{"id":"f1b42c41-0b45-482d-b191-c26c788892db","arxiv_id":"2607.24630","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A spatially smoothed moving reference frame formulation reduces interface velocity discontinuities in propeller simulations while preserving integral propulsion quantities.","lead":"This paper introduces a modified moving reference frame (mMRF) method for ship propellers, in which the modeled rotation rate fades smoothly from the propeller to the domain edge to reduce kinks at the rotating-stationary interface. If it holds up, ship CFD can get cheaper self-propulsion predictions with fewer local flow artifacts than classical MRF methods, at the same computational cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The local-improvement claim is not independently tested: the Taylor-Couette verification cannot activate the new ∇f term, q and k are calibrated against the same SI reference used in Table 8, and Eq. (21) leaves f≈2.5e-3 at the interface.","rationale":"The reader's conditional verdict is the right level. The mMRF construction has real strengths: it has a clean f=1 limit, the open-water and self-propulsion integral quantities track EFD within a few percent, and the grid/time-step sensitivity study (Tables 9/10) shows monotonic convergence. However, the headline local-accuracy claim is less secure than the abstract suggests. The Taylor-Couette verification is explicitly degenerate for the new term: the paper states that u_MRF·∇f=0 there, so it cannot validate the mechanism that is supposed to fix the interface. The first case in which the mechanism acts is also the case used to choose q and k, and the same SI-based reference is used both as the fitting target (Table 5) and as the reference for the local deviation metric (Table 8). In-sample agreement with a fitted parameter is evidence that the method can be tuned, not that the tuning rule is predictive. The additional mismatch between Eq. (21) and the stated f=0 boundary condition is smaller but reinforces the point: the exact compatibility argument is asymptotic, not exact, for the reported parameters. None of this suggests the method is wrong in an engineering sense; it suggests the central claim should be scoped as 'can reduce interface artifacts when f is chosen appropriately', pending an out-of-sample test. Therefore I see no reason to move away from CONDITIONAL.","tokens_in":22112,"tokens_out":14078,"duration_ms":121337,"concrete_test":"Recompute the SP2-SP9 local deviation table (Table 8) with a fixed, non-calibrated f, e.g., q=0.5, k=30 for all MRF fractions, and also with q=0.4, k=40 (which makes f_int≈0), without any SI-based parameter selection. If the disc-averaged error ratios R_ε are not uniformly below 1, or the upstream-plane reduction disappears, the reported improvement is attributable to calibration rather than to the mMRF mechanism itself.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that mMRF restores velocity/pressure continuity and reduces interface artifacts rests on the extra term (∇f·u_MRF)u in Eq. (19) being a faithful model of a partially rotating frame. The only analytic verification, the Taylor-Couette case in Sec. 3.1, has u_MRF·∇f=0 by axisymmetry, so the new term is inactive there; the paper explicitly notes this. The first nontrivial exercise of the term is the JBC self-propulsion case, but the shape of f is not fixed a priori: Sec. 4.3 selects q=0.8,k=30 by comparing KT/KQ to the SI solution of the same configuration that later defines the local deviation metric (Eq. 35, Table 8). This is not a full circularity, since the fit target is integral and the evaluation local, but it is still an in-sample calibration: no independent rule for q,k is provided. Moreover, the chosen f does not actually vanish at the interface: Eq. (21) with q=0.8,k=30 gives f≈(1+e^6)^-1≈2.5e-3 at d_int=0, so Eq. (20) is satisfied only approximately, and 'restoring continuity' overstates the implemented boundary condition. The integral results remain credible; the local-accuracy headline is what needs support.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a modified Moving Reference Frame (mMRF) method for propeller-hull interaction simulations. The rotation rate of the reference frame is scaled by a position-dependent damping function f(r) that is intended to be unity near the propeller and zero at the interface to the stationary domain. The governing equations are derived in Sec. 2.2 and Appendix A, leading to an extra momentum term (∇f·u_MRF)u in Eq. (19). The method is implemented in the RANS solver FreSCo+, verified against the analytical Taylor–Couette solution, and applied to open-water and JBC self-propulsion cases. The paper reports that mMRF reproduces integral propulsion quantities as accurately as classical MRF while markedly reducing interface discontinuities and local flow-field deviations from a sliding-interface reference, at comparable computational cost.","tokens_in":22460,"tokens_out":3811,"duration_ms":36488,"significance":"If the central claim holds, the method offers a practical cost-accuracy trade-off for propeller-hull interaction CFD: it retains the efficiency of MRF while reducing the interface artifacts that limit classical MRF at large MRF fractions. The derivation is self-contained, the reduction to standard MRF for f=1 is explicitly shown, and the open-water grid/time-step convergence study in Appendix B is properly documented with monotonic convergence ratios. The application to the JBC benchmark with validation against experimental integral data is a strength. However, the verification strategy leaves a gap between the governing-equation claim and the numerical evidence: the only case that exercises the new term is precisely the case in which the damping-function parameters are calibrated, so the reported local-accuracy improvement may be partly a calibration effect.","major_comments":[{"comment":"The Taylor–Couette verification in Sec. 3.1 cannot test the new term in Eq. (19), because u_MRF·∇f=0 there by axisymmetry, as the paper itself notes. The first nontrivial exercise of this term is the JBC self-propulsion case, but Sec. 4.3 selects q=0.8 and k=30 by comparing K_T and K_Q against the sliding-interface solution F01 (Table 5), and the same F01 solution is later used as the reference for the disc-averaged deviation metric in Eq. (35) and Table 8. The reported reductions R_ε≈0.58–0.83 are therefore in-sample measures: they compare a calibrated model against the calibration reference. To make the central local-accuracy claim load-bearing, the authors should either provide an independent test case in which ∇f is active and a known or experimentally measured solution exists, or demonstrate that the qualitative conclusions are insensitive to q and k over a wide range, or evaluate the local deviations against an independent reference (e.g., EFD fields) rather than only the SI solution.","section":"§3.1 and §4.3"},{"comment":"With the selected parameters q=0.8 and k=30, Eq. (21) gives f≈(1+e^6)^-1≈2.5×10^-3 at d_int=0, not zero. Hence the compatibility condition (20) is satisfied only approximately at the interface, and the abstract's claim that mMRF \"restores velocity and pressure continuity\" is stronger than what is implemented. The residual discontinuity is small but nonzero, and its magnitude should be quantified in the manuscript. The authors should also discuss whether forcing f to exactly zero at the interface (e.g., by using a compactly supported damping function) would change the reported improvements.","section":"§2.2.1, Eq. (21)"},{"comment":"The derivation of the absolute-velocity formulation (19) is algebraically plausible, but it is presented in a condensed form that is difficult to audit. In particular, the step leading to Eq. (41) involves a rearrangement of the convective term that is not fully explained. Since the entire method rests on this equation, the authors should either expand the derivation in Appendix A to show each cancellation explicitly or provide a supplementary symbolic algebra check. This is not a request for cosmetic changes; it is needed to rule out a hidden sign or factor error in the extra ∇f term.","section":"Eq. (19) and Appendix A"}],"minor_comments":[{"comment":"The phrase \"restoring velocity and pressure continuity\" should be qualified as approximate, given that f does not vanish at the interface for the chosen sigmoid parameters (see major comment).","section":"Abstract and Sec. 2.2.1"},{"comment":"The caption refers to the middle panel as \"an unmodified simulation with a partially rotating grid\"; for clarity it should state that this is classical MRF with n_MRF/n=0.5, consistent with the terminology used elsewhere in the paper.","section":"Fig. 1 caption"},{"comment":"The table reports ΔK_T and ΔK_Q as percentages but uses the notation \"0.944%\" without a plus sign for positive values; using a consistent signed percentage format (e.g., +0.944%) would avoid ambiguity.","section":"Sec. 4.3, Table 5"},{"comment":"The convergence ratios R=0.67 and R=0.40 for the grid and time-step studies are reported without a confidence interval; stating the number of significant digits and the definition of R exactly as in Eq. (44) is fine, but the authors should note that these are single-computation estimates and not based on a Richardson-extrapolation uncertainty calculation.","section":"Appendix B, Tables 9 and 10"},{"comment":"The EFD data in these figures are stated to be time-averaged experimental measurements, while the numerical fields are instantaneous at a common phase (for the deviation metric) or time-averaged over one revolution (for the contour comparisons). The caption should state clearly which averaging is used in each panel, since the mixing of instantaneous and averaged fields can mislead the reader.","section":"Sec. 4.5 and Figs. 21–24"},{"comment":"The reference to Durasević et al. (2022, 2023) is cited in the text as \"Durasevi´c et al. (2022; 2023)\" but appears in the reference list as \"Durasevi´c, S., Gatin, I., Uroi´c, T., and Jasak, H.\"; please ensure consistent spelling and formatting.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The core derivation and the computational study are of reasonable quality, and the paper is likely to be of interest to the ship-CFD community. The main concern is the verification gap: the new term is not exercised in the analytical verification, and the local-accuracy claim is evaluated against the same SI solution used for parameter calibration. I would ask the authors to address this by adding an independent verification case or a sensitivity study that breaks the calibration dependence. If they can do so, I would be willing to accept the paper after the revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a real method-development paper with a clean derivation and honest integral validation, but the local-accuracy claim—the headline—depends on parameters fitted to the same reference solution it is later compared against.\n\nWhat is new: the spatially varying frame-rotation scaling f(r) and the resulting ∇f term in Eq. (19) do not appear in the cited partially-rotating-grid work. The derivation in Sec. 2.2 and Appendix A is algebraic and self-contained, and it reduces to standard MRF for f=1. The open-water grid and time-step study shows monotonic convergence with small changes, and the JBC self-propulsion integrals are within a few percent of EFD; mMRF does not degrade those, and it costs the same as MRF. That is a genuine practical advance for design-loop calculations.\n\nThe soft spots are real but not disqualifying. The Taylor-Couette verification cannot exercise the new term: u_MRF·∇f=0 by axisymmetry, so the case only checks consistency of the standard MRF part. The first real test of the ∇f term is the JBC case, but there the shape of f is chosen by picking q=0.8,k=30 to match the SI thrust and torque (Table 5), and the same SI solution is then the reference for the local deviation metric in Table 8. That is in-sample calibration, not an independent test. It is a mild circularity rather than a fatal one, because the fit target is integral and the evaluation is local, but it means the reported 0.58–0.83 error ratios are partly a calibration effect. And the paper overstates at one point: with q=0.8,k=30, Eq. (21) gives f≈2.5e-3 at the interface, not zero, so 'restoring continuity' is not literally what the implementation does. The compatibility condition is approximate, which is fine, but the wording should be softened.\n\nOne more point: no code or data are shipped, but the JBC case is a public benchmark, so the method is reproducible from the text. The low-J open-water deviation is minor and the authors themselves attribute it to the unexplored parameter set.\n\nWho is this for: people doing ship CFD or rotor-internal-flow simulations that mix resolved motion and MRF. They will get the derivation and a fair assessment of the trade-off. The paper deserves a serious referee; the right outcome is probably 'major revision' with an independent parameter-setting rule or a verification case where ∇f is active and the prediction is checked against SI or EFD without fitting.","headline":"Clean derivation and solid integral validation, but the local-accuracy payoff is calibrated rather than independently tested.","tokens_in":22950,"tokens_out":3196,"would_cite":true,"duration_ms":27597,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A smoothed reference frame removed the velocity jump at propeller-domain interfaces in ship CFD.","keywords":["moving reference frame","partially rotating grid","propeller-hull interaction","self-propulsion simulation","Japan Bulk Carrier","RANS","sliding interface","interface continuity"],"falsifier":"A direct comparison of the mMRF prediction against a sliding-interface reference in a configuration where the transition band cuts through a strongly non-uniform wake, with the parameters q and k fixed a priori (not fitted to the SI solution), and where the term (∇f·u_MRF)u is not small: if the disc-averaged deviation from SI is not reduced below classical MRF, the claimed benefit is a calibration artifact. In particular, the Taylor-Couette verification cannot falsify the model because u_MRF·∇f vanishes there.","tokens_in":21894,"feed_emoji":"🚢","tokens_out":2861,"duration_ms":19244,"temperature":0.7,"pith_summary":"This paper tries to establish that a moving reference frame (MRF) whose rotation rate is spatially damped to zero at the domain boundary can replace the abrupt rotating-stationary interface of classical MRF and restore velocity and pressure continuity. The authors derive the modified momentum equations, implement them in a RANS solver, verify against an analytical Taylor-Couette flow, and test on open-water and self-propulsion simulations of the Japan Bulk Carrier. They report that the modified method reproduces integral propulsion quantities as accurately as classical MRF while markedly reducing local interface discontinuities and non-physical artifacts, especially at large MRF fractions, at essentially the same computational cost.","feed_headline":"Smoothed reference frame removes propeller interface jump","feed_subtitle":"Scaling MRF rotation to zero at the domain boundary cuts flow-field artifacts by up to 42 percent in ship CFD.","key_machinery":"The central object is the modified momentum equation (Eq. 19), which adds the term (∇f·u_MRF)u to the classical MRF formulation, where u_MRF = f Ω_MRF × (r−r0) is the spatially varying reference-frame velocity and f is a sigmoidal damping function (Eq. 21) that transitions from 1 near the rotating propeller surface to 0 at the domain interface. This term is the only new addition and it enforces the compatibility condition at the interface.","core_discovery":"The central claim is that scaling the MRF rotation rate by a smooth scalar function f(r), which is unity near the propeller and zero at the domain interface, eliminates the velocity discontinuity that classical MRF exhibits at the rotating-stationary boundary. The key new term in the momentum equation is (∇f·u_MRF) u, which arises from the spatially varying rotation and ensures that the interface compatibility condition f Ω_MRF × u = f u_MRF·∇u is satisfied automatically where f=0. In practice, the method reduces the disc-averaged deviation from the sliding-interface reference to 58-83% of the classical MRF values across tested planes and rotation ratios, with no additional computational cost.","pith_inferences":["The same smoothing approach could be adapted to other rotating-machine contexts, such as pumps, turbines, or wind turbines, where an MRF interface cuts through a non-uniform wake and classical MRF produces similar discontinuities.","The scaling function f could be optimized rather than hand-tuned: the paper fixes q and k by matching the sliding-interface solution, but a calibration-free choice based on local flow gradients or turbulence length scales might be possible.","The method's benefit likely grows with the non-uniformity of the inflow: in nearly uniform open-water flow, classical MRF already performs well, while the largest gains appear in the ship wake, suggesting the term (∇f·u_MRF)u corrects precisely the missing convection of the velocity jump."],"forward_implications":["Ship self-propulsion simulations can use larger time steps and higher MRF fractions without suffering the interface artifacts that classical MRF produces, making partially rotating grid methods more reliable for hull-propeller interaction studies.","The method offers a favorable cost-accuracy trade-off for adjoint-based optimization, since it requires fewer time steps than sliding-interface simulations while retaining better fidelity than steady MRF.","The mMRF formulation can be applied to configurations with energy-saving devices or pre-swirl ducts, where local flow accuracy at the propeller plane matters.","At very high MRF fractions, the method still produces some flow distortions, so fully modeled rotation should be avoided when accurate local flow prediction is required."],"supporting_citations":[{"why":"Introduces the partially rotating grid method that splits propeller rotation into grid-resolved and MRF components, which the present method modifies.","marker":"Durasević et al. (2022)"},{"why":"Extends the partially rotating grid method to full-scale pre-swirl duct studies, motivating the need to mitigate interface discontinuities.","marker":"Durasević et al. (2023)"},{"why":"Provides the sliding interface method used as the high-fidelity reference solution throughout the verification and application.","marker":"Blades and Marcum (2007)"},{"why":"Supplies the JBC geometry, experimental resistance, open-water, and self-propulsion data used for validation.","marker":"Hino et al. (2020)"},{"why":"Provides the classical MRF derivation and source-term formulation that the modified equations extend.","marker":"Luo et al. (1994)"},{"why":"Supplies the analytical Taylor-Couette solution used to verify the numerical implementation.","marker":"Taylor (1923)"},{"why":"Provides the SST k-omega turbulence model used in all RANS simulations.","marker":"Menter et al. (2003)"},{"why":"Supplies the volume-of-fluid method used for the two-phase free-surface resistance simulation.","marker":"Hirt and Nichols (1981)"}],"fun_headline_variants":["Smooth MRF roll-off eliminates propeller interface jumps","Fading rotation rate repairs propeller CFD boundary","No-cost smoothing of MRF removes ship wake artifacts","Scaled MRF spin ends propeller domain discontinuity","Spatially decaying MRF cleans propeller flow fields"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The single scalar damping function f, applied to the MRF rotation and accompanied by the extra momentum term (∇f·u_MRF)u, is a physically consistent model of a partially rotating reference frame, with its shape parameters q and k chosen for convenience rather than derived from blade motion.","fun_headline_variants_meta":{"raw":{"variants":["Smooth MRF roll-off eliminates propeller interface jumps","Fading rotation rate repairs propeller CFD boundary","No-cost smoothing of MRF removes ship wake artifacts","Scaled MRF spin ends propeller domain discontinuity","Spatially decaying MRF cleans propeller flow fields"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000211,"raw_usage":{"total_tokens":1410,"prompt_tokens":936,"completion_tokens":474,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":401}},"tokens_in":552,"tokens_out":474,"duration_ms":12954,"temperature":1.0,"reasoning_tokens":401,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:25:24.957445+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct comparison of the mMRF prediction against a sliding-interface reference in a configuration where the transition band cuts through a strongly non-uniform wake, with the parameters q and k fixed a priori (not fitted to the SI solution), and where the term (∇f·u_MRF)u is not small: if the disc-averaged deviation from SI is not reduced below classical MRF, the claimed benefit is a calibration artifact. In particular, the Taylor-Couette verification cannot falsify the model because u_MRF·∇f vanishes there.","supporting_citations":[],"review_version":2}