Strain Rate Eigenvectors Research Articles

Turbulence Effects on the Statistical Behaviour and Modelling of Flame Surface Density and the Terms of Its Transport Equation in Turbulent Premixed Flames

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

Lagrangian model for passive scalar gradients in turbulence

The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier–Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. A recent model handles these unclosed terms using a multi-level version of the recent deformation of Gaussian fields (RDGF) closure (Johnson & Meneveau, Phys. Rev. Fluids, vol. 2 (7), 2017, 072601). This model is in remarkable agreement with direct numerical simulations (DNS) data and works for arbitrary Taylor Reynolds numbers $\textit {Re}_\lambda$ . Inspired by this, we develop a Lagrangian model for passive scalar gradients in isotropic turbulence. The equation for passive scalar gradients also involves an unclosed term in the Lagrangian frame, namely the scalar gradient diffusion term, which we model using the RDGF approach. However, comparisons of the statistics obtained from this model with DNS data reveal substantial errors due to erroneously large fluctuations generated by the model. We address this defect by incorporating into the closure approximation information regarding the scalar gradient production along the local trajectory history of the particle. This modified model makes predictions for the scalar gradients, their production rates, and alignments with the strain-rate eigenvectors that are in very good agreement with DNS data. However, while the model yields valid predictions up to $\textit {Re}_\lambda \approx 500$ , beyond this, the model breaks down.

The role of breakup and coalescence in fine-scale bubble-induced turbulence. II. Kinematics

This second part of our research explores the kinematic aspect of fine-scale bubble-induced turbulence (BIT) to (i) present the effect of bubble breakup and coalescence and (ii) compare it against the universal kinematic fine-scale turbulence characteristics reported in the literature. To this end, we simulate a dilute bubbly system of 0.5% void fraction using two distinct numerical simulations. In the volume-of-fluid (VoF) simulation, bubbles undergo breakup and coalescence. In the immersed boundary method (IBM) simulation, however, they act as rigid spheres. We also perform a simulation of classical homogeneous isotropic turbulence (HIT). The first important outcome of this study is that BIT is radically different from HIT in terms of its kinematic fine-scale characteristics. In the vorticity-dominating regions, BIT exhibits a weak vortex stretching. This weak vortex stretching is due to (a) the intermediate strain-rate eigenvalues skewed weakly to positive and (b) the extensive strain-rate eigenvector aligning perpendicular to the vorticity vector. The BIT has, on average, not only a weak enstrophy production but also a weak strain production in strain-dominating regions. The weak strain production is due to (a) the presence of vortex stretching in highly strained fluid elements and (b) the absolute magnitude of compressive strain-rate eigenvalue being as close to the extensive strain-rate eigenvalue. Thus, none of the kinematic fine-scale HIT characteristics is noted for BIT. The second important conclusion is that bubble breakup and coalescence play little to no influence on the kinematics of fine-scale BIT as VoF and IBM simulations produce similar results.

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.

Non-normal effect of the velocity gradient tensor and the relevant subgrid-scale model in compressible turbulent boundary layer

The non-normal effects of the velocity gradient tensor (VGT) in a compressible turbulent boundary layer are studied by means of the Schur decomposition of the VGT into its normal and non-normal parts. Based on the analysis of the relative importance of them, it is found that the non-normal part significantly affects the dynamics of the VGT in the wall-bounded turbulent flow and the relevant non-normal effect has a dominant influence on the enstrophy and dissipation. It is revealed that the deviatoric part of the pressure Hessian is associated with the non-normal effect and the isotropic part is associated with the normal effect. The pressure Hessian significantly influences the vortex stretching. The non-normal effect reinforces the preferences for the vorticity vector to align with the intermediate strain-rate eigenvector and to be perpendicular to the extensive and compressive strain-rate eigenvector in the near-wall region. The non-normal effect also reduces the intermediate eigenvalue of the strain-rate tensor. Furthermore, a subgrid scale (SGS) model that separately considers the normal and non-normal effects is proposed based on the above characters and is verified to give a better prediction of the SGS dissipations in the wall-bounded turbulent flow.

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.

Modeling the pressure-Hessian tensor using deep neural networks

The pressure-Hessian tensor (PHT) is an important factor governing the Lagrangian evolution of velocity gradients in turbulent flows. To help develop a physically consistent model for PHT, we train a tensor basis neural network (TBNN) using velocity gradient information as input. Our trained model is found to be superior to existing models, not just in terms of root-mean-squared error, but also for capturing PHT physical attributes. Our model retrieves almost identical alignment statistics between the pressure-Hessian and the strain-rate eigenvectors when compared with well established direct numerical simulation (DNS) datasets.

Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor (Aij) into the symmetric strain-rate (Sij) and anti-symmetric rotation-rate (Wij) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate (Nij), pure-shear (Hij) and rigid-body-rotation-rate (Rij). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants’ space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude (A2 ≡ AijAij). Especially, shear contribution is dominant in regions of high values of A2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.

Parametric numerical study of passive scalar mixing in shock turbulence interaction

Turbulent mixing of passive scalars is studied in the canonical shock–turbulence interaction configuration via shock-capturing direct numerical simulations, varying the shock Mach number ( ), turbulence Mach number ( ), Taylor microscale Reynolds number ( ) and Schmidt number ( , 1, 2). The shock-normal evolution of scalar variance and dissipation transport equations, spectra and probability density functions (PDFs) are examined. Scalar dissipation, its production and destruction increase across the shock with higher , lower and lower . Mixing enhancement for different flow topologies across the shock is studied from changes in the PDFs of velocity gradient tensor invariants and conditional distributions of scalar dissipation. The proportion of the stable-focus-stretching flow topology is the highest among all the topologies in the flow both before and after the shock. Unstable-node/saddle/saddle topology is the most dissipative throughout the flow domain, despite variations across the shock. Preshock and postshock distributions of the alignment between the strain-rate tensor eigenvectors and the scalar gradient, vorticity and the mean streamwise vector conditioned on flow topology are studied. A novel barycentric map representation is introduced for a more direct visualization of the alignments and conditioned scalar dissipation distributions. Interaction with the shock increases alignment of the scalar gradient with the most extensive eigenvector, decreasing it with the most compressive, which is still dominant. The barycentric map of the passive scalar gradient also reveals that, across the shock, the most probable alignment between scalar gradient and strain eigendirections converges towards the alignment that provides the most dissipation. This also leads to an enhancement of scalar dissipation immediately downstream of the shock.

Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry

This study develops a comprehensive description of local streamline geometry and uses the resulting shape features to characterize velocity gradient ( ) dynamics. The local streamline geometric shape parameters and scale factor (size) are extracted from by extending the linearized critical point analysis. In the present analysis, is factorized into its magnitude ( ) and normalized tensor . The geometric shape is shown to be determined exclusively by four parameters: second invariant, ( ); third invariant, ( ); intermediate strain rate eigenvalue, ; and vorticity component along intermediate strain rate eigenvector, . Velocity gradient magnitude, , plays a role only in determining the scale of the local streamline structure. Direct numerical simulation data of forced isotropic turbulence ( ) is used to establish streamline shape and scale distribution, and then to characterize velocity-gradient dynamics. Conditional mean trajectories (CMTs) in – space reveal important non-local features of pressure and viscous dynamics which are not evident from the -invariants. Two distinct types of – CMTs demarcated by a separatrix are identified. The inner trajectories are dominated by inertia–pressure interactions and the viscous effects play a significant role only in the outer trajectories. Dynamical system characterization of inertial, pressure and viscous effects in the – phase space is developed. Additionally, it is shown that the residence time of – CMTs through different topologies correlate well with the corresponding population fractions. These findings not only lead to improved understanding of non-local dynamics, but also provide an important foundation for developing Lagrangian velocity-gradient models.

Vorticity gradient stretching in the direct enstrophy transfer process of two-dimensional turbulence

In two-dimensional turbulence enstrophy is injected at the forcing scale and transferred down to the dissipative scale where viscosity dominates. On intermediate scales the forward enstrophy cascade is accompanied by a stretching of the vorticity gradient (VG) at the strain rate (SR), resulting in a preferential orthogonality between the VG and the stretching direction. In a coordinate system formed by the SR eigenvectors at a fixed time, we find that the VG statistically turns toward the direction perpendicular to the eigenvector corresponding to the stretching, as shown in the figure.

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.

Structures of turbulent premixed flames in the high Karlovitz number regime – DNS analysis

Lean premixed turbulent methane-air flames have been investigated using direct numerical simulations (DNS) for different Karlovitz numbers (Ka), ranging from 65 to 3350. The flames are imposed to a high intensity small-scale turbulent environment, corresponding to high Ka conditions, and the effect on the flame structure is investigated during the transition from initial laminar flame to highly distorted turbulent flame. The focus is on the internal structure of different sub-layers of these flames. The preheat layer, fuel consumption layer and oxidation layer are characterized by the distribution of formaldehyde, the fuel consumption rate and the CO consumption rate, respectively. Different measures that quantify sub-layer thickness for turbulent flames have been defined and analyzed. The flame brush is broadened with time while the local thickness (excluding large scale wrinkling) of all three layers initially show thinning due to the interaction of the flame with the turbulent flow field. As time passes, the local thickness of the preheat layer and fuel consumption layer are restored while the oxidation layer remains thinned due to suppression of CO consuming reactions. As Ka increases there is an increasing probability of finding thinned, large gradient regions in each of these sub-layers. The contribution to the evolution of flame thickness from normal strain rate, chemical reaction and normal and tangential diffusion is analyzed in terms of a gradient transport equation. The relative size of the terms changes as Ka increase and, in particular, the term due to chemical reactions loses its relative significance. The observed thinning of the local flame structure is attributed to the preferential alignment of the flame normal with the compressive strain rate eigenvectors. Such alignment provides a mechanism for the flame thinning, consistent with the behavior of non-reacting scalars. A preferred angle of about 20 degrees is observed between the flame normal and the compressive strain rate eigenvector.

Lagrangian investigations of vorticity dynamics in compressible turbulence

In this work, we investigate the influence of compressibility on vorticity-strain rate dynamics. Well-resolved direct numerical simulations of compressible homogeneous isotropic turbulence performed over a cubical domain of 10243 are employed for this study. To clearly identify the influence of compressibility on the time-dependent dynamics (rather than on the one-time flow field), we employ a well-validated Lagrangian particle tracker. The tracker is used to obtain time correlations between the instantaneous vorticity vector and the strain-rate eigenvector system of an appropriately chosen reference time. In this work, compressibility is parameterized in terms of both global (turbulent Mach number) and local parameters (normalized dilatation-rate and flow field topology). Our investigations reveal that the local dilatation rate significantly influences these statistics. In turn, this observed influence of the dilatation rate is predominantly associated with rotation dominated topologies (unstable-focus-compressing, stable-focus-stretching). We find that an enhanced dilatation rate (in both contracting and expanding fluid elements) significantly enhances the tendency of the vorticity vector to align with the largest eigenvector of the strain-rate. Further, in fluid particles where the vorticity vector is maximally misaligned (perpendicular) at the reference time, vorticity does show a substantial tendency to align with the intermediate eigenvector as well. The authors make an attempt to provide physical explanations of these observations (in terms of moment of inertia and angular momentum) by performing detailed calculations following tetrads {approach of Chertkov et al. [“Lagrangian tetrad dynamics and the phenomenology of turbulence,” Phys. Fluids 11(8), 2394–2410 (1999)] and Xu et al. [“The pirouette effect in turbulent flows,” Nat. Phys. 7(9), 709–712 (2011)]} in a compressible flow field.

Genesis and evolution of velocity gradients in near-field spatially developing turbulence

This paper investigates the dynamics of velocity gradients for a spatially developing flow generated by a single square element of a fractal square grid at low inlet Reynolds number through direct numerical simulation. This square grid-element is also the fundamental block of a classical grid. The flow along the grid-element centreline is initially irrotational and becomes turbulent further downstream due to the lateral excursions of vortical turbulent wakes from the grid-element bars. We study the generation and evolution of the symmetric and anti-symmetric parts of the velocity gradient tensor for this spatially developing flow using the transport equations of mean strain product and mean enstrophy respectively. The choice of low inlet Reynolds number allows for fine spatial resolution and long simulations, both of which are conducive in balancing the budget equations of the above quantities. The budget analysis is carried out along the grid-element centreline and the bar centreline. The former is observed to consist of two subregions: one in the immediate lee of the grid-element which is dominated by irrotational strain, and one further downstream where both strain and vorticity coexist. In the demarcation area between these two subregions, where the turbulence is inhomogeneous and developing, the energy spectrum exhibits the best$-5/3$power-law slope. This is the same location where the experiments at much higher inlet Reynolds number show a well-defined$-5/3$spectrum over more than a decade of frequencies. Yet, the$Q{-}R$diagram, where$Q$and$R$are the second and third invariants of the velocity gradient tensor, remains undeveloped in the near-grid-element region, and both the intermediate and extensive strain-rate eigenvectors align with the vorticity vector. Along the grid-element centreline, the strain is the first velocity gradient quantity generated by the action of pressure Hessian. This strain is then transported downstream by fluctuations and strain self-amplification is activated a little later. Further downstream, vorticity from the bar wakes is brought towards the grid-element centreline, and, through the interaction with strain, leads to the production of enstrophy. The strain-rate tensor has a statistically axial stretching form in the production region, but a statistically biaxial stretching form in the decay region. The usual signatures of velocity gradients such as the shape of$Q{-}R$diagrams and the alignment of vorticity vector with the intermediate eigenvector are detected only in the decay region even though the local Reynolds number (based on the Taylor length scale) is only between 30 and 40.

Turbulence-flame interactions in DNS of a laboratory high Karlovitz premixed turbulent jet flame

In the present work, direct numerical simulation (DNS) of a laboratory premixed turbulent jet flame was performed to study turbulence-flame interactions. The turbulent flame features moderate Reynolds number and high Karlovitz number (Ka). The orientations of the flame normal vector n, the vorticity vector ω and the principal strain rate eigenvectors ei are examined. The in-plane and out-of-plane angles are introduced to quantify the vector orientations, which also measure the flame geometry and the vortical structures. A general observation is that the distributions of these angles are more isotropic downstream as the flame and the flow become more developed. The out-of-plane angle of the flame normal vector, β, is a key parameter in developing the correction of 2D measurements to estimate the corresponding 3D quantities. The DNS results show that the correction factor is unity at the inlet and approaches its theoretical value of an isotropic distribution downstream. The alignment characteristics of n, ω and ei, which reflect the interactions of turbulence and flame, are also studied. Similar to a passive scalar gradient in non-reacting flows, the flame normal has a tendency to align with the most compressive strain rate, e3, in the flame, indicating that turbulence contributes to the production of scalar gradient. The vorticity dynamics are examined via the vortex stretching term, which was found to be the predominant source of vorticity generation balanced by dissipation, in the enstrophy transport equation. It is found that although the vorticity preferentially aligns with the intermediate strain rate, e2, the contribution of the most extensive strain rate, e1, to vortex stretching is comparable with that of the intermediate strain rate, e2. This is because the eigenvalue of the most extensive strain rate, λ1, is always large and positive. It is confirmed that the vorticity vector is preferentially positioned along the flame tangential plane, contributing to the dominance of cylindrical curvature of the flame front. Finally, the effect of heat release on the turbulence-flame interactions is examined. It is found that heat release has only limited impact on the statistics due to the minor role played by the strain rate induced by heat release rate in the current high Ka flame.

Influence of compressibility on the Lagrangian statistics of vorticity–strain-rate interactions

The objective of this study is to investigate the influence of compressibility on Lagrangian statistics of vorticity and strain-rate interactions. The Lagrangian statistics are extracted from "almost" time-continuous data sets of direct numerical simulations of compressible decaying isotropic turbulence by employing a cubic spline-based Lagrangian particle tracker. We study the influence of compressibility on Lagrangian statistics of alignment in terms of compressibility parameters-turbulent Mach number, normalized dilatation-rate, and flow topology. In comparison to incompressible turbulence, we observe that the presence of compressibility in a flow field weakens the alignment tendency of vorticity toward the largest strain-rate eigenvector. Based on the Lagrangian statistics of alignment conditioned on dilatation and topology, we find that the weakened tendency of alignment observed in compressible turbulence is because of a special group of fluid particles that have an initially negligible dilatation-rate and are associated with stable-focus-stretching topology.

Influence of flow topology and dilatation on scalar mixing in compressible turbulence

The kinematics of passive scalar mixing and its relation to local flow topology and dilatation in compressible turbulence are examined using direct numerical simulations (DNS) of decaying isotropic turbulence. The main objective of this work is to characterize the dependence of various evolution mechanisms of scalar dissipation on local streamline topology and normalized dilatation. The DNS results indicate that the topology has a stronger influence on the nonlinear amplification mechanism than the dilatation level of a fluid element. In its appropriately normalized form, the amplification mechanism is found to be fairly independent of the Mach and Reynolds numbers. Non-focal topologies (the so called unstable-node/saddle/saddle and stable-node/saddle/saddle) are found to be associated with more intense mixing than the focal topologies at almost all dilatation levels. Alignment tendencies (jointly conditioned upon topology and dilatation) between the scalar-gradient vector and the strain-rate eigenvectors are shown to play a key role in shaping the observed behaviour in compressible turbulence. Finally, some modelling implications of these findings are discussed.

Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet

AbstractVortex stretching and compression, which cause enstrophy production by inviscid processes, are investigated near the turbulent/non-turbulent (T/NT) interface in a planar jet by using a direct numerical simulation (DNS). The enstrophy production is investigated by analysing the relationship among a vorticity vector, strain-rate eigenvectors and strain-rate eigenvalues. The statistics are calculated individually for three different interface orientations. The vorticity near the T/NT interface is oriented in the tangential direction to the interface. The enstrophy production is affected by the interface orientation because the intensity of vortex stretching depends on the interface orientation, and the alignment between the vorticity vector and the strain-rate eigenvectors is confined by the interface. The enstrophy production near the T/NT interface is analysed by considering the motion of turbulent fluid relative to that of the interface. The results show that the alignment between the interface and the strain-rate eigenvectors changes depending on the velocity field near the T/NT interface. When the turbulent fluid moves toward the T/NT interface, the enstrophy is generated by vortex stretching without being greatly affected by vortex compression. In contrast, when the turbulent fluid relatively moves away from the T/NT interface, large enstrophy reduction frequently occurs by vortex compression. Thus, it is shown that the velocity field near the T/NT interface affects the enstrophy production near the interface through the alignment between the vorticity and the strain-rate eigenvectors.

Interaction between strain and vorticity in compressible turbulent boundary layer

The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation (DNS) of the compressible Navier-Stokes equations. Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions. It is found that large enstrophy production is associated with high dissipation and high enstrophy, while large enstrophy destruction with moderate ones. The enstrophy production and destruction are also correlated with the dissipation production and destruction. Moreover, the enstrophy producing region has a distinct tendency to be ‘sheet-like’ structures and the enstrophy destroying region tends to be ‘tube-like’ in the inner layer. Correspondingly, the tendency to be ‘sheet-like’ or ‘tube-like’ structures is no longer obvious in the outer layer. Further, the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies. It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer, and the enstrophy production (destruction) mainly on the alignment between the vorticity vector and the extensive (compressive) eigenvector in the outer layer.