Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of full RANS closure. For the non-stratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Transition to chaos in a reduced-order model of a shear layer

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

Experimental observation of the origin and structure of elastoinertial turbulence

Turbulence generally arises in shear flows if velocities and hence, inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases, a state of chaotic motion, “elastoinertial turbulence” (EIT), has been observed in a narrow Reynolds number interval. We here determine the origin of EIT in experiments and show that characteristic EIT structures can be detected across an unexpectedly wide range of parameters. Close to onset, a pattern of chevron-shaped streaks emerges in qualitative agreement with linear and weakly nonlinear theory. However, in experiments, the dynamics remain weakly chaotic, and the instability can be traced to far lower Reynolds numbers than permitted by theory. For increasing inertia, the flow undergoes a transformation to a wall mode composed of inclined near-wall streaks and shear layers. This mode persists to what is known as the “maximum drag reduction limit,” and overall EIT is found to dominate viscoelastic flows across more than three orders of magnitude in Reynolds number.

Entrainment and growth of vortical disturbances in the channel-entrance region

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

Influence of separation structure on the dynamics of shock/turbulent-boundary-layer interactions

Shock/turbulent-boundary-layer interactions (STBLIs) are ubiquitous in high-speed flight and propulsion applications. Experimental and computational investigations of swept, three-dimensional (3-D) interactions, which exhibit quasi-conical mean-flow symmetry in the limit of infinite span, have demonstrated key differences in unsteadiness from their analogous, two-dimensional (2-D), spanwise-homogeneous counterparts. For swept interactions, represented by the swept–fin-on-plate and swept–compression–ramp-on-plate configurations, differences associated with the separated shear layers may be traced to the intermixing of 2-D (spanwise independent) and 3-D (spanwise dependent) scaling laws for the separated mean flow. This results in a broader spectrum of unsteadiness that includes relatively lower frequencies associated with the separated shear layers in 3-D interactions. However, lower frequency ranges associated with the global “breathing” of strongly separated 2-D interactions are significantly less prominent in these simple, swept 3-D interactions. A logical extension of 3-D interaction complexity is the compound interaction formed by the merging of two simple interactions. The first objective of this work is therefore to analyze the more complex picture of the dynamics of such interactions, by considering as an exemplar, wall-resolved simulations of the double-fin-on-plate configuration. We show that in the region of interaction merging, new flow scales, changes in separation topology, and the emergence of lower-frequency phenomena are observed, whereas the dynamics of the interaction near the fin leading edges are similar to those of the simple, swept interactions. The second objective is to evolve a unified understanding of the dynamics of STBLIs associated with complex configurations relevant to actual propulsion systems, which involve the coupling between multiple shock systems and multiple flow separation and attachment events. For this, we revisit the salient aspects of scaling phenomena in a manner that aids in assimilating the double-fin flow with simpler swept interactions. The emphasis is on the influence of the underlying structure of the separated flow on the dynamics. The distinct features of the compound interactions manifest in a centerline symmetry pattern that replaces the quasi-conical symmetry of simple interactions. The primary separation displays topological closure to reveal new length scales, associated unsteadiness bands, and secondary flow separation.

A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

A hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact (HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.

Effects of Mass and Damping on Flow-Induced Vibration of a Cylinder Interacting with the Wake of Another Cylinder at High Reduced Velocities

Flow-induced vibration is a canonical issue in various engineering fields, leading to fatigue or immediate damage to structures. This paper numerically investigates flow-induced vibrations of a cylinder interacting with the wake of another cylinder at a Reynolds number Re = 150. It sheds light on the effects of mass ratio m*, damping ratio, and mass-damping ratio m*ζ on vibration amplitude ratio A/D at different reduced velocities Ur and cylinder spacing ratios L/D = 1.5 and 3.0. A couple of interesting observations are made. The m* has a greater influence on A/D than ζ although both m* and ζ cause reductions in A/D. The m* effect on A/D is strong for m* = 2–16 but weak for m* > 16. As opposed to a single isolated cylinder case, the mass-damping m*ζ is not found to be a unique parameter for a cylinder oscillating in a wake. The vortices in the wake decay rapidly at small ζ. Alternate reattachment of the gap shear layers on the wake cylinder fuels the vibration of the wake cylinder for L/D = 1.5 while the impingement and switch of the gap vortices do the same for L/D = 3.0.

Elastically driven Kelvin–Helmholtz-like instability in straight channel flow

Originally, Kelvin–Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn’s bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers are encountered in many engineering and environmental applications, and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On the other hand, many of the important physical mechanisms in these systems, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of the full RANS closure. For the non-stratified case, the SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.