Length Scales and the Navier-Stokes Equations

1993 ◽  
pp. 267-270
Author(s):  
M. Bartuccelli ◽  
C. D. Doering ◽  
J. D. Gibbon ◽  
S. J. A. Malham
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Length Scales ◽  
Navier Stokes Equations

Characterization of coherent vortical structures in a supersonic turbulent boundary layer

2008 ◽  
Vol 613 ◽  
pp. 205-231 ◽  
Author(s):  
SERGIO PIROZZOLI ◽  
MATTEO BERNARDINI ◽  
FRANCESCO GRASSO
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Stokes Equations ◽  
Supersonic Boundary Layer ◽  
Navier Stokes ◽  
Hairpin Vortices ◽  
Length Scales ◽  
Navier Stokes Equations ◽  
Vortical Structures

A spatially developing supersonic boundary layer at Mach 2 is analysed by means of direct numerical simulation of the compressible Navier--Stokes equations, with the objective of quantitatively characterizing the coherent vortical structures. The study shows structural similarities with the incompressible case. In particular, the inner layer is mainly populated by quasi-streamwise vortices, while in the outer layer we observe a large variety of structures, including hairpin vortices and hairpin packets. The characteristic properties of the educed structures are found to be nearly uniform throughout the outer layer, and to be weakly affected by the local vortex orientation. In the outer layer, typical core radii vary in the range of 5–6 dissipative length scales, and the associated circulation is approximately constant, and of the order of 180 wall units. The statistical properties of the vortical structures in the outer layer are similar to those of an ensemble of non-interacting closed-loop vortices with a nearly planar head inclined at an angle of approximately 20° with respect to the wall, and with an overall size of approximately 30 dissipative length scales.

scholarly journals Length scales for the Navier–Stokes equations on a rotating sphere

2004 ◽  
Vol 324 (2-3) ◽  
pp. 179-184 ◽  
Author(s):  
Yuliya N. Kyrychko ◽  
Michele V. Bartuccelli
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Length Scales ◽  
Navier Stokes Equations ◽  
Rotating Sphere

scholarly journals Length scales in solutions of the Navier-Stokes equations

Nonlinearity ◽  
1993 ◽  
Vol 6 (4) ◽  
pp. 549-568 ◽  
Author(s):  
M V Bartuccelli ◽  
C R Doering ◽  
J D Gibbon ◽  
S J A Malham
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Length Scales ◽  
Navier Stokes Equations

PREDICTABILITY AND THE BUTTERFLY EFFECT IN TURBULENT FLOWS: A SHELL MODEL STUDY

1993 ◽  
Vol 03 (06) ◽  
pp. 1581-1585
Author(s):  
A. CRISANTI ◽  
A. VULPIANI ◽  
M. H. JENSEN ◽  
G. PALADIN
Keyword(s):  
Shell Model ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Length Scales ◽  
Navier Stokes Equations ◽  
Gaussian Shape ◽  
Model Study ◽  
Large Length ◽  
The Mean

We discuss the dynamical growth of a disturbance in turbulent flows based on numerical calculations of an approximative model of the Navier–Stokes equations, a so-called shell model. A disturbance at small length scales is observed to propagate (and increase) towards large length scales by an inverse cascade of duration T, the predictability time. At increasing Reynolds number Re, the mean predictability time Tt is found to decrease proportionally to Re−0.47. Moreover, the probability distribution of (T − Tt)/Tt changes its shape as Re increases: at relatively small values of Re it has an almost Gaussian shape, while at large Re it gets an exponential tail, indicating the possibility of large excursions for Tt.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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