A Novel Flow-induced Motion Energy Harvesting with Coupled Mechanism of Time-varying Stiffness and Passive Turbulence Control

Hao Wu; Yongxi Wu

REVIEW 5 major objections 5 minor 18 references

A Novel Flow-induced Motion Energy Harvesting with Coupled Mechanism of Time-varying Stiffness and Passive Turbulence Control

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that combining passive turbulence strips with time-varying stiffness can double harvesting efficiency to a 57 percent peak, with amplitudes up to 11 times and fluid power up to 2 times larger.

desk verdict The paper's headline numbers rest on an unvalidated variable-stiffness simulation, but the combination of PTC and time-varying stiffness is new and the constant-stiffness validation gives the qualitative trends some credibility. read the letter →

arxiv 2411.16130 v1 pith:WJIQ27SN submitted 2024-11-25 physics.flu-dyn

Yongxi Wu , Hao Wu This is my paper · ORCID

classification physics.flu-dyn

keywords flow-inducedmotionefficientenergyharvestingcoupledmechanismboundarylayermodulationtime-varyingstiffnessbionicspassiveturbulencecontrolvortex-inducedvibration

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a cylinder oscillator can harvest far more energy from a flowing stream if its spring stiffness is made to vary in time while its boundary layer is stirred by roughness strips. In simulations of the coupled system, the authors report peak energy-harvesting efficiency of 57 percent, vibration amplitudes up to 11 times larger, and fluid power output up to 2 times larger than a constant-stiffness bare cylinder. The design is patterned after octopus tentacles, which change stiffness during motion and use suction cups to shape the flow. A sympathetic reader would care because the result points toward low-frequency, broadband ocean-energy harvesters that work at low flow speeds.

What carries the argument

The load-bearing mechanism is the single-degree-of-freedom oscillator whose stiffness $K_{vt}$ is time-varying, driven by a bionic model of octopus tentacle stiffness (SIN: $K_{vt}=K_0/2\sin(m\omega_n t)+10.27$, trapezoid toggling between 20.53 and 10.20), coupled to a PTC sandpaper strip placed at 20, 60, or 80 degrees from the stagnation point. The argument runs through URANS/SST k-omega simulations that reproduce measured amplitudes for constant stiffness within 5 percent error over the tested PTC positions. The time-varying stiffness acts as a parametric excitation that enlarges oscillations and shifts them to lower frequency; the PTC re-energizes the boundary layer and manages local flow instabilities, giving the coupled system global stability and a broader response band.

What would settle it

Change one thing in the paper's own setup: replace the constant spring with a programmable stiffness element that follows $K_{vt}=K_0/2\sin(m\omega_n t)+10.27$, keep the P180 strip at 80 degrees, run at $U=0.192$ m/s in the same Reynolds range, and measure the harvested electrical or mechanical power. If the efficiency does not come close to the simulated 57 percent, or if the amplitude gain is far from 11 times, the central claim is falsified; a cheaper partial check is to reproduce the constant-stiffness amplitude curves at all three PTC positions and confirm the reported under-5-percent agreement.

Watch

Extended reading notes

Core claim

The central discovery is that the two controls are complementary: passive turbulence control (PTC, roughness strips that trip boundary-layer separation) imparts global stability to the oscillator, while time-varying stiffness (SIN or trapezoidal $K_{vt}$ patterns) injects local parametric excitation that raises amplitude and power. The paper finds peak efficiency when the stiffness oscillates at a fraction of the natural frequency with PTC placed downstream of the natural separation point: SIN variable stiffness with PTC at 80 degrees, and trapezoid with PTC at 60 degrees. In these configurations the harvesting efficiency reaches 57 percent, amplitude grows to about 11 times the constant-stiffness value, and extracted fluid power doubles, while the working frequency drops, meaning broader, lower-frequency capture. The authors also compile an energy-transfer characteristic map that classifies amplitude and power effects as weak or strong enhancement or suppression for each PTC position and stiffness pattern.

Load-bearing premise

The whole performance gain depends on the assumption that a spring whose stiffness actually varies in time behaves exactly as the URANS simulation says; the paper only validates the numerics against constant-stiffness experiments, because time-varying stiffness could not be tested physically.

Editorial extensions

If this is right

Peak energy-harvesting efficiency of about 57 percent is attainable with SIN stiffness at 80-degree PTC at the lowest tested velocity (0.192 m/s).
Vibration amplitudes can be increased up to 11 times and fluid power output up to 2 times relative to the constant-stiffness bare cylinder.
The coupled system harvests at lower frequency and over a wider bandwidth, which suits low-speed flows such as shallow rivers and slow sea areas.
The energy-transfer characteristic map gives a design rule: for SIN stiffness, 80-degree PTC gives the strongest enhancement; for trapezoid stiffness, 60-degree PTC is best.
As flow velocity increases, efficiency and power decrease, so the device is most effective at low speeds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the 57 percent efficiency holds in hardware, it approaches the Betz limit of 59.26 percent, leaving almost no room for additional hydrodynamic losses; a physical prototype may therefore show substantially lower efficiency.
The same coupling idea might transfer to other flow-induced devices, such as galloping bodies or flapping foils, where parametric stiffness excitation plus boundary-layer trips could broaden resonance.
The paper's claim that PTC prevents galloping suggests a testable hypothesis: the energy-transfer map could be turned into a control law that adapts $K_{vt}$ in real time to incoming velocity, maintaining high efficiency across a variable current.
Because the authors note that the energy input needed to vary stiffness is small, a fair comparison should subtract that input from the reported output; doing so would lower the net efficiency and should be quantified.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the 57% efficiency, 11x amplitude, and 2x power numbers all come from a variable-stiffness URANS regime that is never directly validated. The constant-stiffness validation in Section 2.2.2 covers the bare cylinder and PTC configurations, not the time-varying stiffness term. If that term is wrong, the central claim falls.

What is genuinely new is the combination itself: passive turbulence control plus time-varying stiffness for FIM energy harvesting. Previous work, including the authors' own papers, did one or the other. Here they sweep two stiffness waveforms (SIN and trapezoid), four frequency ratios, three PTC positions, and five flow speeds—a thorough parametric study. They also validate the constant-stiffness cases against their own experiments with errors mostly below 5%. That is real evidence, and it gives the qualitative trends (larger amplitude, lower frequency, broader bandwidth) more weight. The energy transfer map is a useful design heuristic, even if it is based on simulation.

The main soft spot is exactly the validation gap the authors themselves admit: "the variable stiffness simulation, based on the RANS model, is deemed reliable." That phrase is doing a lot of work. The constant-stiffness comparison checks the flow solver and the baseline oscillator, but not whether the time-varying stiffness is implemented correctly, whether the waveform interacts with the body dynamics as modeled, or whether the URANS closure stays accurate when the natural frequency changes mid-cycle. No mesh-convergence study, no error bars, no code or data release. The efficiency number also ignores the energy needed to modulate the stiffness—the paper says it is small, but does not quantify it. And because the best configurations are picked after the sweep, you are reading a post hoc maximum.

This is a paper for the VIV/FIM energy harvesting community. The qualitative mechanism is plausible and the map could guide future designs, but the quantitative claims should be treated as predictions, not established results. It deserves a serious referee: the combination is new, the baseline validation is decent, and the flaws are fixable with more work. I would send it to review, with the request that the referee push hard on variable-stiffness validation, numerical convergence, and an honest energy budget.

Referee Report

5 major / 5 minor

Summary. The manuscript proposes a novel energy-harvesting concept that couples time-varying stiffness (SIN and trapezoidal waveforms) with passive turbulence control (PTC) on a single-degree-of-freedom cylinder oscillator, inspired by octopus tentacles. The authors present a URANS-based numerical study, validate the constant-stiffness case against their own experiments, and then extend the model to time-varying stiffness. They report a maximum harvesting efficiency of 57%, an up-to-11-fold increase in vibration amplitude, and an up-to-2-fold increase in fluid power output for configurations such as SIN stiffness at 80° PTC or trapezoidal stiffness at 60° PTC. They also propose an energy-transfer mechanism map and claim low-frequency, broadband harvesting. The central claim is that the coupled mechanism yields high, practical energy harvesting.

Significance. If the headline numbers are correct, the paper would represent a substantial advance in flow-induced-motion energy harvesting, particularly for low-velocity ocean and river flows. The systematic parameter sweep over PTC positions, stiffness waveforms, and frequency ratios is a useful contribution, and the phase-plane and spectral analyses help rationalize the proposed mechanism. The paper also explicitly compares with prior work (Ding et al., Sun et al., Xu et al.) and provides experimental validation for the constant-stiffness baseline. However, the significance is tempered by the fact that all headline performance claims are produced by unvalidated variable-stiffness simulations, and the efficiency definition omits the actuation energy required for stiffness modulation. The paper would be significantly strengthened by direct validation or a clear verification framework for the time-varying stiffness mechanism, along with honest reporting of numerical uncertainty.

major comments (5)

[Section 2.2.2] The load-bearing step of the paper is the transition from constant-stiffness validation to variable-stiffness reliability. The text states: "Hence, the variable stiffness simulation, based on the RANS model, is deemed reliable." This inference is not supported. The validation in Fig. 10 covers only constant-stiffness cases (bare and PTC-fitted cylinders) and compares only vibration amplitudes with the experiment. It does not validate the time-varying stiffness term Kvt(t) in Eq. (1), the implementation of the SIN/trapezoidal waveforms in Table 2, or the URANS closure when the natural frequency changes mid-cycle. All the headline quantities (57% efficiency, 11x amplitude, 2x power) are obtained from variable-stiffness simulations (Figs. 20, 21, 31). The authors should either provide a direct experimental or analytical validation of a time-varying stiffness oscillator, or at minimum perform additional verification (e.g., a case with known analytical solution, convergence with time-step and mesh refinement, and sensitivity to the stiffness waveform implementation). Without this, the central claim rests on an unverified assumption.
[Section 2.3, Eq. (9)] The efficiency definition in Eq. (9) does not account for the energy input required to realize the time-varying stiffness. The authors dismiss this energy as "very small and can be ignored" (Section 2.2.2) without providing any estimate. This is a critical omission, especially because the reported maximum of 57% is close to the Betz limit (59.26%); a non-negligible actuation energy would reduce the net efficiency substantially. The manuscript should either quantify the actuation energy and subtract it from the output power, or explicitly report both gross and net efficiency and justify the claim of negligible input energy with a physical or numerical estimate.
[Figures 20, 21, 31 and Sections 4.2, 4.4] The paper does not present any uncertainty quantification for the URANS simulations. There is no mesh-convergence study, no time-step sensitivity analysis, and no error bars or confidence intervals for the reported amplitudes, powers, or efficiencies. Since the best configurations (SIN at 80° PTC with m=1.5, trapezoid at 60° PTC) are selected post hoc from a large parameter sweep, the reported maxima (57%, 11x, 2x) may be inflated by numerical noise or overfitting of the parameter space. The authors should report grid-convergence results (at least for the headline configurations), estimate numerical uncertainty, and ideally perform a small number of repeat simulations with different initial conditions or solver settings to establish the robustness of the claimed maxima.
[Section 4.2 and Conclusion item 2] The relationship between the maximum amplitude and the maximum efficiency is presented ambiguously. In Section 4.2 the highest dimensionless amplitude is reported for wv/wn = 0.5, while in Section 4.4 the highest efficiency is reported for the SIN form with variable-stiffness frequency 1.5 times the natural frequency at 80° PTC. The abstract and conclusion claim "a maximum of 57%, increasing vibration amplitude by up to 11 times" without specifying whether these maxima occur at the same configuration. The paper should clarify whether the amplitude enhancement and efficiency enhancement are simultaneously achievable or are separate optima, and if the latter, which configuration is recommended as the best overall design.
[Equation (1)] Equation (1), the governing ODE for the oscillator, is not displayed in the manuscript text; only the equation number appears. Because the time-varying stiffness term Kvt(t) is central to the paper, the authors must ensure that the full equation is correctly typeset and visible. Without it, the reader cannot assess the formulation of the stiffness modulation or the implementation in the numerical model.

minor comments (5)

[Section 2.2.2] The abbreviation PTC is defined as "Passive Turbulence Control" in the abstract and introduction, but in Section 2.2.2 the text refers to "PTC (Positive Turbulence Control) structures." This is incorrect and should be corrected to "Passive."
[Section 3.2] Two consecutive sections are both numbered 3.2: the first is "PTC Influence on Periphery" and the second is "PTC and Variable Stiffness Coupled Influence on Harvesting Mechanism." The section numbering should be fixed (e.g., 3.2 and 3.3) throughout the manuscript.
[Section 4.5] The caption of Fig. 32 describes an "energy transfer characteristic map" but the criteria for classification are introduced in the text, not in the figure itself. It would be helpful to add these classification boundaries (weak/strong enhancement/suppression) directly to the figure or its caption for reader comprehension.
[References] Reference [20] is cited as "Mazzolai et al. [20]" while the later citation to "Xu et al. [20]" appears in Section 2.2.2. This suggests a numbering inconsistency: the reference list contains no entry for Xu et al. [20]. The citations should be renumbered and checked for consistency.
[Figure 31] The legend of Fig. 31 contains a vast number of curve labels (some overlapping) and the line styles are difficult to distinguish. Showing only the most relevant configurations (e.g., best SIN, best trapezoid, bare cylinder, and comparison curves) would improve clarity and make the efficiency comparison readable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline efficiency and amplitude results are forward URANS outputs of a parameter sweep, not refits of the target data; the self-citation to prior models is backed by in-paper experiments.

full rationale

The central claims about 57% efficiency, 11x amplitude, and 2x power are simulation outcomes from a deterministic forward model. The model inputs (K, zeta, K0, m, PTC positions) are measured or chosen parameters, and the paper reports results across a grid of these inputs rather than fitting them to match the claimed efficiency or amplitude values. Therefore no fitted input is renamed as a prediction. The statement in Section 2.1 that the study 'continues the previous works of Wu et al. [16-19]' is a self-citation for the baseline model and equipment, but it is not load-bearing: Section 2.2.2 independently validates the constant-stiffness oscillator against experiments (Fig. 10) with errors 'predominantly below the 5% threshold.' The extrapolation 'Hence, the variable stiffness simulation, based on the RANS model, is deemed reliable' is a validation gap, not circularity: the time-varying stiffness term in Eq. (1) is not itself verified experimentally, and the dismissal of actuation energy as 'very small and can be ignored' is unquantified. These are correctness and uncertainty risks, not definitional reductions. The efficiency normalization by the Betz limit in Eq. (9) is a convention, not a circular construction. No claim derives a result from a definition that already contains it, and no uniqueness theorem or ansatz is smuggled in via author-only citations.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the URANS model, the transfer of validation from constant to variable stiffness, and the neglect of actuation energy. These are stated assumptions, not derived results. The swept parameters (m and PTC angle) are inputs to the study, not fitted to the reported efficiency, so they do not create circularity. The key added value is the parameter sweep and the classification map.

free parameters (5)

K0 (dimensionless stiffness amplitude) = 20.53
Set equal to the constant-stiffness baseline (Table 2); the time-varying stiffness oscillates around this value.
Damping ratio zeta = 77.432e-3
Fitted from exponential decay of experimental free vibration (Section 2.2.2).
Variable stiffness frequency ratio m = 0.50, 0.75, 1.00, 1.50
Swept values chosen by hand to explore stiffness modulation frequency relative to natural frequency.
PTC position angle = 20, 60, 80 degrees
Swept positions representing pre-separation, separation, and post-separation boundary layer states.
Trapezoid low-level stiffness value = 10.20
Chosen as roughly half of K0 for the trapezoid pattern (Table 2), not derived from first principles.

assumptions (5)

domain assumption URANS with SST k-omega accurately predicts flow-induced vibration of a circular cylinder with PTC at Re 1.2e4 to 2.4e4.
Section 2.2.1 adopts the turbulence model on the basis of general validation claims, but no mesh-convergence or model-form uncertainty study is provided.
ad hoc to paper Variable-stiffness simulations are reliable even though only constant-stiffness simulations are validated against experiment.
End of Section 2.2.2 states 'the variable stiffness simulation, based on the RANS model, is deemed reliable' without a direct validation.
ad hoc to paper The energy input needed to realize time-varying stiffness is negligible.
Section 2.2.2 asserts this energy is 'very small and can be ignored' relative to generated energy; no quantitative support is given.
standard math The Betz limit (16/27) correctly defines the maximum extractable power for this oscillating-cylinder configuration.
Equation (9) normalizes efficiency by Betz limit; this is a standard result, but its application to a bluff-body oscillator is an assumption.
domain assumption A mesh of 500,000 elements with y+ about 1 provides adequate resolution.
Section 2.2.2 describes the mesh but provides no mesh-convergence study across resolutions.

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Cite this review

Pith. "Pith review of A Novel Flow-induced Motion Energy Harvesting with Coupled Mechanism of Time-varying Stiffness and Passive Turbulence Control." pith.science (2026). https://pith.science/paper/WJIQ27SN

@misc{pith2026241116130,
  author       = {Pith},
  title        = {Pith review of: A Novel Flow-induced Motion Energy Harvesting with Coupled Mechanism of Time-varying Stiffness and Passive Turbulence Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WJIQ27SN}},
  note         = {Machine review of arXiv:2411.16130}
}

read the original abstract

The ocean contains a substantial amount of energy, and the efficient harvesting of this energy holds significant importance. Drawing inspiration from the biomimicry of octopus tentacles, this study introduces a synergistic mechanism designed to optimize energy harvesting through flowinduced motions, integrating boundary layer modulation via passive turbulence control (PTC) with dynamic system stiffness adjustments via time-varying stiffness (SIN & Trapezoidal patterns). The implementation of PTC facilitates global stability by managing the local instabilities caused by variable stiffness, culminating in a highly effective energy harvesting capability. Our investigations summarize the requisite conditions for peak energy harvesting efficacy, notably within the SIN 80 degrees PTC and Trapezoid/60 degrees PTC arrangements, which have been demonstrated to double the efficiency of energy harvesting with up to 57%, alongside a reduction in initial harvesting frequency and an enhancement in both instantaneous power output and vibration amplitude. Furthermore, an energy transfer characteristic map has been compiled to illustrate the mechanism coupled between boundary layer modulation and time-varying stiffness. This research not only introduces novel perspectives but also stands as a significant stride in the realm of wide band and efficient energy harvesting in the ocean.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

[1]

PTC-to-FIM

Introduction Many scholars have studied energy harvesting in-depth, but for the actual marine environment, there are some disadvantages of narrow energy harvesting frequency band and low efficiency. To solve such problems, the idea of boundary layer control is introduced and passive turbulence control (PTC) is one of it. PTC can achieve precise regulation...

work page
[2]

PTC and Variable Stiffness Coupled Energy Harvesting Model 2.1 Single-Degree-of-Freedom Fluidic Vibration Model This study continues the previous work s of Wu et al. [16-19]. The mathematical model and experimental equipment used are exactly the same as before. Cylinders subjected to low-turbulence free surface flow undergo a broad spectrum of Reynolds nu...

work page
[3]

Results and Analysis 3.1 PTC Influence on Flow Field The following four figures show the dimensionless displacement and power time -varying curves of the bare cylinder and three different PTC positions and the time -varying screenshots of the flow field taken at four moments in order to analyze the variation of the flow field. The four moments are selecte...

work page
[4]

weak enhancement

Discussion 4.1 Energy Harvesting with PTC Fig.19 shows the motion amplitude and power frequency etc. for different PTC positions at 0.192-0.394m/s (0 represents bare cylinder), and it can be seen that for the amplitude, for all velocities, the 20 degrees PTC is able to increase slightly with respect to the bare cylinder, and is slightly suppressed at both...

work page
[5]

Our proposition introduces a coupled mechanism integrating boundary layer control and system stiffness modulation inspired by octopus tentacles

Conclusion To address challenges related to narrow bandwidth and inefficient energy harvesting . Our proposition introduces a coupled mechanism integrating boundary layer control and system stiffness modulation inspired by octopus tentacles. Realize broadband and efficient harvesting of energy by interaction between local instabilities and global stabilit...

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Achenbach, E. 1971. Influence of surface roughness on the cross-flow around a circular cylinder. Journal of fluid mechanics, 46(2), 321-335. [2 ] üvven, O., Farell, C., & Patel, V . C. 1980. Surface -roughness effects on the mean flow past circular cylinders. Journal of Fluid Mechanics, 98(4), 673-701

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Nakamura, Y ., & Tomonari, Y . 1982. The effects of surface roughness on the flow past circular cylinders at high Reynolds numbers. Journal of Fluid Mechanics, 123, 363-378

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Chang, C. C. J., Kumar, R. A., & Bernitsas, M. M. 2011. VIV and galloping of single circular cylinder with surface roughness at 3.0× 104≤ Re≤ 1.2× 105. Ocean Engineering, 38(16), 1713-1732

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

PTC-to-FIM

Introduction Many scholars have studied energy harvesting in-depth, but for the actual marine environment, there are some disadvantages of narrow energy harvesting frequency band and low efficiency. To solve such problems, the idea of boundary layer control is introduced and passive turbulence control (PTC) is one of it. PTC can achieve precise regulation...

work page

[2] [2]

PTC and Variable Stiffness Coupled Energy Harvesting Model 2.1 Single-Degree-of-Freedom Fluidic Vibration Model This study continues the previous work s of Wu et al. [16-19]. The mathematical model and experimental equipment used are exactly the same as before. Cylinders subjected to low-turbulence free surface flow undergo a broad spectrum of Reynolds nu...

work page

[3] [3]

Results and Analysis 3.1 PTC Influence on Flow Field The following four figures show the dimensionless displacement and power time -varying curves of the bare cylinder and three different PTC positions and the time -varying screenshots of the flow field taken at four moments in order to analyze the variation of the flow field. The four moments are selecte...

work page

[4] [4]

weak enhancement

Discussion 4.1 Energy Harvesting with PTC Fig.19 shows the motion amplitude and power frequency etc. for different PTC positions at 0.192-0.394m/s (0 represents bare cylinder), and it can be seen that for the amplitude, for all velocities, the 20 degrees PTC is able to increase slightly with respect to the bare cylinder, and is slightly suppressed at both...

work page

[5] [5]

Our proposition introduces a coupled mechanism integrating boundary layer control and system stiffness modulation inspired by octopus tentacles

Conclusion To address challenges related to narrow bandwidth and inefficient energy harvesting . Our proposition introduces a coupled mechanism integrating boundary layer control and system stiffness modulation inspired by octopus tentacles. Realize broadband and efficient harvesting of energy by interaction between local instabilities and global stabilit...

work page

[6] [6]

Achenbach, E. 1971. Influence of surface roughness on the cross-flow around a circular cylinder. Journal of fluid mechanics, 46(2), 321-335. [2 ] üvven, O., Farell, C., & Patel, V . C. 1980. Surface -roughness effects on the mean flow past circular cylinders. Journal of Fluid Mechanics, 98(4), 673-701

work page 1971

[7] [7]

Nakamura, Y ., & Tomonari, Y . 1982. The effects of surface roughness on the flow past circular cylinders at high Reynolds numbers. Journal of Fluid Mechanics, 123, 363-378

work page 1982

[8] [8]

Chang, C. C. J., Kumar, R. A., & Bernitsas, M. M. 2011. VIV and galloping of single circular cylinder with surface roughness at 3.0× 104≤ Re≤ 1.2× 105. Ocean Engineering, 38(16), 1713-1732

work page 2011