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Laminar-to-Turbulent Transition of Yield-Stress Fluids in Pipe and Channel Flows

Shivam Prajapati, Prasoon Suchandra, Vivek Kumar, Ardalan Javadi, Suhas Jain, Cyrus Aidun

Abstract

We present direct numerical simulations (DNS) of laminar to turbulent transition in Herschel-Bulkley (HB) yield-stress fluids flowing through pipes and rectangular channels. The simulations employ a Herschel-Bulkley formulation that captures the yield-stress-driven plug, its breakdown, and the emergence of near-wall turbulent structures, enabling direct resolution of the transition mechanisms. The DNS cover a broad range of generalized Reynolds numbers, Re_G = 378 to 5300, allowing us to resolve plug formation, transition onset, and fully turbulent regimes. In pipe flow, the simulations reproduce the characteristic transition sequence, which includes a strong plug and negligible turbulence at low Re_G, a sharp rise in turbulence intensity and u'rms within a narrow transitional window (Re_G ~ 2000 to 3000), and wall-dominated turbulence with a weakened core at higher Re_G. Transition occurs only when local Reynolds stresses exceed the yield stress. The resulting regime boundaries (Re_G < 1735 laminar, 1735 < Re_G < 2920 transitional, and Re_G > 2920 turbulent) align with trends reported for Carbopol fluids. This work provides the first DNS resolving the complete laminar to turbulent transition in HB fluids for both pipe and channel configurations, offering unified insight into plug breakdown, turbulence localization, and the role of yield stress in transition mechanisms. Experimental validation using a 3.6 m acrylic channel with particle image velocimetry (PIV) is planned to further assess the DNS predictions and quantify geometry-dependent transition thresholds.

Laminar-to-Turbulent Transition of Yield-Stress Fluids in Pipe and Channel Flows

Abstract

We present direct numerical simulations (DNS) of laminar to turbulent transition in Herschel-Bulkley (HB) yield-stress fluids flowing through pipes and rectangular channels. The simulations employ a Herschel-Bulkley formulation that captures the yield-stress-driven plug, its breakdown, and the emergence of near-wall turbulent structures, enabling direct resolution of the transition mechanisms. The DNS cover a broad range of generalized Reynolds numbers, Re_G = 378 to 5300, allowing us to resolve plug formation, transition onset, and fully turbulent regimes. In pipe flow, the simulations reproduce the characteristic transition sequence, which includes a strong plug and negligible turbulence at low Re_G, a sharp rise in turbulence intensity and u'rms within a narrow transitional window (Re_G ~ 2000 to 3000), and wall-dominated turbulence with a weakened core at higher Re_G. Transition occurs only when local Reynolds stresses exceed the yield stress. The resulting regime boundaries (Re_G < 1735 laminar, 1735 < Re_G < 2920 transitional, and Re_G > 2920 turbulent) align with trends reported for Carbopol fluids. This work provides the first DNS resolving the complete laminar to turbulent transition in HB fluids for both pipe and channel configurations, offering unified insight into plug breakdown, turbulence localization, and the role of yield stress in transition mechanisms. Experimental validation using a 3.6 m acrylic channel with particle image velocimetry (PIV) is planned to further assess the DNS predictions and quantify geometry-dependent transition thresholds.
Paper Structure (20 sections, 21 equations, 8 figures, 2 tables)

This paper contains 20 sections, 21 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Rheology model
  4. Non-Newtonian Reynolds number
  5. Generalized Reynolds number based on wall viscosity.
  6. Metzner--Reed Reynolds number.
  7. Friction Reynolds number.
  8. Governing equations
  9. Domain discretization
  10. Computational domains and mesh
  11. Pipe flow.
  12. Channel flow.
  13. Results & discussion
  14. Domain-size sufficiency via two-point correlations.
  15. One-dimensional energy spectra
  16. ...and 5 more sections

Figures (8)

  • Figure 1: Pipe flow geometry and coordinate system.
  • Figure 2: Channel flow geometry and coordinate system.
  • Figure 3: Streamwise two-point correlations in the channel for the velocity components $u$, $v$, and $w$: $R_{uu}(r_x;y)$, $R_{vv}(r_x;y)$, and $R_{ww}(r_x;y)$.
  • Figure 4: One-dimensional streamwise energy spectra in the channel at a near-wall location and at the channel center: $E_{uu}(k_x)$, $E_{vv}(k_x)$, and $E_{ww}(k_x)$.
  • Figure 5: Turbulence intensity $I$ (%) as a function of generalized Reynolds number $Re_G$ in Herschel--Bulkley pipe flow. Solid lines with markers show the present DNS, and dashed lines show the experimental data. Results are reported at $r/R=0$, $r/R=0.75$, and $r/R=-0.75$.
  • ...and 3 more figures