Direct Numerical Simulation (DNS) data obtained earlier from two statistically stationary, 1D, planar, weakly turbulent premixed flames are analyzed in order to examine the influence of ...combustion-induced thermal expansion on the flow structure within the mean flame brushes and upstream of them. The two flames are associated with the flamelet combustion regime and are characterized by significantly different density ratios, i.e.
σ
=
7.53
and 2.5. The Helmholtz–Hodge decomposition is applied to the DNS data in order to extract rotational and potential velocity fields. Comparison of the two fields shows that combustion-induced thermal expansion can significantly change the local structure of the incoming constant-density turbulent flow of unburned reactants by significantly increasing the relative magnitude of the potential velocity fluctuations when compared to the rotational velocity fluctuations in the flow. Such effects are documented not only within the mean flame brush, but also well upstream of it. The effect magnitude is increased by the density ratio
σ
, with the effects being well (weakly) pronounced at
σ
=
7.53
(2.5, respectively). Moreover, the potential and rotational velocity fields can cause opposite variations of the local area of an iso-scalar surface
c
x
,
t
=
const
within flamelets by generating the local strain rates of opposite signs.
Abstract
The study of a turbulent premixed flame often involves analysing quantities conditioned to different iso-surfaces of a reactive scalar field. Under the influence of turbulence, such a ...surface is deformed and translated. To track the surface motion, the displacement speed (
$S_d$
) of the scalar field respective to the local flow velocity is widely used and this quantity is currently receiving growing attention. Inspired by the apparent benefits from a simple decomposition of
$S_d$
into contributions due to (i) curvature, (ii) normal diffusion and (iii) chemical reaction, this work aims at deriving and exploring new evolution equations for these three contributions averaged over the reaction surface. Together with a previously obtained
$S_d$
-evolution equation, the three new equations are presented in a form that emphasizes the decomposition of
$S_d$
into three terms. This set of equations is also supplemented with a curvature-evolution equation, hence providing a new perspective to link the flame topology and its propagation characteristics. Using two direct numerical simulation databases obtained from constant-density and variable-density reaction waves, all the derived equations and the term-wise decomposition relations are demonstrated to hold numerically. Comparison of the simulated results indicates that the thermal expansion weakly affects the key terms in the considered evolution equations. Thermal expansion can cause variations in the averaged
$S_d$
and its decomposed parts through multiple routes more than introducing a dilatation term. The flow plays a major role to influence the key terms in all equations except the curvature one, due to a cancellation between negatively and positively curved surface elements.
Complex-chemistry direct numerical simulation (DNS) data obtained earlier from lean hydrogen-air flames associated with corrugated flame (case A), thin reaction zone (case B), and broken reaction ...zone (case C) regimes of turbulent burning are analysed to directly assess capabilities of the flamelet approach to predict mean concentrations of species in a premixed turbulent flame. The approach consists in averaging dependencies of mole fractions, reaction rates, temperature, and density on a single combustion progress variable c, which are all obtained from the unperturbed laminar flame. For this purpose, four alternative definitions of c are probed and two probability density functions (PDFs) are adopted, i.e. either an actual PDF extracted directly from the DNS data or a presumed β-function PDF obtained using the DNS data on the first two moments of the c(x, t)-field. Results show that the mean density and mean mole fractions of H2, O2, and H2O are well predicted using both PDFs for each c, although the predictive capabilities are little worse in case C. In cases A and B, the use of the actual PDF and the fuel-based c also offers an opportunity to well predict mean mole fractions of O and H, whereas the mean mole fraction of OH is slightly underestimated. In the highly turbulent case C, the same approach performs worse, but still appears to be acceptable for evaluating the mean radical concentrations. The use of the β-function PDFs or another combustion progress variable yields substantially worse results for these radicals. When compared to the mean mole fractions, the mean rate of product creation, i.e. the source term in the transport equation for the mean combustion progress variable, is worse predicted even for a quantity (species concentration or temperature) adopted to define c and using the actual PDF. Consequently, turbulent burning velocity is not predicted either.
The present work aims at modeling the entire convection flux
ρ
u
W
¯
in the transport equation for a mean reaction rate
ρW
¯
in a turbulent flow, which (equation) was recently put forward by the ...present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for
ρ
u
W
¯
are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire,
ρuW
¯
, and mean,
ũ
ρW
¯
, convection fluxes is well pronounced, with the turbulent flux,
ρ
u
′′
W
′′
¯
, showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux
ρ
u
W
¯
reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.
The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically ...and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.
The goals of the present review paper are; (i) to introduce experimental facilities and numerical tools applied to investigating inhomogeneously premixed flames, (ii) to summarize recent progress in ...revealing and understanding local phenomena (e.g. back-supported combustion or generation of flame surface area) that stem from the influence of mixture inhomogeneities on flame propagation through flammable reactants, (iii) to show state-of-the-art of unsteady multidimensional RANS and LES research into inhomogeneously premixed turbulent flames and to discuss models invoked for this purpose, and (iv) to highlight issues that still challenge researchers who develop such models.
The present work aims at development and validation of a tool for numerically modeling stratified turbulent combustion in a gasoline direct injection (GDI) engine. For this purpose, an open source ...code called OpenFOAM
®
, which has been attracting growing interests from both industries and academies due to an opportunity to access the source code and to test new models without paying license fees, is further developed by implementing advanced models relevant to stratified turbulent burning. In particular, first, the Flame Speed Closure model of premixed turbulent combustion is implemented in order to simulate flame propagation through inhomogeneously premixed reactants. Second, a newly calculated approximation of the laminar flame speed of gasoline-air mixtures as a function of the equivalence ratio, pressure, and temperature is implemented in order to simulate dependence of burning rate on the local mixture composition. Third, a newly calculated approximation of the combustion temperature of gasoline-air mixtures as a function of the equivalence ratio, pressure, and product enthalpy is implemented in order to allow for dissociation of combustion products and heat losses. Fourth, a presumed mixture-fraction probability density function (PDF) approach is implemented in order to simulate the influence of turbulent fluctuations in the mixture fraction on the local burning rate. In addition to commonly used mass-weighted mixture-fraction PDF, a more consistent model that deals also with the canonical mixture-fraction PDF is developed and the two approaches are compared. Numerical results that show the influence of the aforementioned implementations on computed global characteristics of stratified combustion in a research GDI engine are discussed. The developed numerical tool is quantitatively validated by comparing computed pressure traces in the GDI engine with experimental data obtained in three different cases associated with two different loads, late injection timings, and short time intervals between the injection and spark ignition.
Modeling of premixed turbulent combustion involves averaging reaction rates in turbulent flows. The focus of most approaches to resolving this problem has been placed on determining the dependence of ...the mean rate
w
˜
of product creation on the laminar flame speed
S
L
, the rms turbulence velocity
u
′
, etc. The goal of the present work is to draw attention to another issue: May the input quantity
u
′
for a model of
w
˜
=
w
˜
(
u
′
/
S
L
,
…
)
be considered to be known? The point is that heat release substantially affects turbulence and, hence, turbulence characteristics in premixed flames should be modeled. However, standard moment methods for numerically simulating turbulent flows do not allow us to evaluate the true turbulence characteristics in a flame. For instance, the Reynolds stresses in premixed flames are affected not only by turbulence itself, but also by velocity jump across flamelets. A common way to resolving this problem consists of considering the Reynolds stresses conditioned on unburned (or burned) mixture to be the true turbulence characteristics. In the present paper, this widely accepted but never proved hypothesis is put into question, first, by considering simple model constant-density problems (flame motion in an oscillating one-dimensional laminar flow; flame stabilized in a periodic shear, one-dimensional, laminar flow; turbulent mixing). In all the cases, the magnitude of velocity fluctuations, calculated using the conditioned Reynolds stresses, is affected by the intermittency of reactants and products and, hence, is not the true rms velocity. Second, the above claim is further supported by comparing balance equations for the mean and conditioned Reynolds stresses. The conditioned Reynolds stresses do not characterize the true turbulence in flames, because conditional averaging cuts off flow regions characterized by either high or low velocities.
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