Determination of Constitutive Relationships with Multiple Gauges in Nondivergent Waves

Abstract

Constitutive relationships are calculated from multiple Lagrangian gauge records obtained in one-dimensional wave experiments by integrating the flow equations expressing conservation of mass and momentum along a particle path. Specifically for flow adjacent to a constant state, particle velocity-stress relationships are calculated from multiple stress-time profiles by integrating the combined mass and momentum equations, and specific volume-particle velocity relationships are calculated from multiple particle velocity-time profiles by integrating the continuity equation; but these relationships are in general approximate because the material derivatives required to perform the integrations are generated from gauges separated by finite distances. Steady-state, simple isentropic, and simple nonisentropic waves are shown to be the only flows that allow constitutive relationships among stress, particle velocity, and specific volume to be determined exactly with either a pair of stress gauges or a pair of particle velocity gauges. A general procedure for the determination of constitutive relationships with three gauges is formulated and tested with an exact solution for a strong decaying shock wave to indicate errors resulting from the finite separation of gauges when constitutive relationships cannot be calculated exactly.