Evolution Of Enstrophy Research Articles

Computational Study on Flow Characteristics of Shocked Light Backward-Triangular Bubbles in Polyatomic Gas

This study computationally examined the Richtmyer–Meshkov instability (RMI) evolution in a helium backward-triangular bubble immersed in monatomic argon, diatomic nitrogen, and polyatomic methane under planar shock wave interactions. Using high-fidelity numerical simulations based on the compressible Navier–Fourier equations based on the Boltzmann–Curtiss kinetic framework and simulated via a modal discontinuous Galerkin scheme, we analyze the complex interplay of shock-bubble dynamics. Key findings reveal distinct thermal non-equilibrium effects, vorticity generation, enstrophy evolution, kinetic energy dissipation, and interface deformation across gases. Methane, with its molecular complexity and higher viscosity, exhibits the highest levels of vorticity production, enstrophy, and kinetic energy, leading to pronounced Kelvin–Helmholtz instabilities and enhanced mixing. Conversely, argon, due to its simpler atomic structure, shows weaker deformation and mixing. Thermal non-equilibrium effects, quantified by the Rayleigh–Onsager dissipation function, are most significant in methane, indicating delayed energy relaxation and intense turbulence. This study highlights the pivotal role of molecular properties, specific heat ratio, and bulk viscosity in shaping RMI dynamics in polyatomic gases, offering insights on uses such as high-speed aerodynamics, inertial confinement fusion, and supersonic mixing.

Investigation of aspect ratio effects on flow characteristics and vorticity generation in shock-induced rectangular bubble

In shock-induced Richtmyer–Meshkov instability, the polygonal bubbles, including the rectangular interface can offer favorable circumstances for shock refraction research. Also, the aspect ratio is crucial in characterizing the physics behind this instability. Therefore, the aspect ratio effects on the flow characteristics and vorticity generation in the shock-induced rectangular light gas bubbles are investigated numerically in this study. This investigation is performed for a wide range of aspect ratios varying from 0.25 to 3.0. These effects are highlighted in the interface morphology, wave paradigms, vorticity generation, enstrophy evolution, and a qualitative examination of interface deformation. For simulating two-component gas flows, a high-order explicit modal discontinuous Galerkin approach is employed to solve a two-dimensional system of compressible inviscid Euler equations. Existing experimental results for shock-induced square and cylindrical light bubbles are used to validate the numerical model and solver. The results indicate that the effects of aspect ratio are critical in characterizing the interface morphology during the interaction between the shock wave and rectangular bubble. The interface morphology evolves faster as the aspect ratio increases, and the process of transverse jet formation is observed to be significantly different. The aspect ratio effects result in a substantial change in the flow field with bubble deformation, vortex development, vorticity generation, and transverse jet formation. The effects of aspect ratio are further investigated in detail through the mechanism of vorticity generation and enstrophy evolution. Finally, these effects on shock trajectories and interface characteristics over time are thoroughly explored.

Enstrophy evolution during head-on wall interaction of premixed flames within turbulent boundary layers

The statistical behaviors of mean enstrophy and its evolution during head-on interaction of premixed flames propagating toward a chemically inert flat wall across the turbulent boundary layer have been analyzed using direct numerical simulations for a friction velocity-based Reynolds number of Reτ=110. The enstrophy dynamics have been analyzed for both isothermal and adiabatic thermal wall boundary conditions. The contributions of vortex-stretching and viscous dissipation are found to be leading order source and sink, respectively, to the mean enstrophy transport in both non-reacting and reacting flows irrespective of the wall boundary condition. However, the contributions due to dilatation rate and baroclinic torque play important roles in addition to the leading order contributions of the vortex-stretching and viscous dissipation terms in the enstrophy transport in turbulent premixed flames. The thermal boundary condition has been demonstrated to affect the near-wall behavior of the enstrophy transport contribution due to dilatation rate, which also affects the near-wall distribution of the enstrophy. The magnitudes of the leading order contributors to the enstrophy transport decrease with the progress of head-on interaction for both wall boundary conditions. Moreover, the overall sink contributions to the enstrophy transport dominate over the source contributions, giving rise to a drop in the mean enstrophy with the progress of head-on interaction. The enstrophy distribution changes significantly during flame-wall interaction, which gives rise to a modification of the relative proportion of the coherent structures in the reacting flow turbulent boundary layer compared to the corresponding non-reacting flow features.

Numerical simulations of Richtmyer–Meshkov instability of [formula omitted] square bubble in diatomic and polyatomic gases

The Richtmyer–Meshkov instability of a shock-driven SF6 square bubble in monatomic, diatomic, and polyatomic gases is investigated numerically. The focus was placed on presenting more intuitive details of the flow-fields visualizations, vorticity production, degree of thermal non-equilibrium, enstrophy and dissipation rate evolutions, and interface structures. A mixed-type modal discontinuous Galerkin method is employed for solving the two-dimensional system of physical conservation laws derived from the Boltzmann–Curtiss kinetic equation of diatomic and polyatomic gases. For validation, the numerical results were compared with the existing experimental results. The results revealed that diatomic and polyatomic gases provoke considerable changes in the flow-fields, resulting in complex wave patterns, bubble deformation, and outward SF6 jets formation in contrast to monatomic gas. A detailed investigation on the effects of diatomic and polyatomic gases is carried out through the vorticity production, degree of nonequilibrium, and evolution of enstrophy as well as dissipation rate. Moreover, the length and height of the interface structures are investigated quantitatively. Finally, the effects of thermal non-equilibrium parameters, such as inverse power-law index and bulk viscosity ratio are examined. The present work attempts to enhance the understanding of the RM instability studies in monatomic, diatomic, and polyatomic gases.

Numerical investigation of thermal non-equilibrium effects of diatomic and polyatomic gases on the shock-accelerated square light bubble using a mixed-type modal discontinuous Galerkin method

In this article, a numerical investigation is carried out for analyzing the thermal non-equilibrium effects of diatomic and polyatomic gases on the flow dynamics of a shock-accelerated square light bubble. The simulation emphasis is placed on the flow morphology visualization, wave patterns, degree of thermal non-equilibrium, vorticity generation, and evolution of enstrophy as well as dissipation rate. A two-dimensional system of unsteady physical conservation laws derived from the Boltzmann-Curtiss kinetic equation of diatomic and polyatomic gases is solved by employing an in-house developed mixed-type modal discontinuous Galerkin method with uniform meshes. An explicit third-order SSP Runge-Kutta scheme is employed for the time discretization. The numerical results are compared with existing experimental results for validation, and they are found in good agreement. The results elucidate that the effects of thermal non-equilibrium, including different gas properties play a significant role during the interaction between an incident shock wave and a square light bubble. The effects of diatomic and polyatomic gases cause a significant change in flow morphology, resulting in complex wave patterns, vorticity generation, vortices formation, and bubble deformation. In comparison to monatomic gases, diatomic and polyatomic gases exhibit the formation of larger rolled-up vortex chains, different jet structure and large mixing zones. A detailed investigation on the effects of diatomic and polyatomic gases is explored using the vorticity generation, degree of non-equilibrium, the evolutions of enstrophy and dissipation rate. Finally, the effects of thermal non-equilibrium parameters, including temperature-dependent transport coefficient and bulk viscosity ratio, on the flow dynamics of the shock-accelerated square light bubble are comprehensively investigated.

Influence of gap-ratio on flow dynamics and heat transfer for a square cylinder approaching a moving wall in turbulent regime

Flow past a square cylinder near a moving wall is investigated for 0.1 ≤ G/D (gap-ratio) ≤ 1.0 at a constant Reynolds number of 22,000 using large eddy simulations. Influence of the gap-ratio on various flow features has been studied. It is observed that for G/D ≤ 0.3, a regular Kármán vortex shedding from the cylinder gets suppressed which causes a large change in the flow dynamics. Unlike the case of a stationary wall, no ground vortex is formed in the present case. For G/D = 1.0, turbulence is strong in the near wake region and for low G/D values (≤ 0.3) it gets weaker and shifts downstream. With a decrease in G/D, an early reattachment of the lower shear-layer with the bottom surface of the cylinder occurs while the upper shear-layer is deflected and K-H instability occurs away from the top surface. The so-called ‘extreme events’ which contain high frequency fluctuations are observed for G/D = 1.0 and these disappear for low G/D values. Large coherent structures are observed for high G/D (≥ 0.5) while for low G/D uniformly distributed small structures are formed. Evolution of enstrophy has been examined for G/D = 0.1 and the role of the strain-rate tensor in the enstrophy production has been investigated. The lift coefficients are negative for all G/D values while drag coefficients decrease with a decrement in G/D and are nearly constant for G/D ≤ 0.3. Due to the formation of large coherent structures, power spectra for high G/D follows -5/3 law over a large range of frequency. Unlike the case of a laminar flow, Nusselt number on the cylinder surface monotonically decreases with a decrease in G/D.

Topological evolution near the turbulent/non-turbulent interface in turbulent mixing layer

The topological evolution near the turbulent/non-turbulent interface (TNTI) in turbulent mixing layer is studied by means of statistical analysis of the invariants of velocity gradient tensor (VGT) based on direct numerical simulation data. The dynamics of topological evolution is investigated in terms of the source terms of the evolution equations for the invariants, including the pressure effect term, viscous effect term and interaction term among the invariants. It is found that the local topology of fluid particles at the TNTI evolves from non-focal region to focal region in the plane of the second (Q) and the third (R) invariants of the VGT. The topological evolution is mainly associated with the pressure effect term in the TNTI region. According to the analysis of the evolution of enstrophy and dissipation, the enstrophy increase and the dissipation decrease are revealed in the TNTI region, which are caused by viscous vorticity diffusion near the TNTI. A weak correlation between the strain rate and the rotation rate is found in the TNTI region which is related to the reduction of enstrophy production. The alignments between vorticity and strain near the TNTI are investigated and a strong alignment of the vorticity with the extensive eigenvector direction is identified in the TNTI region.

Numerical study of shock/vortex interaction in diatomic gas flows

The particle-based direct simulation of Monte Carlo(DSMC) was present and validated for the investigation of non-equilibrium effects in diatomic gas flows. All the validations show that the results of the present DSMC is in agreement with the experimental data. Then, the numerical studies of micro scale shock/composite-vortex interactions in diatomic gas flows were conducted. The substantial attenuation of enstrophy in diatomic gas flow is observed. Differ from the sharp decreasing in diatomic gas, the time evolution of enstrophy in monatomic gas flow decrease linearly in the whole process. This study also shows that the vortex deformation through a shock, in particular, is observed to be strongly dependent on the shock and vortex strengths. Also, it is also found that strong interaction can also cause vorticity production in microscale shock/vortex interaction for diatomic gas flow. The attenuation, analogous to DSMC results, overwhelms the vorticity generation only in a limited set of regimes with low shock Mach number, small vortex size, or weak vortex. Besides, in diatomic gas flow, viscous vorticity generation is also most dominant in the three dynamical processes of vorticity transportation, followed by dilatational and baroclinicvorticity generation. The present study conform that shock/vortex present different features in strong and weak interactions for monatomic and diatomic gas flows. Furthermore, it provides a new way for the investigation of non-equilibrium effects.

Vorticity dynamics in turbulence growth

The mechanisms of vorticity amplification in the formation of turbulence are investigated by means of direct numerical simulations of the Navier–Stokes equations with different initial conditions and Reynolds numbers. The simulations show good universality of the enstrophy evolution, that occurs in two stages. The first stage is dominated by the effect of vortex stretching, and it finishes with a k −3 power-law energy spectrum. The second stage is dominated by the action of viscosity on the small scales, and it finishes with a Kolmogorov k −5/3 energy spectrum.

Decaying turbulence in soap films: energy and enstrophy evolution

This experimental study of quasi-two-dimensional grid turbulence in gravity-driven soap-film flow focuses on the differences between the behavior of the flow and the theoretical picture of two-dimensional turbulence. A previously unattainable quality of velocity field acquisition facilitates simultaneous measurement of velocity field features in the scale range spanning over two orders of magnitude. The highly-resolved flow field data are analyzed statistically in terms of velocity structure functions, as well as energy and enstrophy averages at different downstream positions. We find the rate of decay of these averages to be quantifiably greater than the predictions of the two-dimensional turbulence theory. This increased decay is likely to be the manifestation of the extra dissipation mechanism present in soap-film flows and prominent on the larger scales—air drag. The structure function analysis confirms the notion.

Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

We study the vortex-accelerated secondary baroclinic vorticity deposition (VAVD) at late-intermediate times, and dynamics of sinusoidal single-mode Richtmyer–Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three post-shock Atwood numbers (A*), 0.2, 0.635, and 0.9, with Mach number (M) of 1.3. We initialize the sinusoidal interface with a slightly “diffuse” or small-but-finite thickness interfacial transition layer to facilitate comparison with experiment and avoid ill-posed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time tM, which is defined as the time when the extracted medial axis of an interfacial layer first becomes multivalued. For an interval of 11tM beyond tM, the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex roll-up region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher A*. This vorticity deposition is due to misalignment of density gradient across the interface and vortex-centripetal acceleration (secondary baroclinic), and enhanced by the intensification of interfacial density gradient arising from the vortex-induced strain. Our simulation results for A*=0.635 agree with the recent air–sulfur hexafluoride (SF6) experiment of Jacobs and Krivets [Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, (2001)], including several large-scale features of the evolving mushroom structure: The usual interface spike-bubble amplitude growth rate ȧ and the dimensions of the spike roll-up cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate ȧ disagrees with the O(t−1) result of Sadot et al. [Phys. Rev. Lett. 80, 1654 (1998)]. Instead, it approaches a constant which increases with A*(⩽0.9). An adjusting periodic single point vortex model which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to late-intermediate times at low Atwood numbers (A*=0.2,0.635). The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and one-dimensional averaged kinetic-energy spectra are presented at several times.