Experimental observation on surface undulations over ... · Experimental observation on surface...
Transcript of Experimental observation on surface undulations over ... · Experimental observation on surface...
Experimental observation on Experimental observation on ppsurface undulations over surface undulations over
erodible bederodible bed
Annual Workshop of Advanced Modeling on Shear Shallow Flows Annual Workshop of Advanced Modeling on Shear Shallow Flows
on Curved Topography on Curved Topography AMoSSAMoSS
(INRIA(INRIA‐‐MOST 2014MOST 2014‐‐2016) Associated Team Work2016) Associated Team Work
8th July 2015, in Antibes/Nice, France
Yih‐Chin TAI1, Chin‐Kai Cheng1 and Chih‐Yu Kuo21Dept. Hydraulic & Ocean Eng., National Cheng Kung University, Tainan 701, Taiwan
2Research Center for Applied Sciences, Academia Sinica, 115 Taipei, Taiwan
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
Water‐sand mixtureSand material : Ottawa sand (C‐778, diameter: 06 – 0.8 mm)Sand material : Ottawa sand (C 778, diameter: 06 0.8 mm)Plexi‐glass channel : 1.6 m long, 1 cm wideChannel slope : 3 – 5 degreeWater flux : 0.00898 kg/sSand supply : 0.3 kg/s
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
30cm 5cm 45cm20cm
Experimental observation• Steady state• high‐speed camera (fps = 200)Ch l l 0 d• Channel slope: 0 degree
• Bed slope: ca. 2.5 degreeTh f d l ti i hibit d b th St f b ll• The surface undulation is exhibited by the Styrofoam ball
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
• Channel slope: 3 degree, Bed slope: ca. 1 degree, fps = 1,000
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
• Channel slope: 3 degree, Bed slope: ca. 1 degree, fps = 1,000Trough 1 Trough 2 Trough 3Crest 1 Crest 2
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
FrouheFrouhe Number (only approximation)Number (only approximation)• Piecewise linear distribution u uPiecewise linear distribution wu
2 2( )d ,s
b
z
zu z z u h
shh 21 2 3 1 0.5 ,h h h sh h
2Fr cos 3 1u gh u
• Channel slope: 3 degree
s g
p g
Trough 01 0 4874 0 0111 0 0049 1 1612 1 0346
(m / s)u (m)h (m)sh FrTrough 01 0.4874 0.0111 0.0049 1.1612 1.0346
Crest 01 0.5091 0.0125 0.0052 1.1517 1.0387
Trough 02 0.4729 0.0106 0.0057 1.1977 0.9721
Crest 02 0.4986 0.0127 0.0050 1.1451 1.0352
Trough 03 0.4977 0.0106 0.0047 1.1641 1.0473
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
• Channel slope: 5 degree, fps = 1,000
Crest no.1 Trough no.1 Crest no.2 Trough no.2
Crest 01 0.6830 0.0101 0.0040 1.1427 1.2504
(m / s)u (m)h (m)sh Fr
Trough 01 0.6592 0.0091 0.0040 1.1588 1.211
Crest 02 0.6513 0.0101 0.0040 1.1427 1.2303
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
Trough 02 0.6644 0.0096 0.0040 1.1507 1.2268
• Velocity and pressure measurements in undular hydraulic jump after Fawer (1937)after Fawer (1937)
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
Conventional method: Boussinesq‐type modele g Serre (1953) Peregrine (1966) etc
hUth
0
e.g. Serre (1953), Peregrine (1966), etc.
( ) dz
w z u z
bxxxtxhUUUUghhU
xthU
xt
321 3
222
( ) dbz
b
w z u zx
U z zx
Saint‐Venant term non‐hydrostatic term
x
Shear Flow model: Richard and Gavrilyuk (2012, 2013)h h
hghhUhU
hUxt
h
322 1
0
0
Uhh
Uhxt
h
bhghhUxt
2 0
Uh
xt
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN
Open questions forOpen questions forOpen questions for Open questions for discussiondiscussion
• Is the observation a three-dimensionalphenomena?
Looking for optimal model• Looking for optimal model
• The wavy formation at the bottomy
• The impacts of the sediment-water layer.
• Rigid bed and erodible bottom.
Dr.-Ing. Y. C. Tai, Dept. Hydraulic and Ocean Engineering, NCKU, TAIWAN