Heating Control And Global Stability Of Compressible Flow Around A Body

Compressible flow around a body has always been an important topic of scholars home and abroad in fluid mechanics, and never for a moment has the study of its control and stability analysis ceased. The instability phenomena of flow past a locally heated cylinder on its surface are explored, with its rational mechanism interpreted by using wake-type profiles as the inlet boundary conditions. Furthermore, the flow around a slender body of revolution at high angle of attack with heating perturbation control is investigated as well as the global stability of three-dimensional compressible flow around a sphere and a disk.A method of heating the cylinder wall partially for investigating the heating effect is carried out for the first time. Various overheat ratios T*= Tw/T∞= 293.15K) are considered, and the other non-dimensional parameters are fixed at certain values as follows:Re= 60, Mach=0.2. It is found that the heating effects are completely different for various heating locations on the cylinder surface. Heating the windward or leeward side of cylinder surface could reduce or even completely suppress the vortex shedding from the cylinder at supercritical Reynolds numbers. However, when the lateral sides of cylinder surface (perpendicular to the steam-wise direction) are heated at T* = 1.6, a reverse effect is found for the first time that the flow is destabilized and the vortex shedding could be excited at subcritical Reynolds numbers.By means of numerical simulations of variable-density wakes, when the leeward side of the cylinder surface is heated, the density of fluid in the wake decreases, stabilizing the whole flow field; while the lateral sides heated, the density of fluid outside of the wake increases, destabilizing the whole flow field. In addition to the influence of the density, the velocity profile under various temperature contributions has also a significant effect on the vortex shedding. The competition between the stabilizing and destabilizing effects may lead to a completely different or opposite vortex shedding behavior as the overheat ratio changes.Inspired by the problem of flow past a heated cylinder, a new heating control model is proposed for the problem of flow around a slender body of revolution at high angle of attack. The model could eliminate the asymmetry of the grid system, and makes the results more reliable. It is revealed that the side force of the heating model shows a single-periodic bistable changing with the roll angle. Compared with the geometric model, the perturbation introduced by the heating model maybe weaker, and the heating model flow could be easily covered up by the geometric model flow. Global linear stability of three-dimensional compressible flow around a sphere/disk is studied by using a quasi-linearization method on the Navier-Stokes equations, and an implicit restarted Arnoldi approach is adopted to solve the eigenvalue problem. The global stability problem of compressible, three-dimensional basic flows around a sphere/disk is investigated at subcritical and supercritical values of the Reynolds num-ber, with the Mach numbers M= 0.2 and 0.6. Results show that the increasing of Mach number (up to M= 0.6) has no qualitative influence on the transition of flow patterns.