Stability of a laminar pipe flow subjected to a step-like increase in the flow rate

Abstract

We perform the linear modal stability analysis of a pipe flow subjected to a step-like increment in the flow rate from a steady initial flow with the flow rate, Qi, to a final flow with the flow rate, Qf, at the time, tc. A step-like increment in the flow rate induces a non-periodic unsteady flow for a definite time interval. The ratio, Γa=Qi/Qf, parameterizes the increase in the flow rate, and it ranges between 0 and 1. The stability analysis for a pipe flow subjected to a step-like increment in the flow rate from the steady laminar flow (Γa>0) is not reported in the literature. The present work investigates the effect of varying Γa on the stability characteristics of an unsteady pipe flow. The step-like increment in the flow rate for 0≤Γa≤0.72 induces a viscous type instability for a definite duration, and the flow is modally unstable. The non-axisymmetric disturbance with azimuthal wavenumber, m = 1, is the most unstable mode. The flow is highly unstable for Γa=0, and the flow becomes less unstable with an increase in Γa. The flow becomes stable before it attains the steady-state condition for all Γa.