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