PowerPoint Presentation by Cl3Kz1

VIEWS: 2 PAGES: 28

• pg 1
```									    Reynolds Stress Constrained
Multiscale Large Eddy Simulation for
Wall-Bounded Turbulence

Shiyi Chen
Yipeng Shi, Zuoli Xiao, Suyang Pei, Jianchun Wang, Yantao Yang
State Key Laboratory of Turbulence and Complex Systems
College of Engineering, Peking University
and
Johns Hopkins University
Question: How can one directly use
fundamental physics learnt from our
research on turbulence for modeling and
simulation?

Conservation of energy, helicity, constant
energy flux in the inertia range, scalar flux,
intermittency exponents, Reynolds
stress structures…

Through constrained variation principle..
such as decimation theory, renormalized
perturbation theory… physical space?
Test of the Constrained-SGS Model
Forced isotropic turbulence:
DNS: Direct Numerical Simulation. A            DSM: Dynamic Smagorinsky Model
DMM: Dynamic Mixed Similarity Model
(Re=250) data obtained by Pseudo-
spectral method with 5123 resolution.          CDMM: Constrained Dynamic Mixed Model

Comparison of the steady state energy spectra.      Comparison of PDF of SGS dissipation at grid
scale (a posteriori)
Large Eddy Simulation
resolution challenge at high Re

106

108.5

(Piomelli 2002)

Near-wall treatment is key to utility of LES in practice
Hybrid RANS/LES
Detached Eddy Simulation

S-A Model

                                      
Dˆ / Dt  Cb1 1  ft 2  Sˆ   Cw1 f w  Cb1 /  2  ˆ / d       ˆ  ˆ   Cb 2  ˆ  /   f t1U 2
2                                      2
DES-Mean Velocity Profile
DES Buffer Layer and Transition Problem

Lack of small scale fluctuations in the RANS area is the
main shortcoming of hybrid RANS/LES method
Possible Solution to the Transition Problem

Hamba (2002, 2006): Overlap method
Keating et al. (2004, 2006): synthetic turbulence in the interface
Reynolds Stress Constrained Large Eddy
Simulation (RSC-LES)
1. Solve LES equations in both inner and outer layers, the
inner layer flow will have sufficient small scale fluctuations
and generate a correct Reynolds Stress at the interface;

2. Impose the Reynolds stress constraint on the inner layer
LES equations such that the inner layer flow has a
consistent (or good) mean velocity profile; (constrained
variation)

3. Coarse-Grid everywhere

LES        Small scare turbulence
in the whole space

Reynolds Stress Constrained
Control of the mean velocity profile in LES by
imposing the Reynolds Stress Constraint

LES equations
ui   ui u j    p       2ui       ij
SGS

                         
t     x j      xi    x j x j    x j

Performance of ensemble average of the LES equations
 ui        ui u j         p         2 ui            ij
SGS
Rij
LES

                                                    
t           x j         xi        x j x j         x j          x j

where

RANS
Rij     Rij   ij
LES    SGS
Reynolds stress constrained SGS stress model is
adopted for the LES of inner layer flow:

Decompose the SGS model              into two parts:

The mean value               is solved from the Reynolds

stress constraint:

(1) K-epsilon model to solve Rijmod
(2) Algebra eddy viscosity: Balaras & Benocci (1994) and Balaras et
al. (1996)

where

(3) S-A model (best model so far for separation)
For the fluctuation of SGS stress, a Smagorinsky

The interface to separate the inner and outer layer
is located at the beginning point of log-law region, such
the Reynolds stress achieves its maximum.
Results of RSC-LES

Mean velocity profiles of RSC-LES of turbulent
channel flow at different ReT =180 ~ 590
Mean velocity profiles of RSC-LES, non-constrained
LES using dynamic Smagorinsky model and DES
(ReT=590)
Mean velocity profiles of RSC-LES, non-constrained
LES using dynamic Smagorinsky model and DES
(ReT=1000)
Mean velocity profiles of RSC-LES, non-constrained
LES using dynamic Smagorinsky model and DES
(ReT=1500)
Mean velocity profiles of RSC-LES, non-constrained
LES using dynamic Smagorinsky model and DES
(ReT=2000)
Error in prediction of the skin friction coefficient:

C f  C f ,Dean                   wall                        
Error                      100   Cf                C f ,Dean  0.073Reb1 4   (friction law, Dean)
C f ,Dean                     Ub 2
2

% Error                    ReT=590               ReT=1000                ReT=1500            ReT=2000

LES-RSC                       1.6                     2.5                    3.3               0.3

LES-DSM                        15.5                    21.3                   30.2              35.9

DES                          19.7                    17.0                   13.5              14.1
Interface of RSC-LES and DES (ReT=2000)
Velocity fluctuations (r.m.s) of RSC-LES and DNS
(ReT=180,395,590). Small flunctuations generated at the
near-wall region, which is different from the DES method.

RSC-LES                    DNS(Moser)
Velocity fluctuations (r.m.s) and resolved shear
stress:(ReT=2000)
DES streamwise fluctuations in plane parallel to the
wall at different positions:(ReT=2000)

y+=6               y+=38              y+=200

y+=500             y+=1000           y+=1500
DSM-LES streamwise fluctuations in plane parallel to
the wall at different positions:(ReT=2000)

y+=6               y+=38             y+=200

y+=500            y+=1000            y+=1500
RSC-LES streamwise fluctuations in plane parallel to
the wall at different positions:(ReT=2000)

y+=6               y+=38             y+=200

y+=500            y+=1000            y+=1500
Multiscale Simulation of Fluid Turbulence
Conclusions
1. RSC-LES uses the same grids resolution as DES;
2. The inner layer flow solved by RSC-LES possesses
sufficient small scale fluctuations;
3. The transition of the mean velocity profile obtained
by the RSC-LES from the inner layer to the outer
layer at the interface is smooth;
4. RSC-LES is a simple method and may improve DES,
and the forcing scheme…
5. We have used time averaging scheme for non-
uniform systems, RSC-LES works nicely.

```
To top