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At least 883 records · Page 49

Stability Analysis of Streaks Induced By Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗

Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows

In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.

Duck, Peter W.↗

On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully-developed flows

There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmein-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poisseulle flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.

Bennett, James↗

Study Of Disturbances In Rotating Plane Poisseuille Flow

Report describes computer-simulation of instability and transition to turbulence in plane Poisseuille flow in rotating channel. Motions of fluid governed by Navier-Stokes equations of incompressible flow, using periodic boundary conditions in streamwise and spanwise directions. Principal parameters affecting flow are Reynolds and rotation numbers.

Kim, John↗

Stability of Long's vortex at large flow force

Long's self-similar vortex is known to have two solutions for each supercritical value of the flow force. Each of those solutions is shown to have a double structure if the flow force is large. The inertial instabilities of one of those large-flow-force limit solutions are investigated, showing that they are related to the instabilities of the Bickley jet in one regime. However, the swirl in the vortex becomes important for long waves, very strongly modifying the sinuous and varicose, Bickley modes. The asymptotic results obtained agree well with the numerical solutions for the sinuous mode, but not for the varicose mode, the difficulty in the latter case being apparently due to mode jumping.

Foster, M. R.↗

GPU-based simulation of the two-dimensional unstable structure of gaseous oblique detonations

In this paper, the two-dimensional structure of unstable oblique detonations induced by the wedge from a supersonic combustible gas flow is simulated using the reactive Euler equations with a one-step Arrhenius chemistry model. A wide range of activation energy of the combustible mixture is considered. Computations are performed on the Graphical Processing Unit (GPU) to reduce the simulation runtimes. A large computational domain covered by a uniform mesh with high grid resolution is used to properly capture the development of instabilities and the formation of different transverse wave structures. After the initiation point, where the oblique shock transits into a detonation, an instability begins to manifest and in all cases, the left-running transverse waves first appear, followed by the subsequent emergence of right-running transverse waves forming the dual-head triple point structure. This study shows that for low activation energies, a long computational length must be carefully considered to reveal the unstable surface due to the slow growth rate of the instability. For high activation energies, the flow behind the unstable oblique detonation features the formation of unburnt gas pockets and strong vortex-pressure wave interaction resulting in a chaotic-like vortical structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Progress on Understanding Rayleigh–Taylor Flow and Mixing Using Synergy Between Simulation, Modeling, and Experiment

Simultaneous advances in numerical methods and computing, theoretical techniques, and experimental diagnostics have all led independently to better understanding of Rayleigh–Taylor (RT) instability, turbulence, and mixing. In particular, experiments have provided significant motivation for many simulation and modeling studies, as well as validation data. Numerical simulations have also provided data that is not currently measurable or very difficult to measure accurately in RT unstable flows. Thus, simulations have also motivated new measurements in this class of buoyancy-driven flows. This overview discusses simulation and modeling studies synergistic with experiments and examples of how experiments have motivated simulations and models of RT instability, flow, and mixing. First, a brief summary of measured experimental and calculated simulation quantities, of experimental approaches, and of issues and challenges in the simulation and modeling of RT experiments is presented. Implicit large-eddy, direct numerical, and large-eddy simulations validated using RT experimental data are then discussed. This is followed by a discussion of modeling using analytical, modal, buoyancy–drag, and turbulent transport models of RT mixing experiments. The discussion will focus on three-dimensional RT mixing arising from multimode perturbations. Finally, this focused review concludes with a perspective on future simulation, modeling, and experimental directions for further research. Research in simulation and modeling of RT unstable flows, coupled with experiments, has made significant progress over the past several decades. This overview serves as an opportunity to both discuss progress and to stimulate future research on simulation and modeling of this unique class of hydrodynamically unstable turbulent flows.

42 ENGINEERING↗

Analytical study of the origin and behavior of asymmetric vortices

An hypothesis advanced originally to explain computational observations is supported by theoretical considerations: The asymmetric mean flow observed on bodies of revolution at moderate to high angles of attack is the result of a convective instability of an originally symmetric flow to a time-invariant space-fixed disturbance. Additionally, the time-dependent fluctuations characteristic of the flow at higher angles of attack (up to 90 deg) are the result of an absolute instability of an originally steady flow to a small temporal disturbance of finite duration. Within a common domain, the instability mechanisms may coexist. The experimentally confirmed existence of bistable states, wherein the side-force variation with nose roll angle approaches a square-wave distribution, is attributed to the dominant influence of a pair of trailing vortices from the ogival forebody. Their existence is made possible by the appearance of foci of separation in the skin-friction line pattern beyond a critical angle of attack. The extreme sensitivity of the asymmetric flow orientation to nose geometry, demonstrated experimentally, is attributed to the presence of an indeterminate phase in the family of possible solutions for the three-dimensional wave system.

Tobak, Murray↗

Another look at zonal flows: Resonance, shearing, and frictionless saturation

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as L ZF ~f 3/16 (1-$f$) 1/8 ρ $^{5/8}_s$ $l^{3/8}_0$in the (relevant) adiabatic limit (i.e., τ ck k$2\atop{||}$ D || $\gg$1). $f$ is the fraction of turbulence energy coupled to ZF and l 0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E~(γ L /ε c ) 2 , which indicates the extent of the “near-marginal” regime to be γ L <ε c , for the case of avalanche-induced profile variability. Here, ε c is the rate of dissipation of potential enstrophy and γ L is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γ L are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Observations on instabilities of cavitating inducers

Experimental observations of instability of cavitating inducers were made for two different inducers operating at different flow coefficients. In general, instability occurred just before head breakdown. Auto-oscillation and rotating cavitation were observed. Analysis of small-amplitude behavior of the inducer and hydraulic system is carried out, and analytical predictions of stability limits were compared with experiment.

Braisted, D.↗

Fluid flow in a jet and the Ca XIX line profiles observed during solar flares

The present study considers two types of fluid models as methods for reproducing the blueshifts and line broadening observed in soft X-ray lines during the rise of solar flares. The fluid models representing the laminar flow of material in a jet and through a pipe were used to derive the velocity at each location in the flow. The optimal values for the free parameters in the jet model were within the ranges expected for solar flare conditions. The jet was much smaller than typical flare volumes estimated from spatial images, but the resulting densities were consistent with the upper limit of densities derived using density-sensitive line ratios. This supports previous reports of small filling factors and is interpreted as evidence for a chromospheric origin for the flow. Stability analysis indicates that, although the laminar jet can reproduce the observations, instabilities may cause the flow to become turbulent, and that this laminar treatment is not strictly valid.

Bornmann, P. L.↗

Self-similar Reynolds-averaged mechanical–scalar turbulence models for reshocked Richtmyer–Meshkov instability-induced mixing in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing incompressible turbulent Richtmyer–Meshkov instability-induced mixing in planar geometry derived in the small Atwood number limit are extended to construct models for reshocked Richtmyer–Meshkov mixing. In this study, the models are based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ modeled either differentially or algebraically. The three- and four-equation models allow for a simultaneous description of mechanical and scalar mixing, i.e., mixing layer growth and molecular mixing. Mixing layer growth parameters and other physical observables were obtained explicitly as functions of the model coefficients and were used to calibrate the model coefficients. Here, the solutions for the singly shocked Richtmyer–Meshkov case for the mixing layer width and the turbulent fields are used to construct piecewise-continuous generalizations of these quantities for times after reshock. For generality, the post-reshock mixing layer width is not assumed to grow with the same power-law as the pre-reshock width, and an impulsive approximation applied to Rayleigh–Taylor instability growth is used to establish the expression for the post-reshock width. A four-equation model is then used to illustrate the spatiotemporal behavior of the mean and turbulent fields and late-time turbulent equation budgets across the mixing layer. The reference solutions derived here can provide systematic calibrations and better understanding of mechanical–scalar turbulence models and their predictions for reshocked Richtmyer–Meshkov instability-induced turbulent mixing in the very large Reynolds number limit.

42 ENGINEERING↗

Zonal Flow and Self-regulating Mechanism in a Hydrodynamic Disk

This study addresses key aspects of momentum transport in hydrodynamic disks, which is critical for understanding zonal flow generation and turbulence in compressible hydrodynamic disks. We find that nonlinear momentum/density transport leads to the formation of zonal flows from the Rossby wave instability in disks. We analytically derive the generation and location of zonal flows and describe a modified Taylor identity applicable to compressible disk flows. We further present a self-regulation model, revealing a dynamic interplay between zonal flow and fluctuations driven by Rossby wave instability that regulates the nonlinear saturation state. This theoretical framework contributes insights into the dynamics of disks such as protoplanetary disks, shedding light on the intricate processes governing momentum/density transport and the emergence of zonal flows in the saturation of protoplanetary disks.

Astrophysical fluid dynamics↗

GRAVITATIONAL INSTABILITIES IN TWO-COMPONENT GALAXY DISKS WITH GAS DISSIPATION

Growth rates for gravitational instabilities in a thick disk of gas and stars are determined for a turbulent gas that dissipates on the local crossing time. The scale heights are derived from vertical equilibrium. The accuracy of the usual thickness correction, (1 + kH){sup -1}, is better than 6% in the growth rate when compared to exact integrations for the gravitational acceleration in the disk. Gas dissipation extends the instability to small scales, removing the minimum Jeans length. This makes infinitesimally thin disks unstable for all Toomre-Q values and reasonably thick disks stable at high Q primarily because of thickness effects. The conventional gas+star threshold, Q{sub tot}, increases from {approx}1 without dissipation to 2 or 3 when dissipation has a rate equal to the crossing rate over a perturbation scale. Observations of Q{sub tot} {approx} 2-3 and the presence of supersonic turbulence suggest that disks are unstable over a wide range of scales. Such instabilities drive spiral structure if there is shear and clumpy structure if shear is weak; they may dominate the generation of turbulence. Feedback regulation of Q{sub tot} is complex because the stellar component does not cool; the range of spiral strengths from multiple arm to flocculent galaxies suggests that feedback is weak. Gravitational instabilities may have a connection to star formation even when the star formation rate scales directly with the molecular mass because the instabilities return dispersed gas to molecular clouds and complete the cycle of cloud formation and destruction. The mass flow to dense clouds by instabilities can be 10 times larger than the star formation rate.

79 ASTRONOMY AND ASTROPHYSICS↗

The Generation of Smooth High Speed Solar Wind from Plume-Interplume Mixing

Plumes and rays are magnetic field aligned density striations in coronal holes with different values of plasma beta. The overall plasma beta is very small in the low corona but exceeds unity beyond 15-20 solar radius. High speed solar wind reported beyond 0.3 AU is relatively smooth and uniform and known to originate from the much filamented coronal hole. Thus the obvious question is how to generate a smooth solar wind from seemingly filamentary structure. Hence one has to find a mechanism to substantiate this apparent observed (Ulysses) phenomenon. To do this we model plumes as jets (or wakes) of plasma emitted from the solar surface. The shear between a jet and its ambient is known to become unstable to the MHD Kelvin-Helmholtz ("KH") instability if the Alfven Mach number of the jet is greater than one and the uniform external magnetic field is small. Starting with a simple configuration we consider a jet of half thickness R, having uniform density and uniform internal magnetic field. The external medium has also a uniform density and uniform magnetic field. The jet is perturbed at the boundary with a linear amplitude and fixed frequency. We simulate the coronal jet using the 3D ZEUS code. The first results indicate the slab jet is unstable to the MHD KH instability at 5-10 solar radius for some angle of wave propagation. The propagating instability may smooth the filamented flow. It may also produce the entrained Alfvenic fluctuations observed by Ulysses in the high speed wind. We are at present determining the parameters which induce large growth rate. This may clarify the mystery behind the emergence of fast smooth solar wind from very filamentary structures in coronal holes. Also, using the dispersion relation already available for such a flow we obtain some general description of the instability criteria for the KH instability at a jet interface.

Parhi, Shyamsundar↗

Molecular shear heating and vortex dynamics in thermostatted two dimensional Yukawa liquids

It is well known that two-dimensional macroscale shear flows are susceptible to instabilities leading to macroscale vortical structures. The linear and nonlinear fate of such a macroscale flow in a strongly coupled medium is a fundamental problem. A popular example of a strongly coupled medium is a dusty plasma, often modelled as a Yukawa liquid. Recently, laboratory experiments and molecular dynamics (MD) studies of shear flows in strongly coupled Yukawa liquids indicated the occurrence of strong molecular shear heating, which is found to reduce the coupling strength exponentially leading to the destruction of macroscale vorticity. To understand the vortex dynamics of strongly coupled molecular fluids undergoing macroscale shear flows and molecular shear heating, MD simulation has been performed, which allows the macroscopic vortex dynamics to evolve, while at the same time “removes” the microscopically generated heat without using the velocity degrees of freedom. We demonstrate that by using a configurational thermostat in a novel way, the microscale heat generated by shear flow can be thermostatted out efficiently without compromising the large scale vortex dynamics. In the present work, using MD simulations, a comparative study of shear flow evolution in Yukawa liquids in the presence and absence of molecular or microscopic heating is presented for a prototype shear flow, namely, Kolmogorov flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-Temperature Deformation Behavior of Ti-6Al-2Sn-4Zr-2Mo Alloy with Lamellar Microstructure Under Plane-Strain Compression

High-temperature plane-strain compression of a Ti-6Al-2Sn-4Zr-2Mo (Ti-6242) alloy with a lamellar structure was applied by a thermal simulation machine Gleeble 3800 at a temperature of 1223-1370 K and a strain rate of 0.01-10 s{sup −1}. Constitutive relations between the flow stress and strain at different temperatures and strain rates were constructed based on the Arrhenius equation. Processing maps based on the dynamic material model at strains of 0.5, 1.0, and 1.25 were also constructed to analyze the mechanism and instability of high-temperature deformation. Dynamic recrystallization was found to occur at 1223-1313 K and 0.01-0.1 s{sup −1}, with a peak efficiency of power dissipation of 70%. Observations of the microstructure demonstrated that α platelets and dynamic globularization were responsible for dynamic softening in the α + β phase field. Flow instability behaviors occurred at 1263-1343 K/1.78-10 s{sup −1}, 1233-1283 K/0.1-3.16 s{sup −1}, and 1353-1373 K/0.56-1.78 s{sup −1}, and adiabatic shear bands and microcracks were observed in these domains. Thus, for the lamellar Ti-6242 alloy, the recommended hot rolling parameters were 1243-1333 K and 0.01-0.1 s{sup −1}. Electron backscattered diffraction results revealed that the dynamic restoration mechanism in the β phase field was dynamic recovery when the strain rate was as high as 10 s{sup −1}.

36 MATERIALS SCIENCE↗