{"id":"d1924d77-839b-44e4-87f7-c1dc2949bbe9","arxiv_id":"2607.19567","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper derives cavitation acoustic perturbation equations and traces monopole-like tonal noise to near-wall cavity collapse phase-locked to cavity shedding.","lead":"This paper extends acoustic perturbation equations to cavitating flows, embedding vapor mass transfer and mixture compressibility as in-domain sound sources. If the framework holds up, it gives engineers a cheap way to locate the noise sources behind propeller \"singing\" tones.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The singing tonal prediction rests on unresolvable URANS collapse transients; the acoustic source terms inherit a base-flow model whose collapse events are not demonstrated to be physical.","rationale":"The reader's weakest assumption—that the URANS base flow faithfully supplies the acoustic source terms—is indeed the load-bearing concern. The paper's singing mechanism is not an independent physical prediction but a direct consequence of the one-way coupling: the acoustic spectrum must mirror the base-flow source spectrum. Since URANS cannot resolve true collapse transients, the collapse-driven tonal at fc could be a numerical/model artifact. The reader's CONDITIONAL verdict is appropriate; my concern does not change it but sharpens the conditionality. I agree with the reader's identification of the same weakest assumption. The concrete test—a base-flow resolution study—would directly test convergence of the collapse source and the resulting tonal frequency, settling whether the singing claim is robust.","tokens_in":24125,"tokens_out":12284,"duration_ms":107448,"concrete_test":"Re-run the cavitating cylinder case with a finer base-flow mesh (e.g., Mesh 4 of Table 1) and a smaller hydrodynamic time step, then recompute the integral pressure-rate source Sdp(t) (Fig. 18) and the acoustic spectrum at (0,20D). If fc or the Sdp peak amplitude changes by more than ~10%, the collapse-driven singing source is not converged and the tonal prediction is an artifact of the URANS base flow.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that CAPE resolves collapse-driven tonal singing—requires that the URANS base state (Eqs. 36-37 with the Schnerr-Sauer source, §2.3) faithfully reproduces the intermittent, impulsive cavity growth, shedding, and collapse. The source terms h, c²∂ρ0/∂t, and −∂P/∂t (Eqs. 26-29) are evaluated one-way from this base flow (§2.4). But URANS with k-ω SST is intrinsically dissipative and cannot resolve the fine-scale bubble collapse that generates the acoustic transient; the collapse pressure spikes in ∂P/∂t are therefore grid- and model-dependent surrogates. Fig. 11 shows strong intermittency in URANS αl, CD, CL, but this is a RANS-filtered signal, not a resolved collapse. Consequently, the tonal peak at fc in Fig. 15c is a self-consistency: the acoustic spectrum is driven by the URANS source spectrum, so finding fc in both is expected. The paper supplies no external baseline—no experiment or scale-resolving simulation—to confirm that the URANS collapse frequency is the physical singing frequency. Without that, the mechanism claim is conditional on the base-flow model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives and implements the Cavitation Acoustic Perturbation Equations (CAPE) for a homogeneous liquid-vapor mixture. The formulation decomposes the flow into an incompressible URANS base state and small acoustic perturbations, and introduces three cavitation-related source contributions: phase-change mass transfer, mixture-compressibility variation, and the base-pressure time derivative. A segregated finite-volume predictor-corrector scheme with acoustic subcycling and an absorbing PML-type region is presented. Verification is performed on 1D wave propagation (mesh/time-step convergence, PML, frequency preservation, Stokes attenuation), followed by application to non-cavitating and cavitating flow past a cylinder and a cavitating hydrofoil. The non-cavitating case reproduces the dipole directivity of Shen et al.; the cavitating cases show near-axisymmetric/monopole-like radiation and tonal peaks aligned with the cavity-shedding frequency, which the authors interpret as collapse-driven singing.","tokens_in":24475,"tokens_out":8813,"duration_ms":75842,"significance":"The CAPE derivation appears algebraically consistent, and the energy balance in Eq. (43) is a useful device for interpreting the volumetric source. A notable strength is that the acoustic system contains no fitted constants: all parameters (C_c, C_v, n0, d_Nuc, sigma_max, m) belong to the base-flow or numerical setup, not to the acoustic model. The 1D verification is systematic, and the non-cavitating benchmark against Shen et al. provides a credible check of the numerical implementation. If the physical application claims can be secured, the framework would be a valuable, efficient tool for hydroacoustic source analysis in cavitating flows. However, the application-level claims currently rest on unvalidated URANS collapse dynamics, and the Stokes-law verification is incomplete; these are the main barriers to accepting the physical conclusions.","major_comments":[{"comment":"The Stokes-law verification only checks the f² scaling, not the absolute attenuation coefficient. The reported values α ≈ 0.01–0.07 m⁻¹ at 100–200 Hz are orders of magnitude larger than the physical Stokes coefficient for water: α = 2μω²/(3ρc³) ≈ 8×10⁻¹¹ m⁻¹ at 100 Hz for μ ≈ 10⁻³ Pa·s, c ≈ 1500 m/s. Agreement with Eq. (55) therefore reflects numerical/PML dissipation rather than physical viscous attenuation. To support the claim that the solver 'follows Stokes’ law' (abstract and §5), the authors should compare the extracted coefficient with the analytic value, or use a setup in which numerical dissipation is demonstrably subdominant.","section":"§4.2 (Fig. 6b)"},{"comment":"The central claim—that collapse-induced pressure-rate amplification generates tonal singing—is not independently established. All acoustic sources are evaluated one-way from the URANS/Schnerr–Sauer base flow (§2.3–2.4), and Fig. 15(c) shows the acoustic spectrum peaking at exactly the URANS cavity-shedding frequency f_c identified in Fig. 12. This is a necessary self-consistency of the one-way coupling, not a physical prediction. URANS with k-ω SST cannot resolve the impulsive, small-scale collapse transients that Figs. 17–18 identify as the singing trigger; the dP/dt surge is a RANS-filtered, grid-dependent surrogate. Without an experimental singing-frequency baseline, a scale-resolving base flow, or at least a grid/closure sensitivity study of the source statistics, the mechanism claim remains conditional on the base-flow model.","section":"§4.4–§4.5, Eqs. (26)–(39), Figs. 15, 17, 18"},{"comment":"No quantitative validation is provided for the cavitating cases. The only external benchmark is the non-cavitating Re=200 directivity (§4.3, Fig. 9), which is a low-Reynolds, single-phase check. The cavitating SPL levels (e.g., ~126 dB re 1 μPa at 20D in Fig. 16) depend on the prescribed nuclei parameters n0, d_Nuc and mass-transfer coefficients C_c, C_v, none of which are varied or tied to experimental data. The absolute levels and the claimed monopole/singing signatures should be tested against measurements or against parameter sensitivity before being presented as physical predictions.","section":"§4.4–§4.5 (Figs. 16, 21)"}],"minor_comments":[{"comment":"The text says 'attenuation exponents (referred to the general attenuation from 5000 to 12,500)', but the axis is labeled α (m⁻¹). Clarify the normalization and the extraction procedure.","section":"§4.2 / Fig. 6"},{"comment":"Placeholder '(author?)' appears before Ref. [22] in the text and in the Fig. 9 caption; this should be replaced with the actual citation.","section":"§4.3"},{"comment":"The notation ρ_l/ρ_v versus ρ_{0,l}/ρ_{0,v} appears to denote the same quantities; use one set of symbols consistently.","section":"§2.1, Eqs. (13) and (26)"},{"comment":"The added damping terms form an absorbing layer, but the term 'perfectly matched' is not demonstrated analytically (no complex-coordinate stretching or auxiliary variables). If a simple sponge layer is intended, the terminology should be adjusted; the numerical reflection tests are nevertheless useful.","section":"§2.2, Eqs. (32)–(35)"},{"comment":"The density update uses coefficients 1.5 and 0.5 without derivation. Please provide the implicit time-integration formula from which these coefficients arise.","section":"Eq. (51)"}],"recommendation":"major_revision","confidential_remarks":"The paper presents a useful extension, but the current validation status is insufficient for publication as is. I recommend a major revision focusing on (i) correcting or reframing the Stokes-law claim, (ii) adding a comparison or sensitivity analysis for the cavitating singing prediction, and (iii) softening the language from 'resolved collapse' to 'modeled URANS source'."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nWhat you should know: this paper derives a real extension of the acoustic perturbation equations to cavitating multiphase flow, and the derivation is worth referee time. The stronger claims about collapse-driven 'singing' are not as solid as the abstract implies, because the acoustic sources are fed one-way from an incompressible URANS base flow.\n\nThe new content is genuine. Cheng and Jaiman add a phase-change mass-transfer source h, a Wood-type mixture-compressibility closure, and the ∂P/∂t pressure-rate term to APE, and they give an energy balance showing that p′h/ρ0 acts as a monopole-like source. That goes beyond single-phase APE/LPCE. The finite-volume predictor-corrector with subcycling and PML is internally consistent; the non-cavitating cylinder directivity reproduces the Shen et al. result; and the acoustic-sector parameters are prescribed before the acoustics, so no acoustic output is used to fit constants. The framework is a useful starting point, not a repackaging.\n\nThe soft spots are real but not fatal. The Stokes-law verification only demonstrates α∝f². The absolute coefficient matters, and the reported α, 0.01–0.07 m⁻¹ at 100–200 Hz, is orders of magnitude above physical water absorption, so the claim of reproducing Stokes' law is not established. The stress-test concern about URANS collapse transients is fair: the cavitating cylinder and hydrofoil are 2D URANS with Schnerr-Sauer, so individual collapse events are not resolved. The tonal alignment of the acoustic spectrum with fc and its harmonics is a self-consistency of the one-way coupling, because the sources are derived from the same URANS fields. Without an experimental or scale-resolving baseline, the singing mechanism remains a hypothesis. The paper acknowledges the URANS limitation, but the abstract states it more strongly than the evidence supports. Minor: no code/data, and a few reference placeholders (`(author?)`) remain.\n\nMy verdict: the core derivation holds up, and the paper should go to peer review. I would ask for revision, primarily to reframe the physical claims and repair the Stokes-law verification.","headline":"A genuine extension of APE to cavitating multiphase flows with a clean derivation and plausible numerics; peer-review it, but treat the singing-mechanism claims as conditional on the URANS base flow.","tokens_in":24948,"tokens_out":7888,"would_cite":true,"duration_ms":74003,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Cavitation ‘singing’ is traced to near-wall, phase-locked cavity collapse by a new acoustic perturbation formulation whose phase-change and pressure-rate terms carry the sources inside the domain.","keywords":["cavitation noise","acoustic perturbation equations","hydroacoustics","monopole source","singing","multiphase flow","finite volume method","perfectly matched layer"],"falsifier":"Measure or directly simulate the far-field acoustic spectrum of the same cavitating cylinder (Re ≈ 1.1×10^5, σcav = 0.8) and hydrofoil, and check whether the tonal peak sits at the cavity-shedding frequency fc ≈ 0.335 U0/D with a nearly axisymmetric directivity; a tonal line at the vortex-shedding frequency instead, or a dipole-shaped directivity, would falsify the CAPE source attribution.","tokens_in":24010,"feed_emoji":"🔊","tokens_out":6152,"duration_ms":48314,"temperature":0.7,"pith_summary":"The paper derives cavitation acoustic perturbation equations (CAPE) that embed vapor mass transfer, mixture compressibility, and unsteady base-pressure rate directly into the acoustic source terms, so cavitation noise sources are resolved inside the computational domain rather than modeled as equivalent surfaces. In the authors' account, the phase-change term acts as a volumetric monopole-like source while localized collapse events act through amplification of the pressure-rate term, and the framework reproduces the tonal 'singing' of a cavitating cylinder and hydrofoil as phase-locked to the cavity-shedding frequency. A sympathetic reader would care because this is a hybrid formulation that connects cavitation dynamics to radiated sound in a single, efficient solver, exchanging the usual dipole picture for a monopole-dominated one when cavitation sets in. The paper's own scope notes that the base flow is URANS with a Schnerr-Sauer closure and one-way coupling, so the predicted singing mechanism inherits the fidelity of that incompressible base flow.","feed_headline":"Cavitation singing traced to collapse near the wall","feed_subtitle":"Source-resolved acoustic equations tie cavitation tonal hum to phase-locked collapse and monopole radiation.","key_machinery":"The central object is the CAPE system, Eqs. (26)-(29), a set of perturbation equations for ρ′, f = ρ0u′ + ρ′U + ρ′u′, and p′. The load-bearing pieces are the phase-change source h, which injects mass-transfer-driven volume change as a monopole-like term; the mixture compressibility 1/(ρ0c²) built from Wood's relation, which makes the local sound speed collapse where vapor appears; and the base-state terms c²∂ρ0/∂t − ∂P/∂t, which turn unsteady pressure and density changes of the incompressible base flow into acoustic driving. A finite-volume predictor-corrector solver with m = 1000 acoustic substeps per flow step and a perfectly matched layer carries the waves outward and absorbs them at the","core_discovery":"The central claim is the CAPE system, Eqs. (26)-(29): a closed acoustic perturbation system for a liquid-vapor mixture in which the source h carries phase-change mass transfer, the mixture compressibility is set by the Wood-type relation 1/(ρ0c²) = αl/(ρ0,l c_l²) + (1-αl)/(ρ0,v c_v²), and the pressure-rate term c²∂ρ0/∂t − ∂P/∂t enters through the closure ∂p/∂ρ = c². Together these allow cavitation-induced noise to be generated and propagated within the domain, with the energy balance of Eq. (43) showing the phase-change term p′h/ρ0 as a monopole-like volumetric acoustic source. Applied to a Re = 1.11×10^5 cavitating cylinder and a NACA 6412 hydrofoil, the framework finds that the far-field t","pith_inferences":["The paper's energy balance is derived with ρ0 and c locally frozen; treating CAPE source strengths as a rigorous far-field budget would need the full variable-coefficient energy identity, which the paper does not provide.","If collapse is truly the tonal driver, then controlling near-wall inception through surface texturing or micro-ventilation should suppress the singing peak without moving the vortex-shedding frequency—a testable design consequence the paper leaves implicit.","Because the source chain depends on the URANS base flow, repeating the analysis with a scale-resolving base flow (LES or compressible two-phase) would show how much of the intermittent collapse structure—and therefore the predicted singing—is turbulence-model dependent.","The linear interpolation of source terms across each flow step (Eq. 54) may smear the sharpest collapse impulses; checking spectral convergence with larger subcycling ratios would test whether the peak at fc is robust."],"forward_implications":["If CAPE is right, cavitation-induced ‘singing’ is a near-wall collapse phenomenon phase-locked to the cavity-shedding frequency fc, so tonal underwater noise can be attributed to specific collapse events rather than to the wake's vortex shedding.","The same validated solver reproduces dipole radiation in the non-cavitating cylinder benchmark and monopole-like radiation in the cavitating cases, establishing a clean acoustic signature for detecting cavitation noise by directivity.","The acoustic energy balance identifies phase-change mass transfer as a volumetric monopole source, giving a quantitative source map for the sound field, not just far-field levels.","Because the formulation preserves the structure of conventional APE solvers, it can be dropped into existing incompressible cavitation-flow solvers with one-way coupling, making hydroacoustic prediction far cheaper than direct compressible simulation.","The verified Stokes-law attenuation and PML behavior give confidence that the propagation part is physically consistent over a range of frequencies."],"fun_headline_variants":["Cavitation noise equations trace monopole hum to bubble collapse","New framework resolves cavitation noise sources in multiphase flow","Phase change and collapse drive cavitation tones, new model shows","Source-resolved acoustic equations for cavitating flows","Cavitation's acoustic fingerprint decoded in new computational framework"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire prediction rests on the incompressible URANS solution (with the Schnerr-Sauer cavitation model) faithfully supplying the impulse of cavity growth, shedding, and collapse; if the base flow blurs those events, the computed singing follows the model rather than the physics.","fun_headline_variants_meta":{"raw":{"variants":["Cavitation noise equations trace monopole hum to bubble collapse","New framework resolves cavitation noise sources in multiphase flow","Phase change and collapse drive cavitation tones, new model shows","Source-resolved acoustic equations for cavitating flows","Cavitation's acoustic fingerprint decoded in new computational framework"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000185,"raw_usage":{"total_tokens":1209,"prompt_tokens":843,"completion_tokens":366,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":587,"completion_tokens_details":{"reasoning_tokens":284}},"tokens_in":587,"tokens_out":366,"duration_ms":3952,"temperature":1.0,"reasoning_tokens":284,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T12:22:23.439869+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure or directly simulate the far-field acoustic spectrum of the same cavitating cylinder (Re ≈ 1.1×10^5, σcav = 0.8) and hydrofoil, and check whether the tonal peak sits at the cavity-shedding frequency fc ≈ 0.335 U0/D with a nearly axisymmetric directivity; a tonal line at the vortex-shedding frequency instead, or a dipole-shaped directivity, would falsify the CAPE source attribution.","supporting_citations":[],"review_version":1}