Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids

Experimental results reveal that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, appears to have the characteristics of a nonhysteretic, supercritical instability of the laminar base state. Contrary to what was previously believed, classical transition is found to be responsible for returning symmetry to the flow. An absence of evidence of the instability in simulations (either linear or nonlinear) suggests that an element of physics is lacking in the commonly used rheological model for inelastic shear-thinning fluids. These unexpected discoveries raise new questions regarding the stability of these practically important fluids and how they can be successfully modeled.

Figure 1

Variation of asymmetry measures $\overline{\alpha },\overline{r_p}/D$ and $u_{\mathrm{rms}}/U_b$ (closed symbols) and transition indicators $p_{\mathrm{rms}}/\overline{P}$ and $v_{r\theta ,\mathrm{rms}}/U_b$ (open symbols). The solid curve is a power law of the form $\overline{r_p}/D=a{(\mathit{\text{Re}}-{\mathit{\text{Re}}}_c)}^b$, where $b=0.55$. Inset shows dependence of the fluctuations of $\alpha$ on $\mathit{\text{Re}}$.

Figure 2

Time-averaged streamwise velocity profile ($U/U_b$) for laminar ($\mathit{\text{Re}}=300,\overline{\alpha }=0.025$), transitional ($\mathit{\text{Re}}=8000,\overline{\alpha }=0.165$), and turbulent ($\mathit{\text{Re}}=15000,\overline{\alpha }=0.018$) flow, from left to right, respectively.

Figure 3

The time-varying nature of the asymmetric flow pattern at $\mathit{\text{Re}}=8000$ is shown by the time history of asymmetry factor, $\alpha$ (bottom) and instantaneous cross-stream snapshots of the streamwise velocity ($U/U_b$). (a) Asymmetric flow with preferred orientation, (b) temporarily quasiaxisymmetric flow induced by a turbulent puff, and (c) a brief visit to asymmetric flow with an alternative orientation. The experimental duration is approximately 200 s and the SPIV acquisition rate is 5 Hz. The two insets show the location of the peak velocity in the radial-azimuthal plane as the asymmetry returns following the passing of a puff.

Figure 4

The temporary elimination of the asymmetry by a turbulent puff at $\mathit{\text{Re}}=8000$. The top panel shows simultaneous time histories of the nondimensional swirling strength and the asymmetry factor ($\alpha$). The bottom panel shows a visualization of a puff using isosurfaces of swirling strength (${\lambda }_{ci}D/U_b=0.012$); red and blue indicate regions on the isosurface where the local axial vorticity is positive and negative respectively. The SPIV acquisition rate is 200 Hz.

Figure 5

Traces of the peak velocity during the transient processes of axisymmetric-asymmetric transition (left) and asymmetric-axisymmetric relaminarisation (right). Each dot corresponds to an instant in time color coded by its nominal $\mathit{\text{Re}}$ according to $\mathit{\text{Re}}=1960$ (pink), $\mathit{\text{Re}}=3400$ (blue), $\mathit{\text{Re}}=4230$ (red), $\mathit{\text{Re}}=5750$ (green), and $\mathit{\text{Re}}=6740$ (black) with the time delay between each $\mathit{\text{Re}}$ being 30 s. The arrows indicate the direction of movement with time.