Correction: Wang et al. Mechanisms of Flow-Induced Pressure Pulsations in Semi-Open Impeller Sewage Pumps Under Solid–Liquid Two-Phase Flow Conditions. Water 2026, 18, 317

There was an error in the original publication [1]. Following publication, it was brought to the authors’ attention that several references were not sufficiently relevant to the specific subject of the study, namely pressure pulsations in a semi-open impeller sewage pump under solid–liquid two-phase flow conditions. The authors have re-examined these references and agree that they are too broad, indirect, or inadequately justified for the paper’s focus. These references were used only for contextual, comparative, or supplementary discussion, and they did not underpin the numerical model, the core data, the results, or the quantitative conclusions.

To correct the scientific record, the authors have removed all the affected references from the text and the reference list. The removed references are the original references [1–3,12,40,43,44,46–49,51–53]; none of these references is retained. The corresponding text has been deleted or reorganized as detailed below.

1. Section 1, Introduction: Removal of Broad Cross-Disciplinary Analogies and Gas-Liquid Comparison

The paragraph 2 should be reorganized as follows: Pressure pulsation is a primary indicator of internal flow instability and is closely linked to noise generation. A thorough understanding of pulsation characteristics is essential for improving pump performance and operational stability [1]. Spence et al. [2] categorized these pulsations into three types, random, blade-frequency harmonic, and shaft-frequency harmonic, establishing a framework for subsequent research. With advances in numerical methods, Computational Fluid Dynamics (CFD) has become a standard tool for investigating these transient phenomena. For instance, Tang et al. [3] employed unsteady numerical simulations combined with sliding mesh technology to conduct numerical simulations and frequency-domain analyses of the internal flow field and pressure pulsations in the tongue region of pumps under various operating conditions. Their findings offered valuable guidance for flow passage optimization, vibration control, and maintenance strategy development for double-suction centrifugal pumps. Zhang et al. [4], Ding et al. [5], Bai et al. [6], Zhang et al. [7], and Cui et al. [8] analyzed unsteady pressure pulsations and hydrodynamic forces induced by flow instabilities in centrifugal pumps, providing important references for pump design improvement. Furthermore, comparing different types of multiphase flow helps to better understand unsteady flow characteristics.

The paragraph 7 should be reorganized as follows: Despite the large number of studies on pressure pulsations in centrifugal pumps, the mechanisms of flow instabilities in semi-open impeller sewage pumps under solid–liquid two-phase conditions remain insufficiently understood. In particular, the combined effects of particle size, particle volume fraction, and flow rate on pressure pulsation intensity and frequency characteristics in key regions such as the impeller outlet and the volute tongue have not yet been systematically clarified. To address this gap, the present study employs unsteady CFD simulations in combination with time–frequency domain analysis to investigate the evolution of pressure pulsations within a semi-open impeller sewage pump. The results identify pulsation-sensitive regions and reveal the governing laws of pressure pulsation under different particle and flow rate conditions, thereby providing new physical insights and theoretical support for vibration suppression, hydraulic stability enhancement, and operational reliability assessment of sewage pump systems.

2. Section 2.2, Grid Generation and Independence Analysis: Removal of Shock-Train and Film-Hole Mesh Analogies

The paragraph 4 should be reorganized as follows: Scheme 3 with 4.26 million grids was selected because the head coefficient became essentially independent of further grid refinement, with the difference between Schemes 3 and 4 being less than 0.05%. This scheme provides a balance between computational accuracy and cost. The average wall y+ value was maintained within the logarithmic-law region, and scalable wall functions were applied for near-wall treatment. Therefore, the adequacy of the mesh is supported by the authors’ own grid-convergence results, head-coefficient stability, y+ distribution, and wall-function treatment.

3. Section 2.3, Boundary Conditions: Removal of High-Pressure Water-Jet Validation Claims

The paragraph 4 should be reorganized as follows: The Standard k−ϵ turbulence model was adopted for its stability in industrial multiphase simulations. The dispersed-phase wall boundary was treated as a free-slip boundary, which is an idealization that neglects particle-wall friction and inelastic rebound. This limitation has been stated in the paper, and the interpretation of the results is based on the dominant interphase momentum exchange and rotor-stator interaction captured by the present numerical model. The coordinated boundary-condition settings ensure consistent pressure-pulsation simulations under the investigated working conditions and provide flow-field data for subsequent time-frequency analysis.

4. Section 3, Monitoring Point Setup and Analytical Methods: Removal of Radial-Force Clustering and Surrogate-Model Optimization Analogies

The paragraph 2 should be reorganized as follows: The 45° interval for the volute monitoring points was selected to provide sufficient circumferential resolution of the pressure field. The combined arrangement of volute monitoring points Wg and W1–W8 and impeller monitoring points Y1–Y6 allows pressure variations near the volute tongue, along the volute passage, and on the impeller working surfaces to be recorded. This layout is used for subsequent time-domain and frequency-domain analysis of pressure pulsation characteristics under different operating and particle conditions.

5. Section 5.2, Pressure Pulsation Under Different Particle Volume Fraction Conditions: Removal of Water-Entry, Ramjet Droplet-Size, and Brittle Ice-Damage Analogies

The paragraph 2 should be reorganized as follows: Time-Domain Characteristics (Figure 17a): The pulsation periods under the clear water condition and low particle volume fraction conditions are similar, while the C_p fluctuation range expands significantly under high particle volume fraction conditions. Specifically, the fluctuation range is (−0.0418 to 0.0818) for the clear water condition, expands to (−0.0895 to 0.1191) at a 10% volume fraction, and further expands to (−0.1393 to 0.1051) at a 20% volume fraction, representing an approximate 97.73% increase in fluctuation amplitude compared to the clear water condition. It can be seen that the impact of particle volume fraction on the pressure pulsation at Wg is significantly greater than that of particle size. The core reason is that an increase in the number of particles intensifies flow turbulence at the volute tongue, enhances the particle impact effect, and thus leads to a significant increase in pressure pulsation. Although the particle contact model is simplified, it effectively captures the dominant momentum transfer driving the pulsation surge.

The paragraph 11 should be reorganized as follows: This phenomenon is attributed to the following: the impeller outlet area has a high flow velocity and strong rotor–stator interaction effect; moreover, the presence of particles changes the local flow pattern and increases the pressure gradient difference. These factors collectively lead to a significant intensification of pressure pulsation in the outlet area. Physically, this intense pulsation at the impeller outlet is driven by the high-speed impact of solid particles against the blade trailing edge. This mechanism directly mirrors the brittle impact dynamics observed in high-pressure water jet ice-breaking. Frequency-Domain Characteristics (Figure 20b): Under all conditions, the dominant frequency of C_p is concentrated around the first-order blade frequency (95 Hz) and shows an increasing trend with the increase in particle volume fraction. The dominant frequency amplitudes, in ascending order of particle volume fraction (clear water, 1%, 5%, 10%, 20%), are 0.0307, 0.0473, 0.0501, 0.0517, and 0.0627, respectively. At a 20% particle volume fraction, the dominant frequency amplitude reaches 2.04 times that of the clear water condition. In addition, there are many low-frequency signals under the clear water condition; as the particle volume fraction increases, these low-frequency signals gradually weaken and eventually disappear. This indicates that the increase in particle volume fraction makes the flow field more complex and exerts a significant regulatory effect on the pressure pulsation at the impeller outlet.

With this correction, the order of some references has been adjusted accordingly. The authors state that the scientific conclusions are unaffected. This correction has been approved by the Academic Editor. The original publication has also been updated.