Instability of fluid and gas flows during heat input and energy conversion

Based on the conservation laws of mass, momentum, and energy expressed in integral form relative to a moving Lagrangian control volume, a general three–dimensional mathematical model is developed to describe the motion of a continuous medium subjected to localized heat input along a specified two–sided surface. The model is applied to analyze the one–dimensional flow of an inviscid gas, and a set of analytical relationships is derived to characterize the conditions under which flow instability occurs. As another application of the general model, the formation of longitudinal thermoacoustic self–oscillations in a Rijke tube with a heat source located at its inlet is considered. In this case, the excitation of self–oscillations is attributed to an N–shaped dependence (negative resistance) of the viscous friction force along the tube as a function of the velocity of the heated air. • A 3D model is developed for gas flow with localized heat input. • The model uses a Lagrangian control volume and integral conservation laws. • A thermal energy dissipation tensor is introduced via Dirac delta function. • Conditions for flow instability and thermoacoustic oscillations are analyzed. • Application to Rijke tube demonstrates excitation due to negative resistance.