“…, the self-similar form of should be The proposed scaling for results in a collapse of the instantaneous profiles on the self-similar form for in (6.3), suggesting that the scaling is consistent with the DNS data. Additionally, these results agree with the findings from Kulkarni & Bisetti (2021), who found that the turbulent transport term (normalized by ) scales with the integral length scale of the flow.…”
Section: Self-similarity Of Transport Termssupporting
confidence: 91%
“…the error is likely statistical in nature, not systematic. Notably, the scaling proposed here does not agree with the scaling proposed by Kulkarni & Bisetti (2021), who suggest that would scale in the same manner as and . Figure 16.Proposed self-similar scaling of from (6.18), conditioned on ( a ) and ( b ) , as functions of the similarity variable .…”
Section: Self-similarity Of Transport Termscontrasting
confidence: 60%
“…2019; Neamtu-Halic et al. 2020; Kulkarni & Bisetti 2021). This, coupled with the similarity to and above, might suggest that the total iso-surface area is independent of the mixing layer width, i.e.…”
Section: Behaviour Of the Terms In The Iso-surface Area Density Trans...mentioning
confidence: 99%
“…Consider the term responsible for production of iso-surface area due to the fluid strain rate . Self-similar scaling for this term can be deduced by considering that the correlation tangential strain rate of the scalar field, , has been shown to scale with the mean turbulent strain rate (Poinsot & Veynante 2005; Kulkarni & Bisetti 2021). Based on the definition of the transverse Taylor length scale in (4.7), and noting that in the present temporal mixing layer, it can be shown that .…”
Section: Self-similarity Of Transport Termsmentioning
confidence: 99%
“…In a recent study of spherically expanding premixed flames, Kulkarni & Bisetti (2021) examined the evolution of the peak value of mean flame surface area density, , as a function of time and Reynolds number. The resulting analysis suggested that primary contributions to the rate of change of include: the mean velocity field, found to scale with the pressure rise of the flame; the turbulent velocity field, found to scale with the integral length of the flow, ; and the net surface ‘stretch’ (i.e.…”
In this study, the transport equation for scalar iso-surface area density (
$\varSigma$
) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the
$\varSigma$
transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that
$\varSigma$
exhibits self-similar behaviour consistent with the development of the temporal mixing layer (Blakeley et al., J. Fluid Mech., vol. 951, 2022, A44). Accordingly, each of the terms in the
$\varSigma$
transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of
$\varSigma$
(
$\partial \varSigma /\partial t$
) and the advection term scale with
$h\lambda _\varPhi /\Delta U$
, where
$h$
is the width of the mixing layer,
$\lambda _\varPhi$
is the scalar Taylor length scale and
$\Delta U$
is the velocity difference. The production and destruction terms are found to scale with an additional factor
$({Re}\,Sc)^{1/2}$
. In contrast, the molecular diffusion term is found to scale with a factor
$({Re}\,Sc)^{-1/2}$
compared to
$\partial \varSigma /\partial t$
. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as
$\partial \varSigma /\partial t$
and the advection term, which may have a significant impact on how the evolution of
$\varSigma$
is understood and modelled in turbulent flows.
“…, the self-similar form of should be The proposed scaling for results in a collapse of the instantaneous profiles on the self-similar form for in (6.3), suggesting that the scaling is consistent with the DNS data. Additionally, these results agree with the findings from Kulkarni & Bisetti (2021), who found that the turbulent transport term (normalized by ) scales with the integral length scale of the flow.…”
Section: Self-similarity Of Transport Termssupporting
confidence: 91%
“…the error is likely statistical in nature, not systematic. Notably, the scaling proposed here does not agree with the scaling proposed by Kulkarni & Bisetti (2021), who suggest that would scale in the same manner as and . Figure 16.Proposed self-similar scaling of from (6.18), conditioned on ( a ) and ( b ) , as functions of the similarity variable .…”
Section: Self-similarity Of Transport Termscontrasting
confidence: 60%
“…2019; Neamtu-Halic et al. 2020; Kulkarni & Bisetti 2021). This, coupled with the similarity to and above, might suggest that the total iso-surface area is independent of the mixing layer width, i.e.…”
Section: Behaviour Of the Terms In The Iso-surface Area Density Trans...mentioning
confidence: 99%
“…Consider the term responsible for production of iso-surface area due to the fluid strain rate . Self-similar scaling for this term can be deduced by considering that the correlation tangential strain rate of the scalar field, , has been shown to scale with the mean turbulent strain rate (Poinsot & Veynante 2005; Kulkarni & Bisetti 2021). Based on the definition of the transverse Taylor length scale in (4.7), and noting that in the present temporal mixing layer, it can be shown that .…”
Section: Self-similarity Of Transport Termsmentioning
confidence: 99%
“…In a recent study of spherically expanding premixed flames, Kulkarni & Bisetti (2021) examined the evolution of the peak value of mean flame surface area density, , as a function of time and Reynolds number. The resulting analysis suggested that primary contributions to the rate of change of include: the mean velocity field, found to scale with the pressure rise of the flame; the turbulent velocity field, found to scale with the integral length of the flow, ; and the net surface ‘stretch’ (i.e.…”
In this study, the transport equation for scalar iso-surface area density (
$\varSigma$
) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the
$\varSigma$
transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that
$\varSigma$
exhibits self-similar behaviour consistent with the development of the temporal mixing layer (Blakeley et al., J. Fluid Mech., vol. 951, 2022, A44). Accordingly, each of the terms in the
$\varSigma$
transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of
$\varSigma$
(
$\partial \varSigma /\partial t$
) and the advection term scale with
$h\lambda _\varPhi /\Delta U$
, where
$h$
is the width of the mixing layer,
$\lambda _\varPhi$
is the scalar Taylor length scale and
$\Delta U$
is the velocity difference. The production and destruction terms are found to scale with an additional factor
$({Re}\,Sc)^{1/2}$
. In contrast, the molecular diffusion term is found to scale with a factor
$({Re}\,Sc)^{-1/2}$
compared to
$\partial \varSigma /\partial t$
. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as
$\partial \varSigma /\partial t$
and the advection term, which may have a significant impact on how the evolution of
$\varSigma$
is understood and modelled in turbulent flows.
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