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arxiv: 2606.19252 · v1 · pith:LMNEAZDPnew · submitted 2026-06-17 · ⚛️ physics.flu-dyn

Multi-objective Bayesian optimization of rigid and flexible nozzles for energy-efficient pulsed jet propulsion

Paras Singh , Yukesh Karki , Victor Hernandez , Daehyun Choi , Saad Bhamla , Chandan Bose This is my paper

Pith reviewed 2026-06-26 18:56 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords pulsed jet propulsionflexible nozzlesrigid nozzlesBayesian optimizationfluid-structure interactionhydrodynamic impulseenergy efficiencyvortex dynamics
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The pith

Flexible nozzles achieve 1.8 times higher impulse-to-energy efficiency than rigid nozzles in pulsed jet propulsion.

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

The paper compares rigid and flexible nozzle designs for pulsed-jet propulsion using multi-objective Bayesian optimization and three-dimensional fluid-structure interaction simulations. Rigid nozzles produce up to 5 times the impulse of a baseline cylinder but at high energy cost, while flexible nozzles reach about 2.5 times the impulse with markedly better efficiency. The central result is that the maximum normalized impulse-to-energy ratio is about 1.8 times higher for flexible nozzles. This indicates more effective conversion of input energy into propulsive output through distinct flow mechanisms in each geometry.

Core claim

Rigid nozzles achieve the highest impulse amplification, up to 5 times that of a baseline cylindrical nozzle, but at substantially increased energy expenditure. In contrast, flexible nozzles yield lower peak impulse enhancement of about 2.5 times while achieving significantly greater propulsion efficiency. The maximum normalized impulse-to-energy ratio for flexible nozzles is about 1.8 times higher than that of rigid configurations, indicating more effective conversion of input energy into useful propulsive output.

What carries the argument

Multi-objective Bayesian optimization framework integrated with three-dimensional fluid-structure interaction simulations that identifies nozzle designs maximizing hydrodynamic impulse while minimizing jet energy input.

If this is right

  • Rigid nozzles enhance performance through geometry-induced internal entrainment, secondary vortex formation, and contraction-driven jet acceleration, producing stronger vortex circulation and downstream convection.
  • Flexible nozzles use traveling expansion-contraction deformation waves that promote additional entrainment during expansion and accelerate internally entrained fluid during contraction.
  • Flexible nozzles improve pressure recovery, reduce pressure-energy expenditure, and mitigate negative pressure impulse contributions.
  • Flexible nozzles achieve greater propulsion efficiency despite lower peak impulse than rigid nozzles.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The efficiency advantage of flexible nozzles may inform design choices for other underwater propulsion devices that face similar impulse-versus-energy trade-offs.
  • Extending the optimization to include objectives such as maneuverability or durability could identify further nozzle variants.
  • Direct comparison of simulation predictions against laboratory measurements on physical models would test whether the reported efficiency gap persists outside the computational setting.

Load-bearing premise

The three-dimensional fluid-structure interaction simulations accurately capture the performance trade-offs between rigid and flexible nozzle geometries in pulsed-jet propulsion systems.

What would settle it

Physical prototypes of the optimized rigid and flexible nozzles tested in a pulsed-jet experiment to measure actual impulse and energy input and determine whether the normalized impulse-to-energy ratio is 1.8 times higher for the flexible case.

Figures

Figures reproduced from arXiv: 2606.19252 by Chandan Bose, Daehyun Choi, Paras Singh, Saad Bhamla, Victor Hernandez, Yukesh Karki.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of a cylindrical nozzle system with flexible walls that passively expand and contract in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Schematic [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Graphical representation of fluid-structure solver coupling between [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Prescribed inlet pulsed jet velocity profile normalized by [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Two-dimensional nozzle geometry showing the spline control points and the highlighted admissible region within [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Multi-objective Bayesian optimization framework [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Normalized hypervolume (HV) as a function of MOBO generations for rigid and flexible nozzle configurations. The HV [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Pareto fronts obtained from MOBO of (a) rigid and (b) flexible nozzle configurations. Blue markers denote all [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Normalized impulse-to-energy ratio, ( [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Pareto-optimal (a) rigid and (b) flexible nozzle geometries rendered in perspective view corresponding to designs [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. (a) Evolution of normalized out-of-plane vorticity contours (ˆω [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Temporal evolution of the normalized primary vortex circulation Γ, for the baseline and Pareto-optimal rigid [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. (a) Evolution of normalized out-of-plane vorticity contours (ˆω [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Deflection envelopes of the baseline (a) Design 0 and Pareto-optimal flexible nozzle designs: (b) Design 21, (c) [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. (a) Temporal evolution of the normalized primary vortex circulation, Γ, for the baseline and Pareto-optimal flexible [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Temporal history of normalized impulse and jet energy input for the baseline and Pareto-optimal rigid nozzle designs [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Temporal history of normalized impulse and jet energy input for the baseline and Pareto-optimal flexible nozzle [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Validation of the MOBO framework against four standard multi-objective benchmark functions described in III: (a) [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
read the original abstract

The biomechanics of pulsed-jet propulsion in aquatic animals, including squids and jellyfish, provide valuable insights into energy-efficient locomotion. In these organisms, flexible funnel deformation enables rapid acceleration and maneuverability while minimizing energy use. Drawing inspiration from these biological systems, this study investigates performance trade-offs between rigid and flexible nozzle geometries in pulsed-jet propulsion systems. A multi-objective Bayesian optimization framework integrated with three-dimensional fluid-structure interaction (FSI) simulations identifies nozzle designs that maximize hydrodynamic impulse and minimize jet energy input. The optimization reveals fundamentally distinct performance characteristics for rigid and flexible nozzles. Rigid nozzles achieve the highest impulse amplification, up to 5 times that of a baseline cylindrical nozzle, but at substantially increased energy expenditure. In contrast, flexible nozzles yield lower peak impulse enhancement of about 2.5 times while achieving significantly greater propulsion efficiency. The maximum normalized impulse-to-energy ratio for flexible nozzles is about 1.8 times higher than that of rigid configurations, indicating more effective conversion of input energy into useful propulsive output. Analysis of the flow physics shows that optimized rigid nozzles enhance performance through geometry-induced internal entrainment, secondary vortex formation, and contraction-driven jet acceleration. This results in stronger vortex circulation and downstream convection. Flexible nozzles use traveling expansion-contraction deformation waves that promote additional entrainment during expansion and accelerate the internally entrained fluid during contraction to improve pressure recovery, reduce pressure-energy expenditure, and mitigate negative pressure impulse contributions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript applies multi-objective Bayesian optimization coupled to 3D fluid-structure interaction simulations to identify rigid and flexible nozzle geometries that maximize hydrodynamic impulse while minimizing input energy for pulsed-jet propulsion. It reports that optimized rigid nozzles achieve up to 5× the impulse of a baseline cylindrical nozzle (at higher energy cost), while flexible nozzles reach ~2.5× impulse with a maximum normalized impulse-to-energy ratio ~1.8× higher than rigid designs, attributing the difference to geometry-induced entrainment and traveling deformation waves.

Significance. If the 3D FSI predictions are quantitatively reliable, the work would usefully quantify performance trade-offs between rigid and deforming nozzles and identify distinct flow mechanisms (internal entrainment, secondary vortices, expansion-contraction waves) that could guide bio-inspired propulsor design. The Bayesian optimization framework itself is a methodological strength for high-dimensional design exploration. However, the central 1.8× efficiency claim rests entirely on unvalidated simulation outputs, limiting the current significance.

major comments (2)
  1. [Abstract] Abstract: the quantitative multipliers (5× impulse for rigid, 2.5× for flexible, 1.8× normalized impulse-to-energy ratio) are the load-bearing results, yet no mesh-convergence data, time-step independence tests, or experimental benchmarks for the baseline or optimized cases are referenced. Any systematic bias in vortex capture or pressure recovery that differs between rigid and deforming geometries would directly alter the reported 1.8× ratio.
  2. [Methods and Results] Methods/Results sections: the three-dimensional FSI model is used to compute both impulse and energy for the efficiency comparison, but the manuscript supplies no validation (grid resolution, boundary-condition sensitivity, or comparison to known rigid-nozzle experiments) that would confirm the simulations are accurate enough for relative performance statements between the two classes of geometry.
minor comments (2)
  1. [Abstract] Notation for the normalized impulse-to-energy ratio should be defined explicitly (including any normalization constants) the first time it appears.
  2. [Figures] Figure captions should state the number of optimization evaluations or Pareto-front points shown to allow readers to assess sampling density.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on validation requirements for the FSI simulations. We agree that supporting numerical evidence is needed to strengthen the quantitative claims and will revise the manuscript accordingly. Below we respond point by point.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the quantitative multipliers (5× impulse for rigid, 2.5× for flexible, 1.8× normalized impulse-to-energy ratio) are the load-bearing results, yet no mesh-convergence data, time-step independence tests, or experimental benchmarks for the baseline or optimized cases are referenced. Any systematic bias in vortex capture or pressure recovery that differs between rigid and deforming geometries would directly alter the reported 1.8× ratio.

    Authors: We accept that the abstract multipliers require supporting convergence evidence. In the revised manuscript we will add dedicated mesh-convergence and time-step independence studies performed on both representative rigid and flexible geometries, reporting L2 norms or integrated impulse/energy changes under successive refinement. These tests will be placed in a new subsection of Methods and referenced from the abstract and results. Regarding differential bias between rigid and deforming cases, the same solver, turbulence model, and boundary conditions are applied uniformly; any residual discretization error is therefore expected to affect both classes similarly, preserving the relative 1.8× ratio. Experimental benchmarks are outside the present computational scope but will be noted as future work. revision: yes

  2. Referee: [Methods and Results] Methods/Results sections: the three-dimensional FSI model is used to compute both impulse and energy for the efficiency comparison, but the manuscript supplies no validation (grid resolution, boundary-condition sensitivity, or comparison to known rigid-nozzle experiments) that would confirm the simulations are accurate enough for relative performance statements between the two classes of geometry.

    Authors: We agree that explicit validation details are currently insufficient. The revised Methods section will include (i) grid-resolution studies with quantitative convergence metrics for impulse and energy, (ii) boundary-condition sensitivity tests (inlet waveform, far-field placement), and (iii) direct comparison of baseline rigid-nozzle results against published experimental and numerical data for pulsed jets. These additions will be used to justify the reliability of relative performance statements. The multi-objective Bayesian optimization itself samples many geometries under identical numerical settings, providing internal consistency checks on trends. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on independent FSI simulations and optimization

full rationale

The paper derives its central 1.8x impulse-to-energy ratio and performance comparisons directly from outputs of 3D fluid-structure interaction simulations coupled to multi-objective Bayesian optimization. These are external computational procedures whose results are not defined in terms of the target metrics or reduced to self-citations. No equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described methodology. The derivation chain is therefore self-contained against the simulation framework rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are identifiable without the full manuscript.

pith-pipeline@v0.9.1-grok · 5800 in / 1178 out tokens · 41695 ms · 2026-06-26T18:56:20.309241+00:00 · methodology

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Reference graph

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