Study On Instability In Taylor-couette Flow Ofviscoelastic Fluids

The research of hydrodynamic instability is a hotspot topic in fluid mechanics until now. Taylor-Couette flow geometry continues to be a paradigm for exprimental and theoretical studies of hydrodynamic instabilty and transition owing to the the advantages such as its simplicity, containing a closed flow system and gengerating multifarious instability status.Besed on the Taylor-Couette flow, the purpose of this disertation is to get the critical parameters at which flow instability happens, the detailed examination of its structure and evolution, particularly the laminar-turbulent transition regime and the possible machanism of instability by studing the inertia-instability and elastic-instability happened in Newtonian fluids and viscoelastic surfactant solutions (CTAC) from experimental and numerical simulaiton.In experimental studies, firstly, we built the standard Taylor-Couette apparatus with two kinds of radii ratio. Then, using the high speed imaging recording system, we studied the instabilty happened in Taylor-Couette geometry which contains fluids varied from distilled water to CTAC solutions with different concentrations such as 50ppm, 200ppm and 1000ppm. For distilled water, we got the critical Reynolds number of inertia-instabilities induced by inertial force, different instabilities regimes by changing the Reynolds numbers and the influence on wavelength of Taylor vortices when the Reynods numbers and radii ratio change. For different concentrations of CTAC solutions, we got the critical Weissenberg number of elastic-instabilities induced by elastic force and the space-time plots of different flow regimes at varing Weissenberg numbers.In numerical simulation studies, We directly solved the Navier-Stokes equation added by an elastic stress term in cylindrical coordinates. For the convective term of constitutive equation which discribed the relation of elastic stress and conformation in viscoelastic fluids, the optimum scheme named Kurganov-Tadmor scheme was used. The mulitgrid method has also been applied to increase the efficiency of calculation. By direct numerical simulation of flow instabilities in the distilled water and 1000ppm CTAC used in experimental studies, we got the velocity field, pressure field and the conformation field of viscoelastic fluids which was impossoble in experimental studies in Taylor-Couette flow region. The quatitative studies of inertia-instabilities and elastic-instabilities were carried. The experimental and numerical studies were verified because it showed fairly good agreement with each other. Finally, according to the experimental and numerical studies, the possible mechanisms of inertia-instabilities and elastic-instabilities were suggested and the potential inaccuracies of experments and numerical simulations were summarized. In the end, the prospects for possible future work in the study of this research field have been addressed.