is validated for a piloted non-premixed turbulent jet flames (Sandia Flame D and E). The results show that the newly generated REDIM can reproduce the thermo-kinetic quantities very well, and the differential molecular diffusion effect can also be well captured.

scholarly journals Closure Relations for Fluxes of Flame Surface Density and Scalar Dissipation Rate in Turbulent Premixed Flames

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 43 ◽  
Author(s):  
Andrei Lipatnikov ◽  
Shinnosuke Nishiki ◽  
Tatsuya Hasegawa
Keyword(s):  
Dissipation Rate ◽  
Surface Density ◽  
Turbulent Flames ◽  
Tuning Parameter ◽  
Scalar Dissipation ◽  
Flame Surface ◽  
Scalar Dissipation Rate ◽  
Flame Surface Density ◽  
Closure Relations ◽  
Flame Brush

In this study, closure relations for total and turbulent convection fluxes of flame surface density and scalar dissipation rate were developed (i) by placing the focus of consideration on the flow velocity conditioned to the instantaneous flame within the mean flame brush and (ii) by considering the limiting behavior of this velocity at the leading and trailing edges of the flame brush. The model was tested against direct numerical simulation (DNS) data obtained from three statistically stationary, one-dimensional, planar, premixed turbulent flames associated with the flamelet regime of turbulent burning. While turbulent fluxes of flame surface density and scalar dissipation rate, obtained in the DNSs, showed the countergradient behavior, the model predicted the total fluxes reasonably well without using any tuning parameter. The model predictions were also compared with results computed using an alternative closure relation for the flame-conditioned velocity.

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.

scholarly journals Local Strain Rate and Curvature Dependences of Scalar Dissipation Rate Transport in Turbulent Premixed Flames: A Direct Numerical Simulation Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
Y. Gao ◽  
N. Chakraborty ◽  
N. Swaminathan
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Strain Rate ◽  
Dissipation Rate ◽  
Premixed Flames ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Turbulent Premixed Flames ◽  
The Mean ◽  
Turbulent Premixed

The statistical behaviours of the instantaneous scalar dissipation rateNcof reaction progress variablecin turbulent premixed flames have been analysed based on three-dimensional direct numerical simulation data of freely propagating statistically planar flame and V-flame configurations with different turbulent Reynolds numberRet. The statistical behaviours ofNcand different terms of its transport equation for planar and V-flames are found to be qualitatively similar. The mean contribution of the density-variation termT1is positive, whereas the molecular dissipation term(-D2)acts as a leading order sink. The mean contribution of the strain rate termT2is predominantly negative for the cases considered here. The mean reaction rate contributionT3is positive (negative) towards the unburned (burned) gas side of the flame, whereas the mean contribution of the diffusivity gradient term(D)assumes negative (positive) values towards the unburned (burned) gas side. The local statistical behaviours ofNc,T1,T2,T3,(-D2), andf(D)have been analysed in terms of their marginal probability density functions (pdfs) and their joint pdfs with local tangential strain rateaTand curvaturekm. Detailed physical explanations have been provided for the observed behaviour.

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

Sign in / Sign up

Export Citation Format

Share Document