S IMULATIONS (SAS) Lars Davidson, www.tfd.chalmers.se/lada L ARGE E - - PowerPoint PPT Presentation

LES, HYBRID LES-RANS AND SCALE-ADAPTIVE SIMULATIONS (SAS)

Lars Davidson, www.tfd.chalmers.se/˜lada

LARGE EDDY SIMULATIONS

GS SGS SGS In LES, large (Grid) Scales (GS) are resolved and the small (Sub-Grid) Scales (SGS) are modelled. LES is suitable for bluff body flows where the flow is governed by large turbulent scales

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 2 / 58

BLUFF-BODY FLOW: SURFACE-MOUNTED CUBE[1]

Krajnovi´ c & Davidson (AIAA J., 2002)

Snapshots of large turbulent scales illustrated by Q = −∂¯ ui ∂xj ∂¯ uj ∂xi

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 3 / 58

BLUFF-BODY FLOW: FLOW AROUND A BUS[2]

Krajnovi´ c & Davidson (JFE, 2003)

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 4 / 58

BLUFF-BODY FLOW: FLOW AROUND A CAR[3]

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 5 / 58

BLUFF-BODY FLOW: FLOW AROUND A TRAIN[4]

Hemida & Krajnovi´ c, 2006

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 6 / 58

SEPARATING FLOWS

Wall

TIME-AVERAGED flow and INSTANTANEOUS flow

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 7 / 58

SEPARATING FLOWS

Wall

TIME-AVERAGED flow and INSTANTANEOUS flow In average there is backflow (negative velocities). Instantaneous, the negative velocities are often positive.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 7 / 58

SEPARATING FLOWS

Wall

TIME-AVERAGED flow and INSTANTANEOUS flow In average there is backflow (negative velocities). Instantaneous, the negative velocities are often positive. How easy is it to model fluctuations that are as large as the mean flow?

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 7 / 58

SEPARATING FLOWS

Wall

TIME-AVERAGED flow and INSTANTANEOUS flow In average there is backflow (negative velocities). Instantaneous, the negative velocities are often positive. How easy is it to model fluctuations that are as large as the mean flow? Is it reasonable to require a turbulence model to fix this?

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 7 / 58

SEPARATING FLOWS

Wall

TIME-AVERAGED flow and INSTANTANEOUS flow In average there is backflow (negative velocities). Instantaneous, the negative velocities are often positive. How easy is it to model fluctuations that are as large as the mean flow? Is it reasonable to require a turbulence model to fix this? Isn’t it better to RESOLVE the large fluctuations?

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 7 / 58

NEAR-WALL TREATMENT

Biggest problem with LES: near walls, it requires very fine mesh in all directions, not only in the near-wall direction.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 8 / 58

NEAR-WALL TREATMENT

Biggest problem with LES: near walls, it requires very fine mesh in all directions, not only in the near-wall direction. The reason: violent violent low-speed outward ejections and high-speed in-rushes must be resolved (often called streaks).

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 8 / 58

NEAR-WALL TREATMENT

Biggest problem with LES: near walls, it requires very fine mesh in all directions, not only in the near-wall direction. The reason: violent violent low-speed outward ejections and high-speed in-rushes must be resolved (often called streaks). A resolved these structures in LES requires ∆x+ ≃ 100, ∆y+

min ≃ 1 and ∆z+ ≃ 30

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 8 / 58

NEAR-WALL TREATMENT

Biggest problem with LES: near walls, it requires very fine mesh in all directions, not only in the near-wall direction. The reason: violent violent low-speed outward ejections and high-speed in-rushes must be resolved (often called streaks). A resolved these structures in LES requires ∆x+ ≃ 100, ∆y+

min ≃ 1 and ∆z+ ≃ 30

The object is to develop a near-wall treatment which models the streaks (URANS) ⇒ much larger ∆x and ∆z

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 8 / 58

NEAR-WALL TREATMENT

Biggest problem with LES: near walls, it requires very fine mesh in all directions, not only in the near-wall direction. The reason: violent violent low-speed outward ejections and high-speed in-rushes must be resolved (often called streaks). A resolved these structures in LES requires ∆x+ ≃ 100, ∆y+

min ≃ 1 and ∆z+ ≃ 30

The object is to develop a near-wall treatment which models the streaks (URANS) ⇒ much larger ∆x and ∆z In the presentation we use Hybrid LES-RANS for which the grid requirements are much smaller than for LES

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 8 / 58

NEAR-WALL TREATMENT

from Hinze (1975)

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 9 / 58

NEAR-WALL TREATMENT

1 2 3 4 5 6 0.5 1 1.5

x z Fluctuating streamwise velocity at y+ = 5. DNS of channel flow. We find that the structures in the spanwise direction are very small which requires a very fine mesh in z direction.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 10 / 58

HYBRID LES-RANS

Near walls: a RANS one-eq. k or a k − ω model. In core region: a LES one-eq. kSGS model. y x Interface wall wall URANS URANS LES y+

ml

• Location of interface either pre-defined or automatically computed

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 11 / 58

MOMENTUM EQUATIONS

• The Navier-Stokes, time-averaged in the near-wall regions and

filtered in the core region, reads ∂¯ ui ∂t + ∂ ∂xj ¯ ui ¯ uj

• = βδ1i − 1

ρ ∂¯ p ∂xi + ∂ ∂xj

• (ν + νT)∂¯

ui ∂xj

• νT = νt, y ≤ yml

νT = νsgs, y ≥ yml

• The equation above: URANS or LES? Same boundary conditions ⇒

same solution!

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 12 / 58

TURBULENCE MODEL

• Use one-equation model in both URANS region and LES region.

∂kT ∂t + ∂ ∂xj (¯ ujkT) = ∂ ∂xj

• (ν + νT) ∂kT

∂xj

• + PkT − Cε

k3/2

T

ℓ PkT = 2νT ¯ Sij ¯ Sij, νT = Ckℓk1/2

T

LES-region: kT = ksgs, νT = νsgs, ℓ = ∆ = (δV)1/3 URANS-region: kT = k, νT = νt, ℓ ≡ ℓRANS = 2.5n[1 − exp(−Ak1/2y/ν)], Chen-Patel model (AIAA

• J. 1988)

Location of interface can be defined by min(0.65∆, y), ∆ = max(∆x, ∆y, ∆z)

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 13 / 58

STANDARD HYBRID LES-RANS

• Coarse mesh: ∆x+ = 2∆z+ = 785. δ/∆x ≃ 2.5, δ/∆z ≃ 5.

10

1

10

2

10

3

5 10 15 20 25 30

y+ U+

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1

x B(x) standard LES-RANS; DNS; LES

• 0.4 ln(y+) + 5.2

B(x) = u(x0)u(x − x0) urmsurms

• Too high velocity because too low shear stress

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 14 / 58

WAYS TO IMPROVE THE RANS-LES METHOD[5, 6, 7]

The reason is that LES region is supplied with bad boundary (i.e. interface) conditions by the URANS region. The flow going from the RANS region into the LES region has no proper turbulent length or time scales New approach: Synthesized isotropic turbulent fluctuations are added as momentum sources at the interface. The superimposed fluctuations should be regarded as forcing functions rather than boundary conditions.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 15 / 58

FORCING FLUCTUATIONS ADDED AT THE INTERFACE

• Object: to trig the momentum equations into resolving large-scale

turbulence u′

f, v′ f , w′ f

x y URANS region LES region wall interface y+

ml

• For more info, see Davidson at al. [5, 7]

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 16 / 58

IMPLEMENTATION

u′

f

v′

f

An Interface Control Volume LES URANS Fluctuations u′

f, v′ f , w′ f are added as sources in all three

momentum equations. The source is −γρu′

i,fu′ 2,fAn = −γρu′ i,fu′ 2,fV/∆y (An=area, V=volume of the C.V.)

The source is scaled with γ = kT/ksynt

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 17 / 58

INLET BOUNDARY CONDITIONS

Uinlet constant in time; uinlet function of time.

5 10 15 20 25 0.2 0.4 0.6 0.8 1 Uin(y)

y U uin(y, t0)

20 40 60 80 100

u(x, y0, t0)

x

xE

Left: Inlet boundary profiles Right: Evolution of u velocity depending of type of inlet B.C.

• With steady inlet B.C., u gets turbulent first at x = xE.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 18 / 58

EMBEDDED LES (BLUFF BODY FLOWS)

Uin+u′

i(t)

Uout Uout Steady RANS Steady RANS

LES

Uin+u′

i(t) used as B.C. for LES in the inner region.

Examples of inner region: external mirror of a car; a flap/slat; a detail of a landing gear. Often in connection with aero-acoustics.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 19 / 58

INLET BOUNDARY CONDITIONS VS. FORCING

Inlet Ub(y) y u′(y, t) URANS region LES region x Ub(xi, t) u′(xi, t)

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 20 / 58

FULLY DEVELOPED CHANNEL FLOW (PERIODIC IN x)

10

1

10

2

10

3

5 10 15 20 25 30

y+ U+

0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2

uv + y/h no forcing; forcing (isotropic fluctuations)

• 0.4 ln(y+) + 5.2

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 21 / 58

DIFFUSER[5]

Instantaneous inlet data from channel DNS used. Domain: −8 ≤ x ≤ 48, 0 ≤ yinlet ≤ 1, 0 ≤ z ≤ 4. xmax = 40 gave return flow at the outlet Grid: 258 × 66 × 32. Re = UinH/ν = 18 000, angle 10o The grid is much too coarse for LES (in the inlet region ∆z+ ≃ 170) Matching plane fixed at yml at the inlet. In the diffuser it is located along the 2D instantaneous streamline corresponding to yml.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 22 / 58

DIFFUSER GEOMETRY. Re = 18 000, ANGLE 10o

H = 2δ 7.9H 21H 29H 4H 4.7H periodic b.c. convective outlet b.c. no-slip b.c.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 23 / 58

DIFFUSER: RESULTS WITH LES

• Velocities. Markers: experiments by Buice & Eaton (1997)

x = 3H 6 14 17 20 24H x/H = 27 30 34 40 47H

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 24 / 58

DIFFUSER: RESULTS WITH NEW RANS-LES

x = 3H 6 14 17 20 24H x/H = 27 30 34 40 47H forcing; no forcing

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 25 / 58

DIFFUSER: RESULTS WITH NEW RANS-LES

0.5 1 1.5

x = −H

−0.5 0.5 1 −0.5 0.5 1

x = 3H

−0.5 0.5 1 −1.5 −1 −0.5 0.5 1

x = 6H forcing; no forcing

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 26 / 58

SHEAR STRESSES (×2 IN LOWER HALF)

x = 3H 6 13 19 23H x/H = 26 33 40 47H resolved; modelled

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 27 / 58

RANS-LES: νt/ν

x = 3H 6 14 17 20 24H x/H = 27 30 34 40 47H forcing; without forcing At x = 24H, νT,max/ν ≃ 450 At x = −7H νT,max/ν ≃ 11

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 28 / 58

RANS-LES: LOCATION OF MATCHING LINE

• Location of matching line. It is defined along 2D instantaneous

streamline (defined by mass flow). Ub,in,kyml,in,k∆z =

jml,i,k

• 2

(¯ ueAe,x + ¯ veAe,y) This approach has successfully been used for asymmetric plane diffuser as well as 3D hill (Simpson & Byun) Other option: min(0.65∆, y), ∆ = max(∆x, ∆y, ∆z)

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 29 / 58

3D-HILL

3.2H L2 W δ = 0.5H L1 H

• utlet B.C.

x z y Inlet B.C.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 30 / 58

NUMERICAL METHOD

Implicit, finite volume (collocated), Central differencing in space and time (Crank-Nicolson (α = 0.6)) Efficient multigrid solver for the pressure Poisson equation CPU/time step 25 seconds on a single AMD Opteron 244 Time step ∆tUin/H = 0.026. Mesh 160 × 80 × 128 8 000 + 8 000 time steps for fully developed+averaging (10 + 10 through flow or T ∗ = TUb/H = 200 + 200) One simulation (8 000 + 8 000) takes one week

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 31 / 58

SYMMETRY PLANE z = 0

0.5 1 1.5 2 0.5 1

y/H x/H Experiments Hybrid LES-RANS

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 32 / 58

3D HILL: RANS

X

• 1

1 2 3 4 1

Experiments RANS, SST

• Similar results obtained with all other RANS models (k − ω, Low-Re

RSM, EARSM, SA-model etc) [9].

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 33 / 58

STREAMWISE PROFILES AT x = 3.69H [8]

0.5 1 0.2 0.4 0.6 0.8 1

U/Uin

z/H = 0

0.5 1

−0.16

0.5 1

U/Uin

−0.49

0.5 1

−0.81

0.5 1

U/Uin

−1.14

0.5 1

−1.47

0.5 1

U/Uin

−1.79

Hybrid LES-RANS; ◦ Experiments

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 34 / 58

SECONDARY VELOCITY VECTORS AT x = 3.69H

−2.5 −2 −1.5 −1 −0.5 0.5 1

y/H Hybrid LES-RANS

−2.5 −2 −1.5 −1 −0.5 0.5 1

y/H z/H Expts

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 35 / 58

SECONDARY VELOCITY VECTORS AT x = 3.69H

−2.5 −2 −1.5 −1 −0.5 0.5 1

y/H RANS, SST

−2.5 −2 −1.5 −1 −0.5 0.5 1

y/H z/H Expts

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 36 / 58

RANS SST: STREAMWISE PROFILES AT x = 3.69H

0.5 1 0.2 0.4 0.6 0.8 1

U/Uin

z/H = 0

0.5 1

−0.16

0.5 1

U/Uin

−0.49

0.5 1

−0.81

0.5 1

U/Uin

−1.14

0.5 1

−1.47

0.5 1

U/Uin

−1.79

RANS-SST; ◦ Experiments

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 37 / 58

3D HILL: SUMMARY

All RANS models give a completely incorrect flow field LES and hybrid LES-RANS in good agreement with expts. Mesh sizes RANS 0.5 − 1.2 million (half of the domain) Hybrid LES-RANS 1.7 million CPU times RANS, EARSM 1 − 2 days 1-CPU DEC-Alpha LES-RANS 1 week (10+10 T-F)∗ 1-CPU Opteron 244

∗ T-F=Through-Flows

• Hybrid LES-RANS results in Ref. [8]

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 38 / 58

MODELLED DISSIPATION, εM

• The unsteady Navier-Stokes reads

∂¯ ui ∂t + ∂ ∂xj ¯ ui ¯ uj

• = −1

ρ ∂¯ p ∂xi + ∂ ∂xj

• (ν + νT)

∂¯ ui ∂xj + ∂¯ uj ∂xi

• The turbulent viscosity, νT, dampens the fluctuations, via the modelled

dissipation, εM, which reads εM = −τij ∂¯ ui ∂xj = 2νT ¯ sij¯ sij, τij = −2νt¯ sij + 2 3δijk, ¯ sij = 0.5 ∂¯ ui ∂xj + ∂¯ uj ∂xi

• 2000

2050 2100 2150 2200 2250 2300 −2 −1.5 −1 −0.5 0.5 1 1.5 2

time step number ¯ u′ = ¯ u − ¯ u low dissipation high dissipation

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 39 / 58

STEADY VS. UNSTEADY REGIONS

∂¯ ui ∂t + ∂ ∂xj ¯ ui ¯ uj

• = −1

ρ ∂¯ p ∂xi + ∂ ∂xj

• (ν + νT)

∂¯ ui ∂xj + ∂¯ uj ∂xi

• OBJECT:

In regions of fine grid: turbulence resolved by ¯ u′

i, i.e. ∂¯

ui ∂t In regions of coarse grid: turbulence modelled by νT

• PROBLEM: in fine-grid regions, νT increases too much which kills ¯

u′

i

• SOLUTION: when ¯

u′

i starts to grow, reduce νT

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 40 / 58

VON K ´ ARM ´ AN LENGTH SCALE

5 10 15 20 0.2 0.4 0.6 0.8 1

¯ u y Lvk,1D Lvk,3D Lvk,1D = κ ∂¯ u/∂y ∂2¯ u/∂y2 LvK,3D = κ ¯ s |U′′|, ¯ s = (2¯ sij¯ sij)1/2 U′′ = ∂2¯ ui ∂xj∂xj ∂2¯ ui ∂xj∂xj 0.5

• The von K´

arm´ an detects unsteadiness (i.e. resolved turbulence, ¯ u′

i)

and reduces the length scale

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 41 / 58

THE SAS TURBULENCE MODEL[10, 11, 12]

Dk Dt − ∂ ∂xj

• ν + νt

σk ∂k ∂xj

• = νt¯

s2 − c1kω Dω Dt −

• ν + νt

σω ∂ω ∂xj

• transport

= c2¯ s2 − c3ω2 + PSAS νt = c4 k ω, PSAS = c5 L LvK,3D , LvK,3D = c6 ¯ s U′′

• Fine grid ⇒ unsteadiness ⇒ small LvK,3D ⇒ large PSAS ⇒ large ω ⇒

small k and low νt

• SAS: Scale-Adapated Simulation

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 42 / 58

SAS: EVALUATION FROM DNS CHANNEL DATA

• Reτ = 500, ∆x+ = 50, ∆z+ = 12, y+

min = 0.3

0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 100 200 300 400 500

y/δ y+ κ¯ s/U′′ κ

• ∂U/∂y

∂2U/∂y2

• (∆V)1/3
• ∆y

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 43 / 58

DOMAIN, Reτ = uτδ/ν = 2000 (Reb ≃ 80 000)

inlet

• utlet

2δ x y 100δ

• 256 × 64 × 32 (x, y, z) cells. zmax = 6.3δ, ∆x+ ≃ 785, ∆z+ ≃ 393.
• δ/∆z ≃ 5, δ/∆x ≃ 2.5
• MODELS: SAS and no SAS

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 44 / 58

CHANNEL WITH INLET-OUTLET

• Synthesized inlet fluctuations (U′)m, (V′)m, (W′)m with time scale

T = 0.2δ/uτ and length scale L = 0.1δ.

• The streamwise fluctuations are superimposed to a mean profile
• btained from 1D channel flow with k − ω model

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 45 / 58

MEAN VELOCITY

10

1

10

2

10

3

5 10 15 20 25 30

y SAS

10

1

10

2

10

3

5 10 15 20 25 30

no SAS y x = 3δ x = 23δ x = 98δ

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 46 / 58

RESOLVED URMS

0.2 0.4 0.6 0.8 1 1 2 3 4

y SAS

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 3 3.5 4

no SAS y x = 3δ x = 23δ x = 98δ

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 47 / 58

PEAK RESOLVED FLUCTUATIONS

20 40 60 80 100 1 2 3 4 5 6

x SAS

20 40 60 80 100 1 2 3 4 5 6

no SAS x max {u′v′} max {urms} max {wrms} ◦ max {vrms}

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 48 / 58

TURBULENT VISCOSITY νt/ν

0.2 0.4 0.6 0.8 1 50 100 150 200 250 300

y SAS

0.2 0.4 0.6 0.8 1 50 100 150 200 250 300

no SAS y x = 3δ x = 23δ x = 98δ ▽ 1D k − ω

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 49 / 58

EVALUATION OF THE SECOND DERIVATIVE

• Option I: (used) compute the first derivatives at the faces

∂u ∂y

• j+1/2

= uj+1 − uj ∆y , ∂u ∂y

• j−1/2

= uj − uj−1 ∆y ⇒ ∂2u ∂y2

• j

= uj+1 − 2uj + uj−1 (∆y)2 + (∆y)2 12 ∂4u ∂y4

• Option II: compute the first derivatives at the centre

∂u ∂y

• j+1

= uj+2 − uj 2∆y , ∂u ∂y

• j−1

= uj − uj−2 2∆y ⇒ ∂2u ∂y2

• j

= uj+2 − 2uj + uj−2 4(∆y)2 + (∆y)2 3 ∂4u ∂y4

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 50 / 58

SECOND DERIVATIVES

20 40 60 80 100 1 2 3 4 5 6

x SAS: Option I

20 40 60 80 100 1 2 3 4 5 6

SAS: Option II x max {u′v′} max {urms} max {wrms} ◦ max {vrms}

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 51 / 58

SAS: CONCLUSIONS

SAS: A model which controls the modelled dissipation, εM, has been presented It detects unsteadiness and then reduces εM In this way the model let the equations resolve the turbulence instead of modelling it The results is improved accuracy because of less modelling More details in [13]

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 52 / 58

CONCLUSIONS

Flows with large turbulence fluctuations difficult to model with RANS models because u′ ≃ ¯ u Unsteady methods (URANS, DES, SAS, Hybrid LES-RANS, LES) are increasingly being used in universities as well as in industry LES is a suitable method for bluff body flows Methods based on a mixture of LES and RANS are likely to be the methods of the future For boundary layers (Rex → ∞) some kind of forcing needed when going from (U)RANS region to LES region Fluctuating inlet boundary conditions can be regarded as a special case of forcing

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 53 / 58

REFERENCES I

• S. Krajnovi´

c and L. Davidson. Large eddy simulation of the flow around a bluff body. AIAA Journal, 40(5):927–936, 2002.

• S. Krajnovi´

c and L. Davidson. Numerical study of the flow around the bus-shaped body. Journal of Fluids Engineering, 125:500–509, 2003.

• S. Krajnovi´

c and L. Davidson. Flow around a simplified car. part II: Understanding the flow. Journal of Fluids Engineering, 127(5):919–928, 2005.

• H. Hemida and S. Krajnovi´

c. LES study of the impact of the wake structures on the aerodynamics of a simplified ICE2 train subjected to a side wind. In Fourth International Conference on Computational Fluid Dynamics (ICCFD4), 10-14 July, Ghent, Belgium, 2006.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 54 / 58

REFERENCES II

• L. Davidson and S. Dahlstr¨
• m.

Hybrid LES-RANS: An approach to make LES applicable at high Reynolds number. International Journal of Computational Fluid Dynamics, 19(6):415–427, 2005.

• S. Dahlstr¨
• m and L. Davidson.

Hybrid RANS-LES with additional conditions at the matching region. In K. Hanjali´ c, Y. Nagano, and M. J. Tummers, editors, Turbulence Heat and Mass Transfer 4, pages 689–696, New York, Wallingford (UK), 2003. begell house, inc.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 55 / 58

REFERENCES III

• L. Davidson and M. Billson.

Hybrid LES/RANS using synthesized turbulent fluctuations for forcing in the interface region. International Journal of Heat and Fluid Flow, 27(6):1028–1042, 2006.

• L. Davidson and S. Dahlstr¨
• m.

Hybrid LES-RANS: Computation of the flow around a three-dimensional hill. In W. Rodi and M. Mulas, editors, Engineering Turbulence Modelling and Measurements 6, pages 319–328. Elsevier, 2005.

• W. Haase, B. Aupoix, U. Bunge, and D. Schwamborn, editors.

FLOMANIA: Flow-Physics Modelling – An Integrated Approach, volume 94 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer, 2006.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 56 / 58

REFERENCES IV

• F. R. Menter, M. Kuntz, and R. Bender.

A scale-adaptive simulation model for turbulent flow prediction. AIAA paper 2003–0767, Reno, NV, 2003.

• F. R. Menter and Y. Egorov.

Revisiting the turbulent length scale equation. In IUTAM Symposium: One Hundred Years of Boundary Layer Research, G¨

• ttingen, 2004.
• F. R. Menter and Y. Egorov.

A scale-adaptive simulation model using two-equation models. AIAA paper 2005–1095, Reno, NV, 2005.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 57 / 58

REFERENCES V

• L. Davidson.

Evaluation of the SST-SAS model: Channel flow, asymmetric diffuser and axi-symmetric hill. In ECCOMAS CFD 2006, September 5-8, 2006, Egmond aan Zee, The Netherlands, 2006.

www.tfd.chalmers.se/˜lada LES course, 19-21 Oct 2009 58 / 58