DEVELOPMENT AND APPLICATION OF INNOVATIVE …€¦ · hywec 2017 – bilbao, april 3-7, 2017 1/102...

HYWEC 2017 – BILBAO, APRIL 3-7, 2017 1/102

DEVELOPMENT AND APPLICATION OF INNOVATIVE ALGORITHMS ASSOCIATED TO THE HYDRO-DYNAMIC COASTAL MODEL: VALIDATION AND OPTIMIZATION OF COMPUTATIONAL TOOLS THROUGH LABORATORY TESTS

J.M. Blanco, G.A. Esteban, U. Izquierdo, A. Peña,

U. Fernández, I. Bidaguren, I. Albaina

University of the Basque Country (UPV/EHU); School of Engineering.

Alameda Urquijo s/n, Bilbao, Spain


A. Preparation of an experimental wave flume and full CFD benchmark (STARCCM+ & ANSYS FLUENT)

B. Application of the ROM (Reduced order method) of POD (Proper Orthogonal Decomposition) to aerodynamic control and WEC simulation

OUTLINE




OUTLINE


1. INTRODUCTION.

2. EXPERIMENTAL WORK.

3. NUMERICAL STUDY (CFD).



1.1. General objectives

- Validation of commercial codes by means of experimental

results (Wave flume)

- Improve the efficiency of numerical computation in CFD wave-WEC interaction relevant problems by means of Reduced Order Methods (ROM)

1. INTRODUCTION

- Definition of wave interaction with floating structures (WECs) in the range of intermediate deep waters

- Technical support to BIMEP

(Biscay Marine EnergyPlatform)



1.2. BIMEP waves

- Significant wave: H1/3=11,5m (return period of 50 years)

- Maximum wave height: Hmax=22m

- Characteristic period: T = 15 s

- Average energy flow (per meter of wave frontage): P = 21.4 kW/m

- Depth (batimetry): between d = 50 m and d = 90 m

- Direction: North 50º West

- Calculated wave length λ (Airy):

- Intermediate deep waters:

d2tgh

2

gT 2 If d = 50 m: If d = 90 m:

m 6.282

m 3.329

18,06,282

50d

27,03,329

90d

2

1d

20

1

5,0

d05,0



2. EXPERIMENTAL FACILITIES


Wave flume: Overview


2. Experimental facility


Wave flume: Specifications

Wave generation section

70 cm 70 cm 70 cm

Wave analysis section Wave absorption section

Long = 295.5 cm Wide = 40 cm

Hig

h =

50 c

m

Paddle

L1 L2

Depth

= 2

0 c

m

45º

31 cm 54.5 cm




Wave flume: Main components

Linear induction wave maker

- Maximum displacement: 210 mm

- Displacement at operating conditions: 150 mm

- Maximum force: 255 N





Wave elevation measurement section

- Equipment used:

- Piezoresistive level transmitter

- Capacitance level indicator

- Ultrasonic level transmitters





Passive wave absorption zone

- Porous stones bed

- Angle = 45º

- Dpm = 2.0 cm

- Porosity = 0.3




Wave flume: Elevation measurement equipment

Ultrasonic level transmitters

- Detection range: 30 – 500 mm

- Blind zone: 0 – 30 mm

- Response delay: 50 ms


Piezoresistive (strain gauge) level transmitter

- Pressure range: 100 mbar – 10 bar

- Excellent low term stability

- No hysteresis








Capacitance level indicator

- Slow response to fast level changes

- Suitable for detection of solids




Wave flume: Software

Variable Minimum Maximum

Paddle (piston type) Amplitude, Ap [m] 0.01 0.18

Paddle forward motion

Average velocity, Vp [m/s] 0.01 6.0

Acceleration, a [m/s2] 0.01 25.0

Deceleration, d [m/s2] 0.01 25.0

Paddle back motion

Average velocity, Vp [m/s] 0.01 6.0

Acceleration, a [m/s2] 0.01 25.0

Deceleration, d [m/s2] 0.01 25.0

Variables to be specified




Wave flume: Software

Variables to be specified




Wave flume: Experimental and analytical results

Paddle (function of time) Generated waves

Position (x [m]) Wave period at L1, TL1 [s]

Pulse velocity (u [m/s]) Wave period at L2, TL2 [s]

Hydrodynamic force (F [N]) Paddle period, Tp [s]

Period (Tp [s]) Paddle average velocity, Vp [m/s]

Wave propagation velocity, c [m/s]

Wave length, λ [m]

Depth to wave length ratio, d/λ [-]

Wave height, H [m]

Slope of the wave, H/λ [-]




Wave flume: Experimental and analytical results Variables to be specified

- Wave propagation velocity, c [m/s]:

+ Distance between ultrasonic level transmitters: 0.7 m

+ Propagation time for measured for one crest between L1 and L2

- Wave length, λ [m]:

- Depth to wave length ratio, d/λ [-]:

Being d = 0.2 m (constant for all the experiments carried out here)




Laboratory tests Schedule of the tests carried out

VA

RIA

BLES

SP

EC

IFIED

Vp = 0.27 m/s Ap = 0.15 m a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m a = d = 25 m/s2

Vp = 0.09 m/s Ap = 0.05 m a = d = 1.0 m/s2

Vp = 0.07 m/s Ap = 0.05 m a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.04 m a = d = 0.5 m/s2

Vp = 0.04 m/s Ap = 0.025 m a = d = 0.3 m/s2

Comparison of the paddle position

Developing waves in the range of

intermediate depth water, similar to

the ones measured at BIMEP

Experimental conditions for the comparison between

CFD and experimental results




Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2

295 296 297 298 299 3000,14

0,16

0,18

0,20

0,22

0,24

0,26

0,28

0,30

Le

vel

[m]

Time [s] L1 L2

Laboratory tests: Comparison of the paddle position




295 296 297 298 299 300-8

-6

-4

-2

0

2

4

6

8

Force [kg] Position [mm]

Time [s]

Fo

rce [

kg

]

-80

-60

-40

-20

0

20

40

60

80

Po

sit

ion

[m

m]


Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2





295 296 297 298 299 300-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

Velocity [m/s] Position [mm]

Time [s]

Ve

loc

ity

[m

/s]

-100

-80

-60

-40

-20

0

20

40

60

80

100

Po

sit

ion

[m

m]

Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2





Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m

a = d = 25 m/s2

295 296 297 298 299 3000,14

0,16

0,18

0,20

0,22

0,24

0,26

0,28

0,30

Le

vel

[m]

Time [s] L1 L2

441 442 443 444 445 4460,14

0,16

0,18

0,20

0,22

0,24

0,26

0,28

0,30

441 442 443 444 445 4460,14

0,16

0,18

0,20

0,22

0,24

0,26

0,28

0,30

L1 Time [s]

Le

vel

[m]

L2

Higher water volume is moved





295 296 297 298 299 300-8

-6

-4

-2

0

2

4

6

8

Force [kg] Position [mm]

Time [s]

Fo

rce [

kg

]

-80

-60

-40

-20

0

20

40

60

80

Po

sit

ion

[m

m]

441 442 443 444 445 446-8

-6

-4

-2

0

2

4

6

8

Force [kg] Position [mm]Time [s]

Fo

rce [

kg

]

-80

-60

-40

-20

0

20

40

60

80

Po

sit

ion

[m

m]

The movement of the paddle was improved

Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m

a = d = 25 m/s2





295 296 297 298 299 300-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

0,5


Time [s]

Ve

loc

ity

[m

/s]

-100

-80

-60

-40

-20

0

20

40

60

80

100

Po

sit

ion

[m

m]

441 442 443 444 445 446-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

0,5


Time [s]

Ve

loc

ity

[m

/s]

-100

-80

-60

-40

-20

0

20

40

60

80

100

Po

sit

ion

[m

m]

Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m

a = d = 25 m/s2





Vp = 0.27 m/s Ap = 0.15 m

a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m

a = d = 25 m/s2

Paddle on top Paddle at bottom

Wave period at L1, TL1 [s] 1.12 1.18


Paddle period, Tp [s] 1.13 1.18

Paddle average velocity, Vp [m/s] 0.27 0.25

Wave propagation velocity, c [m/s] 1.25 1.05

Wave length, λ [m] 1.41 1.24

Depth to wave length ratio, d/λ [-] 0.14 0.16

Wave height, H [m] 0.11 0.12

Slope of the wave, H/λ [-] 0.07 0.10




Vp = 0.09 m/s Ap = 0.05 m

a = d = 1.0 m/s2

1345 1346 1347 1348 1349 13500,17

0,18

0,19

0,20

0,21

0,22

0,23

0,24

Level

[m]

Time [s] L1 L2

Laboratory tests: waves in the range of intermediate depth water




1345 1346 1347 1348 1349 1350

-2

-1

0

1

2


Fo

rce

[k

g]

-40

-20

0

20

40

Po

sit

ion

[m

m]


Vp = 0.09 m/s Ap = 0.05 m

a = d = 1.0 m/s2




1345 1346 1347 1348 1349 1350

-0,2

-0,1

0,0

0,1

0,2


Time [s]

Ve

loc

ity

[m

/s]

-40

-20

0

20

40

Po

sit

ion

[m

m]


Vp = 0.09 m/s Ap = 0.05 m

a = d = 1.0 m/s2




Vp = 0.09 m/s Ap = 0.05 m

a = d = 1.0 m/s2

Wave period at L1, TL1 [s] 1.06


Paddle period, Tp [s] 1.06

Paddle average velocity, Vp [m/s] 0.09

Wave propagation velocity, c [m/s] 1.42

Wave length, λ [m] 1.51

Depth to wave length ratio, d/λ [-] 0.13

Wave height, H [m] 0.045

Slope of the wave, H/λ [-] 0.03





Vp = 0.07 m/s Ap = 0.04 m

a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.05 m

a = d = 0.5 m/s2

400 401 402 403 404 4050,180

0,185

0,190

0,195

0,200

0,205

0,210

0,215

0,220

0,225

0,230

Lev

el [m

m]

Time [s]

L1 L2

461 462 463 464 465 4660,180

0,185

0,190

0,195

0,200

0,205

0,210

0,215

0,220

0,225

0,230

Le

ve

l [m

m]

Time [s]

L1 L2





461 462 463 464 465 466-1,0

-0,5

0,0

0,5

1,0

1,5

2,0


Fo

rce [

kg

]

-40

-20

0

20

40

Po

sit

ion

[m

m]

Similar forces at different amplitude

400 401 402 403 404 405-1,0

-0,5

0,0

0,5

1,0

1,5

2,0


Fo

rce

[k

g]

-40

-20

0

20

40

Po

sit

ion

[m

m]


Vp = 0.07 m/s Ap = 0.04 m

a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.05 m

a = d = 0.5 m/s2




Similar velocities at different amplitude

400 401 402 403 404 405

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20


Time [s]

-40

-30

-20

-10

0

10

20

30

40

-40

-30

-20

-10

0

10

20

30

40

Velo

cit

y [

m/s

]

Po

sit

ion

[m

m]

461 462 463 464 465 466

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20


Time [s]

-40

-30

-20

-10

0

10

20

30

40

-40

-30

-20

-10

0

10

20

30

40

Velo

cit

y [

m/s

]

Po

sit

ion

[m

m]


Vp = 0.07 m/s Ap = 0.04 m

a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.05 m

a = d = 0.5 m/s2






Paddle period, Tp [s] 1.20 1.40

Paddle average velocity, Vp [m/s] 0.07 0.07

Wave propagation velocity, c [m/s] 1.30 0.90

Wave length, λ [m] 1.57 1.26

Depth to wave length ratio, d/λ [-] 0.13 0.16

Wave height, H [m] 0.03 0.04

Slope of the wave, H/λ [-] 0.02 0.03

Vp = 0.07 m/s Ap = 0.04 m

a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.05 m

a = d = 0.5 m/s2

Similar forces and velocities, but very different waves properties





Vp = 0.04 m/s Ap = 0.025 m

a = d = 0.3 m/s2

102 103 104 105 106 1070,185

0,190

0,195

0,200

0,205

0,210

0,215

Le

ve

l [m

m]

Time [s]

L1 L2





102 103 104 105 106 107-0,5

0,0

0,5

1,0

1,5


Fo

rce [

kg

]

-20

0

20

Po

sit

ion

[m

m]


Vp = 0.04 m/s Ap = 0.025 m

a = d = 0.3 m/s2




102 103 104 105 106 107

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20


Time [s]

-25

-20

-15

-10

-5

0

5

10

15

20

25

-25

-20

-15

-10

-5

0

5

10

15

20

25

Ve

loc

ity

[m

/s]

Po

sit

ion

[m

m]


Vp = 0.04 m/s Ap = 0.025 m

a = d = 0.3 m/s2




Vp = 0.04 m/s Ap = 0.025 m

a = d = 0.3 m/s2



Paddle period, Tp [s] 1.18

Paddle average velocity, Vp [m/s] 0.04

Wave propagation velocity, c [m/s] 1.11

Wave length, λ [m] 1.32

Depth to wave length ratio, d/λ [-] 0.15

Wave height, H [m] 0.02

Slope of the wave, H/λ [-] 0.02





Laboratory tests: SUMMARY

Experiments TL1 [s] TL2 [s] Tp [s] c [m/s] H [m] λ [m] H/λ [-] d/λ [-]

Vp = 0.27 m/s

1.12 1.12 1.13 1.25 0.11 1.41 0.07 0.14 A = 0.15 m

a = d = 25 m/s2

Vp = 0.25 m/s

1.18 1.18 1.18 1.05 0.12 1.24 0.10 0.16 A = 0.15 m

a = d = 25 m/s2

Vp = 0.09 m/s

1.06 1.06 1.06 1.42 0.05 1.51 0.03 0.13 A = 0.05 m

a = d = 1.0 m/s2

Vp = 0.07 m/s

1.40 1.40 1.40 0.90 0.04 1.26 0.03 0.16 A = 0.05 m

a = d = 0.5 m/s2

Vp = 0.07 m/s

1.20 1.20 1.20 1.30 0.03 1.57 0.02 0.13 A = 0.04 m

a = d = 0.5 m/s2

Vp = 0.04 m/s

1.18 1.18 1.18 1.11 0.02 1.32 0.02 0.15 A = 0.025 m

a = d = 0.3 m/s2




Laboratory tests: partial conclusions and future prospects

Partial conclusions

- All the waves obtained in all the experiments carried out are in the

range of intermediate depth water.

- However, the results obtained do not satisfy the theory for linear

waves postulated by Sir George Biddel Airy.

Future prospects

- Fulfil the requirements to obtain linear waves in the range of

intermediate water, by reducing the water level in the wave flume.

- The construction of a higher new wave flume.

- Actual wave flume: 2.95 m (long) · 0.4 m (wide) · 0.5 m (high)

- Future wave flume: 12.0 m (long) · 0.6 m (wide) · 0.65 m (high)




Laboratory tests: future prospects

Future prospects

- The construction of a higher new wave flume.

- Actual wave flume: 2.95 m (long) · 0.4 m (wide) · 0.5 m (high)

- Future wave flume: 12.0 m (long) · 0.6 m (wide) · 0.65 m (high)

Figure. Picture of the wave flume (property of GUNT HAMBURG)


3. CFD – STARCCM+


- Summary:

- Stroke ampitude: Ap=0.15 m

- Stroke period: Tp=1.123 s

- Velocity of the paddle: Vp = 0.267 m/s

- No. of simulated cycles: 24

- Simulated time interval: 26.952 s

- Time step (for each temporal iteration): 0.001 s

- Inner iterations (within each time step): 10

- Bottom gap below the paddle: 3 cm

- Initial depth: d = 0,20 m

VA

RIA

BLES

SP

EC

IFIED

Vp = 0.27 m/s Ap = 0.15 m a = d = 25 m/s2

Vp = 0.25 m/s Ap = 0.15 m a = d = 25 m/s2

Vp = 0.09 m/s Ap = 0.05 m a = d = 1.0 m/s2

Vp = 0.07 m/s Ap = 0.05 m a = d = 0.5 m/s2

Vp = 0.07 m/s Ap = 0.04 m a = d = 0.5 m/s2

Vp = 0.04 m/s Ap = 0.025 m a = d = 0.3 m/s2

Case analysed:


3. CFD – STARCCM+


Geometry

Extinction region

Wave region

Moving paddle

Figure 1. Geometry of the computational 2d-wave flume


3. CFD – STARCCM+


Computational resources

- For this introductory task a Personal Computer of the following characteristics has been used:

I7-4790 3.60 GHz Processor with 4 cores, 16 BG RAM 1600 MHz

- The UPV/EHU (Scientific Computing Service IZO-SGI) offers huge computational resources where massive calculation can be run. This option is considered for future studies with high density meshes. A summary of the calculation capabilities:

http://www.ehu.eus/sgi/computational-resources-2/arina-computational-resources-2/arina-cluster-3?lang=en

“Arina has 1926 cores distributed in 1774 xeon cores, 128 Itanium2 cores and 24 opteron codes with RAM memory ranging from 16 to 512 GB per node. 4 of the xeon nodes have 2 Nvidia Tesla cards each and other node 2 Nvidia Kepler. There are 3 high performance file systems based on Lustre, one with 4.2 TB for the Itanium2 and Opteron nodes and other 2 with 22 and 40 TB for the Xeon nodes. All the nodes are connected with a high bandwidth and low latency Infiniband network”

The service is available for Internal Users but for public Institutions an Companies as well with the corresponding rates. The authors thank for technical and human support provided by IZO-SGI SGIker of UPV/EHU and European funding (ERDF and ESF).

















3. CFD – STARCCM+


Mesh

Figure 2. Mesh detail: Complete flow field.

General base size: 1 cm

Base size above and below the

free surface (12 cm thick): 2 mm

Base size in the bottom gap flow

(cylinder 8 cm radius) : 2 mm

Base size close to the

gate region: 2 mm

220000 quadrilateral cells

- Wave region: 194000 cells - Extiction region: 26000 cells


3. CFD – STARCCM+


Mesh

Figure 3. Mesh detail: Region close to the gate.


3. CFD – STARCCM+


Mesh



3. CFD – STARCCM+


Boundary conditions

Figure 6. Boundary conditions.

“Superior”

“Floor”

“Vertical 1” “Vertical 2”

“Interface” “Paddle”

- Vertical 1 & 2: Fixed wall (viscous non-slip condition)

- Floor: Wall (viscous non-slip condition). Cells can slide along the surface

- Velocity of the paddle: Vg = 0.267 m/s

- Gate: Moving wall (viscous non-slip condition). User defined field function to describe the motion

- Superior: Pressure outlet (atmospheric pressure)

- Interface: contact plane between continuos medium and porous medium


3. CFD – STARCCM+


Physical models:

- Eulerian mixing multiphase model

- “Volume of fluid model” (equations):

i

ii

i

ii

i

i

iip

p

cc

(density)

(viscosity)

(specific heat)

Conservation of each volume fraction:

Properties of the mixture

dVDt

DSad)vv(dV

dt

d

A

i

i

i

Agi

Vi i

Local accumulation term Convective term Source term Compressibility term

v

: fluid velocity

gv

: grid velocity


3. CFD – STARCCM+


Physical models:

- Gravity model:

(to obtain the static pressure pstat from the calculated piezometric pressure ppiez)

- Segregated flow: continuity equation and momentum equation are solved separately , and

then coupled by a “prediction – correction” method (Rhie & Chow based on SIMPLE [1])

- Unsteady flow: a certain time step is defined to update the boundary conditions and to solve

numerically the conservation equations by inner iteration for each time interval. For this calculation a discretization algorithm of 1st order has been selected for the non-steady tem of the equations. (Numerical diffusion has not been observed in the definition of the surface layer according to the cell size).

- Realizable k-epsilon two-layer turbulence model: The realizable k-epsilon model is

the standard k-epsilon turbulence model but with a modified tranport equation of dissipation rate ε and the closure coefficient Cμ is not directly given as a constant but it is defined from mean flow and turbulence properties. This mathematical approach fulfils certain constrints on the normal stresses consistent with the physics of turbulence (realizability). Two-layer approach the two turbulent parameters of dissipation rate ε and eddy viscosity μt are modelled as a function of the wall distance in the near-wall layer, whereas in the outer layer the two parameters are computed from the corresponding transport equations. The two different calculations are blended smoothly by using a certain function.

)zz(gpp 0refstatpiez


3. CFD – STARCCM+


Physical models:

- Realizable k-epsilon two-layer turbulence model:

- Turbulent kinetic energy transport equation (for each phase i):

ij

iji

)ij(

jijV

kr

i

k

i

M

i0ii

b

i

k

i

c

iiA

i

k

t

iii

Agiii

Viii )kmkm(dVSS)Y)((GGfadkad)vv(kdVk

dt

d

Local accumulation term Convective term Molecular

diffusion

Turbulent

transport

Turbulent

generation

source term

Buoyancy

generation

source term

Dissipation

Compressibility

User defined

Source

Particle

induced Source

Interaction

between phases

- Turbulent viscosity: from turbulent kinetic energy and dissipation rate

i

2

i

i

t

i

kC


3. CFD – STARCCM+


Physical models:


- Dissipation rate transport equation (for each phase i):

Local accumulation term Convective term

Molecular

diffusion

Turbulent

transport Turbulent

generation

source term

Buoyancy

generation

source term

Dissipation User defined

Source

Particle

induced Source

Interaction

between phases

ij

iji

)ij(

jijV

r

ii0ii2

ii

ib

i31

i

i1

c

iiA

i

k

t

iii

Agiii

Viii )mm(dVSS)(C

k)GCC(

kSCfadad)vv(dV

dt

d

- Clossure coefficients: σk, Cμ, Cε1, Cε2, Cε3


3. CFD – STARCCM+


Physical models:

- Turbulent viscosity:

- Dissipation rate :

- Turbulent viscosity:

A

Reexp1CRe

y4/1

yt

70A

09,0C

42,0

ykRey

l

k 2/3

A

Reexp1ycl

y

l

lc2A

4/3

l Cc

2

t

kC


- Two Layer all y+ wall treatment (Wolfstein [2]):


3. CFD – STARCCM+


Physical models:

- Interaction between phases: Multiphase interaction, surface tension force:

- Water-air surface tension: σ = 0.074 N/m

- Porous medium (packed bed extinction region):

- Forchheimer equation:

- Ergun model for a packed bed (porous media):

- Permeability (m2):

- Forchheimer coefficient (m-1):

vvvk

pp

“Darcy” lineal

term (viscous)

quadratic term

(inertial effects)

pk (m2) permeability of the porous medium

(m-1) Forchheimer coefficient

2

p

3

2

p D

)1(150

k

1

p

3D

)1(75,1

Dp = 3 cm Mean diameter of particles in the porous medium

Volume porosity 3.0


3. CFD – STARCCM+


Results and Discusion:

- Conditions applied for the calculation:

- Stroke ampitude: Ap=0.15 m

- Stroke period: Tp=1.123 s

- Velocity of the paddle: Vp = 0.267 m/s

- No. of simulated cycles: 24

- Simulated time interval: 26.952 s

- Time step (for each temporal iteration): 0.001 s

- Inner iterations (within each time step): 10

- Bottom gap below the paddle: 3 cm

- Initial depth: d = 20 cm


3. CFD – STARCCM+



- Volume fraction (1st period / stroke cycle):


3. CFD – STARCCM+



- Volume fraction (2nd period / stroke): t = T


3. CFD – STARCCM+



- Pressure(3rd period / stroke): t = 2T


3. CFD – STARCCM+



- Pressure (4th period / stroke):

t = 3T


3. CFD – STARCCM+



- Velocity vectors (5th period / stroke):

t = 4T


3. CFD – STARCCM+



- Effect of the stroke on the paddle:

Figure 7. Pressure field (left) and velocity vector field (right) close to the bottom passage.


3. CFD – STARCCM+



- Level meters (L1, located at x = 1.01 m from the left verical wall x=0):

Figure 8. Position y (m) of the free surface at x = 1.01 m: Iso-volume fraction lines of 0.9, 0.7, 0.5, 0.3, 0.2, 0.1


3. CFD – STARCCM+



- Level meters (L2, located at x = 1.71 m from the left verical wall x=0):

Figure 9. Position y (m) of the free surface at x = 1.71 m: Iso-volume fraction lines of 0.9, 0.7, 0.5, 0.3, 0.2, 0.1


3. CFD – STARCCM+



- Level meters (L1 & L2 together):

Figure 10. Position y (m) of the free surface at x = 1.01 m and x = 1.71 m. 24 cycles.


3. CFD – STARCCM+



- Level meters (L1 & L2 together):

Figure 11. Position y (m) of the free surface at x = 1.01 m and x = 1.71 m. 8 first cycles.


3. CFD – STARCCM+



- Distance between level meters: Δx = 0.7 m

- Wave travelling time between level meters: Δt=0.550 s

- Wave propagation velocity:

- Wave period: T=1.123 s

- Wave length:

- Depth: d=0.2 m

- Depth to wave length ratio:

- Intermediate deep waters: (BIMEP range)

- Wave height: H(L1)=0.064 m , H(L2)=0.054 m (evolving wave)

m/s 273.1t

xc

m 43.1Tc

140.0/d

2/1/d20/1

- Computational results:


3. CFD – STARCCM+



- Calculated hydrodinamic to produce the gate stroke:

Figure 12. Hydrodinamic force in the gate motion. 24 cycles.


3. CFD – STARCCM+



- Comparison CFD and experimental results (L1):

Figure 13. Position y (m) of the free surface at x = 1.01 m: Simulation (CFD) and Experimental.

0,14

0,16

0,18

0,2

0,22

0,24

0,26

0,28

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Leve

l [m

]

Time (s)L-1 Simu L-1 Exp


3. CFD – STARCCM+



- Comparison CFD and experimental results (L2):

0,14

0,16

0,18

0,2

0,22

0,24

0,26

0,28

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Leve

l [m

]

Time [s]L-2 Simu L-2 Exp

Figure 14. Position y (m) of the free surface at x = 1.71 m: Simulation (CFD) and Experimental.


3. CFD – STARCCM+



- Comparison CFD and experimental results (Force):

Figure 15. Force delivered to the moving gate: Simulation (CFD) and Experimental.

-100

-50

0

50

100

150

0 2 4 6 8 10 12 14 16

Forc

e [N

]

Time [s]

Calculated force (N) Experimental force (N)


3. CFD – ANSYS-FLUENT (SUMMARY)


Figure 16. Geometry in ANSYS-FLUENT.

Figure 17. Mesh detail close to the gate in ANSYS-FLUENT.




Figure 18. Hydrodinamic force in the gate motion.




Figure 19. Hydrodinamic momentum in the gate motion.




Figure 20. Position y (m) of the free surface at x = 1.01 m (left) and x = 1.71 m (right).

Wave generation section

70 cm 70 cm 70 cm

Wave analysis section Wave absorption section

Long = 295.5 cm Wide = 40 cm

Hig

h =

50 c

m

Paddle

L1 L2

Depth

= 2

0 c

m

45º

31 cm 54.5 cm




Figure 21. Comparative for free surface at x = 1.01 m

0,14

0,16

0,18

0,2

0,22

0,24

0,26

0,28

0 1 2 3 4 5 6 7 8 9

Level [m]

t (s)

L 1

Fluent L-1 Exp


3. CFD – STARCCM+ and ANSYS FLUENT


Conclusions:

- The main parameters of the wave {period T, wave length λ, velocity of propagation c, depth d, d/λ ratio, wave slope H/ λ} are successfully derived from the CFD simulation.

- Some disparities between experiments and CFD simulations have been detected regarding the wave height (in the crest not the trough) and the peak force withstood by the paddle. The main reasons are being analysed and constitute a key issue for future research (CFD: order of numerical discretization and dependence on the mesh density,... / Experimental facility: precise adjustment of the sensibility coefficients of the level sensors, influence of spray from the wave crest, hysteresis,...)

- The evolution of the wave height between level sensors indicates that the wave produced is evolving along the propagation direction and it is directly influenced from the wave maker (paddle) region. Different configurations at lower water depth is a matter of future research to succeed in describing analytically (e. g. by Airy, 2nd order Stokes theory,...) the propagation of fully developed waves.


3. CFD – STARCCM+ and ANSYS FLUENT


Future work:

- Once the correct characterization of the waves is finished, the analysis of the interaction of floating devices (WEC’s) will be modelized and validated through the experimental facility aiming a fully understanding of the hydrodinamic behaviour of such devices.




OUTLINE


MOTIVATION

• POD technique optimality improvement pointwise (feasibility study).

- POD gives optimal aproximate solution in average.

- But, it can be improved locally (pointwise) by some coupling.

• Snapshot-based ROM accuracy improvement by snapshot location optimization.

- Bringing technique from Local Mesh Adaptivity

B. Application of the ROM (Reduced order method) of POD (Proper Orthogonal Decomposition)


is an evolutionary PDE, where L is any space differential operator and f is a source term.

where Λ be a space of parameters (design parameters, flying conditions, etc...).

is a set of solutions (snapshots) of equation (1) for parameters γi respectively.



where K is the correlation matrix and ( , ) is L2 dot product.

Now, we define the POD reduced basis modes Ψi as:

Where λi,j are the components of the i-th eigenvector.

By multiplying (1) by Ψi we obtain



The projection of the initial problem (1) solution on the POD space gives

Finally, building the POD solution reduces to solve for Yj (t) and we obtain a quadratic dynamical system of the form:



OPTIMALITY OF POD BASIS

The POD optimality is guaranteed in the sense of average over the parameters space as it is shown in the theorem.

This optimality is not satisfied pointwise.



To illustrate the idea in a very simple example, let's consider 3 vectors in the R3, as in next Figure.



Applying the POD method into a 2D model, we will get two orthogonal vectors spanning the plan passing between the horizontal one and the third vector:

But, for vectors close or belonging to the horizontal plan the best approximation is to use the horizontal plan.



ALTERNATIVE BASIS:

SORTED GRAM-SCHMIDT (SGS)

Based in an intuitive idea, we propose to use the classical Gram-Schmidt process, with sorting the snapshots in order to minimize the transformations. This gives:



- We calculate the error along a given vector as the length of the vector measured

by the hessian metric T.

- The goal of the adaptation is to equi-distribute the error computed as:

- Algorithm starts with a uniform mesh and a first solution is used to estimate error.

- Then mesh adaptation operations: node movement, edge refinement, coarsening and swapping.

- The error on the consecutive adapted mesh is interpolated on the original one considered as a background mesh.



TEST CASE




LOOCV (Leave-One-Out Cross-Validation) in: Zhao Zhan, Wagdi G Habashi, and Marco Fossati. “Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems". In: AIAA JOURNAL 53.8 (2015), pp. 2174-2185.


CURRENT WORK • Applying Snapshot location improvement to a 2D EULER flow around WELLS

turbine type simmetry profile blade(NACA 0012).

• Flow Mach and Angle of Attack as parameters.

– Mach from 0.5 to 1

– Angle of Attack from 0º to 1.5º



• BCAM CFD research line BBIPED solver used for feeding the initial POD reduced model.

Stipcich, G., A. Ramezani, V. Nava, I. Touzon, M. Sanchez-Lara, and L. Remaki. "Numerical investigation of the aerodynamic performance for a wells-type turbine in a wave energy converter." VI International Conference on Computational Methods in Marine Engineering. MARINE 2015.

• POD vs BBIPED validation

• New Snapshot location improvement and testing new POD model’s computational wealth.



CONCLUSIONS AND FUTURE WORK

• Alternative (SGS) basis is built based on an optimality criterion that minimizes the transformation of the initial set of shots.

• The POD optimality theorem is optimal only in average. It is possible to improve it locally (pointwise) by coupling with SGS.

• Local mesh adaptivity techniques are used for systematic optimization of snapshots location.

• POD-projection approach for error estimate is proposed as an alternative to LOOVC, that needs to build the basis system for each snapshot location.

• Current work in collaboration with BCAM using BBIPED as CFD solver, modeling an EULER flow around a symmetric 2D profile.



THANKS FOR YOUR

ATTENTION!

DEVELOPMENT AND APPLICATION OF INNOVATIVE …€¦ · hywec 2017 – bilbao, april 3-7, 2017 1/102...

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