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Assessment of Turbulence Modeling for Compressible Flow
Around Stationary and Oscillating Cylinders
by Alejandra Uranga
Supervisors: Drs Nedjib Djilali and Afzal Suleman Dept. of Mechanical Engineering - University of Victoria
August 21, 2006
A p p l i e d V e h i c l e
Technologies
Outline
Introduction
Simulation Methodology
Stationary Cylinder
Oscillating Cylinder
Conclusions
Introduction
Periodic pattern of counter-rotating vortices caused by unsteady separation from a bluff body
Kármán Vortex Street
Introduction Methodology Stationary Oscillating Conclusions
Introduction
Periodic pattern of counter-rotating vortices caused by unsteady separation from a bluff body
Kármán Vortex Street
Introduction Methodology Stationary Oscillating Conclusions
NASA satellite image 1999
Introduction
Interaction between 3 shear layers - Boundary layer - Free shear layer - Wake
Flow Around a Circular Cylinder
Introduction Methodology Stationary Oscillating Conclusions
Introduction
Interaction between 3 shear layers - Boundary layer - Free shear layer - Wake
Flow Around a Circular Cylinder
Introduction Methodology Stationary Oscillating Conclusions
Transition to turbulence in - Wake ReD 200 → 400 - Free Shear layer ReD 400 → 150x103 - Boundary layer ReD 150x103 → 8x106
Introduction
Simulation of turbulent flow around circular cylinders - Stationary ReD = 3900 - Oscillating ReD = 3600
Compare accuracy of turbulence models using same numerical procedure with respect to experiments
and other simulations
Scope
Introduction Methodology Stationary Oscillating Conclusions
Methodology
Numerical Simulation of Turbulent Flows
Methodology
Example: Incompressible Momentum Equation
Applying an average or filter operator (overbar) to the momentum equation yields
The terms , , are solved for
The cross terms are unknown closure problem
Introduction Methodology Stationary Oscillating Conclusions
The Need for Turbulence Models
Methodology
Introduction Methodology Stationary Oscillating Conclusions
Simulation of Turbulence
DNS Direct Numerical
Simulation
Solve all Scales
very thin grid required €
ui
URANS Unsteady
Reynolds Averaged Navier-Stokes
(One-point closure)
mean fluctuating
Solve mean quantities
Model Reynolds stresses
€
u i
LES Large Eddy Simulation
large scale Subgrid-Scale
Solve large scale eddies
Model subgrid-scale stress €
u i
Methodology
URANS - One equation Spalart-Allmaras - K-tau Speziale et al.
Large Eddy Simulation (LES) - Smagorinsky-Lilly
Very Large Eddy Simulation (VLES) - Adaptive k-tau Magagnato & Gabi (uses a URANS type subgrid-scale model)
Introduction Methodology Stationary Oscillating Conclusions
Turbulence Models Considered
Methodology
SPARC Structured PArallel Research Code
Finite Volume, Cell Centered, Block-Structured, Multigrid
Simulations are 3D Unsteady Compressible Viscous
Introduction Methodology Stationary Oscillating Conclusions
Computational Code
Stationary Cylinder
Stationary Circular Cylinder in a Uniform Flow
Stationary Cylinder
Cylinder diameter D = 1m Flow velocity U0 = 68.63m/s Mach number Mach 0.2 Reynolds number ReD = 3900
Problem Setup
Introduction Methodology Stationary Oscillating Conclusions
Stationary Cylinder
2D figures: x-y plane at span center
Computational Domain
Introduction Methodology Stationary Oscillating Conclusions
Stationary Cylinder URANS : Average Fields
Introduction Methodology Stationary Oscillating Conclusions
SA Sp
u/U0
ωzD/U0
Stationary Cylinder URANS : Average Streamlines
Introduction Methodology Stationary Oscillating Conclusions
SA Sp
Stationary Cylinder URANS : Average Profiles
Introduction Methodology Stationary Oscillating Conclusions
u/U0 at x/D = 1.54
cp around cylinder
cf around cylinder
Stationary Cylinder LES-VLES : Streamlines
Introduction Methodology Stationary Oscillating Conclusions
LES VLES
Stationary Cylinder LES-VLES : Average Fields
Introduction Methodology Stationary Oscillating Conclusions
LES VLES
u/U0
ωzD/U0
Stationary Cylinder LES-VLES : Average Profiles
Introduction Methodology Stationary Oscillating Conclusions
u/U0 at x/D=1.54
cp around cylinder
cf around cylinder
Stationary Cylinder 3-Dimensionality
Streamwise velocity iso-surfaces
Introduction Methodology Stationary Oscillating Conclusions
URANS Sp LES
Stationary Cylinder Comparison
Introduction Methodology Stationary Oscillating Conclusions
Oscillating Cylinder
Circular Cylinder in Cross-Flow Oscillations
Oscillating Cylinder
Vertical sinusoidal motion
2D URANS k-tau Speziale
Reynolds number 3600
Lock-in: vortex shedding frequency matches cylinder motion frequency
Motion and Cases
Introduction Methodology Stationary Oscillating Conclusions
Oscillating Cylinder URANS Sp Fields
Introduction Methodology Stationary Oscillating Conclusions
ωzD/U0 u/U0
Case IV fc / f0 = 0.800
Oscillating Cylinder Lock-in
Introduction Methodology Stationary Oscillating Conclusions
46%
40% 2%
1%
63%
32%
motion frequency fc/f0
sheddi
ng f
requ
ency
fS/f
0
Conclusions
Summary and Further Work
Conclusions
comparison of results from different turbulence models with same numerical procedure
Spalart-Allmaras model - error in separation point flow remains attached too long small recirculation zone low back pressure large drag
- Accurate Strouhal number
Introduction Methodology Stationary Oscillating Conclusions
Conclusions
K-tau Speziale model - Good mean global quantities Strouhal number, drag, back pressure, separation point velocity profiles along the wake
LES and VLES - reveal secondary eddies - LES resolves dynamics in boundary layer
Oscillating Cylinder
- No other numerical results in same regime
- Lock-in over large range of motion frequencies
- Further investigation required
Introduction Methodology Stationary Oscillating Conclusions
Conclusions
Better averages on LES and VLES
LES with Dynamic and Dynamic Mixed subgrid-scale models
LES of oscillating cylinder
Further Work
Introduction Methodology Stationary Oscillating Conclusions
Questions