Shock Theory of a Bubbly Liquid in a Deformable Tube

Shock propagation through a bubbly liquid filled in a deformable cylindrical tube is considered. Quasi-onedimensional bubbly flow equations that include fluid-structure interaction are formulated, and the steady shock relations are derived. Experiments are conducted in which a free-falling steel projectile impacts the top of an air/water mixture in a polycarbonate tube, and stress waves in the tube material are measured. The experimental data indicate that the linear theory cannot properly predict the propagation speeds of shock waves in mixture-filled tubes; the shock theory is found to more accurately estimate the measured wave speeds.