[Paper Review] Dynamics of propagating turbulent pipe flow structures. Part II: Relaminarization

Andrew Duggleby, Kenneth S. Ball+1 more|arXiv (Cornell University)|Aug 25, 2006

Fluid Dynamics and Turbulent Flows9 references3 citations

TL;DR

This study investigates the dynamics of relaminarizing turbulent pipe flow using direct numerical simulation and Karhunen-Lofle decomposition, revealing that high-frequency outer-layer modes decay first, triggering chugging cycles where transient turbulent states re-emerge via energy transfer from wall modes to lift modes. The key finding is that the outer region's high-frequency modes are essential for sustaining turbulence, and their decay initiates relaminarization, with three chugging cycles observed before complete relaminarization at Reτ = 95.

ABSTRACT

The dynamical behavior of propagating structures, determined from a Karhunen-Lo`eve decomposition, in turbulent pipe flow undergoing reverse transition to laminar flow is investigated. The turbulent flow data is generated by a direct numerical simulation started at a fully turbulent Reynolds number of Re_τ=150, which is slowly decreased until Re_τ=95. At this low Reynolds number the high frequency modes decay first, leaving only the decaying streamwise vortices. The flow undergoes a chugging phenomena, where it begins to relaminarize and the mean velocity increases. The remaining propagating modes then destabilize the streamwise vortices, rebuild the energy spectra, and eventually the flow regains its turbulent state. Our results capture three chugging cycles before the flow completely relaminarizes. The high frequency modes present in the outer layer decay first, establishing the importance of the outer region in the self-sustaining mechanism of wall bound turbulence.

Motivation & Objective

• To understand the dynamical mechanisms behind relaminarization in turbulent pipe flow, particularly the role of propagating flow structures.
• To investigate how energy transfer among modes influences the transition from turbulence to laminar flow under decreasing Reynolds number.
• To determine the contribution of different flow structures—especially high-frequency outer-layer modes—to the self-sustaining nature of wall turbulence.
• To examine the role of triad interactions and mode coupling in the re-emergence of turbulence during chugging cycles.
• To clarify why relaminarization initiates in the pipe center and propagates inward, linking it to energy cascade failure.

Proposed method

• Direct numerical simulation (DNS) of turbulent pipe flow at Reτ = 150, gradually reduced to Reτ = 95 over 12,000 t+ units.
• Karhunen-Lofle (KL) decomposition applied to extract propagating turbulent flow structures and their energy spectra.
• Analysis of time-resolved energy transfer between wall, lift, asymmetric, and ring modes via energy spectra and phase lag analysis.
• Identification of triad interactions among KL modes through Fourier representation, where m + m' + m'' = 0 and n + n' + n'' = 0, indicating energy transfer pathways.
• Use of spectral element algorithm with high spatial resolution (Δr+ ≈ 0.49 near wall, Δz+ = 4.0 streamwise) to ensure accurate flow field resolution.
• Energy flow chart constructed to visualize the catalytic role of ring and asymmetric modes in transferring energy from wall to lift modes.

Experimental results

Research questions

• RQ1 How do the decay dynamics of high-frequency modes in the outer layer influence the onset of relaminarization in pipe flow?
• RQ2 What role do triad interactions among KL modes play in the re-establishment of turbulence during chugging cycles?
• RQ3 Why does relaminarization initiate in the pipe center and propagate inward, and what structural changes precede this?
• RQ4 How does the energy transfer from wall modes to lift modes sustain the turbulent inertial subrange, and what breaks this cycle?
• RQ5 What is the significance of the n=3 traveling wave mode in the re-emergence of turbulence during chugging events?

Key findings

• Three distinct chugging cycles were observed during relaminarization, each involving transient recovery of turbulent energy spectra before final relaminarization at Reτ = 95.
• High-frequency modes in the outer layer decayed first, indicating their critical role in maintaining the turbulent inertial subrange and self-sustaining mechanism.
• The lift modes, responsible for turbulence near the pipe center, lost energy first during chugging, leading to a drop in Reynolds stress and rms velocity profiles near the centerline.
• Energy transfer from wall modes to lift modes—catalyzed by ring and asymmetric modes—failed during relaminarization, breaking the energy cascade and initiating flow decay.
• The n=3 traveling wave mode was the most energetic during the re-emergence of turbulence in each chugging cycle, confirming its importance in the self-sustaining process.
• The final relaminarization began near t+ = 8000, after which no further turbulent recovery occurred, indicating complete loss of turbulent energy cascade.