#### Date of Award

7-1984

#### Degree Type

Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Nuclear Engineering

#### Supervisor

Professor S. Banerjee

#### Abstract

Finite amplitude pressure waves were investigated in a horizontal air-water system to determine the multidimensional propagation characteristics. Five classes of waves were analysed in this system of which four occurred in the water phase. The duct used to investigate these waves was square, 9 cm on a side, and 5 m in length.

Weak shock waves of finite length were used in the gas phase. Theory by Whitham accurately predicted the attenuation.

Pressure wave propagation in the water was dominated in all cases by characteristics associated with a Klein-Gordon equation. This equation is derived assuming a free surface but is found to play a role even when the surface of the water has an applied pressure.

Pressure waves in the water under a free surface were studied in the system. Amplitudes of this class of waves were found to be small and they travel quickly throughout the system.

An impulsive applied pressure to the water at a vertical wall can generate two types of waves depending on the period of the pressure pulse. If it is longer than a cutoff period defined by the Klein-Gordon dispersion relation, amplitudes decay as tˉ½, where t is the time, and exponentially with distance. If the period is less than cutoff, pressure waves in the water can propagate down the duct under a free surface. Pressure amplitudes in the water at the vertical wall can be large due to additive effects from the applied surface pressure.

The water region beneath the shock can act as a three dimensional waveguide. This phenomenon depends on the depth of the water. High pressure amplitudes can occur in the water relative to the shock. The frequency source needed to drive the waveguide is conjectured to be a Klein-Gordon wave packet which remains steady with the shock.

If bubbles are present in the water so that the effective sound speed in the water is less than the speed of the shock, high amplitudes will exist in the water accompanying the shock since energy cannot quickly disperse away from the shock region.

#### Recommended Citation

Stone, Terry Wayne, "Pressure Wave Propagation in a Horizontal Air-Water System" (1984). *Open Access Dissertations and Theses.* Paper 1409.

http://digitalcommons.mcmaster.ca/opendissertations/1409