Forced Nonlinear Acoustic Damping in a Rijke Tube and its Application to Combustion Instability Control

Abstract

Nonlinear unsteady energy transport theory predicts that when multiple coupled oscillatory acoustic modes are unstable, only one of these modes may dominate. This phenomenon produces unusual experimental results in propulsion systems as small changes may alter the stability of many modes, thereby altering their interactions as well. These nonlinear interactions create instances where unstable modes appear to switch, where, in fact, multiple modes are unstable. Understanding this phenomenon is critical in diagnosing combustion instability and in developing damping techniques in unstable systems. In order to verify this predicted phenomenon a forced Rijke tube experiment was performed. This experiment shows that the first mode instability caused by the Rijke tube is eliminated when higher modes are driven. This effect only occurs near the natural frequencies of the Rijke tube and is likely not the result of changes in the Rijke tube operation itself. The positive results of this experiment have applications in the development of new innovative combustion instability damping techniques in propulsion systems as well as validating the analytical methods applied. With this process, a fundamentally new way of damping is presented as it is possible to eliminate low frequency oscillations by either destabilizing higher frequency modes or by directly driving those higher modes. I. Nomenclature Rm= amplitude of oscillation for mode, m αm = normalized linear energy transfer rate for mode, m A = nonlinear energy transfer factor Emnl = nonlinear coupling matrix ω1 = first longitudinal frequency ζm = driven energy transfer rate p1 = unsteady pressure P0 = mean flow pressure ηm = time dependent function km = mode number II. IntroductionNERGY transferred from the bulk fluid flow into the unsteady field manifests as a growing acoustic pressure amplitude. This is the fundamental source of instability in all systems. Once in the unsteady field, nonlinear unsteady energy transport theory 1, 2 defines the flow of energy between unsteady modes. This results in a nonlinear energy cascade and limit cycle behavior. It is this behavior that is responsible for the appearance of harmonic modes and wave steepening 1 .In 2010 3 it was predicted that if the first two modes in a system were both unstable it was possible (given a strong enough second mode instability) for the second mode to stabilize the first mode. This is due to nonlinear coupling between the modes. These observations were explored experimentally by driving higher mode harmonics in a selfexcited Rijke tube in 2012 and presented in 2013 7 . Initial results were promising and the a-priori theoretical prediction 1 Engineer, 112 Mitchell Blvd, Tullahoma, TN, AIAA Member 2 Engineer, 112 Mitchell Blvd, Tullahoma, TN, AIAA Member E Downloaded by UNIVERSITY OF NEW SOUTH WALES on August 2, 2015 | http://arc.aiaa.org |