Centrifugal pumps play a crucial role in industrial operations involving fluid transport. The quest for optimizing efficiency and reducing energy usage is a driving force behind research into their performance. The literature continues to offer opportunities for the creation of models that accurately depict the head generated by pumps, with a particular focus on impellers. The current pumps, however, are still far from being completely optimized. The idea of this paper is to conduct an analysis of energy losses and propose a mathematical expression to represent the head produced by a radial impeller, P23 model, working with water flow, considering that head is influenced by losses due to recirculation, shock/incidence, internal friction. The head losses are quantitatively evaluated from experimental data acquired via particle image velocimetry, which provides information on velocity vector direction and wall shear stress, both useful for the analysis. Our results reveal that the loss due to friction is the most significant, accounting for 40–90% of the total head loss, while shock and recirculation losses are restricted to 35% and 25%, respectively. Friction factors vary from 1.0 to 26 depending on the flow rate, as a result of wall shear stresses reaching up to 430 N/m2, mainly influenced by pressure and pseudoforces. The head calculated through the new proposed expression is finally compared with the actual head generated by the impeller, measured via experiments dedicated to assess the pump performance. According to our results, the relative deviations between the calculated and measured heads are limited to 5%. Although our results have been validated for a single P23 impeller geometry, the methodology developed here can be extended to other impellers in the future. The results may thus represent a step forward for designing more efficient and power-saving pumps.
Month: February 2025
Experimental and theoretical modeling of droplet break-up on W/O emulsion flow in ESPs
The behavior of water-in-oil emulsions flow within Electrical Submersible Pumps (ESPs) is of significant interest in the oil and gas industry due to its complex rheological characteristics, which are influenced by operational parameters and the chemical properties of both phases. Operational parameters such as dispersed phase fraction, temperature, flow rate, and pump design were investigated experimentally in this work. Improved semi-empirical models for mean and maximum droplet diameter estimation were also proposed. Through extensive experimentation and statistical analysis, this study reveals that smaller droplets form with increasing dispersed phase fraction and the flow geometry significantly affects droplet breakage intensity. The proposed models integrate the dispersed phase fraction, dimensionless flow rate, specific speed, and energy dissipation rate, exhibiting commendable alignment with experimental findings. This not only helps predict effective viscosity but offers valuable insights for further analyses, particularly regarding catastrophic phase inversion (CPI) prediction. These aspects have significant importance in the oil and gas industry and can enable the optimization of production systems and processing facilities.
Theoretical and numerical comparison between the pseudopotential and the free energy lattice Boltzmann methods
The pseudopotential and free energy models are two popular extensions of the lattice Boltzmann method for multiphase flows. Until now, they have been developed apart from each other in the literature. However, important questions about whether each method performs better needs to be solved. In this work, we perform a theoretical and numerical comparison between both methods. This comparison is only possible because we developed a novel approach for controlling the interface thickness in the pseudopotential method independently on the equation of state. In this way, it is possible to compare both methods maintaining the same equilibrium densities, interface thickness, surface tension and equation of state parameters. The well-balanced approach was selected to represent the free energy. We found that the free energy one is more practical to use, as it is not necessary to carry out previous simulations to determine simulation parameters (interface thickness, surface tension, etc). In addition, the tests proofed that the free energy model is more accurate than the pseudopotential model. Furthermore, the pseudopotential method suffers from a lack of thermodynamic consistency even when applying the corrections proposed in the literature. On the other hand, for both static and dynamic tests we verified that the pseudopotential method is more stable than the free energy one, allowing simulations with lower reduced temperatures. We hope that these results will guide authors in the use of each method.
Particle image velocimetry in the impeller of a centrifugal pump: Relationship between turbulent flow and energy loss
Turbulent flows play a dominant role in the operation of centrifugal pumps, which find widespread use in industrial settings and various aspects of human life. The dissipation rate of turbulent kinetic energy emerges as a key parameter within these devices, with its local values exerting a significant influence on centrifugal pump performance. Recent advances in particle image velocimetry (PIV) techniques have expanded the ability to analyze complex turbulent flows across a broad spectrum of scales. In this context, this paper aims to deepen our understanding of the turbulent flow field and its correlation with energy loss in centrifugal pump impellers. To achieve this, experiments were conducted using PIV on a transparent pump operating under different conditions. Statistics of the turbulent flow were then obtained from phase-ensemble averages of velocities, vorticity, turbulence production, and local dissipation of turbulent kinetic energy. To overcome the limited spatial resolution constraint of PIV, the large-eddy PIV (LES-PIV) method was employed to estimate the local dissipation rate. In this method, it is assumed that the motion of larger scales is measured by the PIV technique, while the smaller scales (unresolved scales) are modeled by a sub-grid scale model, calculated from the strain rate tensors obtained from the measured fields. Energy losses in the impeller were studied using two methodologies: (i) a conventional method based on power measurements, and (ii) an alternative approach based on the budget of turbulent kinetic energy. Our results reveal that turbulent loss caused by turbulence production is the main source of energy loss in the pump impeller, and it is particularly pronounced in low-flow operating conditions characterized by large-scale structures. On the other hand, in situations where flow rates exceed the best efficiency point (BEP) condition, the predominant flow structures are marked by small-scale features, mainly attributed to local dissipation of turbulence. Our findings clarify the characteristics of energy losses in centrifugal pump impellers and their relationship with the turbulent flow field, and, in addition, providing a methodology for calculating the local turbulent dissipation rate and its limitations when derived from PIV measurements.
Particle image velocimetry in a centrifugal pump: Influence of walls on the flow at different axial positions
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.
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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