Experimental and numerical study of primary instability of a two-phase stratified flow in a circular pipe

The onset of the primary instability of two-phase air-water stratified flow in a circular pipe was studied experimentally by two independent non-intrusive techniques. The techniques analyze the steady or oscillatory response of either a laser beam passing through the air-water interface or of an echo of an ultrasound wave reflected from the interface. The experiments are accompanied by linear stability analysis performed in both Cartesian and bipolar coordinates, thus yielding two independently obtained numerical results for comparison. The critical values of the phases’ superficial velocities corresponding to the flow primary instability calculated numerically by the two independent methods agree well with each other. The computed stability diagram shows that instability sets in owing to long-wave disturbances at large holdups, while at smaller holdups, the most unstable perturbations appear as finite-length (short) waves. A comparison of the experimental and numerical results shows a good agreement for the long-wave instability. For the short-wave instability, the measured critical superficial velocities are below the computed ones, while the frequencies found experimentally for supercritical oscillatory flow states agree with the numerical predictions. Several additional peaks in the frequency spectra are observed in the experiments. By comparing these frequencies with the numerical spectra, we argue that they correspond to stable eigenmodes with close to zero decay rates, which can be triggered either by non-linear mechanisms, or become unstable because of experimental imperfections.