Computational Modelling of Free Surface Flows: wave interaction with fixed and floating bodies
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1 Computatonal Modellng of Free Surface Flows: wave nteracton wth fxed and floatng bodes Dere Causon, Clve Mngham, Lng Qan Zheng Zheng Hu and Hanbn Gu Department of Computng & Mathematcs Centre for Mathematcal Modellng and Flow Analyss
2 CMMFA Team Photo B Wang, ZZ Hu, Y Zhang, D Causon, J Armesto, K Bennett, L Qan Bac S Hggns, N Subramanam, F Gao, J Shach and C Mngham Front
3 Outlne Shallow water code AMAZON-CC Surface capturng Naver Stoes code AMAZON-SC Wave overtoppng and wave energy converters Further methods development Hgh Performance Computng the GPU Future wor Research lns
4 Wave Overtoppng: Hazards
5 Wave Energy The Pelams Manchester Bobber
6 AMAZON two-flud solver Incompressble Naver-Stoes solver Based on an artfcal compressblty solver. Surface-capturng method Treats the free surface as a contact dscontnuty n the densty feld, allowng the use of modern hgh resoluton shoc capturng methods. Fully two phase approach whch solves n both the ar and the water flud regons. Boundary ftted va Cartesan cut cell method
7 Cut Cell Method overlay Cartesan grd
8 Cut cells wor for any doman adaptve cut cell grd for an sland
9 AMAZON-CC: generaton of oblque waves usng cut cells
10 3D ncompressble, Euler equatons wth varable densty: T I T I T I T z I y I x I T S w p w vw uw w v vw p v uv v u uw uv p u u n n n p w v u s t 0 g ,, where h g f B h g f F Q B F n Q s the coeffcent of artfcal compressblty Governng equatons
11 Convectve fluxes The convectve flux F s evaluated usng Roe s approxmate Remann solver. I 1 F 2 F I Q F I Q R LQ Q To ensure second order accuracy, MUSCL reconstructon s used Q x, y, z Q,, Q,, r where x,y,z s a pont nsde the cell,,, r s the vector from the cell centre to the pont x,y,z, Q,, s the cell centre data and s the slope lmted gradent. Q,,
12 Tme dscretsaton The mplct bacward Euler scheme s used together wth an artfcal tme varable to ensure a dvergence free velocty feld and a lnearsed RHS. I m V n R Q Q 1, m Q n 1, m 1 Q n 1, m I ta Q n 1, m Q t n, m V R Q n 1, m where I m dag 1 1 t 1 1 t 1 1 t 1 The resultng system s solved usng an approxmate LU factorsaton. A Jameson-type dual tme teraton s used to elmnate at each real outer teraton.
13 AMAZON-SC 2D smulaton ar/water Overtoppng event occurred 142 seconds nto the experment. Seaward boundary located 2m from wall. Landward boundary s transmssve. Assume: flat water for ntal condtons.
14 3D Cartesan Cut Cell Method Merged cell Cut cell
15 Computatonal doman and boundary condtons Numercal Tan Non-reflectng Free surface Non-reflectng Ar Body Wave maer Water Non-reflectng Wall Reflecton boundary the fctonal cell R: v p R R R v p 2 v gn n n 2 v n n z RO b
16 Results A. Fxed Body B. Movng Body C. Wave propagaton and Extreme waves
17 A. Fxed Body Cases 1. A vertcal cylnder n a 1 st order wave maer 2. A horzontal cylnder n a 1 st order wave maer 3. The Dam brea flow past varous bodes a rght cube, a sewed cube, a bottom mounted and truncated cylnder 4. A bottom mounted and truncated cylnder n regular waves 5. A Pelams-type Geometry n regular waves
18 2. Horzontal Cylnder A regular 1 st order wave mposed at the nlet: u ga cosh z hcos x cosh h t w gasnh z hsn x cosh h t Acos x t Experments and Theoretcal analyses conducted by A.G. Dxon et al and W.J. Easson et al as well as used the STAR CCM by J. Westphalen
19 2. Horzontal Cylnder Relatve vertcal force Relatve vertcal force Relatve vertcal force Case1: d= 0.0m Theoretcal force Expermental force Present result t/t Case 2: d= m Theoretcal force Expermental force present result t/t 1.00 Case 3: d= -0.15m Theoretcal force 0.20 Expermental force 0.10 present result t/t Vertcal force vs tme
20 5. Fxed Pelams-type geometry n regular waves Pelams: m Tan: m Water depth: 0.45m Grd sze: Wave gauges: at front of Pelams CPU about 25 days for 8s Input velocty = Asn t A=-0.1, =2, T =1s
21 5. Pelams Tests Setch of the reference of three trm angles 0º, -9.6º, 9.6º A horzontal poston of front Pelams bac Setch of the Pelams splt to 9 sectons Tan: 13.0m 1.0m 3.5m and the water depth:h=2.8m The front end of the cylnder s placed at 5.0m from the wave maers Input ampltude: A=0.025,0.05,0.1 & 0.15, wave perod: T=1.78s, wave maer number: =1.277, wave length: L=5.0m the angular frequency: w=3.534 and frequency: f= the radus of cylnder: a=0.095m, the total length of Pelams=1.40m
22 Tme hstory of wave run up on the front of Pelams
23 B. Movng Body Cases 1. Oscllatng cone descrbng a vertcal Gaussan wave pacet moton blnd test valdaton 2. Water entry of varous rgd bodes a wedge; Bobber-type shape; sphere shape; cone shape at a prescrbed velocty 3. Regular wave nteracton wth a vertcal floatng bobber
24 1. Oscllatng Cone usng AMAZON-2D axsymmetrc code The vertcal poston of the cone followed the form of a Gaussan wave pacets Experments conducted by K. Drae et al.2008 Test case: A=50mm and m=9 The dead-rse angle s 45º Tan: 2.0m 1.6m, the water depth: h=1.02m and the ntal draught of the cone s z=0.148m Dmensons: a =0.228m, d=0.2281m, b=0.05m The tme step= a the CPU for coarse mesh dx=dy=0.02m 15 hours the CPU for fne mesh dx=dy=0.01m 41 hours z b d
25 Non-dmensonal vertcal forces non-dmensonalsed vertcal force m=9 AMAZON 001 AMAZON 002 expermental data CV-FE AMAZON Δ=0.01 AMAZON Δ=0.02 Expermental data t/t t/t Comparson wth expermental data K. Drae et al and numercal result for non-dmensonal vertcal forces on cone aganst tme
26 2. Water entry of varous rgd bodes
27 Water entry of 3D rgd wedge Body moves vertcally downwards towards an ntally calm water surface at a velocty V=1.19m/s Experments conducted by Tvetnes et al.2008 Tan: 2.0m 0.4m 2.0m and the water depth: h=1.0m The dead-rse angle s 45º Unform mesh: =102,400 dx=dy=dz=0.025m Dmensons: breadth=0.6m, length=0.3m, heght=0.3m A tme step=0.0002s and total CPU about 3 days and 6 hours t=1s
28 Force N Expermental data Present result z d z/d Comparson wth expermental data Tvetnes et al and numercal result for water entry forces
29 Water ext of 3D rgd wedge
30 3. Sngle and multple floatng Bobbers n regular waves mf=1.2 g float mass mc=0.4 g counterweght mass Pulley radus=0.0175m Bobber geometry: a=0.074m, b=0.06m and c=0.07m, Sx = 4a, the water depth =0.46m Intal free surface a b Beam sea drecton Sx c Manchester Bobber Head sea drecton Radus a Beam sea drecton wave maer number : =6.63 Wave perod: T=0.78s Wave length: L=0.95m frequency: f=1.28 ampltude: A=0.013 Head sea drecton K=8.36 T=0.69s Wave length: L=0.75m f=1.44 A=0.013
31 3a. Free-decay for the Manchester Bobber flat-bottomed and concal-topped float a 3 Mc Mf * a3 pnz ds Mc Mf g Mf pnz ds M = 3.1g Mc Counterweght mass=1.0g float mass=2.1g 6 1 M s b U m= 1.1g f mg 3 s b
32 Vertcal dsplacement m Vertcal dsplacement m Case 1: mf=2.1g, mc=1.0g Expermental data Present result a. The drop test tme s Case 2: mf=2.1g, mc=1.2g Expermental data Present result tme s Comparson: expermental data T. Stallard 2008 and current results for decay rate
33 Vertcal dsplacement m vertcal dsplacement m Case 1: mf=2.1g, mc=1.0g b. The rse test Expermental data Present result tme s Case 2: mf=2.1g, mc=1.2g Expermental data present result tme s Comparson: expermental data T. Stallard 2008 and current results for decay rate
34 Sngle and multple hemsphercal Bobbers n regular waves mf=1.2g,mc=0.4g the water depth =0.46m The radus of a=0.075m, b=0.07m The floats separated by Sx = 4a Head sea drecton Beam sea drecton Sx Radus a Intal free surface b a Beam sea drecton wave maer number : =6.63 Wave perod: T=0.78s Wave length: L=0.95m frequency: f=1.28 ampltude: A=0.013 Head sea drecton K=8.36 T=0.69s Wave length: L=0.75m f=1.44 A=0.013
35 Isolaton a. Head seas drecton
36 Vertcal force N Vertcal velocty m/s Vertcal dsplacement m Dsplacement vs tme Bobber 1 Isolaton tme s Vertcal velocty vs tme Bobber 1 Isolaton Comparson: The Bobber at same poston n solaton and array tme s Vertcal force vs tme Bobber Isolaton tme s
37 dt/a dt/a dt/a dt/a dt/a Exp. data Present result float 1 Dsplacement n head seas drecton t/t Exp. data present result float t/t Exp.data Present result float t/t Exp. data Present result float Exp.data Present result float t/t t/t Comparson: expermental data T. Stallard 2008 and present results for dsplacement vs wave perod
38 Isolaton b. Beam seas drecton
39 Vertcal velocty m/s Vertcal force N Vertcal dsplacement m Dsplacement vs tme Bobber 1 Isolaton tme s Vertcal force vs tme Bobber 1 Isolaton tme s Comparson: The Bobber at same poston n solaton and array Vertcal velocty vs tme Bobber 1 Isolaton tme s
40 dt/a dt/a dt/a dt/a dt/a Exp.data Present result float 1 Dsplacement n beam seas drecton t/t Exp.data Present result float Exp. data present result float t/t t/t Exp.data Present result float t/t Exp. data Present result float Comparson: expermental data T. Stallard 2008 and present results for dsplacement vs wave perod t/t
41 C. Devces n Extreme waves 1. Wave propagaton n empty tan for comparson of the experments conducted by Gao Extreme wave n empty tan for comparson of the experments conducted by Nng et al Extreme wave maer wth a vertcal floatng bobber
42 Inlet condton for New Wave extreme wave: sn cosh snh N t t x x h h z ga w N t t x x A cos N N t t x x A t t x x A A t t x x A A cos2 cos cos cos cosh cosh N t t x x h h z ga u cos2 cosh 2 cosh 2 ] cos[ cosh cosh ] cos[ cosh cosh N N t t x x h h z D G A t t x x h h z D G A A t t x x h h z D G A A u sn 2 cosh 2 snh 2 2 ] sn[ cosh snh ] sn[ cosh snh N N t t x x h h z D G A t t x x h h z D G A A t t x x h h z D G A A w
43 Surface elevaton m 0.58 present result 1st order present result 1st+2nd order Physcal Exp tme s Comparson wth expermental data by Nng et al and present numercal results for free surface elevaton at x=3.0 m The focus pont at x =3m maxmum elevaton mnmum elevaton Physcal Exp. by Nng et al t=9.2s Present result 1 st order t =9.147s t=8.557s Present result 1 st + 2 nd order t =9.147s t=8.557s
44 Bobber Devce n Extreme Waves Input velocty under case 2 1 st +2 nd order Tan: 13.0m 0.48m 1m wth the water depth: h=0.5m The ntal poston of the apex of Bobber n the tan s 3.0m=the focus pont 0.24m 0.35m The radus of the hemsphercal base: a=0.15m, the heght of cylndrcal secton: b=0.15m and non-unform mesh: =374,000 and the refned regons=0.02m The mass of the Bobber = the volume of the hemsphercal m=ρ2 a3/3=7.068g,whch s a lttle larger than the ntal mmersed volume Wave gauges: 3.48m,3.68m and the front sde of the Bobber A tme step=0.0003s and CPU near 25 days up to t=12s b Intal free surface a
45 Heave force N Heave force N Surface elevaton m Surface elevaton m Case 2: Case 3: Case Case tme s tme s Tme hstory of wave run-up on the front sde of the Bobber Case tme s Case tme s Tme hstory of the heave force on the Bobber
46 Vertcal dsplacement m Vertcal dsplacement m Vertcal velocty m/s Vertcal velocty m/s Case 2: Case 3: Case Case tme s tme s Tme hstory of the vertcal velocty of the Bobber Case tme s Case tme s Tme hstory of the dsplacement of the Bobber
47 Case 2: Case 3: The Manchester Bobber
48 Improved Resoluton of Free Surface Ln et. al. Two step proecton method Fnte dfference Fast marchng partcle level set Partal cell + LRS local relatve statonary method Non-unform structured rectangular mesh
49 Volent Sloshng: Model Requrements Fnte Volume Invscd Compressble Flow Change of State Thermodynamcs Ar/Water Accurate model of Free Surface
50 Compressble Flow Equatons Fnte Volume Euler Equatons
51 1D Shoc Tube Problem wth Cavtaton Intal Condtons LEFT STATE ρ = g/m3 u = -10 m/s p = 0.9 bar T = K e = J/g K RIGHT STATE ρ = g/m3 u = 10 m/s p = 0.9 bar T = K e = J/g K
52 1D Shoc Tube wth Cavtaton: Flow solver wth no change of state thermodynamcs 1 Δt
53 1D Shoc Tube wth Cavtaton: Flow solver wth no change of state thermodynamcs 1 Δt
54 1D Shoc Tube wth Cavtaton: Flow solver wth no change of state thermodynamcs 1 Δt
55 Physcs of Aerated Water
56 Change of State Thermodynamcs Equaton of State for Water Tat Equaton of State for Ar Ideal Gas
57 Change of State Thermodynamcs Equaton of State for Saturated Two Phase Mxture
58 Oldenbourg Polynomals Propertes of Mxtures
59 Modellng Change of State Thermodynamcs For p: replace EoS by Call Thermoρ, e, p, c, α Wthn SUBROUTINE Thermo: Enter wth ρ, e Solve saturated mxture equaton for T usng Secant Method Calculate ρsat_lqud and ρsat_vapour If ρ > ρsat_lqud then use Tat EoS for water Ifρ < ρsat_vapour then use Ideal gas EoS Else use saturated mxture relatons wth p = psat Calculate mxture speed of sound, c Calculate water vapour tracton, α Return wth p, c and α
60 1D Shoc Tube wth Cavtaton: Flow solver wth change of state thermodynamcs 10 Δt
61 1D Shoc Tube wth Cavtaton: Flow solver wth change of state thermodynamcs 10 Δt
62 1D Shoc Tube wth Cavtaton: Flow solver wth change of state thermodynamcs 120Δt
63 1D Shoc Tube wth Cavtaton: Flow solver wth change of state thermodynamcs 120Δt
64 1D Shoc Tube wth Cavtaton: Flow solver wth change of state thermodynamcs 120Δt
65 Schmdt et. al. Results ECCOMAS CFD 2006
66 Further Mult-component Test Problems
67 The Sugmura Problem: Mult-component RCM
68 Hgh Performance Computng Mult-core hgh spec des-top PC NEC SX-8 vector supercomputer UK Natonal Supercomputng facltes Graphcal Processor Unt GPU NVIDIA Tesla C-870 wth 2 GPU boards NVIDIA CUDA software development t SDK Rac of NVIDIA Tesla S1070 systems url:
69 Executon tme n seconds for 20,000 tme steps 32x32 64x64 128x128 RADIX TILED UNTILED SX Three problem szes wth number of real partcles used beng 32x32, 6x64, 128x128 Code : SX8: means executed on 1 processor of the NEC SX8, all others executed on one board of the NVIDIA Tesla C-870 GPU worstaton.
70 2D Dambrea wth Obstacle usng a Smoothed Partcle Hydrodynamcs Code
71 Conclusons 2D shallow water and fully 3D cut cell free surface capturng codes have been developed for the smulaton of volent wave loadngs on fxed and floatng bodes such as seawalls and wave energy devces. A number of test cases have been used to valdate the codes. The underlyng method s generc and can be appled to any applcaton area nvolvng free surfaces and statonary/movng bodes ncludng complant bodes e.g. LPG carrer n steep waves.
72 Further Wor and Issues Full flud-structure-nteracton capablty wth wave loads and derved motons under regular and extreme wave condtons ncludng movng cargo and resolve volent sloshng ssues n both physcs and numercs. Extensons of our wor on wave energy converters, greenwater overtoppng of fxed and floatng vessels and scour. More use of GPUs.
73 Further Detals and Publcaton References
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