Session: 10.5 - Non-Newtonian fluid flows

Paper Number: 170319

170319 - Direct Numerical Simulation of Relaminarization in Pipe Flow of a Herschel--Bulkley Fluid 

Abstract: 

This work presents the first direct numerical simulation (DNS) of turbulent-to-laminar transition in pressure-driven pipe flow of a yield-stress shear-thinning fluid, covering Reynolds numbers (Re) from 378 to 4488. It analyzes turbulence decay mechanisms in yield-stress fluids, providing fundamental insights into the stabilization of Herschel–Bulkley flows through rheological modification. This study systematically examines various flow regimes, ranging from laminar to fully turbulent, through detailed analysis of radial velocity profiles, velocity fluctuations, and distributions of turbulence intensity. Our results indicate that transition occurs only when the Reynolds stresses exceed the yield stress, effectively breaking the plug region before turbulence develops. Unlike previous DNS studies, which focus on sustained turbulence, we resolve the complete transition dynamics solving the full Navier–Stokes equations. The fluid rheology is characterized by yield stress (τ_Y), consistency index (K), and power index (n), with parameter validation against experimental benchmarks for 0.1% Carbopol solutions available in the literature.

The turbulent intensity was plotted against the generalized Reynolds number (Re_G) at both the centerline and radial positions r/R = ±0.75. During relaminarization, a sudden change in turbulent intensity occurs uniformly across the pipe section. Additionally, we observe that the turbulent intensity begins to increase at r/R = ±0.75 at significantly lower Reynolds numbers than at the centerline. Simulations reveal a critical Reynolds number, Re_crit ≈ 1735, below which turbulence is suppressed, leading to flow relaminarization, consistent with experimental observations available in literature. Three distinct flow regimes emerge: (1) sustained turbulence with modified coherent structures at Re > 2920; (2) progressive decay of turbulence production mechanisms in the transitional range (1735 < Re < 2920); and (3) yield-stress-dominated laminar flow with plug-like velocity profiles at Re < 1735. DNS results quantitatively reproduce transitional trends and velocity profiles from experiments, confirming the influence of shear-thinning rheology on flow regime transitions.

The Herschel–Bulkley model in OpenFOAM is validated against fully developed pipe flow DNS data at Re_τ = 180 and rectangular channel simulations from previous studies. Additional simulations of high-yield-stress fluids at various Reynolds numbers, with 0% and 1% fiber content, further reveal modifications in transition dynamics.

Presenting Author: Shivam Prajapati Georgia Institute of Technology

Presenting Author Biography: Shivam Prajapati is a 2nd year PhD student in Mechanical Engineering department in Georgia Tech under Dr. Cyrus Aidun. He did his undergrad from National Institute of Technology, Agartala from India in Mechanical Engineering. His research interest lies in studying the rheology of non Newtonian fluids.