Study of wave wind interaction at a seawall using a numerical wave channel

Study of wave wind interaction at a seawall using a numerical wave channel tài liệu, giáo án, bài giảng , luận văn, luận...

Accepted Manuscript Study of Wave – Wind Interaction at a Seawall Using a Numerical Wave Channel Phung Dang Hieu, Phan Ngoc Vinh, Du Van Toan, Nguyen Thanh Son PII: DOI: Reference: S0307-904X(14)00208-X http://dx.doi.org/10.1016/j.apm.2014.04.038 APM 9980 To appear in: Appl Math Modelling Received Date: Revised Date: Accepted Date: 28 November 2012 13 January 2014 15 April 2014 Please cite this article as: P.D Hieu, P.N Vinh, D Van Toan, N.T Son, Study of Wave – Wind Interaction at a Seawall Using a Numerical Wave Channel, Appl Math Modelling (2014), doi: http://dx.doi.org/10.1016/j.apm 2014.04.038 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain Study of Wave – Wind Interaction at a Seawall Using a Numerical Wave Channel Phung Dang Hieu 1* , Phan Ngoc Vinh2, Du Van Toan1, Nguyen Thanh Son3 Research Institute for management of Seas and Islands, 125 Trung Kinh Str., Cau Giay, Hanoi, Vietnam Institute of Mechanics, 264 Doican, Hanoi, Vietnam Faculty of Hydro-Meteorology and Oceanography, Hanoi University of Science, 334 Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam * Corresponding author: Fax:+84-4-3259-5429 E-mail address: phunghieujp@gmail.com (Phung D Hieu) Abstract This paper presents the study on wind and waves interactions at a seawall using a numerical wave channel The numerical experiments were conducted for wave overtopping of a ¼ sloping seawall using several conditions of incident waves and wind speeds The numerical results were verified against laboratory data in a case for wave overtopping without wind effects The interaction of waves and wind was analyzed in term of mean wave quantities, overtopping rate and variation of wind velocity at some selected locations The results showed that the overtopping rate was strongly affected by wind and the wind field was also significantly modified by waves There exists an effective range of wind speed in comparison with the local shallow wave speed at the breaking location, which gives significant effects to the wave overtopping rates The maximum of wind adjustment coefficient f w for wave overtopping rate was strongly related to the mean overtopping rate in the case for no wind This study also showed that when the mean overtopping rate was greater than × 10 −4 m3/s/m, the maximum of wind adjustment coefficient f w approached to a specific value of about 1.25 Keywords: Wave overtopping; Two-phase model; Overtopping rate; Seawall; Wind effect Introduction Accurate assessment of wave overtopping at seawall or coastal structures is a key requirement for effective design of coastal defenses Wave overtopping has been studied extensively over the last 30 years (Besley et al [1], Goda et al [2], Owen [11], Van de Meer and Waal [15]) The knowledge on the wave overtopping of seawalls has contributed significantly to the practical industry and published in some distinct guide books so far Among those, it could be mentioned such as “EuroTop Wave Overtopping of Sea Defenses and Related Structures” [10], TAW (2002) [14] and so on However, strong waves dangerous for coastal structures are mostly appeared during the storm weather with the presence of strong wind Whereas, formulae for the estimation of wave overtopping have been empirically formed using experimental data which were measured indoor from experiments done in wave flumes without presence of wind Therefore, wave overtopping in practice may be significantly affected by wind and different from which estimated by using those empirical formulae In the guide book [10], it is pointed out that wind may affect overtopping processes and thus discharges by: changing the shape of the incident wave crest at the structure resulting in a possible modification of the dominant regime of wave interaction with the wall; blowing up-rushing water over the crest of the structure (for onshore wind) resulting in possible modification of mean overtopping discharge and wave-by-wave overtopping volumes; modifying the physical form of the overtopping volume or jet, especially in terms of its aeration and break-up resulting in possible modification to post-overtopping characteristics such as throw speed, landward distribution of discharge and any resulting post-overtopping loadings [10] However, very few experimental studies of wind effect on wave overtopping have been found so far Iwagaki et al [6] studied the wind effect on wave overtopping of vertical seawalls by doing experiments in a small scale wave flume with a wind tunnel Their results confirmed that the wind effects on the rate of wave overtopping on vertical seawalls were very important However, they commented that their results were of only some cases for vertical seawalls and not sufficient to apply to practical purposes Ward et al [16, 17] carried out experiments using a physical wave flume with wind facilities to study the effects of strong onshore winds on run-up and overtopping of coastal structures Although, it is widely assumed that onshore winds significantly result in increasing run-up and overtopping, very few formulae and experimental data estimating the wind effects on run-up and overtopping have been published [8] Thus, further studies with more systematic investigations need to be carried out to disclose the mechanism of wave overtopping Numerical simulation of wave overtopping is very difficult due to the complex process of the wave overtopping itself and in the treatment of the overturning free surface in a numerical model [5] For a decade, the numerical model based on the Navier-Stokes equations together with the volume of fluid (VOF) method has been known as a potential tool for the simulation of wave breaking and wave overtopping However, the simulation of wave overtopping with wind effect is still limited Recently, Li and He [7] have studied the wind effects on wave overtopping by using a two-phase solver Their results showed the capability of the two-phase model in simulation of wind and wave movement and therefore showed the wind effects on wave overtopping of a structure Hieu et al [3], Hieu and Tanimoto [4], Hieu and Vinh [5] proposed a numerical VOFbased two-phase flow model for wave breaking, wave-structure interaction and wave overtopping of seawall supported by porous structures Their studies on verification of the model for wave breaking, wave structure interaction and wave overtopping showed that the model has good capability in making numerical experiments on wave motion and wave structure interaction including wave breaking and overtopping In this study, the proposed model [4, 5] is used as the core of a numerical wave channel for carrying out numerical experiments on wind-wave interaction and studying wind effects on wave overtopping of a slopping seawall Firstly, the numerical wave channel is used to carry out an experiment in the condition similar to the experiment done in a laboratory wave flume in order to verify the numerical wave channel Then, a series of numerical experiments are carried out for the investigation of wind effects on wave overtopping and wave quantities as well as for the study of wind modification by wave motion Numerical wave channel and experiment setup 2.1 Numerical wave channel The numerical model proposed by Hieu and Tanimoto [4] and Hieu and Vinh [5], which was based on the Navier-Stokes equations extended to porous media (Sakakiyama and Kajima, [12]) and the Smagorinsky turbulence model [13], was applied as the core of the numerical wave channel for conducting numerical experiments The numerical wave channel used a source wave maker method in order to minimize the reflection of waves at the wave maker boundary The source wave maker consists of two parts the source function and the damping zone The source function is added to the mass conservation equation in order to generate the desired incident waves While the damping zone works as an energy dissipation one by adding a resistance force proportional to the flow velocity to the momentum equations (refer to [4], [9] for more detail) Fig presents a schematic view of the numerical wave channel 2.1.1 Governing equations The governing equations for the numerical wave channel in a 2-dimensional model are briefly written as follows: Continuity equation: ∂γ xu ∂γ zw + = qmγv ∂x ∂z (1) Modified Navier-Stokes equations: λv λv γ ∂p ∂  ∂u ∂λ x uu ∂λ z wu  ∂u   ∂   ∂u ∂w   + + =− v + γ xν e    + γ zν e  +  − D x u − R x + q u ∂t ∂x ∂z ρ ∂x ∂x   ∂x   ∂z   ∂z ∂x   (2) ∂w ∂λxuw ∂λz ww γ ∂p ∂   ∂w ∂u  ∂ + + =− v + γ xν e  +  + ρ ∂z ∂x  ∂t ∂x ∂z  ∂x ∂z  ∂z (3)   ∂w    − Dz w − Rz − γ v g + qw γ zν e   ∂z   Advection equation for the volume of fluid fractional function: ∂γ v F ∂uγ x F ∂wγ z F + + = qF ∂t ∂x ∂z (4) Equation for the estimation of density and viscosity for the two-phase flow model: ρ = (1 − F ) ρ a + Fρ w (5) ν = (1 − F )ν a + Fν w (6) where t: time, x and z are the horizontal and vertical coordinates, u, w: horizontal and vertical velocity component respectively, ρ: density of the fluid, ρ a : air density, ρ w : water density, ν a and ν w are molecular kinematic viscosity of air and water, respectively, p: pressure, νe: kinematic viscosity (summation of molecular kinematic viscosity and eddy kinematic viscosity), g: gravitational acceleration, γv: porosity, γx, γz: areal porosities in the x and z projections, q m is the source of mass for wave generation qu, qw is the momentum source in x and z direction F is the volume of fluid fractional function; qF is the source of F due to the wave maker source method Dx, Dz: Coefficient of energy damping in the x and z directions respectively Rx, Rz : Drag/resistance force exerted by porous media λv, λx, λz are defined from γv, γx, γz respectively using following relationships λv = γ v + (1 − γ v )C M   λ x = γ x + (1 − γ x )C M  λ z = γ z + (1 − γ z )C M  (7) where CM is the inertia coefficient The resistance force Rx and Rz are described by the following equations Rx = CD (1 − γ x )u u + w 2 ∆x (8) Rz = CD (1 − γ z )w u + w 2 ∆z (9) where ∆x, ∆z are the horizontal and vertical grid size in porous media and CD is the energydamping coefficient The source of mass has the form as follow: q at the source location qm =  s others 0 (10) The momentum source in x and z direction (here we neglect the momentum source contributed by the viscous terms) is respectively given as qu = uq m , q w = wq m 2.1.2 Initial and boundary conditions At the initial time, still water is assumed inside the computation domain There are two kinds of boundaries, namely, interface boundary and domain boundary The interface boundary represents the boundary between the air zone and the water zone while the domain boundary represents variables at virtual cells adjacent to real cells of the computation domain The interface boundary is automatically solved and satisfied the kinematic boundary condition by solving the advection equation (4) The dynamic boundary condition for the free surface is automatically satisfied with the Modified Navier-Stokes equations (2) and (3) For the domain boundary, at the computational cell adjacent to the solid cell, the no-slip boundary condition is adopted At the top boundary, where the computational domain is connected to the open air above, the continuative conditions are applied for velocity and pressure These conditions mean that the velocity components fully satisfy the continuity equation and the gradient of pressure at the boundary set equal to the hydrostatic pressure gradient 2.1.3 Solution method The governing equations are discretized by a finite difference scheme on a staggered grid mesh The velocity components are evaluated at cell sides while scalar quantities are evaluated at the cell center The SMAC method (Simplified Marker and Cell Method) is used to get the time evolution solution of the governing equations The resultant Poisson equation of pressure correction due to the SMAC method is solved using a Bi-conjugate gradient method Here the brief explanation is given as follows (for more detail, see [3, 4]): (a) Give initial values for all variables; (b) Give boundary conditions for all variables; (c) Solve explicitly the momentum equations for the predicted velocities; (d) Solve the Poisson equation for the pressure corrections; (e) Adjust the pressure and velocity; (f) Solve the advection equation of VOF function using the PLIC algorithm for tracking the free surface (g) Calculate the new density and kinematic viscosity based on the VOF values (h) Calculate the turbulence eddy viscosity Return to step (b) and repeat for next time step until the end of specified time 2.2 Experiment setup In the numerical wave channel, a sloping seawall was set on the horizontal bottom with the water depth of 0.6m The seawall had a slope of ¼ connecting a vertical wall at the level of 0.7m to the bottom The point located at the toe of the slope was set as the reference point called x0 (i.e 10m far from the wave source location), where a porous structure was set on The porosity of the porous body was 0.42 The crest height of the vertical wall relative to the still water level was 0.16m Wind was input to the numerical wave channel by using a wind tunnel set at a distance of 0.2m above the still water level and 8m far from the wave source location The wind tunnel was 1m long and 0.49m wide Fig presents the sketch of the experiment setup In the numerical experiment, the overtopping water was measured easily by calculating the total water contained behind the vertical wall Therefore, the accumulated overtopping water and averaged overtopping rate can be obtained The numerical experimental wind speeds, incident wave heights and wave periods are presented in Table In order to validate the numerical wave channel in conducting the experiments on wave overtopping, an experiment with the conditions similar to the experiment N1 was carried out by using the physical wave flume at Department of Coastal Engineering, Water Resource University, Hanoi, Vietnam The wave flume equipped by Delft, The Netherlands was 40m Figure Captions (Hieu et al figures) Fig 1: Schematic view of the numerical wave channel Fig 2: Sketch of the numerical experimental condition using the numerical wave channel Fig 3: Comparison of water surface elevation between simulated results and measured data: a) at the wave gauge G1; b) at the wave gauge G4 Fig 4: Cross shore distribution of wave quantities nearby the seawall Fig 5: Accumulated water volume of wave overtopping at the seawall Fig 6: Variation of relative overtopping rate versus normalized wind speed Fig 7: Variation of wind adjustment coefficient f w versus mean overtopping rate without wind effect q Fig 8: Wind effects on breaking wave crests Fig 9: Vertical distribution of maximum horizontal wind speed from the still water level: a) at x – x0 = 0.5m; b) at x – x0 = 1.5m; c) at x – x0 = 2.84 m at the vertical wall Fig 10: Time variation of wind velocity components at the level z = 40 cm above the still water level: a) x – x0 = 0.5m; b) x – x0 = 1.5m; c) x – x0 = 2.84 m at the vertical wall Fig 11: Snapshot of wind field above waves on the slope 19 Table Captions (Hieu et al Tables) Table 1: Experimental conditions Table 2: Name and location of wave gauges 20 Damping zone Open boundary Wave generation source Solid boundary Air zone Water zone Free surface boundary Porous structure Hieu et al Fig 1: Schematic view of the numerical wave channel Vertical direction (cm) Wind W = - m/s 150 L =102cm 100 stone 6cm SWL 50 d = 40cm h =60cm 70 cm   1/2 10 11 12 13 14 Horizontal direction (m) Hieu et al Fig 2: Sketch of the numerical experimental condition using a numerical wave channel water surface elevation (m) 0.2 Simulated results Expt data 0.15 0.1 0.05 -0.05 -0.1 -0.15 (a) -0.2 10 15 20 25 30 35 20 25 30 35 water surface elevation (m) time (s) 0.2 Simulated results Expt data 0.15 0.1 0.05 -0.05 -0.1 (b) -0.15 -0.2 10 15 time (s) Hieu et al Fig 3: Comparison of water surface elevation between simulated results and measured data: a) at the wave gauge G1; b) at the wave gauge G4 40 Simulated wave crest Vertical distance (cm) 30 Simulated wave height 20 10 Simulated mean water level wave height (expt data) -10 -20 -30 wave crest (expt data) wave trough (expt data) Simulated wave trough -40 -50 -60 -400 -300 -200 -100 100 200 300 400 Horizontal distance (cm) Hieu et al Fig 4: Cross shore distribution of wave quantities nearby the seawall Accumulated overtopping water Q (cm3/cm) 500 Expt Data (averaged) Expt Data Expt Data Expt Data Simulated Q 400 300 200 100 0 10 12 14 16 18 20 t/T Hieu et al Fig 5: Accumulated water volume of wave overtopping at the seawall 0.030 0.025 Hi =17.3 cm, T=1.6s Hi=17cm, T=2.0s Hi =15cm, T=1.3s 0.020 Hi =12cm, T=2.0s Hi =15cm, T=2.0s 0.015 Hi =15cm, T=1.6s Hi = 13cm, T=1.6s Hi = 17cm, T=1.3s Hi =15cm, T=2.2s Hi = 22.6cm, T=2.2s 0.010 0.005 Hi = 12.5cm, T=2.2 0.000 10 Hieu et al Fig 6: Variation of relative overtopping rate versus normalized wind speed fw 1.5 0.5 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 q (m3/s/m) Hieu et al Fig 7: Variation of wind adjustment coefficient f w versus mean overtopping rate without wind effect q Crest at breaking point ( Hi =15cm, T=1.6s) Crest at breaking point ( Hi =15cm, T=2.0s) Crest at breaking point ( Hi =15cm, T=2.2s) Wave crest (cm) 20 15 10 0 10 Wind velocity (m/s) Hieu et al Fig 8: Wind effects on breaking wave crests 8 Numerical results a) Ln(z/zo) y = 0.8768x + 1.6456 0.0 2.0 4.0 6.0 8.0 10.0 Umax (m/s) Numerical results b) Ln(z/zo) y = 0.9906x + 1.2169 0.0 2.0 4.0 6.0 8.0 10.0 Umax (m/s) Numerical results c) Ln(z/zo) y = 0.1814x + 4.6925 0.0 2.0 4.0 6.0 8.0 10.0 Umax (m/s) Hieu et al Fig 9: Vertical distribution of maximum horizontal wind speed from the still water level: a) at x – x0 = 0.5m; b) at x – x0 = 1.5m; c) at x – x0 = 2.84 m at the vertical wall Wind velocity (m/s) 10 U (horizontal wind) a) V (vertical wind) -2 0.25 0.5 0.75 1.25 1.5 1.75 t/T Wind velocity (m/s) 10 U (horizontal wind) b) V (vertical wind) -2 0.25 0.5 0.75 1.25 1.5 1.75 t/T Wind velocity (m/s) 10 U (horizontal wind) c) V (vertical wind) -2 0.25 0.5 0.75 1.25 1.5 1.75 t/T Hieu et al Fig 10: Time variation of wind velocity components at the level z = 40 cm above the still water level: a) x – x0 = 0.5m; b) x – x0 = 1.5m; c) x – x0 = 2.84 m at the vertical wall 10 Vertical direction (cm) m/s Hi = 15cm, T = 1.6s, Wind velocity = m/s a) 100 50 h =60cm d = 40cm   1/2 10 11 12 13 14 Horizontal direction (m) Vertical direction (cm) m/s Hi = 15cm, T = 1.6s, Wind velocity = m/s b) 100 50 h =60cm d = 40cm   1/2 10 11 12 13 14 Horizontal direction (m) Vertical direction (cm) c) m/s Hi = 15cm, T = 1.6s, Wind velocity = m/s 100 50 h =60cm d = 40cm   1/2 10 11 12 13 14 Horizontal direction (m) Hieu et al Fig 11: Snapshot of wind field above waves on the slope 11 Hieu et al Table 1: Experimental conditions Wind speed No Set Hi (cm) T (s) W (m/s) 4.5 17.3 1.6 N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 15 1.6 N12 N13 N14 N15 N16 N17 N18 N19 N20 N21 N22 13 1.6 N23 N24 N25 N26 N27 N28 N29 N30 N31 N32 N33 17 2.0 N34 N35 N36 N37 N38 N39 N40 N41 N42 N43 N44 15 2.0 N45 N46 N47 N48 N49 N50 N51 N52 N53 N54 N55 12 2.0 N56 N57 N58 N59 N60 N61 N62 N63 N64 N65 N66 17 1.3 N67 N68 N69 N70 N71 N72 N73 N74 N75 N76 N77 15 1.3 N78 N79 N80 N81 N82 N83 N84 N85 N86 N87 N88 22.6 2.2 N89 N90 N91 N92 N93 N94 N95 N96 N97 N98 N99 10 15 2.2 N100 N101 N102 N103 N104 N105 N106 N107 N108 N109 N110 11 12.5 2.2 N111 N112 N113 N114 N115 N116 N117 N118 N119 N120 N121 Hieu et al Table 2: Name and location of wave gauges Name of wave gauges Relative distances from the reference point x0 (m) G1 G2 G3 G4 G5 G6 G7 G8 G9 X1 = -3.2 X2 = 0.0 X3 = 1.0 X4 = 1.5 X5 = 1.6 X6 = 1.7 X7 = 2.3 X8 = 2.4 X9 = 2.79 ... measured data: a) at the wave gauge G1; b) at the wave gauge G4 40 Simulated wave crest Vertical distance (cm) 30 Simulated wave height 20 10 Simulated mean water level wave height (expt data)... overtopping of a ¼ sloping seawall using a numerical wave channel for several conditions of incident waves and wind speeds The numerical results were verified against laboratory data in a case for wave. . .Study of Wave – Wind Interaction at a Seawall Using a Numerical Wave Channel Phung Dang Hieu 1* , Phan Ngoc Vinh2, Du Van Toan1, Nguyen Thanh Son3 Research Institute for management of Seas and