Influence of breaking waves on wave induced flow around vertical cylinders Erik Damgaard Christensen and Erik Asp Hansen

Influence of breaking waves on wave induced flow around vertical cylinders Erik Damgaard Christensen and Erik Asp Hansen 1

Plan 1. Investigation of breaking waves on scour 2. An engineering tool to estimate scour development, under development 3. Summary 2

Breaking waves. There is a lack of knowledge about the scour depth under breaking waves, (caused by the presence of the windmill itself or by general bed level changes). A few papers are found for example Carreires et al 2000) and Bijker and Bruyn 1988. In general it is difficult to divide, the bed changes a) caused by the presence of the pile, and b) the general bed level changes. This problem illustrated by fig D taken from Carreiras and fig e taken from Bijker and Bruyn. In the conclusion by Bijker and Bruyn 1988 is written Normally waves will not increase, but even decrease the scour around a structure as compared with that of current only. The depth of this scour is in the order of 1.5 times the pile diameter. In case of breaking waves this value can be, however, considerably higher. ' 3

Scour depth time developments and equilibrium bed profile taken from Carreiras it al 2000 4

Typical scour profiles taken Bijker and Bruyn In the conclusion by Bijker and Bruyn 1988 is written Normally waves will not increase, but even decrease the scour around a structure as compared with that of current only. depth of this scour is in the order of 1.5 times the pile diameter. In case of breaking waves this value can be, however, considerably higher. 5

Introduction to scour in waves No scour for KC lower than 6 Scour associated with free vortices Illustrations from: Sumer and Fredsøe (2002) 6

Example of the computational grid The multiblock structure of the computational domain 7

Example of a breaking wave on a cylinder 8

9 Test cases 50 01:20 3.757 0.9392 10 57.5 0.67 8.93 2 8 4 6 10 50 01:20 3.757 0.9392 10 57.5 0.67 4.47 4 8 4 6 9 25 01:20 3.757 0.9392 10 57.5 0.67 8.93 2 8 4 6 8 25 01:20 3.757 0.9392 10 57.5 0.67 4.47 4 8 4 6 7 15 01:20 3.757 0.9392 10 57.5 0.67 8.93 2 8 4 6 6 15 01:20 3.757 0.9392 10 57.5 0.67 4.47 4 8 4 6 5 10 01:20 5.383 0.9794 16 87.9 0.458 8.93 2 9 5.496 12 4 10 01:20 5.383 0.9794 16 87.9 0.458 4.47 4 9 5.496 12 3 10 01:20 3.757 0.9392 10 57.5 0.67 8.93 2 8 4 6 2 10 01:20 3.757 0.9392 10 57.5 0.67 4.47 4 8 4 6 1 Dist Slope H_in.bound (m) Ks D_in (m) L_cyl Hcyl/D_cyl KC Dia (m) T (s) H_cyl (m) D_cyl (m) Case

Effect of water depth 10

Influence of distance on the breaking wave 11

Effect of diameter Test case 1 KC= 4.5 Test case 2 KC= 9.0 Test case 8 KC= 9.0 12

Friction velocity at the bed Wave breaks before center-line Wave breaks at the center-line 13

Inclusion of a scour hole in the analyses 14

Friction velocity at the bed 15

Engineering scour development model Calculation of the time development of a scour hole Motivation Discussions during this project initiated the development of the tool In cases with large wave forces might not coincidence with the largest scour hole The time scale of scour hole development should be included 16

Basic Hypotheses. If a wind turbine foundation is under a constant influence of waves and currents a scour hole will reach an equilibrium. If the hole is larger than the state of equilibrium the hole will be filled Otherwise, if the hole is smaller than the equilibrium the scour hole will increase 17

Equlibrium scour depth Generally the equilibrium scour depth depends on D: Diameter Hs,Tp,β,w: Significant wave height, Peak periode, Wave direction, Wave spreading Vc,βc: Current speed, and direction D15,d50,d85: Grain size, and distribution s : Settling velocity s: Relative density of sediment n: Porosity 18

Time Scale for scour development under constant flow conditions S( t) = S eq ( t / T 1 exp ) 1T 2T Typical scour development under constant flow conditions 19

S D = 1.3 1 0.03( KC 6) ( e ) for KC > 6 Equilibrium scour, Circular pile. Live bed condition, taken from Sumer at al. 1992 20

Co-directional and perpendicular combined waves and current Equilibrium scour depth in co-directional and perpendicular combined waves and current, Circular pile. Live bed condition, taken from Sumer and Fredsøe (2002) 21

22 Time Development + = + scale eq T t W W dt t W dt t W ), ( ) ( ), ( ), ( θ θ θ θ + = + scale eq T t S S dt t S dt t S ) ( ) ( ) (

Shields Parameter θ = τ ρ g( s 1) d 50 Shields parameter is the ratio between the hydrodynamic and gravity forces acting on a sediment grain 2 τd 50 ρg( s 1) d 3 50 23

Time Development of Horizontal scour hole Equilibrium W(t+dt) W(t) 24

Example D=4.2 m Pile Diameter D50=0.3mm Mean grain size S=2.65 Relative density h=12m Water depth 25

Example cont Scour depth during a storm much lower than max scour Low Time scale, the scour depth follows the eq. depth 26

General Comments Model results not better than the input, mainly based on small scale experiments The scour depth becomes smaller during a storm, than in pure current (could this be included in fatigue calculations?) 27

Summary The literature is not clear in distinguishing between scour and local morphology changes Numerical analyses indicates that the influence of breaking waves on the sediment transport is relatively low. As wave generated scour in general is small, so will the total scour from breaking waves be as well Development of an engineering tool for scour hole development has been initiated 28

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Equilibrium scour depth in co-directional combined waves and current, Circular pile. Live bed condition, taken from Sumer and Fredsøe(2002) 31

System udviklet hvor af bølge randbetingelser overføres fra en Boussinesq bølge model d Boussinesq bølge model ydre bølge felt NS3, Navier-Stokes løser omkring fundamentet 32

Bestemmelse af vandets påvirkning på en fast hav vindmølle består af to trin 1) Bølger, strøm &Vandstand irregulære bølger 3 dimensionale bølger påvirket af havbunden påvirket af vinden bølger og strøm påvirker hinanden (I store parker kan der være påvirkning fra de andre møller) 2) Påvirkninger på Møllen Globale Kræfter/Momenter Lokale påvirkninger, Slamming Bølgeopløb Evt. Erosion Evt. erosionsbeskyttelsen 33

Traditionel Bestemmelse af Hydrodynamisk Kraft 1) Design bølgerne/strøm bestemmes. (Fra Målinger/ Simuleringer) 2)Bølgerne regnes ud fra bølgeteori (Regelmæssig, Højde og periode er givet) 3) Strøm og bølger adderes. 4) Kraft findes vha. Morision s formel med Strøm og Inerti kraft koefficienter 5) Evt. Tillæg for brydning 34

Eksempler: Morision s formel ikke er god nok Hastighed & acceleration I hullet?? Erosions beskyttelse Bundhældning 35

Boussinesq Bølge Model, (hurtig tilnærmet model) Hastigheder antages variere parabolsk fra top til dal, 3 ubekendte Vandstand Vandføring i x retning Vandføring i y retning ( z) ( h + z) U w 2 = x + d U xxx +L η P = u( z) h dz U P = h +η c 1 u( z) = U + c1u xx + c2u xxxx 1 2 1 2 1 1 2 = h η hη + z + hz 3 6 3 2 +L d 36

Basis viden om bølgeopløb skal etableres 37

NS3 Beregninger af bølgeopløb An example of the run-up for a case with sloping bed in front of the vertical circular cylinder. 38