- Active Reflection Compensation (ARC)


A significant improvement in the wave field in flumes and wave basins can be made by equipping the wave generator with the Active Reflection Compensation (ARC) functionality. The aim of the ARC functionality is to reduce unwanted re-reflections of waves against the wave board by absorbing the waves coming from the flume or basin at the moment they reach the wave board. ARC is running simultaneously with generation of the target incident waves, so the wave board generates the target incident waves and absorbs the unwanted waves at the same time.

Equipping a wave generator with the ARC functionality requires additional hardware and software, and a real-time connection to the wave generator control system. The additional hardware concerns ARC wave gauges mounted to the wave boards and the related wave signal data acquisition. The AukePC/ARC software computes real-time the additional motion that the wave generator must make in order to absorb the undesired waves. This information must real-time be transferred to the wave generator control system.

The ARC functionality can be incorporated in existing wave generators, provided they satisfy certain hardware and software characteristics. Please use the contact information in this document for more on this.

In case of buying a new wave generator, we recommend to purchase a Bosch Rexroth wave generator and equip it with the ARCH functionality. Here, ARCH stands for Active Reflection Compensation HyPCoS. In the ARCH software, the Active Reflection Compensation software by Deltares cooperates with the HyPCoS wave generator control software by Bosch Rexroth. From experience (Marin, Coppetec, Deltares (two machines), Hannover), we know that the Bosch Rexroth hardware (wave generators) and software (HyPCoS) operate very well with the AukePC/ARC software.

Installation of the ARC functionality in your wave maker system leads to a tremendous reduction of the re-reflections in a facility (flume or basin). As a consequence, the resulting wave field is much more similar to the desired wave field than in case no ARC is employed.

Motivation for using Active Reflection Compensation
Active reflection compensation (ARC) in the present context refers to the use of the wave maker not only as a wave generating device, but also as a wave absorbing device. Wave generation and active wave absorption can be executed simultaneously. In fact, this is the default way of working. There are various reasons for employing ARC:

  • To avoid spurious re-reflections from the wave maker, thereby spoiling the target incident waves.
  • To reduce the flume or basin stilling time between tests substantially (say, from an hour to a couple of minutes) by quickly removing the otherwise slowly damped low-frequency oscillations.
  • To prevent resonant oscillations in the flume or basin, which reduce the maximum test operation.
  • To make the experimental results less sensitive to the placing of artificial boundaries constituted by wave makers, and thus to make them easier to interpret.

In order to explain the necessity of having ARC in a facility, consider first the prototype situation, see Figure 1. This is the real-life situation somewhere out there in the field. The wave field near the structure (a harbour, a breakwater, a dike, a coastline, etc) always consists of an incident part (the incoming waves) propagating towards the structure, and the reflected waves propagating seawards (away) from the structure.

The next step is to make a laboratory model of the prototype situation. It is inevitable that additional model boundaries are introduced. These boundaries are formed by the side-walls of the facility and by the wave maker. The model boundaries lead to unwanted (because not present in the prototype situation) reflections. Therefore, at the side-walls of basins often gravel beaches are employed to provide additional damping (passive). Also the wave board itself gives – without ARC – significant reflections. In other words, in a facility the wave field consists of two parts:

  • The wanted part. This consists of the target incoming waves (provided by the wave maker) and the reflected waves (the target waves that have reflected at the structure, and may interact with the target incoming waves).
  • The unwanted part. This part consists of the re-reflected waves (reflection of the reflected waves at the wave board), the re-re-reflected waves (reflection of the re-reflected waves at the structure), the re-re-re-reflected waves (reflection of the re-re-reflected waves at the wave board), and so on.

This leads to a polluted wave field, as graphically depicted in Figure 2.

In case ARC is employed, the re-reflection at the wave board is significantly reduced. Of course, also the subsequent re-re-reflections are reduced significantly, to a point of non-existence. This leads to a much less spoiled wave field, as depicted in Figure 3.

To estimate the amount of wave field pollution due to the absence of ARC, and the effect that inclusion of ARC has, a crude model is devised. Let the wave height of the wanted wave field be indicated by , and the wave height of the unwanted wave field by . Furthermore, let the reflection coefficient (defined in terms of wave height) at the structure be denoted by , and the reflection coefficient at the wave board by . It is precisely this coefficient that ARC aims to reduce. It is not hard to prove that the ratio between the wanted wave height and the unwanted wave height is given by:

The value for should be as small as possible, with being the ideal situation. Let’s now insert some representative values. Assume a value for the reflection coefficient of the structure: = 0.4. As mentioned, the influence of ARC lies in the coefficient .

  • With ARC included. With a typical value of = 0.1, we get: = 0.04. This means that the wave field is hardly spoiled with undesired re-reflections. This is considered as acceptable
  • No ARC included. With a typical value of = 0.9, we get: = 0.39. This means that the wave field is significantly spoiled. This situation must be considered as unacceptable.

ARC software and hardware
Getting ARC operational in a facility, requires installation of the ARC software and hardware. The ARC software uses the surface elevation measured by a wave gauge mounted at each wave board segment, and computes a real-time correction to the wave board motion, see the figure.

Here, is the offline wave board signal as computed by AukePC/Generate. The ARC correction is added to the offline signal, leading to the online signal . The factor , which is unity by default, controls the relative influence of the ARC motion on the total signal. The wave board signal leads to a mechanical motion of the wave board, with representing the mechanical transfer function. The motion of the wave board leads, through the Biésel transfer function, to a target incident wave . The measured total wave signal at the wave board, , contains not only the target incident wave ( ), but also the reflected wave . The latter needs to be absorbed. This is done by suitable adjustment of the total wave board signal. The ARC routine computes the required correction to the wave board signal.

Expected performance
The performance of ARC, i.e. the amount in which re-reflections at the wave board are suppressed (i.e. the value of ), depends on various aspects, such as the type of wave generator (piston or flap), the quality of the hardware and software, the stiffness of the machine, the power of the machine engines, the machine electronics etc. Also, the ARCH performance of a given system varies somewhat with the water depth and the wave conditions.

Based on results in the past, typical values of range between 5% and 15% for the most relevant wave conditions. Some results obtained in a flume which is perfectly equiped for ARC (the Scheldt flume at Deltares) are shown in the figure.

As mentioned above, the un-wanted re-reflections can cause a significant amount of undesired wave field ‘pollution’. The figure shows a target spectrum (in black) and two measured spectra. The green line is obtained with ARC on, while the red line is obtained with ARC switched off. The strong spurious peaks occur at the resonance frequencies of the basin. These peaks constitute significant deviations from the target wave field.

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