The Physics of Structure-Structure Impact in Free Surface Flowtsunami.orst.edu/workshop/2006/doc/CaoYim_StructureImpact.pdf · 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 Effects on Bridges

Dec. 26, 2004 – Banda Aceh, Indonesia


Storm Surge Effects on Bridges

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


Tsunami/Storm Surge Effects on Bridges

Dec. 26, 2004Banda Aceh, Indonesia

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


Tsunami/Storm Surge Effects on Bridges

Dec. 26, 2004Banda Aceh, Indonesia

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


Tsunami Effects on Bridges

Dec. 26, 2004 – Southeast India


Storm Surge Effects on Bridges

Aug. 29, 2005 – Mobile, AL


Tsunami transported bridge at Jantang, Aceh (Sumatra)

Higman


Navier-Stokes Equations

1 iji ij i

j j

u uu ft x x

σρ∂∂ ∂

+ = +∂ ∂ ∂

0i

i

ux∂

=∂



3D Model of an Oregon Coastal Bridge


3D Model of an Oregon Coastal Bridge


PFEM 2D Fluid-Structure Interaction Examples (CIMNE)






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∂∂′ ′− = + −

∂ ∂


Structure-Structure Impact• Structure - structure

impact in a fluid medium

• At low relative speed• At high relative

speed • Free surface effects• Computational

Aspects


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


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


Boundary Layer

Laminar and turbulent shear in the near wall region


Boundary Layer

Typical velocity profile for a turbulent boundary layer





• Singular point may appear• “Overlapping”/interacting

boundary layers• Reversed flow directions


V2

V1 Singular point

U





• Singular point may appear • “Overlapping”/interacting



V2

V1

P

y2y1















V2

V1 Singular point

U


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

• Turbulent boundary layer on each structural surface


• Singular point may appear • Overlapping/interacting



• Cavitation may occur





• Singular point may appear• Overlapping/interacting








• Singular point may appear • Overlapping/interacting












V2

V1 P









V2

V1


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


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





• Singular point may appear• Interaction of free surface












V2

V1

P=constant














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


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

Documents

The Physics of Structure-Structure Impact in Free Surface Flowtsunami.orst.edu/workshop/2006/doc/CaoYim_StructureImpact.pdf · The physics of structure-structure impact in free surface