Corrigendum to’Analysis of pressure pulsation and its correlation to energy dissipation in centrifugal pump with bionic optimal impeller base on proper orthogonal decomposition’ [Thermal Science and Engineering Progress 64, August 2025, 103822

To improve the accuracy and reduce the calculation cost for the inverse problem of centrifugal pump impeller, the new inverse method based on proper orthogonal decomposition (POD) is proposed. The pump blade shape is parameterized by quartic Bezier curve, and the initial snapshots is generated by introducing the perturbation of the blade shape control parameters. The internal flow field and its hydraulic performance is predicted by CFD method. The snapshots vector includes the blade shape parameter and the distribution of blade load. The POD basis for the snapshots set are deduced by proper orthogonal decomposition. The sample vector set is expressed in terms of the linear combination of the orthogonal basis. The objective blade shape corresponding to the objective distribution of blade load is obtained by least square fit. The Iterative correction algorithm for the centrifugal pump blade inverse method based on POD is proposed. The objective blade load distributions are corrected according to the difference of the CFD result and the POD result. The two dimensional and three dimensional blade calculation cases show that the proposed centrifugal pump blade inverse method based on POD have good convergence and high accuracy, and the calculation cost is greatly reduced. After two iterations, the deviation of the blade load and the pump hydraulic performance are limited within 4.0% and 6.0% individually for most of the flow rate range. This paper provides a promising inverse method for centrifugal pump impeller, which will benefit the hydraulic optimization of centrifugal pump.

As an important auxiliary equipment for ships, the stable operation of centrifugal pumps has a significant impact on the safe operation of ships, so monitoring the operation of marine centrifugal pumps is particularly urgent. In this paper, a marine centrifugal pump is studied for four cases: the normal state, the initial stages of broken state, the intermediate stages of broken state, and the late stages of broken state. The Delayed Detached Eddy Simulation (DDES) with a nonlinear eddy viscosity model is used for the nonstationary calculation of the whole channel, aiming to study the performance of the centrifugal pump in the broken state. A comprehensive analysis of the hydrodynamic characteristics of the centrifugal pump, such as external characteristics, flow situation, pressure pulsation, and flow analysis based on the proper orthogonal decomposition (POD) method, was carried out. Taken together, these results suggest that as the number of broken blades increases, the corresponding head and efficiency gradually decrease. Blade loss mainly affects the uniformity and stability of the flow field, so that the centrifugal pump performance loss increases, which in turn causes the centrifugal pump head and efficiency to decline. It also leads to an increase in radial force during operation, which in turn causes an increase in the amplitude of pump vibration. The results of the study provide some references for the fault diagnosis of centrifugal pumps.

HIGHLIGHTS • Effectiveness of vice blades flow control method. • Improvement mechanism of flow control method on centrifugal pump. • Energy redistribution of multi-scale turbulence by flow control method. • Design strategy for high-performance centrifugal pump. The demand for the high-performance centrifugal pumps has grown considerably in order to address various working conditions and application scenarios. Here, a high-performance centrifugal pump capable of great hydraulic and anti-cavitation performance, and low-pressure pulsation and vibration, is realized by adding drainage vice blade to the conventional blade type. The multi-scale turbulence in centrifugal pumps is characterized by the Hybrid RANS/LES method, then the energy distributions are obtained by the proper orthogonal decomposition (POD) method. The experimental methods are employed to study the pressure pulsation and vibration characteristics. The new-type of blades can reconstruct the energy of multi-scale turbulence in centrifugal pump by concentrating the energy on low-frequency large-scale flow structures, while reducing the energy of high-frequency small-scale flow structures. A higher energy of large-scale flow structures can enhance the energy transportation and hydraulic performance in centrifugal pump. The small-scale flow structures with lower energy can suppress high-frequency excitation in flow to avoid the hydraulic resonance, which is essential to improve the dynamic characteristics of the centrifugal pumps. We propose a flow control method that can reconstruct the energy distribution of multi-scale turbulence which can greatly improve its overall performance, suggesting a broad range of promising applications.

Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor

The method of proper orthogonal mode decomposition (POD) or KarhunenLoeve decomposition (KLD) is a means of extracting spatial information from a set of time-series data available from a set of sensing locations over a domain. The POD can be used to obtain low-dimensional models or discrete or distributed dynamical systems by computing an orthogonal set of eigen-functions through a finite-dimensional eigenvalue problem that is obtained by post processing of time-series measurements at different spatial locations. Interestingly enough, these eigenfunctions form an orthogonal basis (irrespective of the linear or nonlinear nature of the measured signals) which is optimal in the sense that fewer POD modes are needed to capture a given amount of energy of the measured signal than any other linear set of modes, including vibration modes [219]. Moreover, the eigenvalue corresponding to a given eigenfunction quantifies the amount of energy of the measured signal that is captured by the specific POD mode. Hence, the POD method not only provides a linear orthogonal basis of modes, but also a quantitative measure of the relative importance of these modes with regard to the energy of the signal captured by the POD analysis. This feature of the method makes it a valuable tool in the analysis, system identification and order reduction of the dynamics of engineering systems. As pointed by Kerschen [102] the POD analysis resembles the Singular Value Decomposition Method, with the later method providing additional information related to amplitude modulations of the identified waveforms.

The use of artificial intelligence methodologies in a variety of real-world applications has been around for some time. However, the application of such methodologies to thermal science and engineering is relatively new, but is receiving ever-increasing attention in the published literature since the mid 1990s. Such attention is due essentially to special requirements and needs of the field of thermal science and Engineering (TSE) in terms of its increasing complexity and the recognition that it is not feasible to approach many critical problems in this field by the use of traditional analysis. The purpose of the present brief review is to point out the recent advances in the artificial intelligence (AI) field and the successes of such methodologies to the current problems in thermal science and engineering. Some shortfalls and prospect for future applications will also be indicated.

Today, the fuel and energy complex (FEC) is the basis of Russian economy. It includes the most dynamically developing industries, such as petrochemical, oil refining, etc., associated with the production, transportation and processing of various fuels, as well as industries engaged in the production and distribution of electricity: thermal engineering, hydropower engineering and nuclear power engineering. The nomenclature of FEC centrifugal pumps includes a wide list of names: singleand multistage centrifugal pumps of low, medium and high pressure for clean water, water with impurities and various aggressive media [1, 2], pumps for oil production and transportation (trunk, booster, electric centrifugal production pumps, pumps for pumping leaks, etc.) and special pumps used in oil refining (cracking, cantilever chemical, etc.) [3]. The development of technical solutions aimed at improving energy efficiency as well as reliability and durability is one of the trends in the development of centrifugal pumps FEC that are most widely covered in engineering literature [4.9]. Along with this, reducing the complexity and cost of production of these pumps due to the automation of the design process remain just as important. In the given article, questions of development of a method of automated profiling of components of flow passage of centrifugal pumps for needs of FEC are considered. The description of the proposed method and the results of its approbation on the example of profiling of the flow passage of the impeller of the centrifugal cantilever chemical pump AH 12.5/50 are presented. Comparison with other known methods is carried out. The estimation of time costs for design works is carried out. It has been found that the automated profiling of the flow passage of the impeller according to the presented method took 720 times less time than manual profiling using conventional methods.

In this paper, we present the newly developed open-source density-based solver pisoCentralDyMFoam and investigate an application of the Proper Orthogonal Decomposition (POD) algorithms for industrial turbomachinery-related problems. POD is implemented in Apache Spark framework for distributed data processing. This solver is based on hybrid Kurganov-Tadmore/PISO scheme. The research was conducted for geometry close to its real prototype with known resonance frequencies. The solver was previously validated on simple industrial case ERCOFTAC centrifugal pump. The POD coefficient matrices were constructed using data set of the snapshots representing each saved time-step of the whole Navier-Stokes numerical model. Several hundred consecutive snapshots of the static pressure field on the impeller wheel surface as well as the velocity field were used for computation of the POD modes. The eigenvalues determined by POD method corresponds to the kinetic energy contained in each mode. The spatial coefficients represents contribution of each elementary volume to the whole mode and helps to locate the region having influence on the mean flow at specific frequencies after Fast-Fourier-Transform (FFT) applied to time-dependent coefficients of the decomposition. The POD modes were sorted by kinetic energy and the zeroth mode was most energetic representing mean flow with relatively small amplitudes. The described concept was extensively validated using computationally cheap 2D-case and then extended to the high-speed centrifugal pump of the small-scale turbojet. It was found that the third mode of the flow has first peak at 12970 Hz right between 2 construction resonance points at 12000 Hz and 13700 Hz. The third and fourth modes represent pressure fluctuations in the wakes region in the diffuser behind vanes. The demonstrated approach allows engineers to analyze flow dynamics more effectively compare to traditional FFT at certain points or cross-section. In addition, it can be useful for data compression and Reduced-Order Model development.

To investigate the spatiotemporal characteristics of vortex structures within a centrifugal pump and explore the application of modal decomposition techniques in three-dimensional vortex feature extraction, this study employs computational fluid dynamics (CFD) to numerically simulate the unsteady flow in a centrifugal pump under flow rates of 80 m 3 /h (low-flow condition), 100 m 3 /h (design flow condition), and 120 m 3 /h (high-flow condition). By integrating the Omega-Liutex method with modal decomposition techniques, including Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), a detailed characterization of the vortex structures is performed. The results indicate that, compared to other vortex identification criteria, the Omega-Liutex vortex identification technique effectively captures the flow structures within the centrifugal pump. By applying the POD method to analyze the vortex characteristics in the impeller region under three different flow conditions, the analysis revealed that tip vortices and wake vortices dominate the energy distribution across all flow conditions, with an energy proportion ranging from 34.7% to 40.3%. Additionally, under both low-flow and design-flow conditions, the first and second-order modal structures of the vortex in the impeller region demonstrate periodic behavior. The dominant vortex structures in the volute region exhibit significant variations under different flow conditions. Under low-flow and design-flow conditions, the primary vortex structures in the volute region include the tongue-shedding vortex and the wall-attached vortex, with a nonlinear interaction observed between the first and second-order modes. Under high-flow conditions, the primary energetic vortex structure in the volute region is the recirculating vortex in the diffuser section. A comparison of the vortex areas for all modes in the impeller and volute regions under three different flow conditions reveals that the primary mode exhibits the smallest vortex area. The first-order mode obtained through the DMD method clearly reveals the overall flow characteristics within the centrifugal pump. Among the first four modes, there are always two modes exhibiting identical vortex structures. In the comparison of vortex feature extraction, the POD method can identify large-scale vortices with relatively low energy in the impeller and volute regions, whereas the DMD method extracts vortex structures more clearly and comprehensively.

Fast prediction of the performance of the centrifugal pump based on reduced-order model

phenomena with the aid of interdisciplinary imaging science and technology. This particular issue contains ten contributed papers and six photogravure pages, which fall broadly within the area of fluids and thermal science and engineering. As is well known, visual observation was already playing an important role in diagnosing various flows more than a hundred years ago; a typical example was the O. Reynolds' experiment of laminar-to-turbulent flow transition in a pipe. This fact can be recognized as a quite reasonable consequence, if one is aware that any physical interpretation of flow phenomena should need knowledge on the degree of spatial extension of phase relationship, e.g., two-point correlation of flow variables. However, it was only about a decade ago that qualitative flow visualization had grown to powerful quantitative measurement techniques such as particle imaging velocimetry and Laser induced fluorescence. It was almost the same time that large-scale numerical simulation of complex flow phenomena such as turbulent and multiphase flows had become another research tool to explore detailed physics in fluid and thermal problems. Currently, both experimental and computational flow visualization techniques are being used extensively in analyzing and exploring flow and transport phenomena, and also in designing various mechanical devices and equipment. This trend will continue to grow, and the use of sophisticated visualization techniques should be indispensable for the future progress in fluids and thermal engineering. I hope these papers herein published provide a nice collection of some of the best contemporary research in visualization of fluid and heat flow.

In this paper, a frequently employed technique named the sparsity-promoting dynamic mode decomposition (SPDMD) is proposed to analyze the velocity fields of atmospheric motion. The dynamic mode decomposition method (DMD) is an effective technique to extract dynamic information from flow fields that is generated from direct experiment measurements or numerical simulation and has been broadly employed to study the dynamics of the flow, to achieve a reduced-order model (ROM) of the complex high dimensional flow field, and even to predict the evolution of the flow in a short time in the future. However, for standard DMD, it is hard to determine which modes are the most physically relevant, unlike the proper orthogonal decomposition (POD) method which ranks the decomposed modes according to their energy content. The advanced modal decomposition method SPDMD is a variant of the standard DMD, which is capable of determining the modes that can be used to achieve a high-quality approximation of the given field. It is novel to introduce the SPDMD to analyze the atmospheric flow field. In this study, SPDMD is applied to extract essential dynamic information from the 200 hPa jet flow, and the decomposed results are compared with the POD method. To further demonstrate the extraction effect of POD/SPDMD methods on the 200 hPa jet flow characteristics, the POD/SPDMD reduced-order models are constructed, respectively. The results show that both modal decomposition methods successfully extract the underlying coherent structures from the 200 hPa jet flow. And the DMD method provides additional information on the modal properties, such as temporal frequency and growth rate of each mode which can be used to identify the stability of the modes. It is also found that a fewer order of modes determined by the SPDMD method can capture nearly the same dynamic information of the jet flow as the POD method. Furthermore, from the quantitative comparisons between the POD and SPDMD reduced-order models, the latter provides a higher precision than the former, especially when the number of modes is small.

Insights into turbulent flow structure and energy dissipation in centrifugal pumps: A study utilizing time-resolved particle image velocimetry and proper orthogonal decomposition

In Memoriam: Professor Arthur E. Bergles (1935–2014), the Pioneering Advocate of Enhanced Heat Transfer and Energy Conservation

A centrifugal pump is one type of pumps that widely used in industries. Its mechanism which creates pressure changes may cause cavitation. Cavitation phenomenon that is not properly maintained may results fatal breakdown leading to high economic losses. Therefore, research is needed to find and develop a method that can detect early cavitation phenomena and identify it at several levels as well. This paper presents a method that can detect cavitation by monitoring the vibrations level of the pump based on statistical analysis of time domain and Principal Component Analysis (PCA). Vibration data is collected, trained and tested for each cavitation level. Training data is normalized and trained for each cavitation level using PCA which produces data loading matrix. The loading matrix is then multiplied by the testing data which gives a score matrix used to classify cavitation level of the centrifugal pump. The result shows that the method of domain-based PCA is successful in transforming the original data of 7 statistical parameters to 7 principal components (PC) with maximum variant. Three PCs gives 93.68% variants which can clearly identify and classify the differences between normal, early, intermediate and fully developed cavitation in the centrifugal pumps.