Large Scale Simulations of Turbulent Flows for Industrial Applications Lakhdar Remaki BCAM- Basque Centre for Applied Mathematics

Outline

p  Flow Motion Simulation p  Physical Model p  Finite-Volume Numerical Method

p  CFD in Industry n  Bloodhound SSC project

n The project n Spray Drag Simulation

n  BCAM-BALTOGAR CFD Platform n The project n Preliminary results

CFD - Computational Fluid Dynamic

CFD - Industry

Aerospace, automotive, ventilation, power generation, chemical manufacturing, polymer processing, petroleum exploration, medical research, meteorology, ….

)2()()()( Dvfpvvvt µλρρρ ••• ∇+∇∇+=∇+⊗∇+∂

[ ] )2()(()()()( ) vDvfpvpEE vvt µλθκρρρ ••••• ∇+∇∇+∇∇+=∇++∇+∂ •

Continuity equation

Momentum equation

Energy equation

p  Navier-Stokes Equations

0)( =∇+∂ • vt

ρρ

ijk

k

i

j

j

iij x

vxv

xvD δ

∂

∂−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂=

31

21

Navier-Stokes Equations

Navier-Stokes Equations: Weak formulation

3,2,1)()( =−= ∫∫∫ ααα

αα

SSV

SSV dnQGdnQFQddtd

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

Euuu

Q

3

2

1

ρ

ρ

ρ

ρ

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

+

+

+

+

=

α

αα

αα

αα

α

α

δρ

δρ

δρ

ρ

upEpuupuupuu

u

F

)(33

22

11

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

−

=

ααβ

α

α

α

α

τ

τ

τ

τ

qu

G

3

3

2

1

0

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∂+

∂+

∂−=

β

α

α

ββαβα µδµτ

xu

xu

xu

k

k

32

Stress tensor

βα x

Tkq∂

∂−=

Average heat flux

Equations Discretization p  Finite Volume Method

n  Cell vertex finite volume solution (Dual mesh) n  Time discretization: explicit multi-stage Runge Kutta n  Convergence acceleration to steady state by local time

stepping and an agglomerated multigrid process.

Inviscid flux Approximation

∑∫Λ∈

≈IJIJFdnQF ~)(

S

Sαα

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+

+

+

+

=

IJ

IJIJ

IJIJ

IJIJ

IJ

IJ

qpEpnqupnqupnqu

q

F

)(

~

313

22

11

ρ

ρ

ρ

ρ

αα IJIJ nuq =

p  Riemann Problem

p  Most popular Riemann approximation solvers n  Roe solver n  Osher-Solomon n  HLLC solver

Inviscid flux Approximation

⎩⎨⎧

>

<=

=∂

∂+

∂

∂

00

),0(

0)(~

sifQsifQ

sQ

QFs

Qt

J

I

IJ

Extension to second order p  Modification of the left and right values in Riemann problem

p  Scheme Accuracy and stabilization n  Accurate Riemann solver n  Accurate Gradient reconstruction method n  Robust limiter: Limit the gradient in the vicinity of

discontinuities (for instance to ensure local extremum diminishing (LED))

JIJJI

IJIIJ

QQQQ

Δ+=

Δ+=

Bloodhound SSC Project p  Constructing a vehicle to take the World Land Speed Record

to 1000 mph

BLOODHOUND SSC 1000 mph

M=0.0 M=1.0 M=0.5 M=1.5

SUBSONIC TRANSONIC SUPERSONIC HYPERSONIC

THRUST SSC 763 mph

THRUST2 633 mph

BABS 171 MPH

BLUEBIRD 174 MPH

Subsonic to Supersonic

Thrust SSC: 763mph Bloodhound SSC: 1000mph

Bloodhound SSC Project

Bloodhound SSC Project

Spay Drag Model for Bloodhound SSC Vehicle

Pressure Shocks around the vehicle

Spay Drag Model for Bloodhound SSC Vehicle

Governing Equations

[ ]TonU pppt .00)( ×Ω=⋅∇+∂ φφ

gUUPUUUp

fpfpf

p

ppppppt

)1()()()(ρ

ρφβ

ρ

φφφ −+−+∇−=⊗⋅∇+∂

⎪⎪

⎩

⎪⎪

⎨

⎧

≥−

<−

+

=− 8.0

43

8.075.1150

65.2

2

2

fpp

fpfpd

fp

fpfp

pf

fp

ifD

UUC

ifD

UUD

φφρφ

φρφ

φ

µφ

β

f

fpfp

e

UUDR

p ν

φ −=

⎪⎩

⎪⎨

⎧ <+=

else

RifRRC pp

p

eeed

4.0

1000)15.01(24 687.0 g

Particle Reynolds number Drag coefficient

Gravity

Solid phase

1=+ fp φφ

[ ]TonU ffffft .00)( ×Ω=⋅∇+∂ ρφρφ

gUUPUUU fffpffffffffft

ρφβτφρφρφ +−−∇+−∇=⊗⋅∇+∂ )(.)()(

Fluid phase (Navier stokes-equations)

Equations Discretization

p  The cell vertex (dual mesh) finite volume scheme described before is used to solve the whole system

n  Fluid phase: Solve the conservative form n  Solid phase: the non-conservative form of the momentum

equations is solved.

[ ]TongUUPUUUp

ffpf

ppppt ,0,)1()(1)()( ×Ω−+−+∇−=⊗⋅∇+∂

ρ

ρβ

ρ

Validation

Y. Kliafas, M. Holt, LDV measurements of a turbulent air-solid two phase flow in a 90 bend. Experiments in Fluids 5, 7385.

Experimental Apparatus: (a) General Flow System, (b) Geometry of the curved square duct

Validation

Hybrid used mesh and Volume Fraction profile for the curved duct

Station θ=0 Station θ=15

Station θ=45 Station θ=30 90 Bend case: Mean Stream fluid and particles velocity comparison to experimental results for different stations

Validation

The delimited area using normal velocity gradient criterion

Bloodhound SSC Supersonic Car: Hybrid mesh

Application to Bloodhound SSC

Application to Bloodhound SSC

Volume fraction profile

Sand particles dust Cloud-Fraction volume variable

Application to Bloodhound SSC

Residual convergence (a)

(b)

Drag convergence before and after injecting sand particles: (a) Volume Fraction= 1.5e-3, Drag increases by 5%. (b) Volume Fraction = 5e-3, Drag increases by 10%.

BCAM-BALTOGAR Project p  BCAM-BALTOGAR CFD Platform for Tubomachinery Design

BALTOGAR centrifugal turbofan BALTOGAR Axial turbo an

Selected BALTOGAR Products

BCAM-BALTOGAR CFD Platform

Mesh Generator

Unsteady-RANS Solver

Rotating Effects

Post-Processing tools

URANS

LES-SST

POD- Model Reduction

Aero-Acoustics Models

Optimization Tools

Aero-Elastics Models

BCAM-BALTOGAR CFD Platform

Mesh Generator

Unsteady-RANS Solver

Rotating Effects

Post-Processing tools

SU2 (Stanford

University)

NetGen (Johannes Kepler University Linz)

p  Multiple Reference Frame Method n  Rotating frame

p  The sliding mesh method

p  The snapshot method

Rotating Simulation

BALTOGAR centrifugal turbofan

Rotor Volute+Rotor

p  BC + Drag force approach Rotating Simulation

BALTOGAR centrifugal turbofan: Rotating part

Rotating direction

AVCF dd2

21

ρ=BC on Blades: Fluid Velocity =Rotating velocity

p  Approach 1: Consider dual cells as discs

p  Approach 2: Use the rotating frame technique with one blade and estimate numerically the drag coefficient

Drag Coefficient Estimation

I

K

IΩ

KΩAVCF d2

21

ρ=

p Axial Turbofan Preliminary Results

p BALTOGAR Centrifugal Turbofan Preliminary Results