Sound generation by coaxial collision of two vortex rings

2000 ◽  
Vol 424 ◽  
pp. 327-365 ◽  
Author(s):  
O. INOUE ◽  
Y. HATTORI ◽  
T. SASAKI
Keyword(s):  
Vortex Ring ◽  
Sound Pressure ◽  
Stokes Equations ◽  
Near Field ◽  
Time Integration ◽  
Relative Strength ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Sound Waves ◽  
Change Of Direction

Sound pressure fields generated by coaxial collisions of two vortex rings with equal/unequal strengths are simulated numerically. The axisymmetric, unsteady, compressible Navier–Stokes equations are solved by a finite difference method, not only for a near field but also for a far field. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The results show that the generation of sound is closely related to the change of direction of the vortex ring motion induced by the mutual interaction of the two vortex rings. For the case of equal strength (head-on collision), the change of direction is associated with stretching of the vortex rings. Generated sound waves consist of compression parts and rarefaction parts, and have a quadrupolar nature. For the case of unequal strengths, the two vortex rings pass through each other; the weaker vortex ring moves outside the stronger vortex ring which shows a loop motion. The number of generated waves depends on the relative strength of the two vortex rings. The sound pressure includes dipolar and octupolar components, in addition to monopolar and quadrupolar components which are observed for the case of a head-on collision.

Sound generation by shock–vortex interactions

1999 ◽  
Vol 380 ◽  
pp. 81-116 ◽  
Author(s):  
OSAMU INOUE ◽  
YUJI HATTORI
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Early Stage ◽  
Near Field ◽  
Time Integration ◽  
Flow Fields ◽  
Navier Stokes ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Reflected Shock

Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier–Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.

Dynamics of a vortex ring in a rotating fluid

1996 ◽  
Vol 317 ◽  
pp. 215-239 ◽  
Author(s):  
R. Verzicco ◽  
P. Orlandi ◽  
A. H. M. Eisenga ◽  
G. J. F. Van Heijst ◽  
G. F. Carnevale
Keyword(s):  
Vortex Ring ◽  
Stokes Equations ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Swirl Flow ◽  
Degree Of Polarization ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Rotating Fluid ◽  
Translation Velocity

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier–Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a ‘degree of polarization’.If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown.Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.

Study of Interaction between Unsteady Supersonic Jet and Vortex Rings Discharged from Elliptical Cell

2018 ◽  
Vol 910 ◽  
pp. 137-142
Author(s):  
Kazumasa Kitazono ◽  
Hiroshi Fukuoka ◽  
Nao Kuniyoshi ◽  
Minoru Yaga ◽  
Eri Ueno ◽  
...  
Keyword(s):  
Laser Ablation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Supersonic Jet ◽  
Pulsed Laser ◽  
Pulsed Laser Ablation ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Thermodynamic Conditions

Pulsed laser ablation with an elliptical cell gives well-defined thermodynamic conditions to the growth of high-quality thin films. The unsteady supersonic jet formed by the shock tube with small high-pressure chamber was used as a simple alternative model of pulsed laser ablation. The vortex ring formed by the shock wave is important to reveal behavior of unsteady supersonic jet discharged from elliptical cell. However, there has been little effort to investigate the interaction between the vortex ring and the jet. The purpose of the present study is to investigate the behavior of the vortex rings and the jet. The experiment and numerical calculation were carried out by schlieren method and by solving the axisymmetric two-dimensional compressible Navier-Stokes equations, respectively. The system of the calculation and the experiment is a model of laser ablation of a certain duration followed by a discharging process through the exit. Moreover, a parametric study was performed to demonstrate the effect of pressure ratio on the interaction among vortex rings and the supersonic jet. The interaction between the supersonic jet and the vortex rings increased the velocity of the supersonic jet up to the magnitude of the velocity at the center of the vortex rings. Closing a distance between the vortex ring and the jet is higher interaction between the vortex rings.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

2001 ◽  
Vol 11 (04) ◽  
pp. 565-599 ◽  
Author(s):  
CRISTIAN A. COCLICI ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Outer Region ◽  
Navier Stokes ◽  
Far Field ◽  
Computational Domain ◽  
Linearized Euler Equations ◽  
Naca0012 Airfoil

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

scholarly journals Competing Lagrangians for incompressible and compressible viscous flow

2019 ◽  
Vol 6 (1) ◽  
pp. 181595 ◽  
Author(s):  
F. Marner ◽  
M. Scholle ◽  
D. Herrmann ◽  
P. H. Gaskell
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Deterministic Model ◽  
First Integral ◽  
Dissipative Systems ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Irreversible Processes ◽  
Time Averaging ◽  
Sound Waves

A recently proposed variational principle with a discontinuous Lagrangian for viscous flow is reinterpreted against the background of stochastic variational descriptions of dissipative systems, underpinning its physical basis from a different viewpoint. It is shown that additional non-classical contributions to the friction force occurring in the momentum balance vanish by time averaging. Accordingly, the discontinuous Lagrangian can alternatively be understood from the standpoint of an analogous deterministic model for irreversible processes of stochastic character. A comparison is made with established stochastic variational descriptions and an alternative deterministic approach based on a first integral of Navier–Stokes equations is undertaken. The applicability of the discontinuous Lagrangian approach for different Reynolds number regimes is discussed considering the Kolmogorov time scale. A generalization for compressible flow is elaborated and its use demonstrated for damped sound waves.

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