Simulation of tsunamiinduced boundary layers and scour around monopiles David R. Fuhrman Isaac A. Williams Bjarke Eltard Larsen Cuneyt Baykal B. Mutlu Sumer
Boundary layer model Fuhrman, D.R., Schløer, S. & Sterner, J. (2013) RANS-based simulation of turbulent wave boundary layer and sheet-flow sediment transport processes. Coast. Eng. 73, 151 166. MatRANS model (Fuhrman et al. 2013) Implemented in Matlab Reynolds-averaged Navier-Stokes (RANS) equations One-dimensional vertical (1DV) New transitional k-w turbulence closure Finite difference discretization Time stepping with Matlab s ode15s routine
Model validation Solitary wave experiments of Sumer et al. (2010) Smooth beds Periods ranging from T=7 9.4 s u 0 U 1m 2, T au1 Re sech m 2 a t U 1m
Summary of experimental conditions (Sumer et al. 2010)
Velocity profiles Re 7.110 (laminar) 4 Re 1.810 turbulent 6
Bed shear stresses (Laminar theory from Liu et al. 2007)
Simulation of tsunami-scale boundary layers Assumed conditions Offshore: T=15 min, H 0 =1 m, h 0 =4000 m Wave conditions shoaled (linear shallow water theory) to 13 depths, as shallow as h=10 m Four sediment sizes: d=smooth, 0.3 mm, 1.5 mm, 3 mm k s =2.5d Reynolds numbers: 10 4 10 9 Roughness: a/k s =500 4 10 5
Synthetic (idealized) tsunami wave descriptions Three different wave forms Single wave (solitary like, but free period) Sinusoidal 2 2 N-wave (Madsen & Schaffer 2010): u U m sech t t t 0 1 sech
Tohoku (2011): Measured tsunami signals Appoximated using superposition of single waves (Chan and Liu, 2012): 3 2 t H sech t t t u t t n1 n n 0 n 0 g h Indian Ocean (2004):
Summary of simulated conditions 13 depths 5 waves 4 grain sizes 260 simulations
Tsunami boundary layer thickness Williams, I.A. & Fuhrman, D.R. (2016) Numerical simulation of tsunami-scale wave boundary layers. Coast. Eng. 110, 17 31. y a Smooth (solid lines) Rough (dashed lines) Re=7.0x10 8 (black) Re=2.2x10 7 (red) d Even at h=10 m, d 5 m i.e. BL not depth limited!
Scour model sedimorph model (Jacobsen et al. 2014) OpenFOAM environment Fully-coupled (RANS + Turbulence (k-w) + Sediment transport + Morphology) Bed and suspended sediment transport Morphology using moving mesh algorithm Model validated and well tested Current scour around a monopile (Baykal et al. 2015) Wave-induced pipeline scour and backfilling (Fuhrman et al. 2014) Wave-plus-current scour (Larsen et al. 2016)
Pipeline scour (KC = 30) g s t* 2 D 1 d 3 t
Level 1 Level 2 Example computational mesh
Tsunami scales Mercator yacht signal, measured off the coast of Thailand (2004) approximated as sinusoidal Period T=13 min Wave height H=5 m Depth h=14 m Velocity U=2.1 m/s Sediment d=0.3 mm Wave boundary layer thickness d =2.4 m Monopile diameter D=5 m
Model scale similarity Froude similarity (ensures similarity in adverse horizontal pressure gradients) Fr D U gd 0.30 D model D D full model 0.10 m 0.30 m/s Dimensionless boundary layer thickness (governs size of horseshoe vortex in steady currents) 50 U model d D 0.47 d model 0.047 m Tmodel 52.9 s
Model scale similarity (2) Keulegan-Carpenter number: KC full UT D 328 KCmodel 157 Period-to-scour time scale ratio: T T T * s s full T s 0.54 g 1 3 0.7 s 1d 1 d 1. 5 D 2 O 400 D T T s model 0.69 (New expression, based on reanalysis of experimental data of Sumer et al. 1992)
Summary of model and full tsunami scales Full scale Model scale D 5 m 0.1 m d 0.3 mm 0.17 mm T 13 min = 780 s 52.9 s U m 2.1 m/s 0.297 m/s U f 0.0745 m/s 0.0146 m/s d 2.36 m 0.047 m T s 1449 s 76.4 s S 1.49 m 0.0297 m s 2.65 2.65 Fr D 0.30 0.30 d/d 0.47 0.47 KC 328 157 Re D =U m D/ 10 7 3 10 4 m 1.1 0.078 T/T s 0.54 0.69 S/D 0.297 0.297
Animation of tsunami-induced scour
Scour time series (leading wave) 2 u/u1m 0-2 0 10 20 30 40 50 60 Scour ceases slightly after peak New scour process begins after flow reversal
Scour time series (3 successive periods) Scour grows to an equilibrium value Scour depth is significantly less than for steady current (S/D 1.3)
Scour evolution:
Scour evolution (cross-sections)
Importance of boundary layer thickness on horseshoe vortex Figure from: Sumer, B.M. & Fredsøe, J. (2002) Mechanics of Scour in the Marine Environment. World Scientific, Singapore.
Practical method for predicting tsunami-induced scour Strategy: Combine existing steady current expressions, but invoke tsunami wave boundary layer thickness (Tsunami-induced flows are both current-like and wave-like!) Equilibrium scour, taking into account finite d: S D d S d S 0 0 1 exp 0.55 0.296, 1.3 0.7 D D D Scour depth, taking into account time evolution: S S d t 1 exp s, t D D Ts S yields 0.15,0.22,0.26 D s nt, 1 for n 1, 2,3 S S d t
Comparison of predicted vs. simulated results Steady current (Baykal et al. 2015) t=2t t=3t t=t
Conclusions Tsunami boundary layers: Boundary layer model developed capable of reaching full geophysical scales Tsunami-induced boundary layers are both: current-like (long durations) wave-like (unsteady, finite boundary layer thickness) Sinusoidal, single wave, and N-wave forms are all reasonable idealizations Parameterized boundary layer thickness, turbulence, and bed shear stresses Tsunami-induced scour: Advanced fully-coupled CFD model developed for simulating tsunami-induced scour processes around a monopile foundation (relevant for wind farms) Methodology developed for maintaining hydrodynamic and morphologic similarity for model and full scales Practical methodology developed for engineering prediction of tsunamiinduced scour around monopile foundations
DTU publications (acknowledging ASTARTE) Published: Sumer, B.M., Guner, H.A.A., Hansen, N.M., Fuhrman, D.R. & Fredsøe, J. (2013) Laboratory observations of flow and sediment transport induced by plunging waves. J. Geophys. Res. 118, 1 22. Sumer, B.M., Baykal, C., Fuhrman, D.R., Jacobsen, N.G. & Fredsøe, J. (2014) Numerical calculation of backfilling of scour holes. 7th Int. Conf. on Scour and Erosion, Perth, Australia. Fuhrman, D.R., Baykal, C.B., Sumer, B.M., Jacobsen, N.G. & Fredsøe, J. (2014) Numerical simulation of waveinduced scour and backfilling processes beneath submarine pipelines. Coast. Eng. 94, 10 22. Baykal, C.B., Sumer, B.M., Fuhrman, D.R., Jacobsen, N.G. & Fredsøe, J. (2015) Numerical investigation of flow and scour around a vertical circular cylinder. Phil. Trans. Roy. Soc. A 373, 20140104. Submitted or in preparation: Williams, I.A. & Fuhrman, D.R. (2016) Simulation of tsunami-scale wave boundary layers. Coast. Eng. 110, 17 31. Larsen, B.E., Fuhrman, D.R., Baykal, C. & Sumer, B.M. (2016) Tsunami-induced scour around monopiles. (in preparation). Eltard-Larsen, B., Fuhrman, D.R. & Sumer, B.M. (2015) Simulation of wave-plus-current scour beneath submarine pipelines. J. Waterw. Port Coast Offshore Eng.-ASCE (in press). Madsen, P.A., Schaffer, H.A., Fuhrman, D.R. & Toledo, Y. (2015) Uniform asymptotic approximations for transient waves due to an initial disturbance. J. Geophys. Res. (in press). Baykal, C., Sumer, B.M., Fuhrman, D.R., Jacobsen, N.G. & Fredsøe, J. (2015) Numerical simulation of waveinduced scour and backfilling processes around a cylindrical monopile. (in review).
Wind wave-induced flow, sediment transport, and scour/backfilling around a monopile foundation (Baykal et al. 2016, submitted)
Simulation of tsunamiinduced boundary layers and scour around monopiles David R. Fuhrman Isaac A. Williams Bjarke Eltard Larsen Cuneyt Baykal B. Mutlu Sumer
Single wave evolution to large Reynolds numbers Re=10 7 Re au m U mt, a 2 Re=2 10 6 t (deg)
Turbulent kinetic energy k 1 2 u 2 v 2 w 2 k U a 0.068 max 2 1m k s 0.22 Smooth (solid lines) Rough (dashed lines) Re=7.0x10 8
Bed shear stresses
b,max 1 2 f w Tsunami wave friction factor diagrams U 2 1m Smooth: Rough: f w 0.04Re 0.16 f w exp 5.5 a k s 0.16 0.67 Existing expresions are relatively accurate, even when extrapolated to tsunami scales!
b,max 1 2 f w U 2 1m Comparison with synthetic signals Tohoku (2011): Indian Ocean (2004): The various synthetic wave forms represent real-life tsunamis reasonably!