Extensive Principal Strain Rate Research Articles

Effects of dilatation and turbulence on tangential strain rates in premixed hydrogen and iso-octane flames

The tangential strain rate in premixed flames impacts significantly the flame surface area generation and thus the combustion process. Studies on incompressible isotropic turbulence have revealed that the mean tangential strain rate at material and iso-scalar surfaces is positive and exhibits a universal value when normalized by the Kolmogorov time. This is associated with the preferential alignment of the surface normal with the most compressive principal strain rate. The present study investigates such effects in premixed hydrogen and iso-octane flame kernels using direct numerical simulations. It is shown that the normalized mean tangential strain rate of the investigated flames has a very similar value compared with the incompressible flows. However, in the reaction zone, the flame surface normal aligns preferentially with the most extensive principal strain rate. Furthermore, this alignment depends on the reaction progress variable and the Lewis number, while the tangential strain rate remains independent of these parameters. Such counter-intuitive behaviour is systematically investigated by decomposing the effects of dilatation and residual solenoidal turbulence. It is found that the solenoidal turbulence influences significantly the tangential strain rate. A general effect of turbulence on the tangential strain rate is identified, which is consistent with incompressible flows and independent of the Lewis number and the reaction progress variable. This is a remarkable finding indicating that models of the tangential strain rate developed based on incompressible flows apply also to premixed flames with different Lewis numbers, and, for the modelling, only the solenoidal turbulence should be considered.

Alignment statistics of pressure Hessian with strain rate tensor and reactive scalar gradient in turbulent premixed flames

The relative alignment of the eigenvectors of pressure Hessian with reactive scalar gradient and strain rate eigenvectors in turbulent premixed flames have been analyzed for Karlovitz number values ranging from 0.75 to 126 using a detailed chemistry three-dimensional direct numerical simulations database of H2–air premixed flames. The reactive scalar gradient preferentially aligns with the most extensive strain rate eigendirection for large Damköhler number and small Karlovitz number values, whereas a preferential collinear alignment between the reactive scalar gradient with the most compressive strain rate eigendirection is observed in flames with small Damköhler number and large Karlovitz number. By contrast, the eigenvectors of pressure Hessian do not perfectly align with the reactive scalar gradient, and the net effect of the pressure Hessian on the evolution of the normal strain rate contribution to the scalar dissipation rate transport acts to reduce the scalar gradient in the zone of high dilatation rate. The eigenvectors of pressure Hessian and the strain rate are aligned in such a manner that the contribution of pressure Hessian to the evolution of principal strain rates tends to augment the most extensive principal strain rate for small and moderate values of Karlovitz numbers, whereas this contribution plays an important role for the evolution of the intermediate principal strain rate for large values of Karlovitz number. As the reactive scalar gradient does not align with the intermediate strain rate eigenvector, the influence of pressure Hessian contributions to the scalar–turbulence interaction remains weak for large values of Karlovitz number.

Principal strain rate evolution within turbulent premixed flames for different combustion regimes

The statistical behaviors of the principal strain rates and its evolution in turbulent premixed flames have been analyzed using a three-dimensional direct numerical simulations dataset of statistically planar turbulent premixed flames with different turbulence intensities spanning from the corrugated flamelet regime to the thin reaction zone regime. It has been found that the scalar gradient predominantly aligns collinearly with the most extensive principal strain rate eigendirection within the flame for large values of Damköhler numbers and small values of turbulence intensities and Karlovitz numbers. However, this tendency weakens with the increasing turbulence intensity, which, for a given integral length scale, amounts to a decrease (an increase) in the Damköhler (Karlovitz) number. Moreover, it has been observed that the terms due to molecular diffusion, pressure Hessian, and the correlation between pressure and density gradients play key roles in the evolution of principal strain rates for flames with large values of Damköhler numbers and small values of Karlovitz numbers. However, the relative importance of the terms arising from the correlation between pressure and density gradients and the pressure Hessian relative to the strain rate and vorticity contributions of the principal strain rate transport diminishes with the increasing Karlovitz number and decreasing Damköhler number. The statistical behaviors of the mean values of the terms of the transport equation of the principal strain rate have been explained based on the relative alignments of principal strain rate eigenvectors with vorticity, pressure gradient, and the eigenvectors of the pressure Hessian tensor. The findings of the current analysis suggest that the pressure gradient and pressure Hessian tensor play key roles in the evolution of principal strain rates within premixed turbulent flames, and their influence needs to be accounted for high fidelity modeling of the tangential strain rate and scalar–turbulence interaction terms of the flame surface density and scalar dissipation rate transport equations, respectively. This provides possible explanations for the modification in the alignment of the reactive scalar gradient with local principal strain rates in premixed flames in comparison to that in non-reacting turbulent flows.

Surface density function evolution and the influence of strain rates during turbulent boundary layer flashback of hydrogen-rich premixed combustion

The statistical behavior of the magnitude of the reaction progress variable gradient [alternatively known as the surface density function (SDF)] and the strain rates, which govern the evolution of the SDF, have been analyzed for boundary layer flashback of a premixed hydrogen-air flame with an equivalence ratio of 1.5 in a fully developed turbulent channel flow. The non-reacting part of the channel flow is representative of the friction velocity based Reynolds number Reτ = 120. A skeletal chemical mechanism with nine chemical species and twenty reactions is employed to represent hydrogen-air combustion. Three definitions of the reaction progress variable (RPV) based on the mass fractions of H2, O2, and H2O have been considered to analyze the SDF statistics. It is found that the mean variations of the SDF and the displacement speed Sd depend on the choice of the RPV and the distance away from the wall. The preferential alignment of the RPV gradient with the most extensive principal strain rate strengthens with an increase in distance from the cold wall, which leads to changes in the behaviors of normal and tangential strain rates from the vicinity of the wall toward the middle of the channel. The differences in displacement speed statistics for different choices of the RPV and the wall distance affect the behaviors of the normal strain rate due to flame propagation and curvature stretch. The relative thickening/thinning of the reaction layers of the major species has been explained in terms of the statistics of the effective normal strain rate experienced by the progress variable isosurfaces for different wall distances and choices of RPVs.

Insights into the Bending Effect in Premixed Turbulent Combustion Using the Flame Surface Density Transport

ABSTRACTThe bending effect of turbulent flame speed variation (i.e., the deviation from the linear increase of flame speed with increasing root-mean-square turbulent velocity fluctuation) has been investigated based on a Direct Numerical Simulation database of statistically planar turbulent premixed flames propagating into forced unburned gas turbulence. The validity of Damköhler’s first hypothesis has been utilized to analyze the bending effect in terms of generalized Flame Surface Density (FSD) evolution. The volume-integrated value of the tangential strain rate term of the FSD transport equation remains positive, whereas the volume-integrated value of the curvature term assumes negative values. Under statistically stationary state, the positive value of the volume-integrated tangential strain rate term remains in equilibrium with the negative value of the volume-integrated curvature term. It has been found that the contribution of the normal strain rate to the flame surface area remains negative for small turbulence intensities, which eventually become positive for large turbulence intensities. This is a consequence of the change of collinear alignment of the reaction progress variable gradient from the most extensive principal strain rate direction to the direction of the eigenvector associated with the most compressive principal strain rate with increasing turbulence intensity. An increase in turbulence intensity increases the width of the probability density functions of flame curvature, and thereby increases the surface-averaged curvature squared values. This eventually makes the FSD curvature term due to the tangential diffusion component of displacement speed as the major contributor to the negative contribution of the volume-integrated curvature term in the FSD transport equation for large turbulence intensities. However, the negative contribution of the volume-integrated FSD curvature term does not increase indefinitely with increasing turbulence intensity and the inner cut-off scale, which also limits the maximum possible value of the volume-integrated FSD strain rate term under statistically stationary state, governs the maximum possible destruction of flame surface area. It has been argued that the upper limits of the flame surface area generation and destruction are responsible for the bending effects in the variations of turbulent flame speed and flame surface area.

Effects of heat release and imposed bulk strain on alignment of strain rate eigenvectors in turbulent premixed flames

The impact of combustion heat release and bulk compressive strain on local alignment between the flame front normal and strain rate eigenvectors (principal strain rates) are investigated using simultaneous laser-induced fluorescence imaging of OH and tomographic particle image velocimetry in turbulent premixed CH4/O2/N2 counterflow flames with Karlovitz numbers (Ka) of 1.3 and 2.7. The bulk strain rate imposed by the counterflow introduces a preferential alignment of the most compressive principal strain rate, s3, with the flame normal, n. Dilatation induced by heat release acts as a competing mechanism that promotes the alignment of the most extensive principal strain rate, s1, with n. In the counterflow flames, the preferential s3-n alignment prevails and remains dominant across the entire flame. This alignment stands in stark contrast to observations from previous studies in turbulent Bunsen flames or flames in isotropic turbulence, indicating the significance of bulk strain rate in determining local strain-flame alignment. The effects of increasing turbulence intensity on strain rate-flame front alignment are twofold; on the one hand, turbulence diminishes the s3-n preferential alignment that is associated with the bulk strain field by increasing flame surface wrinkling and reducing the tendency of the flame front normal and s3-eigenvectors to align with the axis of the counterflow. On the other hand, turbulence reduces the impact of heat release and enhances preferential s3-n alignment approximately 1 mm ahead of the flame front, reflecting the characteristic alignment of compressive strain and scalar gradients in turbulent non-reacting flows. The effects of bulk strain are also observed in strain rate alignment statistics based on the fluctuating velocity fields, although the impact is less pronounced than for the statistics based on the full velocity fields.As a result of this complex interplay between heat release, turbulence, and bulk strain rate, the flame-tangential strain rate is on average extensive, and the flame-normal strain rate is dominantly compressive except for an approximately 0.8 mm wide region near the flame front where it is extensive due to dilatation. The compressive bulk strain in the counterflow was also shown to compress the length scales over which the strain rate and its alignment are affected by flame heat release. The present finding is important for developing turbulent flame models to accommodate the effect of bulk strain rate that is inherently associated with practical burner geometries, and the length scale dependence of the bulk strain effect could be a consideration for determining the cutoff scale in the context of large-eddy simulations.

Scale locality of the energy cascade using real space quantities

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighboring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Reλ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales, allowing one to determine the fluxes between these scales and to interrogate the role of nonlocal (in physical space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale Lω are stretched mostly by straining structures of size 3Lω to 5Lω, and the stretching by eddies of sizes larger than 10Lω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Reλ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.

Life of flame particles embedded in premixed flames interacting with near isotropic turbulence

Flame particles are surface points that always remain embedded on, by comoving with a given iso-scalar surface within a flame. Tracking flame particles allow us to study the fate of propagating surface locations uniquely identified throughout their evolution with time. In this work, using Direct Numerical Simulations we study the finite lifetime of such flame particles residing on iso-temperature surfaces of statistically planar H2–air flames interacting with near-isotropic turbulence. We find that individual flame particles as well as their ensemble, experience progressively increasing tangential straining rate (Kt) and increasing negative curvature (κ) near the end of their lifetime to finally get annihilated. By studying two different turbulent flow conditions, flame particle tracking shows that such tendency of local flame surfaces to be strained and cusped towards pinch-off from the main surface is a rather generic feature, independent of initial conditions, locations and ambient turbulence intensity levels. The evolution of the alignments between the flame surface normals and the principal components of the local straining rates are also tracked. We find that the surface normals initially aligned with the most extensive principal strain rate components, rotate near the end of flame particles’ lifetime to enable preferential alignment between the surface tangent and the most extensive principal strain rate component. This could explain the persistently increasing tangential strain rate, sharp negative curvature formation and eventual detachment.

On the alignment of fluid-dynamic principal strain-rates with the 3D flamelet-normal in a premixed turbulent V-flame

Statistics of the alignment of fluid-dynamic principal strain-rates and the local flamelet-normal in a premixed turbulent V-flame (methane-air, Ret=450, φ=0.8) were measured experimentally using simultaneous stereoscopic particle image velocimetry (SPIV) and planar laser-induced fluorescence of OH (OH-PLIF). The use of a second OH-PLIF sheet, oriented in a crossed-plane imaging configuration enabled conditioning of the statistics with respect to through-plane flame orientation. The statistics show the geometric alignment changes significantly with the distance between the flame and the location where the strain-rate field is evaluated. It was observed that approximately 30η upstream of the flame, the fluid-dynamic principal strain-rates show no preferential alignment with the flamelet. With increasing proximity to the flame, the most extensive principal strain-rate is observed to align preferentially perpendicular to the local flamelet-normal. In the immediate vicinity of the flame, where local fluid-dynamics are dominated by dilatation, the principal extensive strain-rate is observed to align preferentially parallel to the local flamelet-normal. The realignment of the principal strain-rates in the immediate vicinity of the flame is clearly the result of local flow acceleration caused by heat-release at the reaction zone. As the most extensive principal strain-rate tends to align preferentially perpendicular to the local flamelet-normal outside the region of heat-release, the data indicate that high scalar gradients observed ahead of the flamelet are produced by the local turbulent flow-field, rather than destroyed by it.

INVESTIGATION OF FLAME STRETCH IN TURBULENT LIFTED JET FLAME

DNS data of a laboratory-scale turbulent lifted hydrogen jet flame has been analyzed to show that this flame has mixed mode combustion not only at the flame base but also in downstream locations. The mixed mode combustion is observed in instantaneous structures as in earlier studies and in averaged structure, in which the predominant mode is found to be premixed combustion with varying equivalence ratio. The non-premixed combustion in the averaged structure is observed only in a narrow region at the edge of the jet shear layer. The analyzes of flame stretch show large probability for negative flame stretch leading to negative surface averaged flame stretch. The displacement speed-curvature correlation is observed to be negative contributing to the negative flame stretch and partial premixing resulting from jet entrainment acts to reduce the negative correlation. The contribution of turbulent straining to the flame stretch is observed to be negative when the scalar gradient aligns with the most extensive principal strain rate. The physics behind the negative flame stretch resulting from turbulent straining is discussed and elucidated through a simple analysis of the flame surface density transport equation.

Alignment statistics of active and passive scalar gradients in turbulent stratified flames

The scalar gradient alignment statistics for active and passive scalar gradients (e.g., fuel mass fraction gradient and mixture fraction gradient) are presented here for turbulent stratified flames. It has been shown that, under some conditions, the active scalar gradient may align with the most extensive principal strain rate in contrast to the passive scalar gradient that remains aligned with the most compressive principal strain rate even when the active scalar gradient aligns preferentially with the most extensive principal strain rate. Physical explanations are provided for the observed behaviors.

The Scalar Gradient Alignment Statistics of Flame Kernels and its Modelling Implications for Turbulent Premixed Combustion

The effects of mean flame curvature on reaction progress variable gradient, \(\nabla c\), alignment with local turbulent strain rate are studied based on three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame kernels with different initial radii under decaying turbulence. A statistically planar flame is also considered in order to compare the results obtained from the kernels with a flame of zero mean curvature. It is found that the dilatation rate effects diminish with decreasing kernel radius due to defocusing of heat in the positively curved regions. This gives rise to a decrease in the extent of reaction progress variable gradient alignment with most extensive principal strain rate with decreasing kernel radius. The modelling implications of the statistics of the alignment of \(\nabla c\) with local strain rate have been studied in terms of scalar dissipation rate transport. A new modelling methodology for the contribution of the scalar-turbulence interaction term in the transport equation for the mean scalar dissipation is suggested addressing the reduced effects of dilatation rate for flame kernels and the diminished value of turbulent straining at the small length scales at which turbulence interacts with small flame kernels. The performance of the new models is found to be satisfactory while comparing to DNS results. The existing models for the dilatation contribution and the combined chemical reaction and molecular dissipation contributions to the transport of mean scalar dissipation, which were originally proposed for statistically planar flames, are found to satisfactorily predict the corresponding quantities for turbulent flame kernels.

Effects of Lewis number on the reactive scalar gradient alignment with local strain rate in turbulent premixed flames

The effects of Lewis number Le on the reactive scalar gradient alignment with the local strain rate have been studied using Direct Numerical Simulation data of freely propagating statistically planar turbulent premixed flames with Le ranging from 0.34 to 1.2. The alignment characteristics of the reaction progress variable gradient are explained using the statistics of dilatation rate, and flame normal and tangential strain rates. The strength of dilatation rate is shown to increase with decreasing Le and this effect becomes particularly strong for the flames with Le<1 because of thermo-diffusive instability. The dilatation rate is shown to be responsible for the preferential alignment of the reactive scalar gradient with the most extensive principal strain rate in the reaction zone for flames with Le close to unity, contrary to the alignment of scalar gradient with the most compressive principal strain rate in turbulent passive scalar transport. However, stronger dilatation rate effects in Le≪1 flames (e.g. Le=0.34) gives rise to the preferential alignment of the reactive scalar gradient with the most extensive principal strain rate for the major portion of the flame-brush. The scalar gradient alignment with local strain rate plays an important role in the transport of scalar dissipation rate and the flame surface density. The observed alignment with the most extensive principal strain rate destroys the scalar gradient and the magnitude of this sink is found to increase with decreasing Lewis number for a given turbulent Reynolds number and Damköhler number.

Influence of the Damköhler number on turbulence-scalar interaction in premixed flames. I. Physical insight

Scalar dissipation rate is a central quantity in turbulent flame modeling as it is closely related to the reaction rate. It is well known that turbulence-scalar interaction plays a vital role in turbulent flows with scalar mixing and thus on the scalar dissipation rate. This interaction process is characterized by the tensor inner product between the scalar gradient vector and the turbulence strain rate tensor and it is found to depend strongly on the Damköhler number, Da. Two direct numerical simulation data sets are analyzed in detail in order to understand the physics of Da dependence. The well known alignment of scalar gradient with the most compressive principal strain rate resulting in production of the scalar gradient by turbulence is observed for low (Da&amp;lt;1) Damköhler number flame, whereas the turbulence dissipates the scalar gradient in high Da flame. This dissipation of the scalar gradient in the high Da flame is because of its preferential alignment with the most extensive principal strain rate. Even for Da&amp;lt;1 flame, in the regions of intense heat release the scalar gradient has a tendency to align with the most extensive strain rate. This distinct change is because of strong competition between chemical strain rate, due to dilatation from the flame front and the local fluid dynamic strain rate. The alignment characteristics affect flame normal and tangential strain rate statistics. The flame normal strain rate is found to be positive throughout the flame brush when Da&amp;gt;1, whereas it is predominantly negative when Da&amp;lt;1. Despite this difference the mean tangential strain rate remains positive yielding flame surface area production. However, the production results via different physical mechanisms. Possible implications of these differences on the modeling of turbulent premixed flames are identified and explained.

Interaction of turbulence and scalar fields in premixed flames

The interaction of turbulence with progress variable, c, field in a premixed flame is studied. This interaction is characterized by the correlation c,ieijc,j¯, where the overbar denotes an appropriate averaging process, c,i is the gradient of c in spatial direction i and eij is the turbulence strain rate. The importance of this term is recognized via a transport equation for the square of the magnitude of the scalar gradient in turbulent premixed flames. It is also shown that the above correlation forms a natural part of the tangential strain rate which appears in the flame surface density, Σ, equation. It is well known that this correlation is negative signifying the scalar gradient production by incompressible turbulence via the preferential alignment of the scalar gradient with the most compressive principal strain rate. This physical picture is commonly adopted for turbulent premixed flames also. Contrary to this, analyses of direct numerical simulation data for a turbulent premixed flame having flamelet combustion characteristics show the preferential alignment of the scalar gradient with the most extensive principal strain rate. This preferential alignment is because of flame influence on the flow via dilation. The above alignment pulls the isoscalar surfaces from each other yielding positive values for the above correlation inside the flame brush. Thus the turbulence, in addition to the molecular dissipation process, dissipates the scalar gradients in premixed flames when the Damköhler number (Da) is large. These dissipation processes are counteracted by chemical reactions which produce the scalar gradients. A simple RANS model for the above correlation is obtained by decomposing it into contributions from flame front and nonflame front regions of the flow as suggested by the DNS results. The model obtained here involves Da and represents the dissipation of the scalar gradients by the turbulence when Da is larger than unity. This model also recovers the production of the scalar gradient by the turbulence when Da is less than unity. Comparison of this model prediction with the DNS data of large Da flame is reasonable. The turbulence-scalar interaction in low and moderate Damköhler number flames still needs to be explored.