Recently, a simple model for evaluating turbulent scalar flux in premixed flames was developed and validated using six experimental data sets obtained from flames stabilized in impinging jets ...(Sabelnikov and Lipatnikov, Combust. Sci. Technol.
183
, 588–613,
2011
; Sabelnikov and Lipatnikov, Flow Turbulence Combust.
90
, 387–400,
2013
). The model addresses the flamelet regime of premixed turbulent combustion and yields an algebraic expression for the mean velocity conditioned to unburned mixture, while turbulent scalar flux is evaluated substituting this conditioned velocity into the well-known Bray-Moss-Libby (BML) expressions. The present work aims at further assessment of the aforementioned model against two well-known 3D DNS databases obtained from statistically planar, 1D premixed turbulent flames characterized by various density ratios (7.53, 5.0, 3.3, and 2.5). For the highest density ratio, an excellent agreement between the model and DNS data was obtained. This result is particularly encouraging, because the experimental data used earlier to test the model are associated with approximately the same (7-8) density ratios. However, the DNS data obtained for lower density ratios indicate a trend, not addressed by the original model, i.e. a model parameter is not a constant but decreases with decreasing density ratio, with the dependence of the model parameter on the density ratio being roughly linear for three flames addressed by one DNS database. Implementation of this linear fit into the model makes it consistent both with the DNS and with all experimental data used earlier to validate the original model.
Balance equations for mass, velocity, and Reynolds stresses conditioned either to an unburned or to a burned mixture are derived from standard mass conservation, Navier–Stokes, and combustion ...progress variable balance equations by assuming that the probability of finding intermediate states of a reacting mixture is much less than unity. The derived equations contain three unclosed terms controlled by flamelet structure and flamelet statistics, whereas other unclosed terms are not straightforwardly affected by heat release and have counterparts in models of nonreacting flows. Equations of this type offer an opportunity to facilitate modeling the effects of heat release on turbulence. The modeling of these effects is further simplified if flamelet structure perturbations by turbulent eddies are neglected.
A common approach to modeling the influence of turbulent fluctuations in the mixture fraction f on the burning rate in a partially premixed flame consists of invoking a presumed Favre (mass-weighted) ...probability density function (PDF)
. In the present work, two issues relevant to such an approach are addressed. First, averaging of a dependence q(f), where q is an arbitrary quantity, e.g., the laminar flame speed S
L
, requires modeling of the canonical PDF P(f) if q is not proportional to the density
. Second, because the shape of
is not known a priori in a typical case, the presumed PDF approach can be a predictive tool only if the mean quantities
are weakly sensitive to the PDF shape. To study the two issues, dependencies of
and
, computed for gasoline surrogate-air mixtures under elevated temperatures and pressures, associated with the conditions in a gasoline direct injection spark ignition engine, are averaged invoking either beta function or double-Dirac delta function Favre or canonical PDFs. Moreover, a simpler approach is proposed to evaluate
. The approach consists of expanding
in Taylor series with respect to
, followed by averaging. The mean quantities
and
obtained for various Favre first
and second
moments using the aforementioned alternative methods are compared with each other and with
and
, respectively. The following conclusions are drawn. First, when averaging
under conditions of the present study, the difference between the Favre and canonical beta-function PDFs may be disregarded for simplicity. Second,
is sensitive to the shape of presumed PDF
if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently large. Third, if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently low in order for the mean laminar flame speeds obtained invoking the beta-function and double-Dirac delta-function PDFs to be approximately equal to one another, then,
can also be evaluated using the Taylor-expansion approach.
A simple model is proposed to evaluate (a) the divergence of velocity vector conditioned on unburned mixture, and (b) the vector component normal to the mean flame brush in the flamelet regime of ...premixed turbulent combustion. The model involves a single constant and does not invoke an extra balance equation. To perform the first test of the model, six flames stabilized in impinging jets and experimentally investigated by 4 research groups were numerically simulated. In the computations, (a) approximations of the measured axial profiles of the mean combustion progress variable were invoked, (b) the well-known (Bray et al.,
1998
, and
2000
) statistically steady and 1-dimensional Favre-averaged continuity and Euler equations were numerically integrated in order to approximate the measured axial profiles of the mean axial velocity, and, then, (c) the approximations were utilized in order to evaluate conditioned velocities and turbulent scalar flux using the proposed model supplemented with the BML approach and balance equation for the Favre-averaged combustion progress variable. The obtained agreement between the measured and computed axial profiles of the conditioned axial velocities or axial turbulent scalar flux was encouraging, thus, indicating that the proposed simple model is promising. Since the correlation between fluctuations of velocity and unity normal vectors, conditioned to flamelet surface, plays a key role in the model, the encouraging test results call for studying this correlation in future DNS. Moreover, further research into the difference in velocity conditioned on unburned mixture and velocity conditioned on the unburned side of flamelets is necessary for improving the model at the leading edge of a turbulent flame brush.
When a premixed flame propagates in a turbulent flow, not only does turbulence affect the burning rate (e.g., by wrinkling the flame and increasing its surface area), but also the heat release in the ...flame perturbs the pressure field, and these pressure perturbations affect the turbulent flow and scalar transport. For instance, the latter effects manifest themselves in the so-called countergradient turbulent scalar flux, which has been documented in various flames and has challenged the combustion community for approximately 35 years. Over the past decade, substantial progress has been made in investigating (
a
) the influence of thermal expansion in a premixed flame on the turbulent flow and turbulent scalar transport within the flame brush, as well as (
b
) the feedback influence of countergradient scalar transport on the turbulent burning rate. The present article reviews recent developments in this field and outlines issues to be solved in future research.
The influence of countergradient transport on the speed of a statistically stationary, planar, 1D premixed flame that propagates in frozen turbulence is studied theoretically and numerically by ...considering the normalised magnitude N
B
of the countergradient flux to be an input parameter. Spectra of admissible flame speeds are analytically determined and explicit travelling wave solutions are found for two algebraic relations widely used to close the mean rate of product creation. A problem of selecting the physically relevant solution that is approached for sufficiently steep initial conditions is addressed. It is argued that, if N
B
is larger than an analytically determined critical number N
cr
B
, then the type of the physically relevant solution is drastically changed. If N
B
< N
cr
B
, the physically relevant solution is of pulled wave type, i.e. its speed is controlled by processes localised to the leading edge of the flame brush and can be determined within the framework of a linear analysis at the leading edge. If N
B
> N
cr
B
, the physically relevant solution is of pushed wave type, i.e. its speed is controlled by processes in the entire flame brush. Analytical expressions for the speed of the physically relevant solution as a function of N
B
and the density ratio are obtained. For N
B
> N
cr
B
, the mean flame brush thickness and the spatial profile of the Favre-averaged combustion progress variable are also determined analytically. These results are validated by numerical simulations. Both analytical expressions and numerical data indicate that (i) both turbulent flame speed and thickness are decreased when N
B
is increased and (ii) the direction of total scalar flux (i.e. the sum of countergradient and gradient contributions) is strongly affected not only by N
B
, but also by the shape of the dependence of the mean rate of product creation on the mean combustion progress variable.
In order to experimentally study whether or not the density ratio
σ
substantially affects flame displacement speed at low and moderate turbulent intensities, two stoichiometric ...methane/oxygen/nitrogen mixtures characterized by the same laminar flame speed
S
L
= 0.36 m/s, but substantially different
σ
were designed using (i) preheating from
T
u
= 298 to 423 K in order to increase
S
L
, but to decrease
σ
, and (ii) dilution with nitrogen in order to further decrease
σ
and to reduce
S
L
back to the initial value. As a result, the density ratio was reduced from 7.52 to 4.95. In both reference and preheated/diluted cases, direct images of statistically spherical laminar and turbulent flames that expanded after spark ignition in the center of a large 3D cruciform burner were recorded and processed in order to evaluate the mean flame radius
R
̄
f
t
and flame displacement speed
S
t
=
σ
−
1
d
R
̄
f
dt
with respect to unburned gas. The use of two counter-rotating fans and perforated plates for near-isotropic turbulence generation allowed us to vary the rms turbulent velocity
u
′
by changing the fan frequency. In this study,
u
′
was varied from 0.14 to 1.39 m/s. For each set of initial conditions (two different mixture compositions, two different temperatures
T
u
, and six different
u
′
)
, five (respectively, three) statistically equivalent runs were performed in turbulent (respectively, laminar) environment. The obtained experimental data do not show any significant effect of the density ratio on
S
t
. Moreover, the flame displacement speeds measured at
u
′/
S
L
= 0.4 are close to the laminar flame speeds in all investigated cases. These results imply, in particular, a minor effect of the density ratio on flame displacement speed in spark ignition engines and support simulations of the engine combustion using models that (i) do not allow for effects of the density ratio on
S
t
and (ii) have been validated against experimental data obtained under the room conditions, i.e. at higher
σ
.
The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001 is ...generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.
A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is ...performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.
The statistics of fluid velocity components conditional in unburned reactants and fully burned products in the context of Reynolds Averaged Navier Stokes (RANS) simulations have been analysed using a ...Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames for both high and low values of Damköhler number for different values of heat release parameter. It has been found that the contributions arising from chemical reaction to the conditional mean velocities and the conditional Reynolds stresses remain strong under high values of Damköhler number. The expressions for conditional mean velocity components and conditional Reynolds stresses, which are derived based on bi-modal probability density function of reaction progress variable for unity Lewis number flames, are modified in this study in such a manner that the new expressions can be used for low Damköhler number flames where bi-modal distribution is not realised. Suitable models for conditional surface-averaged velocity components and the Reynolds stresses have been identified, which are shown to work satisfactorily for all values of Damköhler number and heat release parameter considered in this analysed.
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