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Understanding of energy conversion and losses in a centrifugal pump impeller

Abstract

As energy consumption saving becomes an urgent need in the contemporary world, the demand for improving pump energy efficiency is attracting increasing attention. This paper presents an extensive numerical investigation of energy transfer and dissipation in a centrifugal pump impeller, with the aim of elucidating the underlying mechanisms of loss and revealing the energy conversion processes in the impeller. The turbulent flows of the impeller are studied using very large eddy simulation under nominal flow rate and two part-load conditions. A new loss assessment model, which quantifies total loss by mean-flow viscous loss and turbulent loss, is proposed based on a detailed analysis of the budgets of the mean-flow kinetic energy and turbulent kinetic energy (_TKE_). Results show that the turbulent loss supplied by _TKE_ production is the main part of the total loss in all investigated cases. The mean-flow viscous dissipation related loss decreases significantly under part-load conditions. Energy conversion processes and their relevance to the flow structures have been revealed by investigating the spatial distributions of _TKE_ production, mean-flow viscous dissipation and turbulent dissipation. Finally, the contributions of each subcomponent of the _TKE_ production term to _TKE_ production have been explored.

Introduction

Pumping systems are one of the prominent areas of energy consumption. According to the International Energy Agency and the European Commission [1], electric motors consume 46% of the electricity generated in the world, and pumping systems consume over 22% of the energy supplied by electric motors. Due to loss in processes of energy transformation, the practical efficiency of pump units is 40–90% [2], and it may even be less than 20% for the ultra-low specific speed centrifugal pumps operating at part-load conditions [3,4]. With the rapid growth of global energy consumption, the energy saving and consumption reduction of pump units and pumping systems has received increasing attention. The hydraulic loss in different hydraulic components of the pump, particularly in the impeller, is an essential part of the total loss of the pump units. Therefore, it is of great importance to explore the mechanism of losses and understand the related energy conversion processes in the pump impeller, especially for high-performance pump model innovation and energy saving of pumping systems.

Since the losses are directly related to the complex three-dimensional flows, the features of flow in centrifugal pump impellers have long attracted the attention of researchers [[5], [6], [7], [8], [9], [10]]. Based on the Particle Image Velocimetry (PIV) system, Pedersen et al. [6] measured the flow structures inside a six-blade centrifugal impeller at part-load conditions. They found a “two-channel” phenomenon which consists of alternate stalled and unstalled passages in the impeller at quarter-load condition, and there were obvious recirculation structures at the inlet and strong shear flows near the outlet of the stalled passage. However, PIV observations show that in deep stalled conditions, the recirculation in a five-blade centrifugal impeller propagates in different flow passages in the opposite direction to the impeller rotation [11]. Li et al. [12] studied the effects of flow structures in the impeller on the performance of a low-specific speed centrifugal pump by PIV technique and computational fluid dynamics (CFD) simulation. The results showed that recirculations on the pressure side (PS) and suction side (SS) of the blade rotate oppositely. The PS recirculation enhances the hydraulic performance of the impeller, while the SS recirculation has a negative impact. Luo et al. [13] compared the performance of centrifugal impellers with different blade leading-edge shapes, and found that optimized blade leading-edge could reduce the range of low-pressure zone caused by the recirculation at the inlet of the impeller passage and improve the efficiency of the pump. Although abundant research results have elucidated the flow features of centrifugal pump impellers, the links between the losses and the flow structures have still not been deeply analyzed.

For the evaluation of energy loss in centrifugal pump and impeller, in the conventional method, a quantitative calculation of the total loss is usually conducted by taking the difference between input power and output power [2]. This method is effective in calculating the loss of different pump components and assessing the effects of geometry optimization on the energy loss and efficiency of the pump [14,15]. Unfortunately, it cannot establish the concrete connections between losses and flow structures, as well as to elucidate the mechanisms for losses and energy conversion processes. To obtain the local distribution of losses, from the perspective of energy dissipation, Kock et al. [13] proposed a local entropy generation method to study the losses in the flow field. In this method, the relations between losses and flow structures is established based on the local entropy distribution obtained by CFD or accurate measurements and the amount of energy loss can be quantified by the spatial integral of the local entropy generation rate over the flow domain. Neglecting the heat transfer effects, the local entropy consists of the mean-flow viscous dissipation and the turbulent dissipation [16,17]. The former characterizes the process of converting mean-flow kinetic energy (_MKE_) into internal energy through the effects of fluid viscosity; while the latter corresponds to the process of converting turbulent kinetic energy (_TKE_) into internal energy and dominates in highly turbulent flow regions. In recent years, as summarized by Zhou et al. [18], the local entropy generation method has been applied to analysis energy loss in hydraulic machinery [[16], [17], [18], [19], [20], [21]], and it was found that the major sources of turbulent dissipation occurred mainly in near-wall region, the blade suction side recirculation, backflow and blade wake. However, the local entropy generation method requires the turbulent dissipation information of the flow field. It shows limitations in the cases in which the dissipative scales cannot be precisely presented, especially in the near-wall region [22,17,23,24].

From an energy conversion perspective, in the turbulent flow of a centrifugal pump impeller, part of _MKE_ is converted into _TKE_ and finally dissipated into heat via dissipative structures [25]. Consequently, the total loss also can be determined by summing up the amounts of mean-flow viscous dissipation (energy conversion from mean-flow into heat) and _TKE_ production (energy conversion from mean-flow into turbulent motion) in the impeller. The _TKE_ production is related to the mean shear and velocity fluctuation of the flow and is mainly affected by the large-scale turbulence structures [26]. Thus, theoretically, evaluating the energy loss corresponding to turbulent dissipation by computing the _TKE_ production is not necessary to resolve the dissipative scales as rigorously as in the local entropy generation method.

Inspired by this concept, the current work focuses on the analysis of energy conversion processes in a centrifugal pump impeller and the distribution of losses in the flow field. The primary goals are to clarify the mechanisms of loss and to uncover details of the energy conversion in the impeller. The Very Large Eddy Simulation (VLES) method [27], a scale-resolving simulation technique which can resolve the large-scale turbulent structures, is adopted to simulate the complex turbulent flow in the impeller. Regarding the strong anisotropic characteristics of turbulent flow in centrifugal impeller under rotation and complex curved boundary, we developed a new turbulence resolution control function for the VLES model. Based on the energy conversion analysis, we proposed a quantitative model, namely mean-flow kinetic energy loss analysis model (MKE-LAM), for energy loss prediction. Flow characteristics, energy loss, and links between energy conversion and flow structures in a low specific speed centrifugal impeller under nominal flow conditions and two part-load conditions are extensively investigated. This study sheds light on the energy conversion processes between _MKE_ and internal energy and provides a reference for optimal design and efficiency improvement of centrifugal impellers.

Governing equations

The governing equations for the isothermal and incompressible turbulent flow encountered in this research are the unsteady Reynolds-Averaged Navier-Stokes (URANS) equations for the conservation of mass and momentum, which are presented in the following forms [26]:∂u i‾∂x i=0∂u i‾∂t+u j‾∂u i‾∂x j=−1 ρ∂p‾∂x i+μ ρ∂2 u i‾∂x j∂x j−∂τ i j U R A N S∂x j τ i j U R A N S=u i u j‾−u i‾u j‾=u i″u j″‾where ρ is density, μ is the fluid dynamic viscosity, τ i j U R A N S is the modeled turbulent Reynolds stress and u i″ represents the modeled

Results and disscustion

In the current work, unsteady flows under the nominal flow rate (1.0 _Q_ _d_) and two part-load conditions (0.6 _Q_ _d_ and 0.25 _Q_ _d_) are investigated. In this section, the results of numerical simulations are presented and the mean-flow structures, energy loss and energy conversion processes are discussed.

Conclusions

In this paper, we have used Very Large Eddy Simulation (VLES) method, a scale-resolving simulation technique, to analyze the unsteady flow within a low specific speed centrifugal pump impeller. To improve the efficiency and accuracy of the methodology for resolving the complex flow in the impeller, a new resolution control function for the VLES model was constructed by accounting for the turbulence anisotropy and strong shear effect of the turbulent flow in the impeller. The validity and

Credit Author Statement

Weisheng Chen: Conceptualization, Methodology, Validation, Investigation, Data curation, Writing – original draft. Yaojun Li: Conceptualization, Methodology, Validation, Supervision, Writing – review & editing. Zhuqing Liu: Conceptualization, Supervision, Funding acquisition, Writing – review & editing. Yiping Hong: Methodology, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Acknowledgement

The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China (No. 61511013 and No. 51679240).