Wave Tank Testing
Wave tank testing - The joy of working with water waves
At Evergreen Innovations Prototyping, we have done a lot of wave tank testing. Wave tank testing is exciting and fun, and we want to share some of our experience here. We have undertaken wave tank testing at the David Taylor Basin at U.S. Navy facility at Carderock (NSWCCD), the Imperial College London hydrodynamic lab, the LIR deep-ocean basin at the University College Cork, the FloWave TT wave-current tank in Edinburgh, the Kelvin Hydrodynamics Laboratory at Strathclyde University, the Alfond W2 Ocean Engineering Lab at the University of Maine, the Hydraulic Wave Basin Facility at the University of Iowa, the LHEEA facility at Ecole Centrale Nantes and many others. If you have never been to a wave tank before, this video (Copyright U.S. Department of Defense) is a great introduction.
Evergreen Innovations has helped many wave energy developers in prototyping and testing their technologies. Most recently we have worked with AWS Ocean Energy, CalWave Power Technologies and Checkmate Sea Energy (Anaconda technology). Developing renewable wave energy technology is challenging but also great fun. To give you an idea of the type of work this involves, have a look at the U.S. Wave Energy Prize video below (Copyright with the U.S. Navy). Evergreen Innovations supported team Waveswing America (third place) during the Wave Energy Prize competition.
A little wavemaking background
Good quality model testing requires an understanding of the wave tank environment, most importantly the wave maker and the beach. A wave maker is similar to most other structures moving in the ocean, and is actually very similar to a wave energy converter. For most applications, a simple closed-analytical theory describes the wave maker to good accuracy. This theory is based on the assumptions of inviscid, incompressible and irrotational flow. A velocity potential can be formulated that satisfies the following boundary conditions:
Here, ϕ(x, z) is the velocity potential in the coordinate system (x, z), and the horizontal (u) and vertical (w) velocities can be expressed as
u = ∂ϕ/∂x
w = ∂ϕ/∂z
The general form of the velocity potential for the wave maker solution is
ϕ(x, z, t) = A0cosh k0(h + z)sin (k0x − ωt) + ∑j = 1…∞Cjexp ( − kjx)cos kj(h + z)cos (ωt)
The first part of this solution represents a progressive water wave, and the second part represents so-called evanescent modes. The evanescent modes are also often referred to as standing wave modes. The wave numbers k0 and kj can be found as the solution to two forms of dispersion equations, which are illustrated below.
In the above figure, the horizontal axis represents a non-dimensional water depth. In shallow water (left of figure), a typical wave maker produces mostly progressive waves (ϕp). In deeper water (right of figure), the wave maker also produces a large amount of evanescent waves.
First, with little evanescent wave modes, the wave elevation (normalized by the progressive wave amplitude) looks fairly consistent:
However, when the wave maker introduces evanescent modes, the wave field can become spatially non-homogeneous:
The second animation shows a wave field that is quite different at the wave maker compared to further downstream. For this reason, any model placed in the wave tank should be a sufficient distance away from the wave maker. As a rule-of-thumb, a distance of 2-3 water depth is generally sufficient. For example, if the water depth in the wave basin is 2.0m, then placing the model 6.0m away from the wave maker is sufficient.
Absorbing wave makers
Very similar to wave energy converters, wave makers can also be used to absorb energy. This is useful when part of the wave reflects from the testing model or the beach. An absorbing wave maker can remove some of this reflected energy from a wave tank, and avoid a long-term built-up of reflected content. There are numerous ways to implement absorption control. At Evergreen Innovations, we most often implement force control. For the wave maker example, this leaves us with two possible control strategies, which are shown in a simplified form below.
The absorption controller can be optimized to closely approximate a complex conjugate (impedance matching) controller – see publications for details. To tune this controller, the wave maker hydrodynamic coefficients are required. For most wave maker types, these coefficients can be determined analytically.
For example, the radiation damping for a piston wave maker is
d(ω) = ρgc0/(ωk0)tanh k0h
The added mass for a piston wave maker is
m(ω) = ρg/ω2∑cj/kjtanh kjh
where the coefficients cj can also be calculated analytically. Typical coefficients for a piston wave maker are shown in the following figure.
The below video shows a wave tank that uses two wave makers, one at each end. The wave makers can, at the same time, generate and absorb waves. The overall effect is that they produce a standing wave. Once the wave makers are switched off, the wave tank settles very quickly due to absorption control.
An understanding of standing waves and wave absorption (beach and wave maker) are important parts of wave tank testing. We will very soon add further topics to this blog, for example the use of deterministic (finite repeat time) vs. fully random wave generation techniques.
Standardization of wave tank testing
Johannes Spinneken presently leads the international standardization efforts in wave energy testing as international co-convenor with the IEC. Johannes and the IEC team recently published the first consensus-based international standard for wave energy testing – IEC TS 62600-103. Contact us if you would like to find out more about standardization in wave energy.