The acoustic pressure distribution generated within the NPL Reference Cavitating Vessel has been modelled using Finite Element (FE) techniques. This work predicts the spatial distribution of the 25 kHz field for a range of operating temperatures, and enables estimation of effects such as sensor spatial averaging to be made.

The FE method consists of approximating the vessel and its contents in small domains (finite elements), each of which has specific material properties. By setting boundary and driving conditions, output quantities such as acoustic pressure can be obtained over the vessel volume. The model exploits the cylindrical symmetry of the vessel, and so only requires a 10th of the vessel to be investigated: the vessel transducers are modelled as Tonpiltz sources. The figure shows the model configuration, and the resulting acoustic pressure distribution in the plane corresponding to the central transducer row.

Good qualitative agreement is seen between prediction and experimental data. The plots below illustrate the effect of changing the water temperature in the vessel model, showing the predicted pressure distributions at 25 °C, 27 °C and 29 °C (left to right). A strong dependence of the pressure field on temperature is seen. Such changes are not seen experimentally, and indicate the significant complexity of modelling the vessel accurately. They probably arise from the model having a high modal density – a significant number of vibrational modes are possible over a small temperature and acoustic wavelength range.

Sensor spatial averaging

The effect of using a sensor of finite size to measure the acoustic field distribution is shown below. Here, two pressures profiles across the vessel are predicted, determined using a point receiver, and using a 30 mm diameter, 22 mm high cylindrical surface analogous to the Cavitation Sensor. The 'sensor' does spatially average, as expected, but does not have a significant effect on the local structure in the field.

For further information on the PAFEC modelling work, and to discuss your own modelling requirements, contact Pierre Gélat