Instabilities in Pulsating Pipe Flow of Shear-Thinning and Shear-Thickening Fluids

• Main Author: Sadrizadeh, Sasan
• Format: Others
• Language: English
• Published: Linköpings universitet, Mekanisk värmeteori och strömningslära 2012
• Subjects: Stability; Pulsatile pipe; Transient Growth; Floquet Multiplier; Modal and non-Modal Stability
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-82037

In this study, we have considered the modal and non-modal stability of fluids with shear-dependent viscosity flowing in a rigid straight pipe. A second order finite-difference code is used for the simulation of pipe flow in the cylindrical coordinate system. The Carreau-Yasuda model where the rheological parameters vary in the range of 0.3 < n < 1.5 and 0.1 < λ < 100 is represents the viscosity of shear- thinning and shear thickening fluids. Variation of the periodic pulsatile forcing is obtained via the ratio Kω/Kο and set between 0.2 and 20. Zero and non-zero streamwise wavenumber have been considered separately in this study. For the axially invariant mode, energy growth maxima occur for unity azimuthal wave number, whereas for the axially non-invariant mode, maximum energy growth can be observed for azimuthal wave number of two for both Newtonian and non-Newtonian fluids. Modal and non-modal analysis for both Newtonian and non-Newtonian fluids show that the flow is asymptotically stable for any configuration and the pulsatile flow is slightly more stable than steady flow. Increasing the maximum velocity for shear-thinning fluids caused by reducing power-low index n is more evident than shear-thickening fluids. Moreover, rheological parameters of Carreau-Yasuda model have ignored the effect on the peak velocity of the oscillatory components. Increasing Reynolds number will enhance the maximum energy growth while a revers behavior is observed by increasing Womersley number.