Wall entropy ratio as a diagnostic indicator for centrifugal pump blade fracture: Linking dissipation and excitation-response

According to the deficiency of the traditional centrifugal pump inverse method, the partial differential equation is used to generate the centrifugal pump blade surface, and then the blade design problem is transformed into the boundary-value problem of partial differential equation. According to the blade streamline equation, when the distributions of blade angle on boundary are given, the angular coordinates of dispersed points on pump blade boundary would be calculated. And so the boundary condition of the partial differential equation is determined. The blades geometries can be controlled by adjust the distribution of the blade angle on hub and shroud. A new distribution function is introduced to control the blade angle on hub and shroud. The gradient optimizing technology is also used to find the optimum control parameters in distribution function. The relations between the pump blade model and the pump design parameters are built, so the clipping drawing of the pump impeller is unnecessary when designing the impeller, and the parameterized design of blade is achieved. The calculation case shows that the inverse method of centrifugal pump blade presented here is rational, and it is of great value both in theory and in engineering practice.

The inverse problem is always one of the important issues in the field of fluid machinery for the complex relationship among the blade shape, the hydraulic performance, and the inner flow structure. Based on Bayesian theory of posterior probability obtained from known prior probability, the inverse methods for the centrifugal pump blade based on the single-output Gaussian process regression (SOGPR) and the multioutput Gaussian process regression (MOGPR) were proposed, respectively. The training sample set consists of the blade shape parameters and the distribution of flow parameters. The hyperparameters in the inverse problem models were trained by using the maximum likelihood estimation and the gradient descent algorithm. The blade shape corresponding to the objective blade load can be achieved by the trained inverse problem models. The MH48-12.5 low specific speed centrifugal pump was selected to verify the proposed inverse methods. The reliability and accuracy of both inverse problem models were confirmed and compared by implementing leave-one-out (LOO) cross-validation and extrapolation characteristic analysis. The results show that the blade shapes within the sample space can be reconstructed exactly by both models. The root mean square errors of the MOGPR inverse problem model for the pump blade are generally lower than those of the SOGPR inverse problem model in the LOO cross-validation. The extrapolation characteristic of the MOGPR inverse problem model is better than that of the SOGPR inverse problem model for the correlation between the blade shape parameters can be fully considered by the correlation matrix of the MOGPR model. The proposed inverse methods can efficiently solve the inverse problem of centrifugal pump blade with sufficient accuracy.

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.

Parameter equation study for screw centrifugal pump

Cavitation is a complex multiphase flow phenomenon, and the generation of transient phase transitions between liquid and vapor during cavitation development leads to multi-scale vortex motion. The transient cavitation dynamics and centrifugal pump’s rotor–stator interaction will induce pressure fluctuations in the impeller and the volute fluid of the centrifugal pump, resulting in a complex flow field structure. Based on the Schnerr–Sauer cavitation model and SST k-ω turbulence model, this paper studies the transient characteristics of the cavitation-induced unsteady flow in the centrifugal pump and the excitation response to the pressure pulsation in the volute under different flow conditions, taking the large vertical double-volute centrifugal pump as the research object. The results indicate the following: As the impeller rotates, in the external excitation response, the jet-wake flow structure at the centrifugal pump blade outlet shows an increase in the blade frequency signal. This is evident near the measurement points of the volute tongue and separator. When severe cavitation occurs, the maximum amplitude at the blade frequency in the volute shifts from the pump tongue (30°) to the downstream of the tongue (45°). The value of fpmax is 3.1 times that when NPSHa = 8.88 m. By applying the Omega vortex identification method, it can be seen that the interaction between the vortices at the blade trailing edge and the stable vortex in the volute tongue undergoes a process of elongation, fusion, separation, and recovery. This represents the downstream influence of the impeller on the volute. When Q = 0.9Qd, the process of the blade passage vortex tail detaching and dissipating in the impeller flow path can be observed, demonstrating the upstream influence of the volute on the impeller.

Centrifugal pumps are essential in various industrial applications, and their stable and efficient operation has a direct impact on the overall performance of the system. This study simulates different lengths of fractures at the LE (leading edge) of a single blade to conduct an in-depth analysis of their effects on internal flow and transient characteristics. The study reveals that the most significant effects of blade LE fractures on pump performance occur near a flow rate of 0.8Qd, where the head and efficiency can decrease by up to 6.19% and 3.77%, respectively, compared to the original blades. Blade fractures lead to deterioration of flow on the pressure and suction sides, creating vortices and inducing leakage flow, while entropy production significantly increases in this area. A 230.1% increase in the distribution angle and a 26.6% increase in the maximum radial force reflect changes in the radial force distribution. Also, LE fractures make the wall pressure pulsations stronger at the SPF (shaft passing frequency), and they make the amplitude of the pulsations on the blade surface much bigger at both SPF and 3SPF frequencies. Finally, LE fractures change the way vibrations behave at radial measurement points in both the x and y directions in a big way. The acceleration amplitudes at SPF and 3SPF frequencies go up by 125.8%, 193.1%, and 62.5%, 184.6%, respectively. These findings provide an important theoretical basis for the early warning and diagnosis of blade fracture failures.

In this research, a new inverse method for centrifugal pump blade based on free form deformation is proposed, the free form deformation is used to parametric the pump blade. The blade is implanted to a trivariate control volume which is equally subdivided by control lattice. The control volume can be deformed by moving the control lattice, thereupon the object is deformed. The flow in pump is solved by using a three dimensional turbulent model. The lattice deformation function is constructed according to the gradient distribution of fluid energy along the blade and its objective distribution. Deform the blade shape continually according to the flow solve, and we can get the objective blade shape. The calculation case shows that the proposed inverse method based on FFD method is rational.

The impeller, as a key component of artificial heart pumps, experiences high shear stress due to its rapid rotation, which may lead to hemolysis. To enhance the hemolytic performance of artificial heart pumps and identify the optimal combination of blade parameters, an optimization design for existing pump blades is conducted. The number of blades, outlet angle, and blade thickness were selected as design variables, with the maximum shear stress within the pump serving as the optimization objective. A back propagation (BP) neural network prediction model was established using existing simulation data, and a grey wolf optimization algorithm was employed to optimize the blade parameters. The results indicated that the optimized blade parameters consisted of 7 impeller blades, an outlet angle of 25 °, and a blade thickness of 1.2 mm; this configuration achieved a maximum shear stress value of 377 Pa-representing a reduction of 16% compared to the original model. Simulation analysis revealed that in comparison to the original model, regions with high shear stress at locations such as the outer edge, root, and base significantly decreased following optimization efforts, thus leading to marked improvements in hemolytic performance. The coupling algorithm employed in this study has significantly reduced the workload associated with modeling and simulation, while also enhancing the performance of optimization objectives. Compared to traditional optimization algorithms, it demonstrates distinct advantages, thereby providing a novel approach for investigating parameter optimization issues related to centrifugal artificial heart pumps.

The centrifugal pump holds significant prominence as a widely adopted power machinery in mechanical industries. This study aims to uncover the influence of blade trailing edges on the energy performance of centrifugal pumps. Sixteen types of blade trailing edge models, including Bezier trailing edges, rounded pressure side, cut suction side, and original blade trailing edges, are examined both numerically and experimentally. Entropy production power and energy loss for each domain with different trailing edge models are computed using entropy production theory and the pressure drop method, respectively. The correlation between them and the interaction of energy loss in various domains are determined through Spearman correlation analysis. Furthermore, the energy loss and efficiency of the centrifugal pump are decomposed and explored. Finally, the impact of different trailing edges on each component of shaft power is analyzed. The study findings indicate that increasing the radius of the trailing edge leads to higher head, while a thinner trailing edge enhances efficiency. Consistent trends are observed in entropy production and energy loss across different blade trailing edges. Modifying the impeller trailing edge significantly affects not only the impeller but also the cavity, diffuser, and outlet chamber, with minimal impact on the inlet chamber. Thinning the blade trailing edge can decrease energy loss and entropy production. Proper design of the blade trailing edge can effectively reduce the pressure pulsation near the impeller outlet in the stator. This study serves as a valuable reference for the design and research of centrifugal pump blade trailing edges.

The centrifugal pump is the common mechanical equipment, which is extensively applied in the water conservancy, ships and other projects, and the blade structure is a very important part in the centrifugal pump. In this paper, the stress distribution and concentration of single blade in the impeller are analyzed under the different pressure field of the blade structure surface, and the fatigue failure of blade is also studied. The research results show that the we can get the stress and strain of the blade accurately and intuitively through the analysis for the blade structure, the stress concentration of the centrifugal pump blade is mainly in the root and junction of the wheel cover, and the import value of stress concentration is larger than the outlet; the stress concentration may be caused easily as the stress increases rapidly in the blade, which has a great impact on the fatigue strength, the fatigue limit of the blade with the stress concentration is decreased more obviously than the fatigue limit of the smooth blade.

The marine centrifugal pump is one of the most energy-intensive pieces of equipment in ship auxiliary machinery, and the efficient design of its hydraulic components can effectively reduce the total energy consumption of the ship system. Aiming at the complex three-dimensional twisted blade profile structure of the marine centrifugal pump, this paper optimized the clonal selection algorithm and constructed an automatic hydraulic optimization design method for the high-efficiency centrifugal pump impeller. Considering the multi-condition operation characteristics of the marine centrifugal pump, a performance test platform for the marine centrifugal pump was built, and the actual operating conditions of the model pump were tested to obtain its performance characteristics under operating conditions. The numerical simulation method was employed to capture and analyze the internal flow field and flow characteristics of the model pump. Addressing the design challenges of the marine centrifugal pump impeller, which involve multiple parameters with significant interactions, a traditional clonal selection algorithm was enhanced using a Slime Mold Algorithm, and a hybrid Clonal Selection Algorithm integrated with Slime Mold and Tangent Flight mechanisms was established. Based on the MATLAB and ANSYS platforms, an automated hydraulic optimization design framework for the centrifugal pump impeller was established. Using the optimized clonal selection algorithm, with the operational efficiency of the model pump as the optimization objective and controlling ten key geometric parameters of the blade profile through Bézier curves, the blade profile optimization design was achieved. The pump hydraulic efficiency under the rated flow condition increased by 7%. The unsteady internal flow efficiency of the optimized marine centrifugal pump was significantly improved. The blade optimization alleviated flow separation phenomena on the tangential surface of the impeller and in partial regions of the volute, reduced the flow loss area, and significantly decreased overall flow losses.

The blade fracture of horizontal centrifugal pump will not only affect the hydraulic performance of the pump, but also affect the safety and stability of the whole unit. In this paper, for horizontal centrifugal pumps, five single-blade fracture schemes are designed and numerical simulations are carried out under different operating conditions. The results show that with the increase of fracture size, the influence on the hydraulic characteristics of the pump shows a decreasing trend, and it will also affect the turbulent kinetic energy distribution near the impeller inlet, so that the internal flow becomes complex and the flow loss increases. The radial force on the impeller changes periodically, and its magnitude shows a nonlinear decreasing change with the increase of the fracture size. The pressure pulsation analysis of several monitoring points in the worm shell shows that as the fracture size increases, the amplitude of the lobe frequency slowly rises, and the shaft frequency, which is second only to the lobe frequency, becomes higher and higher and begins to dominate. A study of the rotor system shows that the maximum deformation of the impeller occurs at the edge of the impeller cover and the maximum equivalent stress occurs at the blade exit; blade fracture causes a significant reduction in the latter third-order intrinsic frequency.

Pump as turbine (PAT) is one of the micro-hydro system components. It can be used alone as a generator in remote areas without power supply, and in hydraulic networks instead of pressure-reducing valves. However, its hydraulic optimization still remains an open research problem. One of the optimization techniques is the rounding of the sharp edges at the blade periphery. Existing studies are mostly based on prototype experiments to obtain the optimization effect. In order to more intuitively analyze the influence of this structural optimization on the internal flow of PAT, this paper uses the CFD method to study the influence of the leading edge of the centrifugal pump blade and the fillet of the impeller on the turbine performance. By simulating the PAT performance at different flow rates and speeds, the internal hydraulic performance changes caused by the inverted circular blade are analyzed. Simulation results show that, under various operating conditions, the impeller inverted circle improves the efficiency of PAT to different degrees. At the speed of 1500 rpm, the efficiency is most obviously improved, which can reach 8.09%. Internal flow results show that the efficiency increases along with the decrease in impeller inlet resistance and the flow separation region in the impeller. This paper provides an effective method for studying the PAT hydraulic optimization problem.

To improve the prediction accuracy of the surrogate model and reduce the calculation cost for hydraulic optimization design of centrifugal pump impeller, an inverse design and optimization method based on adaptive proper orthogonal decomposition (APOD) hybrid model was proposed. Initial samples were designed by perturbing blade control parameters of the original model. The samples were classified using the K-means clustering algorithm, and the adaptive samples were selected according to the category of the objective sample. The snapshot set is composed of blade shape parameters and the CFD flow field data in impeller, which is decomposed into a linear combination of orthogonal bases by the proper orthogonal decomposition (POD) method to predict the objective parameters. According to the objective load distribution, the low specific speed centrifugal pump was inversely designed by using the APOD model, and its initial blade was obtained. And then, the flow field corresponding to disturbed blade shape was predicted using the APOD method, so as to evaluate the gradient of the objective function to design variables. Finally, the initial blade was optimized by the gradient descent method. The results show that the APOD hybrid model method can be employed to accomplish the blade inverse design and the flow field prediction in the optimization design of centrifugal impeller, which significantly reduces the numerical calculation cost and improves the accuracy of the flow field prediction.

In order to improve the cavitation resistance of centrifugal pump, bionic groove surface structure was arranged on the suction surface of centrifugal pump blade which is the most prone to cavitation. Numerical simulation method was used to study the influence of different-shape groove blade on cavitation performance of centrifugal pump. The results showed that the head and efficiency of the centrifugal pump with circular grooved surface blades were close to the smooth surface blade centrifugal pump and higher than those with triangular grooved surface blades and rectangular grooved surface blades. The low pressure area of the circular groove blade was the smallest and the cavitation resistance was the best. At the critical cavitation margin point, circular groove blade can effectively reduce the probability of negative incidence, and the cavitation inhibition effect was the most obvious.