the physics of structure-structure impact in free surface...

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim1

The Physics of Structure-Structure Impact in Free Surface Flow

Solomon YimGang Cao

Dept. of Civil EngineeringOregon State University

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim2

Tsunami Effects on Bridges

Dec. 26, 2004 – Banda Aceh, Indonesia

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim3

Storm Surge Effects on Bridges

Aug. 29, 2005 – Biloxi, MS, Gulf of Mexico

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim4

Tsunami/Storm Surge Effects on Bridges

Dec. 26, 2004Banda Aceh, Indonesia

Aug. 29, 2005Biloxi, MS, Gulf of Mexico

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim5

Tsunami/Storm Surge Effects on Bridges

Dec. 26, 2004Banda Aceh, Indonesia

Aug. 29, 2005Mobile River, AL, Gulf of Mexico

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim6

Tsunami Effects on Bridges

Dec. 26, 2004 – Southeast India

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim7

Storm Surge Effects on Bridges

Aug. 29, 2005 – Mobile, AL

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim8

Tsunami transported bridge at Jantang, Aceh (Sumatra)

Higman

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim9

Navier-Stokes Equations

1 iji ij i

j j

u uu ft x x

σρ∂∂ ∂

+ = +∂ ∂ ∂

0i

i

ux∂

=∂

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim10

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim11

3D Model of an Oregon Coastal Bridge

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim12

3D Model of an Oregon Coastal Bridge

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim13

PFEM 2D Fluid-Structure Interaction Examples (CIMNE)

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim14

PFEM 2D Fluid-Structure Interaction Examples (CIMNE)

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim15

PFEM 2D Fluid-Structure Interaction Examples (CIMNE)

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim16

RANS with k-epsilon closure model0i

i

Ux

∂=

∂

iji ij i

j j i

U U PU ft x x x

τρ⎡ ⎤ ∂∂ ∂ ∂

+ = − +⎢ ⎥∂ ∂ ∂ ∂⎢ ⎥⎣ ⎦

t ij i j

j j k j j

Uk k kU u ut x x x x

μρ ρ μ ρ ρεσ

⎡ ⎤⎛ ⎞ ∂∂ ∂ ∂ ∂ ′ ′+ = + − −⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

2

1 1 2 2t i

j i jj j j j

UU f C u u f Ct x x x k x kε ε ε ε

ε

με ε ε ε ερ ρ μ ρ ρσ

⎡ ⎤⎛ ⎞ ∂∂ ∂ ∂ ∂ ⎛ ⎞ ′ ′+ = + − −⎢ ⎥⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦

( ) 2( ) ( )3

ji kij t ij

j i k

UU Uwhere kx x x

τ μ μ μ ρ δ∂∂ ∂

= + + − +∂ ∂ ∂

2( )3

jii j t ij

j i

UUu u kx x

ρ μ ρ δ∂∂′ ′− = + −

∂ ∂

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim17

Structure-Structure Impact• Structure - structure

impact in a fluid medium

• At low relative speed• At high relative

speed • Free surface effects• Computational

Aspects

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim18

Wall damping function (LRN)

20.0165R 20.51 1k

t

where f eRμ

− ⎛ ⎞⎡ ⎤= − +⎜ ⎟⎣ ⎦

⎝ ⎠

3

10.051f

fεμ

⎛ ⎞= + ⎜ ⎟⎜ ⎟

⎝ ⎠

2

2 1 tRf eε−= −

1/ 2

kk yand Rν

=

2

tkwhere Rνε

=

2

tkf Cμ μμ ρε

=

• Explicitly boundary layer dependent coefficients

• Implicitly boundary layer dependent coefficient

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim19

Structure-Structure Impact at Low Relative Speed (Low Re)

• Laminar boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • Overlapping of boundary

layers• Reversed flow directions

and opposite singular effect during separation

V2

V1

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim20

Boundary Layer

Laminar and turbulent shear in the near wall region

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim21

Boundary Layer

Typical velocity profile for a turbulent boundary layer

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim22

Structure-Structure Impact at Low Relative Speed (Low Re)

• Laminar boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear• “Overlapping”/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

V2

V1 Singular point

U

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim23

Structure-Structure Impact at Low Relative Speed (Low Re)

• Laminar boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • “Overlapping”/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

V2

V1

P

y2y1

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim24

Structure-Structure Impact at Low Relative Speed (Low Re)

• Laminar boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • “Overlapping”/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim25

Structure-Structure Impact at Low Relative Speed (Low Re)

• Laminar boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • Overlapping of boundary

layers• Reversed flow directions

and opposite singular effect during separation

V2

V1 Singular point

U

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim26

Structure-Structure Impact at High Relative Speed (High Re)

• Turbulent boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • Overlapping/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

• Cavitation may occur

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim27

Structure-Structure Impact at High Relative Speed (High Re)

• Turbulent boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear• Overlapping/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

• Cavitation may occur

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim28

Structure-Structure Impact at High Relative Speed (High Re)

• Turbulent boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • Overlapping/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

• Cavitation may occur

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim29

Structure-Structure Impact at High Relative Speed (High Re)

• Turbulent boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • “Overlapping”/interacting

boundary layers• Reversed flow directions

and opposite singular effect during separation

• Cavitation may occur

V2

V1 P

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim30

Structure-Structure Impact at High Relative Speed (High Re)

• Turbulent boundary layer on each structural surface

• Fluid “jets” in both orthogonal directions during approach

• Singular point may appear • Overlapping of boundary

layers• Reversed flow directions

and opposite singular effect during separation

• Cavitation may occur

V2

V1

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim31

Cavitation• The same phenomenon

happens in the tip and root of a propeller blade. The corrosion caused by the implosion of bubbles will crack the blade when sustained cavitation occurs

• Well studied in propeller analysis literatureCavitation in propeller blades

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim32

Effects of Free Surface

• Constant pressure at free surface

• Preferred fluid “jet”direction during approach

• Singular point may appear • Interaction of free surface

with boundary layers• Cavitation may occur and

interact with free surface

V1

V2

P=constant

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim33

Effects of Free Surface

• Constant pressure at free surface

• Preferred fluid “jet”direction during approach

• Singular point may appear• Interaction of free surface

with boundary layers• Cavitation may occur and

interact with free surface

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim34

Effects of Free Surface

• Constant pressure at free surface

• Preferred fluid “jet”direction during approach

• Singular point may appear • Interaction of free surface

with boundary layers• Cavitation may occur and

interact with free surface

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim35

Effects of Free Surface

V2

V1

P=constant

• Constant pressure at free surface

• Preferred fluid “jet”direction during approach

• Singular point may appear • Interaction of free surface

with boundary layers• Cavitation may occur and

interact with free surface

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim36

Effects of Free Surface

• Constant pressure at free surface

• Preferred fluid “jet”direction during approach

• Singular point may appear • Interaction of free surface

with boundary layers• Cavitation may occur and

interact with free surface

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim37

Computational Aspects• Which normal distance is

valid when using damping functions? y1 or y2?

• When the solid is very close to the wall, say, when y1 and y2 are overlapped, how to calculate y1? Directly use the law for linear layer?

• After the contact elements are generated in numerical code, can we just neglect this boundary layer?

P

V2

V1y1 y2

Tsunami Workshop, 26-28 DEC 2006, Hilo, Hawaii Solomon C. Yim38

SummaryThe physics of structure-structure impact in free surface

flow have been examined. The following are important issues that need to be addressed:

• Interaction between boundary layers around the structures needs to be taken into account for both low and high Re flows

• Cavitation in high Re flow (propeller literature)• Free surface interaction with structural boundary layers• Free surface interaction with cavitation