PRES Large Eddy Simulation(1)

KIT – University of the State of Baden-Wuerttemberg and

National Research Center of the Helmholtz Association www.kit.edu 35th IAHR World Congress

Wolfgang Rodi

Institute for Hydromechanics

Karlsruhe Institute of Technology

Karlsruhe, Germany

Large-Eddy Simulation in Hydraulics -

the method and its potential



2 35th IAHR World Congress Prof. Wolfgang Rodi

New Book in IAHR Monograph Series

Large-Eddy Simulation in Hydraulics

Wolfgang Rodi Karlsruhe Institute of

Technology, Germany

George Constantinescu The University of Iowa,

USA

Thorsten Stoesser Cardiff University, UK

Published June 27, 2013

by CRC Press, Taylor & Francis Group

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Eddies in Turbulence

Surface of stirred tank Energy spectrum of turbulence

• Large eddies dominate mean-flow behaviour

• Small eddies dissipate energy

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Large eddies in shallow mixing layer

courtesy of

W. Uijttewaal

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Flow in flood plain with vegetation

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Large eddies in groyne field

From Weitbrecht, Socolofsky &

Jirka (2008)

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Flow over rectangular structure/roughness

element

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Flow over gravel bed

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Coherent structures – bursts/streaks – near wall

From Nezu and Nakagawa (1993) Courtesy of T. Stoesser

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Calculation approaches for turbulent flows

Starting point: Navier Stokes equations:

0,1

)(2

i

i

jj

i

i

ji

j

i

x

u

xx

u

x

puu

xt

u

• Direct Numerical Simulation (DNS):

Numerical solution of exact time -

dependent Navier-Stokes equations

No. of grid points ~ Re3

• Large-Eddy Simulation (LES):

Numerical resolution of only the larger

eddies; subgrid-scale model for effect

of smaller eddies

• Solution of Reynolds - averaged

Navier-Stokes equations (RANS):

Turbulent fluctuations averaged out.

Effect of all turbulent motions accounted

for by turbulence model: Main method

used in practice, economical, but poor on handling complex phenomena

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DNS – LES – RANS – Spectral Perspective

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Difference large/small eddies – the idea of LES

• The idea of LES is to calculate explicitly the large scales by solving the 3D

unsteady equations – and to model the motion of the small scales

• This avoids problem of having to model the large-scale, problem - dependent

motion - and at the same time of having to resolve the small-scale dissipative

motion, thus removing restriction to low Re

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Concept of LES – Scale Separation

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Spatial averaging / filtering

0,1

)(2

i

i

jj

i

i

ji

j

i

x

u

xx

u

x

puu

xt

u

Starting point: Navier-Stokes equations:

• RANS introduces time averaging/

filtering

• In LES small-scale motion removed

by spatial averaging or filtering.

Aproaches:

• Averaging over control volume of mesh:

is Schumann‘s volume-balance method

=> discrete balance equations for each CV

• Filtering:

e.g. top hat or

Gaussian filter:

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15 35th IAHR World Congress Prof. Wolfgang Rodi 29.08.2013




Filtered / averaged equations – SGS stresses

appearing in filtered/ averaged equations

• This needs to be modeled (SGS model) – effect mainly dissipative – can be

achieved by numerical dissipation (ILES method)

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• Originally the non-linear convection term is 𝑢𝑖𝑢𝑗 ≠ 𝑢 𝑖𝑢 𝑗

• Difference is subgrid-scale (SGS) stress




Effect of filter width / cut-off boundary

Fairly large filter width - relatively large

unresolved scales requiring more SGS model

effort → VLES

Small filter width, most scales resolved,

only smallest scales to be modeled →

Simple SGS model ok

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Subgrid-scale Models

Strain tensor:

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• In shallow water 2 range spectrum

- 2D LES resolving only large-scale

horizontal motion possible

- Sub-depth-scale model necessary,

e.g.:

- 2D LES not covered here

(see Hinterberger et al, JHE 2008)

3D/2D LES

• Away from walls LES not restricted to low Re

• At high Re near walls, such as bed, important

scales small → No. of grid points ~ Re2

- near-wall model necessary

- either wall functions or RANS treatment in

Hybrid approach

• Genuine LES is 3D

- large computing times

*hut

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Boundary conditions/near-wall treatment

Walls:

• Wall-resolved LES: no slip

(not for high Re)

• High Re: wall model needed

- Wall functions

(log/exponential velocity)

- RANS near wall –

Hybrid approach, e.g.

Detached Eddy Simulation

(DES)

Free surface:

• Usually rigid lid approximation

- Surface elevations suppressed, effects simulated via pressure variations

→ ok when surface deviations from mean small

inflow

free

surface

bed/walls

outflow

LES

RANS

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Inflow and outflow conditions

Inflow:

• In addition to mean values,

realistic fluctuations must be

provided

- Periodic conditions when

flow periodic (developed)

- Precursor calculation of

developed flow in channel

of inflow cross section

- Synthetically generated turbulence

superimposed on measured or guessed

velocity distribution

Outflow: Convective condition used - solving 1D equation in flow direction -

allows disturbances to leave domain freely

periodic conditions

inflow

outflow

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Hybrid LES – RANS Methods

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• Two-layer methods

near-wall layer calculated by RANS

different eddy-viscosity models in the 2

regions

sharp or smeared interface

• Detached Eddy Simulation (DES)

also RANS near wall

same ν𝑡model in 2 regions,

length-scale determination different

• Embedded LES

only where complex

flow LES applied

main problem is

coupling




LES of open channel flow at Reτ = 590, Reh = 11000

Hinterberger et al (2008) • grid 8 Mio cells

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Channel flow with sediment erosion

A B

A B

Instantaneous velocity and sediment concentration in cross-sectional plane

Courtesy of Jing Bai and Hongwei Fang, Tsinghua University, Beijing

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Channel flow over 3 layers of spheres

computational set-up

• LES of Stoesser et al (2007 – Proc. 32nd IAHR Congress)

In analogy to PIV measurements from Aberdeen University (Dr. D. Prokrajac)

Domain: 5.3H x 3.5H x H, 18 x 12 spheres per layer, H/D=3.42

200,15Re

Hub

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Instantaneous Streamwise Velocity –

Longitudinal Plane

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Perturbation vectors (u’-w’)

Slice a

Ejections

Slice b

Sweeps

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DNS of moveable bed motion

Calculations of A. Kidanemariam and M. Uhlmann,

Institute for Hydromechanics, KIT

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Periodic dunes – Flow structure 1

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Periodic dunes – instantanous velocity

vectors

a) instantaneous velocity perturbations in a longitudinal plane

b) snapshot of instantaneous velocity perturbations near surface

c) snapshot of instantaneous velocity vectors near bed

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Periodic dunes – 3D flow structures

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From Omidyeganeh and Piomelli (2011)




Flow through vegetation

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From Stoesser et al (2010)




Flow structures at river confluence

Momentum ratio Mr ≈ 1 Momentum ratio Mr ≈ 5

Vortical structures in horizontal plane near surface

• DES of Miyanaki, Constantinescu et al (2010)

• Re = UD/ ν = 18 000, 4 Mio grid cells

A3

A1

A

C

(a) (b)

20D

N A3

A1

A

C

wzD/U

0.50

0.25

0.00

-0.25

-0.50

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Flow structure at river confluence 2

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Flow past cylinder in shallow water

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Flow past bridge pier with deformed bathymetry

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LES of Kirkil et al (2008)




Flow past bridge abutment

near surface near bed

high Re low Re

from Koken and Constantinescu (2009)

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Flow past bridge abutment – u* time series

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Groyne field – instantaneous flow field

Snapshot of instantaneous vectors

of velocity perturbation

Top: PIV measurements

Bottom: LES

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Groyne field – flow and mass exchange

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Groyne field – mass exchange

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Concluding remarks

• LES allows to predict and study flows with complex behaviour

• Method yields information on unsteady features, resolves large-

scale eddies

• Superior to RANS whenever large-scale structures dominate

flow and scalar transport

• Well-resolved LES feasable only at low Re – at high Re near-

wall region needs to be bridged by wall functions

or simulated by RANS in Hybrid method (e.g. DES)

• Embedded LES promising for large-scale problems

• With increasing computer power LES and in particular Hybrid

LES-RANS will be used more and more in Hydraulics

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Documents

PRES Large Eddy Simulation(1)