EN 
BR For almost a century, humans have relied on centrifugal pumps for the transport of low-viscous fluids in commercial, agricultural, and industrial activities. Details of the fluid flow in impellers often influence the overall performance of the centrifugal pump and may explain unstable and inefficient operations taking place sometimes. However, most studies in the literature were devoted to understanding the flow in the midaxial position of the impeller, only with a few focusing their analysis on regions closer to solid walls. This paper aims to study the water flow in the vicinity of the front and rear covers (shroud and hub) of a radial impeller to address the influence of these walls on the fluid dynamics. For that, experiments using particle image velocimetry (PIV) were conducted in a transparent pump at three different axial planes, and the PIV images were processed to obtain the average velocity fields and profiles, as well as turbulence levels. Our results suggest that: (i) significant angular deviations are observed when the velocity vectors on the peripheral planes are compared with those on the central plane; (ii) the velocity profiles close to the border are similar to those in the middle, but the magnitudes are lower close to the hub than to the shroud; (iii) the turbulent kinetic energy on the periphery is up to eight times greater than that measured at the center. Our results bring new insights that can help propose mathematical models and improve the design of new impellers. A database and technical drawings of the centrifugal pump are also available in this paper so that other researchers can perform numerical simulations and validate them against experimental data.
Month: February 2025
Particle image velocimetry in the impeller of a centrifugal pump: A POD-based analysis
The flow field within the channels of a centrifugal pump impeller is usually complex, containing turbulent structures in a wide range of time and length scales. Identifying the different structures and their dynamics in this rotating frame is, therefore, a difficult task. However, modal decomposition can be a useful tool for detecting coherent structures. In this paper, we make use of proper orthogonal decomposition (POD) of time-resolved flow fields in order to investigate the flow in a centrifugal pump. For that, we carried out experiments using time-resolved particle image velocimetry (TR-PIV) in a pump of transparent material operating at different conditions and obtained the statistical characteristics of the turbulent flow from phase-ensemble averages of velocities and turbulent kinetic energy. The results reveal that at the pump’s best efficiency point (BEP) the flow is well-organized, with no significant flow separation. For flow rates below the BEP, flow separation and vortex structures appear in the impeller channels, making the flow unstable. At flow rates above the BEP, intense jets appear close to the suction blades, while small instabilities occur on the pressure side. The POD analysis shows that at low flow rates, the flow is dominated by large-scale structures with intense energy levels, while at the BEP and higher flow rates, the flow is dominated by small-scale structures. Our results shed light on the turbulence characteristics inside the impeller, providing relevant information for reduced-order models capable of computing the flow in turbomachinery at much lower costs when compared to traditional methods.
A low-order preconditioner for high-order element-wise divergence constant finite element spaces
Mixed finite element problems are a class of problems that arises when modeling several physical phenomena, such as in computational fluid dynamics, structural analysis, optimization, etc. Designing efficient iterative schemes for such a family of approximations has been the subject of several works in the past decades. However, its success is intimately related to the proper definition of a preconditioner, i. e., the projection of the original algebraic system to an equivalent one with better spectral properties. In recent work, we have proposed a new class of H(div)-conforming finite element spaces with element-wise constant divergent. This family of elements was designed to improve reservoir simulation computational cost and are obtained by choosing the lower order space with piece-wise constant normal fluxes incremented with divergence-free higher-order functions. In this work, we propose an iterative scheme to solve problems arising in the context of the above mentioned element- wise constant divergence approximation spaces. The strategy consists on using the matrix of linear fluxes as a preconditioner to solve the higher-order flux problem. The latter is solved iteratively by means of a conjugate gradient scheme. In the presented numerical tests, this strategy has shown to be convergent in a few iterations for different problems in 2D and 3D. In addition, as internal fluxes are condensed, only boundary variables need to be computed. This strategy relates to the MHM technique and can be efficiently used to access fast multi-scale approximations in future work.
Recent advances in a multiscale flux-based method for simulating flow in fractured porous media.
Computational simulation of reservoir flow is an important tool that provides valuable insight into the decision process in oil extraction. Several types of commercial software have been developed over the years for this application, the majority using low-order schemes, which can become prohibitive for very large models. This issue becomes more apparent since, nowadays, the accuracy of a simulator is dominated by the accurate simulation of the multiscale characteristics of a reservoir such as permeability heterogeneity. To capture these multiscale features in low-order schemes, very refined models are required. Therefore, developing a high-order scheme able to simulate fractured reservoir flow that is accurate and can efficiently capture the multiscale features of the reservoir is of great value for the field. With this motivation, this presentation reports on recent advances in a methodology to simulate flow in highly heterogeneous fractured porous media using the Multiscale Hybrid-Mixed (MHM) method with H(div)-confirming flux approximations. This method is particularly appealing because of its inherent properties such as local mass conservation, multiscale features, and strong divergence-free enforcement for incompressible flows. Flow in the porous media is modeled with traditional Darcy’s equations and the coupling between flow in the porous media and fractures is based on the conceptual Discrete-Fracture-Matrix representation, where the fractures are idealized as lower-dimensional elements at the interface of matrix elements. The methodology is compared with benchmark examples to demonstrate its robustness, accuracy, and efficiency.
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