large scale experiments as a tool for numerical …towards a balanced methodology in european...

Towards a Balanced Methodology in

European Hydraulic Research 10-1

10. LARGE SCALE EXPERIMENTS AS A TOOL FOR NUMERICAL MODEL DEVELOPMENT

Jens Kirkegaard1, Erik Asp Hansen1, Jesper Fuchs1, Hemming A. Schäffer1, Harry

Bingham2 and Erik D. Christensen1 1 DHI Water & Environment, Hørsholm, Denmark, 2 MEK, DTU, Lyngby, Denmark

Abstract

Experimental modelling is an important tool for study of hydrodynamic phenomena. The applicability of experiments can be expanded by the use of numerical models and experiments are important for documentation of the validity of numerical tools. In other cases numerical tools can be applied for improvement of the reliability of physical model results.

This paper demonstrates by examples that numerical modelling benefits in various ways from experimental studies (in large and small laboratory facilities). The examples range from very general hydrodynamic descriptions of wave phenomena to specific hydrodynamic interaction with structures.

The examples also show that numerical model development benefits from international co-operation and sharing of high quality results.

10.1 Introduction

Marine structures are exposed to complex environmental forces during construction as well as during their service life. The exposure to hydrodynamic forces is site dependent and a general design manual is therefore limited to specification of design methods. For this reason experiments and studies are much more important parts of the design process than for any other type of construction – maybe with space programs as a notable exception. In the second half of the 20th century scale experiments and numerical models have developed to a mature state and the methods are now used extensively for quantitative assessment of structural designs.

A popular belief is that computational methods are now so developed that any problem can be solved by the computer. Computer games with fancy visualisation of real life situations give the impression that the involved processes are adequately computed / modelled, but often they are nothing but graphic deception. A computer animation of a sea surface shown on a screen does not in itself provide more quantitative insight than watching the natural sea. To constitute a reliable tool for the professional design process we need to know the kinematics ‘inside’ the wave and near the bottom of the sea or river. Models that are capable of describing these processes are extremely complicated as they need to respect all laws of physics and need to respect the hydrodynamic interaction between the water, soil and structures. On the other hand, the numerical models can be used to quantify possible differences between the reduced scale experiment and the nature. For example due to differences between full scale and model scale Reynolds numbers.

Because hydraulic structures are essential for the society, be it in relation to transportation, exploitation of natural resources, safety against disasters and long term

Kirkegaard, Hansen, Schäffer, Fuchs, Bingham and Christensen Budapest, 22-23 May 2003



environmental impacts, a huge research effort has been spent on development of adequate models and in particular the effort has concentrated on hydrodynamic numerical models. Although large accomplishments have been achieved it is important to realise that improvements are still needed, especially when considering the modelling of fluid-structure interaction.

For certain processes the application of numerical models only would represent a step ‘backwards’ relative to more traditional modelling by experiments. Numerical modelling is normally considered to be relatively inexpensive, but cost saving cannot justify a more simplistic model if the most important physical factors are not realistically represented. There are large potential synergies between the different methods in physical and numerical modelling as described in HYDRALAB’s strategy paper (The HYDRALAB Consortium, 2003) and this is why we need to care for further advances of all the available study tools.

This paper aims at describing by examples how experimental hydraulic models can be used in connection with development and verification of new numerical models and thereby help creating the synergy described above. The examples are from development activities at DHI Water & Environment in Denmark. Similar examples could be drawn from the activities of other research and development institutions throughout the world. It is important to realise that interaction between the different research groups – as facilitated for example through the EU-supported research programmes and international conferences – stimulates the advances of methodologies and should thus be continued.

10.2 Scope of Experimental Support to Numerical Modelling

Physical models are scaled down representations of natural processes to fit into a laboratory environment. They can either be designed to describe specific physical processes (process models) or they can be established to describe a range of processes governing the flow situation in a geographical area or around a complete structure (design models). The laboratory environment provides controllable boundary conditions so that test conditions can be decided by the researcher and tests can be repeated under identical conditions. This is rarely possible in full scale.

Experiments can be used in various ways in connection with development and application of numerical models:

• Identification and description of processes • Validation of numerical models • Interaction with numerical models (hybrid and composite modelling)

The following examples illustrate these applications primarily in the context of wave hydrodynamics and wave-structure interaction.

10.3 Deepwater Risers

DHI has been engaged in the challenging task of developing methods and tools for the prediction of deepwater riser behaviour and has performed a large number of riser model tests for the Norwegian Deepwater Programme. The objective was to study the interaction of long vertical risers exposed to steady current.

The programme comprised tests under strict two-dimensional conditions, ie the risers were modelled as spring mounted rigid pipe segments and the steady current was perpendicular to the pipe axis (See Figure 10-1).




Pair of Smooth Riser Pair of Helical Risers

Figure 10-1. Experimental set-up for riser tests

Typically, risers are arranged in linear arrays although details of the arrangements depend on the production platform concept. The ocean current may approach the riser array such that the individual risers are located in the wake of each other. The riser motions are a combination of a low frequency wandering (wake induced oscillations (WIO)), and vortex induced vibrations (VIV) at a frequency much higher than the WIO.

The two-dimensional test conditions made the project well suited to calibrate and validate numerical tools for riser analysis (Christensen and Deigaard, 2001). Such tools are often based on two-dimensional force coefficients and traditional strip theory formulations: Each section of the model is analysed assuming two-dimensional conditions locally and the full response is found solving the three-dimensional structural riser model as illustrated in Figure 10-2

FLOW

FLOW

FLOW

3D Structural

Figure 10-2. Principles of numerical riser model




10.4 Volume of Fluids - Complex Fluid-Structure Interactions

Wave induced forces on offshore platform decks has become an important issue in the design and reassessments of older platforms. Due to seafloor subsidence the lower deck of an offshore platform may be subject to wave impact during the most severe storms.

A series of model tests with wave loading on different types of deck elements have been performed in the large wave channel (GWK) at Forschungszentrum Küste in Hannover, Germany. The following types of deck elements have been considered:

a) tubular elements b) plate profiles c) HEB beam profiles.

The tests have been performed with individual elements and arrays of elements. Tests

have also been performed with an array of beam elements covered with deck plating. A large range of different wave types, air gaps, and inundation's have been tested. Regular waves with wave height ranging from 1.4 m to 1.8 m, irregular waves and wave packages with crest heights ranging from 0.9 m to 1.6 m have been tested. During the tests the following parameters were measured: Wave elevations, deck element inundation, wave kinematics profile, and wave forces on the individual deck elements. The model test results have been analysed to provide hydrodynamic load coefficients to a wave-in-deck load calculation programme. The formulation includes time varying forces and reduction factors due to shielding.

The very complex flow pattern and the associated forces has until now primarily been studied experimentally. However, using the VOF-technique to handle the free surface it is in fact possible to study the complex flow of a wave hitting one or more structural elements of a platform deck numerically (Nielsen and Mayer, 2001), Figure 10-3.

Figure 10-3. Snap shot numerical simulations of 3 HEB beam profiles hit by a large wave




Upstream

Middle

Downstream

Horizontal Vertical

Figure 10-4. Comparison between numerical simulated and measured forces for 3 HEB beam

profiles hit by a large wave

10.5 Wave-induced Oscillation of Moored Ships

WAMSIM is a numerical model for predicting the wave-induced motion of a restrained floating body in restricted water, see Bingham (1998). A combination of established methods is used in an attempt to account for the most important physical processes involved in this complicated problem, while keeping the computational burden modest.

Potential theory is invoked to describe both the wave transformations over the bathymetry of the harbour, and the hydrodynamic interaction between the waves and the floating structure. However, the solution procedure is split into two steps where modified Boussinesq theory is used to predict the transformation of the waves as they propagate from deep water into the harbour or bay where the vessel is moored. The WAMIT model (Newman et al. 1995), based on linear potential theory, describes the hydrodynamic interaction between the fluid and the floating body, with the free-surface and body boundary conditions satisfied to first-order. In order to include non-linear forces due to the mooring system, as well as estimates for the neglected hydrodynamic effects in the form of empirical coefficients, the equation of motion is solved directly in the time domain.

The model is validated for the linear problem, and non-linear calculations are compared with experimental measurements for a ship moored in an L-shaped harbour in free decay response of the moored ship, Figure 10-5. The response of a moored ship is the surge, sway and yaw modes that are typically dominated by the natural periods introduced by the mooring system. These natural periods tend to be very long, as the ships mass is very large relative to the spring constants of the mooring system. At such long periods wave making (wave radiation damping) is very small, which means that other forms of damping which is missing from the ideal model are: viscous fluid forces, and mechanical friction in the mooring system.




The best way to quantify these effects is to use the free decay tests in open water mooring condition.

Figure 10-5. The figure illustrates the experimental setup at full scale, the lengths are in

meters, and the water depth is 24 m. From Bingham (1998)

The equations for the viscous damping that includes constant friction damping, linear,

quadratic, and cubic damping is:

∑=

+++=6

1

33210 )(|)(|)()()(k

kjkkkjkkjkjj txBtxtxBtxBBtF &&&&

In principal this leads to 114 coefficients that has to be estimated through the experiments. However, a simplified approach where only three out of six of the components in is assumed to be of significant interest. Further no cross-term affects the damping, i.e. surge movements does not influence on the sway damping etc.

3210 ,,, jkjkjkj BBBB

)(tFj

During preliminary test cases it was realised that the model apparently lacks important damping in the surge, sway, roll and yaw modes near the peak of the resonant response. This can be seen clearly by looking at free decay tests of the moored ship in these modes i.e., the ship is displaced in one mode and released, after which the response is measured. Figure 10-6 compares the measured and computed decay response in these four modes.




Figure 10-6. Decay test of the moored ship without damping other than linear wave radiation

damping, from Bingham (1998)

Note that although the individual lines and fenders are linear springs, the resulting motion especially in the sway mode is non-linear. There are a number of possible sources for the missing damping: The mooring system acts to dampen the surge motion due to friction as the ship moves tangentially along the fenders. Friction also acts at the pulleys over which the potentiometer lines run providing some damping to all modes. Higher-order hydrodynamic effects, primarily slow-drift damping (Grue and Biberg, 1992) may account for some of the sway and yaw damping. Some separation of the flow at the hull bottom is also a possibility with the quay wall so close to the ship. These effects warrants further investigation, but a crude approximation of all the missing damping in the model can be made by including linear coefficients of dynamic friction in the calculations, and using the decay tests to estimate their magnitude. From these curves, we estimate a fender friction coefficient of approximately 1 MN/(m/s) acting in phase with the velocity of the ship along the fender when the ship is in contact with the fender. This force will act to oppose both the surge velocity and the roll angular velocity. In sway and yaw, we estimate the total damping coefficients to be 2 MN/(m/s) m and 5.5×103 MNm/(rad/s), respectively. Including these coefficients in the




calculations produces the decay test results shown in Figure 10-7. Note that the fender friction appears to provide the correct roll damping as well.

Figure 10-7. Decay test of the moored ship with the estimated damping coefficients included

in the calculations, from Bingham (1998)

10.6 Long wave Response of Harbour Basin

Wave conditions in harbour basins are often a combination of the diffracted short-period primary wave field and low-frequency oscillations caused by irregular features of the primary waves (wind waves and swell). The low-frequency oscillations may be generated as a result of wave shoaling and breaking near the harbour by which wave energy is transferred into sub-harmonics and super-harmonics. Various processes may subsequently release this energy as free long waves that will give rise to harbour oscillations.

These integrated processes need to be adequately resolved in numerical and physical models because the periods of low–frequency waves may interfere with the natural




frequencies of port basins and moored ships. A combination of models is often the optimal strategy in cases where bathymetry and harbour layouts are complex.

An example of such situation is a study of harbour oscillations in a new marina in Beiruth (Kofoed-Hansen et al, 2000). In this case the physical model was used interactively with the numerical model (MIKE21 BW) for wave conditions with breaking waves on the submerged reef outside the harbour entrance. The reef is seen as a shelf outside the harbour in Figure 10-8.

Model Scale 1 : 60

Artificial Reef

Caisson Front

Marina Basin

Figure 10-8. Bathymetry in numerical and physical models

In the physical model there is a risk of creating an unrealistic amplification of long wave energy between the wave generator and the harbour model. The numerical model is used to identify such problems and to help designing the optimal physical model.

The low frequency oscillations in the harbour basin are shown in Figure 10-9, which is a wave recording from the physical model. The incident wave train has a peak period of 15 s. As shown in Figure 10-9, this gave rise to low frequency oscillations of about 60 s and 400 s.

Recorded signal

Filtered signal (T > 20 s)

Figure 10-9. Time series of measured and filtered surface elevation (m) in the physical model – typical long wave periods are 60 s and 400 s

Initially, the numerical model was used to investigate the natural frequencies of the marina and the entire laboratory test basin. This was done by imposing a white noise spectrum at the offshore boundary of the numerical model. For comparison a white noise spectrum was used




as a boundary condition placed at the location corresponding to the wave generator in the physical model. By this method it is possible to determine a position of the wave generator that will not distort or misrepresent the long wave phenomena in the marina. An example of the agreement between wave conditions in the numerical and physical model is shown in Figure 10-10.

0,0001

0,001

0,01

0,1

1

0,001 0,010 0,100

Frequency [Hz]

Spec

tral d

ensi

ty [m

2 /Hz]

3D Model Tests Mike 21 BW

Figure 10-10. Frequency spectra in harbour basin obtained from physical and numerical

models

Once it has been demonstrated that the low frequency response is well represented in the physical model, this model can be used for detailed assessment of wave disturbance and ship movements in the harbour.

10.7 Near-shore Development of Wave Fields

Deterministic modelling of wave transformation in the near-shore region is an example of a field where numerical and physical models often compete. Both approaches have their strengths and weaknesses, and the best choice depends on the specific situation. On the other hand physical and numerical wave experiments also provide invaluable support for each other. Laboratory tests are essential for the validation of numerical wave models. Numerical models may in turn support physical experiments for example by taking over the outer region of a model area that is too large to fit into the laboratory at an acceptable model scale. Below, we show three examples of the use of laboratory data for qualitative and quantitative validation of a Boussinesq wave model results.

Figure 10-11 shows wave-wave interaction over a submerged bar. The incident waves are regular and no wave breaking occurs. Due to non-linearity, bound second harmonics are generated as the waves shoal up the bar. These second harmonics are gradually released and propagate as free waves behind the bar, where the situation becomes essentially bi-chromatic and linear. The top panel gives a perspective time-space representation of the computed surface elevation (time increasing upwards, covering two wave periods). The middle panel shows the bottom profile. The bottom panel shows the computed and measured variation of the first and second harmonics. The two different phase speeds of the primary wave (the first




harmonic) and the free second harmonic show up as the cross pattern on the down wave side of the bar (see top panel). The measurements were taken by Luth et al (1994).

2nd harmonic

Measurements

Boussinesq result

1st harmonic

Measurements

Boussinesq result

Figure 10-11. Wave-wave interaction over a submerged bar

Figure 10-12. Wave breaking and refraction around a detached breakwater Figure 10-12 shows wave breaking and refraction of regular waves on a beach with a

detached breakwater. The left panel shows a snapshot of the surface elevation computed by a Boussinesq model with wave breaking (Sørensen, Schäffer and Madsen, 1998). The right panel shows a photo from experiments by Mory and Hamm (1997). Note the kink in the wave fronts seen in the experiment as well as in the computation. This kink is supposedly due to interaction between the incoming waves and a wave-induced vortex created by variations in wave setup behind the breakwater.




Experiments by Cox et al. (1991)Pierson-Moskowitz spectrum:Hm0 = 6.45 cm, Tp = 1.0 s

Surface elevation at WG 11 (h = 5 cm)

Boussinesq result

Measurement

Measurement

Swash oscillation (vertical displacement)

Boussinesq result

Figure 10-13. Irregular waves breaking on a beach

Figure 10-13 shows time series of surface elevation and run-up of irregular breaking

waves. The numerical results were obtained by a Boussinesq model including wave breaking and the laboratory measurements were made by Cox et al. (1991). The measurements were shifted upwards by 0.08m for clarity. The middle panel shows the surface elevation at a still water depth of 5cm (wave gauge 11 in Cox et al., see top panel), which is well inside the breaking zone. The bottom panel shows the motion of the shoreline converted into vertical displacement. The agreement is seen to be quite good. The shoreline motion is dominated by low frequency oscillations, which is to be expected because the wave breaking for this case is dominated by spilling breakers. For the present computations a finite element Boussinesq model was applied (Sørensen, Schäffer and Sørensen, 2003), but the resemblance between measurements and model results is similar to what was previously reported using a finite difference model, see Madsen, Sørensen and Schäffer (1997).

10.8 Ship Collisions on Bridge Piers

In recent decades there have been many cases of ships colliding against bridge piers. Several cases have been with fatal consequences such as loss of lives. Today the design of any bridge across navigable waters with commercial traffic is done with due attention to collision risks and impacts. The bridge piers are either designed to withstand collision impact loads, pre-emptive measures are taken against collisions or, more often, a combination of these is applied in the design.

The bridge design process therefore requires that ship impact loads are accurately predicted, or that measures, that can prevent or reduce the risk of impact or reduce the impact




loads, are identified and optimised. One such measure is artificial islands (Havnø and Knott, 1986).

The design problem is multi-disciplinary, involving ship hydrodynamics and structural engineering, hydraulics, soil mechanics and bridge dynamics. For this reason the design problem cannot be solved by any single model, whether physical or numerical.

Hydrodynamic scale experiments are used in many cases to assist in the design process. The experiment poses a number of scaling challenges for which standard scaling methods do not cater. However, in combination with numerical modelling the scale experiment is an indispensable and often the only feasible tool.

An experimental set-up often applied is for the optimisation of a protective structure such as an artificial island surrounding the pier, Figure 10-14. The tests aim to establish a design that secures that ship collision with the pier proper is avoided, and to identify impact forces transmitted to the pier through the soil media.

Figure 10-14. Model test of ship collision against protection island for a bridge pier. The bridge pier structure is mounted on a load cell

In the experiment model ships are navigated towards the protective structure. The tests can

easily cover a wide range of relevant parameters such as navigation conditions (impact speed and relative direction), ship loading conditions and island layout, and demonstrate penetration depths, deflection capabilities and impact forces in pier as well as in ship.

Two main scaling problems are inherent: the soil properties and the ship stiffness (energy absorption). Neither of the two can be scaled correctly in the experimental set-up (Havnø and Knott, 1986, Sterndorff and Pedersen, 1995). Certain scaling problems can be overcome or reduced by combining the experimental model with numerical models. This applies to both the soil mechanics and to the ship stiffness. Thus, a numerical model that simulates the experimental model can be calibrated from the experimental results, and the calibrated model can then subsequently be used to represent prototype conditions, see Figure 10-15. Other types of experimental models can overcome other scaling problems. Thus, in a centrifuge experiment certain of the soil mechanics scaling problems can be overcome, but the model can not represent the overall collision scenario like the above outlined model set-up, which relies primarily on Froude scaling.




Penetration, distance from pieras a function of time

Impact forces

Ship

Pier

Figure 10-15. Numerical model of protection island and computed results of vessel

penetration and forces

It is important to emphasise that neither experimental models nor numerical models can

overcome all scaling and modelling problems and provide the correct description of the physics and mechanics involved. By a combination of the two types of models, however, one is able to achieve the goal with sufficient accuracy.

10.9 References

Bingham, H.B,( 2000):”A hybrid Boussinesq-panel method for predicting the motion of a moored ship”, Coastal Engineering, Vol 40, pp 21-28

Christensen, E.D. and R. Deigaard (2001):” Large eddy simulation of breaking waves”, Coastal Engineering, Vol. 42, pp 53-86

Cox, D.T., H. Mase and T. Sakai (1991). An experiment on the effect of fluid acceleration on seabed stabilty. Report No. 91-HY-01. Kyoto University, Japan.

Grue, J., Biberg, D., (1992): “Wave forces on marine structures with small speed in water of restricted depth”, Appl. Ocean res. Vol 15, pp 121-135.

Havnø, K. and M Knott (1986). Risk analysis and protective island design for ship collisions. Proc. International association for Bridge and Structural Engineering (IABSE) colloquium. Tokyo, Japan. IABSE Reports – Vol. 51, 181-188.

Kofoed-Hansen, H., P. Sloth, O.R. Sørensen and J. Fuchs (2000). Combined numerical and physical modelling of seiching in exposed new marina. Proc. ICCE 2000, 3600-3613.

Luth, H.R, G. Klopman and N. Kitou (1994). Project 13G: Kinematics of waves breaking partially on an offshore bar; LDV measurements for waves with and without a net onshore current. Delft Hydraulics Report H1573, 40 pp.

Madsen. P.A., O.R. Sørensen and H.A. Schäffer (1997). Surf zone dynamics simulated by a Boussinesq type model. Part II: Surf beat and swash oscillations for wave groups and irregular waves. Coastal Eng. 32, 289-319.

Mory, M, aand L. Hamm (1997). Wave height, setup and currents around a detached breakwater submitted to regular and random wave forcing. Coastal Eng. 31, 77-96.

Newman J.N, Lee, C.H., Korsmeyer, F.T. (1995),”A radiation –Diffraction Panel program for Wave-Body Interactions”, Dept- of Ocean Eng., MIT, Cambridge, MA





Nielsen K.B. and Mayer S. (2001a): VOF simulations of green water load problems. 4th Numerical Towing Tank Symposium, September, Hamburg, Germany 2001.

Sterndorff, M.J. and P. Terndrup Pedersen (1995). Large-scale grounding experiments on soft bottoms. Int. Conf on Technologies for Marine Environment Preservation, Tokyo, Japan, Sept. 24-29, 1995.

Sørensen, O.R., H.A. Schäffer and P.A. Madsen (1998). Surf zone dynamics simulated by a Boussinesq type model. Part III. Wave-induced horizontal nearshore circulations. Coastal Eng. 32, 155-176.

Sørensen, O.R., H.A. Schäffer and L.S. Sørensen (2003). Boussinesq-type modelling using an unstructured finite element technique. Submitted to Coastal Eng.

The HYDRALAB Consortium (2003). The Future Role of Experimental Methods in European Hydraulic Research.

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