Effect of Sudden Changes in Flow Area on Pressure Waves of Finite Amplitude

Abstract

Previous investigations of the flow of gases through sudden area changes in pipes are briefly reviewed, both unsteady and steady flow conditions being considered. The present paper concerns the effects of such area changes on single pressure waves of finite amplitude, and covers incident wave amplitudes greatly in excess of those previously investigated. Theoretically, the flow at the area change is assumed to be quasi-steady and one-dimensional, and two alternative treatments are presented. These are based respectively on reversible adiabatic (isentropic) and, more accurately, irreversible adiabatic conditions. Experiments using a simple shock tube confirm the validity of the more accurate theoretical treatment over the range of area and incident pressure ratios considered, namely, 8.1 and 2.4 respectively. The theoretical treatment based on the assumption of isentropic flow at the section change, however, is inadequate in some respects. Discrepancies between theory and experiment are observed when considering, firstly, the reflected wave at an enlargement and, secondly, the transmitted wave at a contraction. Steady flow experiments in which the discharge coefficient for flow through a sudden contraction is measured are also described, this coefficient being required in the theoretical analysis.