scholarly journals Eroding dipoles and vorticity growth for Euler flows in : axisymmetric flow without swirl

2016 ◽  
Vol 805 ◽  
pp. 1-30 ◽  
Author(s):  
Stephen Childress ◽  
Andrew D. Gilbert ◽  
Paul Valiant
Keyword(s):  
Mirror Symmetry ◽  
Axisymmetric Flow ◽  
Vortical Structures ◽  
Piecewise Constant ◽  
Constant Vorticity ◽  
Vortex Dipole ◽  
Euler’S Equations ◽  
Euler Flows ◽  
Euler's Equations ◽  
Structurally Stable

A review of analyses based upon anti-parallel vortex structures suggests that structurally stable dipoles with eroding circulation may offer a path to the study of vorticity growth in solutions of Euler’s equations in $\mathbb{R}^{3}$. We examine here the possible formation of such a structure in axisymmetric flow without swirl, leading to maximal growth of vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the $t^{4/3}$ growth mimics an exact solution of Euler’s equations representing an eroding toroidal vortex dipole which locally conserves kinetic energy. The dipole cross-section is a perturbation of the classical Sadovskii dipole having piecewise constant vorticity, which breaks the symmetry of closed streamlines. The structure of this perturbed Sadovskii dipole is analysed asymptotically at large times, and its predicted properties are verified numerically. We also show numerically that if mirror symmetry of the dipole is not imposed but axial symmetry maintained, an instability leads to breakup into smaller vortical structures.

Analytical and Numerical Study of a Swirling Submerged Jet Flow

2010 ◽  
Author(s):  
H. Alighanbari ◽  
M. Amiralaei ◽  
S. Savtchenko
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Vortical Structures ◽  
Piecewise Constant ◽  
Constant Vorticity ◽  
Submerged Jets ◽  
Helical Vortices ◽  
Helical Vortex ◽  
Upstream Flow

The present study is conducted to investigate the details and characteristics of swirling submerged jets when transferred into a system of helical vortices downstream in a bathtub-like flow. Both analytical and numerical results are presented. In the analytical solution, upstream flow is considered to be two-dimensional with piecewise-constant vorticity profile. The instability of such a flow leads to the formation of two-dimensional dipolar or tripolar vortical structures. It is shown that the size of the vortexless annular area inside the initial vortex is a critical parameter in the two dipolar unstable or tripolar stable structure formations, and that such tripolar flow transforms downstream to a three-dimensional steady helical vortex system, which rotates as a whole and propagates in the downstream direction. The mechanism of screwing vortex filaments into a steady system of helical vortices is also presented. The numerical simulations also confirm the initiation and generation of dipolar vortex structures.

scholarly journals Convergence of Vortex Methods for Euler's Equations

1978 ◽  
Vol 32 (143) ◽  
pp. 791 ◽  
Author(s):  
Ole Hald ◽  
Vincenza Mauceri Del Prete
Keyword(s):  
Vortex Methods ◽  
Euler’S Equations ◽  
Euler's Equations

A physics-based turbocharger model for automotive diesel engine control applications

2018 ◽  
Vol 233 (7) ◽  
pp. 1667-1686 ◽  
Author(s):  
Kang Song ◽  
Devesh Upadhyay ◽  
Hui Xie
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Turbine Rotor ◽  
Variable Geometry ◽  
Gas Velocity ◽  
Euler’S Equations ◽  
Variable Geometry Turbine ◽  
Euler's Equations ◽  
Compressor Power

Control-oriented models of turbocharger processes such as the compressor mass flow rate, the compressor power, and the variable geometry turbine power are presented. In a departure from approaches that rely on ad hoc empirical relationships and/or supplier provided performance maps, models based on turbomachinery physics and known geometries are attempted. The compressor power model is developed using Euler’s equations of turbomachinery, where the gas velocity exiting the rotor is estimated from an empirically identified correlation for the ratio between the radial and tangential components of the gas velocity. The compressor mass flow rate is modeled based on mass conservation, by approximating the compressor as an adiabatic converging-diverging nozzle with compressible fluid driven by external work input from the compressor wheel. The variable geometry turbine power is developed with Euler’s equations, where the turbine exit swirl and the gas acceleration in the vaneless space are neglected. The gas flow direction into the turbine rotor is assumed to align with the orientation of the variable geometry turbine vane. The gas exit velocity is calculated, similar to the compressor, based on an empirical model for the ratio between the turbine rotor inlet and exit velocities. A power loss model is also proposed that allows proper accounting of power transfer between the turbine and compressor. Model validation against experimental data is presented.

GRAPHIC TREATMENT OF EULER'S EQUATIONS

Science ◽  
1927 ◽  
Vol 66 (1700) ◽  
pp. 114-115
Author(s):  
C. Barus
Keyword(s):  
Euler’S Equations ◽  
Euler's Equations

scholarly journals Existence of capillary-gravity water waves with piecewise constant vorticity

2014 ◽  
Vol 256 (8) ◽  
pp. 3086-3114 ◽  
Author(s):  
Calin Iulian Martin ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Water Waves ◽  
Piecewise Constant ◽  
Constant Vorticity

On the wake dynamics of a propeller operating in drift

2014 ◽  
Vol 754 ◽  
pp. 263-307 ◽  
Author(s):  
A. Di Mascio ◽  
R. Muscari ◽  
G. Dubbioso
Keyword(s):  
Axisymmetric Flow ◽  
Operating Conditions ◽  
Tip Vortex ◽  
Streamwise Direction ◽  
Vortical Structures ◽  
Actual Operating ◽  
Oblique Flow ◽  
The Subject ◽  
Flow Variables

AbstractThe onset and the nature of dynamic instabilities experienced by the wake of a marine propeller set in oblique flow are investigated by means of detached eddy simulations. In particular, the destabilization process is inspected by a systematic comparison of the wake morphology of a propeller operating in pure axisymmetric flow and in drift with angle of 20°, under different loading conditions. The wake behaviour in oblique flow shows a markedly different character with respect to the axisymmetric condition: in the latter, the destabilization is triggered by an increasing interaction of the main vorticity confined in the tip vortex; whereas, in the former, the role of the secondary vorticity (oriented in the streamwise direction) as well as the hub vortex seems to be crucial. The features of the wake have been investigated by the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\lambda _{2}$ criterion (Jeong & Hussain, J. Fluid Mech., vol. 285, 1995, pp. 69–94) and typical flow variables (pressure, velocity and vorticity), for both the averaged and instantaneous flow fields. Moreover, in order to further inspect the evolution of the vortical structures, as well as their interaction and destabilization, the spectra of the kinetic energy have been considered. This investigation aims to broaden the knowledge from previous works on the subject of rotor wake instabilities, focusing on the differences between an ideal (axisymmetric) and actual operating conditions occurring in typical engineering applications.

Sign in / Sign up

Export Citation Format

Share Document