Three-dimensional Eddy Research Articles

Comparative analysis of four types of mesoscale eddies in the Kuroshio-Oyashio extension region

Oceanic mesoscale cyclonic (anticyclonic) eddies usually have cold (warm) cores and counterclockwise (clockwise) flow fields in the Northern Hemisphere. However, “abnormal” cyclonic (anticyclonic) eddies with warm (cold) cores and counterclockwise (clockwise) flow fields have recently been identified in the Kuroshio-Oyashio Extension (KOE) region. Here, traditional cyclonic cold-core eddies (CCEs) and anticyclonic warm-core eddies (AWEs) are termed normal eddies, and cyclonic warm-core eddies (CWEs) and anticyclonic cold-core eddies (ACEs) are called abnormal eddies. Applying a vector geometry-based automatic eddy detection method to the Ocean General Circulation Model for the Earth Simulator reanalysis data (OFES), a three-dimensional eddy dataset is obtained and used to quantify the statistical characteristics of these eddies. Results illustrate that the number of CCEs, AWEs, CWEs, and ACEs accounted for 38.46, 36.15, 13.40, and 11.99%, respectively. In the vertical direction, normal eddies are concentrated in the upper 2,000 m, while abnormal eddies are mainly found in the upper 600 m of the ocean. On seasonal scales, normal eddies are more abundant in winter and spring than in summer and autumn, with the opposite trend found for abnormal eddies. Potential density changes modulated by normal eddies are dominated by eddies-induced temperature anomalies, while salinity anomalies dominate the changes modulated by abnormal eddies. This study expands the types of eddies and enriches their understanding in the KOE region.

Effects of streamwise gust amplitude on the flow around and forces on two tandem circular cylinders

Three-dimensional large eddy simulations are carried out to investigate the effect of streamwise gust amplitude ratio AR on the flow structure around and dynamic forces on two tandem circular cylinders at a subcritical Reynolds number of Re = 1 × 103. The center-to-center space L between the two cylinders is fixed at 3.5D, where D is the cylinder diameter. The velocity U of sinusoidal streamwise gust is set as U = U0 (1+ARsin2πfut), where the velocity amplitude ratio AR is varied from 0 to 0.25, U0 is the mean velocity, fu is the frequency of the sinusoidal streamwise gust, and t is the time. In order to enhance the understanding of the streamwise gust effect on the physical properties of the flow around the two tandem cylinders, the shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), unsteady forces, and phase lag (φ) between the fluctuating lift forces of the two cylinders are explicated. The results show that the flow structure around the cylinders is sensitive to AR. A change in AR thus leads to modification of reattaching flow (AR ≤ 0.15) to co-shedding flow (AR ≥ 0.20). The St, fluctuating forces and φ thus jumps at the boundary between the reattaching and co-shedding regimes. A stronger gust effect appears on the fluctuating drag of the upstream cylinder than that of the downstream cylinder. Besides the dominant component of the fluctuating lift induced by the vortex shedding, two other components are observed with the frequencies equaling to the superposition and subtraction of the gust and vortex-shedding frequencies, respectively. In addition, two more cases with L/D = 1.5 and 6.0 are conducted for deeper understanding of AR effects.

Flow dynamics in lateral vegetation cavities constructed by an array of emergent vegetation patches along the open-channel bank

The hydrodynamics in a straight rectangular open channel containing novel lateral cavities constructed by an array of square emergent vegetation patches discontinuously distributed along the bank were explored numerically using three-dimensional large eddy simulations (LES). Five vegetation densities (Φ), ranging from 0.02 to 0.25, as well as the traditional lateral cavities created by impermeable solid media, were tested. The effects of the cavity aspect ratio (AR) were also examined. The LES results showed that the mean recirculation pattern inside the vegetation cavities and coherent structures in the horizontal shear layer were closely dependent on Φ and AR. When Φ ≥ 0.06, a main recirculation vortex that formed inside the vegetation cavities resembled that within solid media cavities, whereas the extent of the former increased upstream as Φ increased. Compared with the solid cases, the vegetation cavities exhibited a higher turbulent intensity within the shear layer and wider regions of enhanced turbulent kinetic energy, which decreased with increasing Φ. The penetration depth of the elevated turbulent kinetic energy into the cavities also decreased with increasing Φ, whereas a deeper penetration was expected at larger AR values. The interfacial turbulence was dominated by “cavities field”-scale coherent vortices at Φ ≤ 0.06, whereas “cavity element”-scale at Φ ≥ 0.15. When Φ = 0.1, the shear vortices of both scales contributed to the enhancement of the interfacial turbulence. The mean mass exchange showed a non-monotonic relationship with Φ and reached maximum values at Φ = 1. The total momentum transport efficiency decreased monotonically with increasing Φ. Despite the AR and Φ values, the turbulent motions dominated the momentum transport over most of the cavity length.

Large eddy simulation on a square cylinder near a plane boundary

Steady flow around the square cylinder with a plane boundary has been investigated through three-dimensional large eddy simulation in the present work. The influence of the gap ratio at high Reynolds number has been summarized by analysing hydrodynamic characteristics around the square cylinder with a plane wall boundary. A three-dimensional numerical mesh is built through structured mesh with multiple meshing strategies. The numerical results have a good agreement with the experimental results at high Reynolds number scenario. The influence of the plane boundary on the pressure distributions and averaged hydrodynamic characteristics has been quantified. The refinement of the meshing in the vicinity and the wake provides a solution to accurate predict the hydrodynamic forces and the flow structures for a near-wall square cylinder. A sharp pressure recovery is found next to the leading edge is ascribed to the flow reattachment at the lower surface. The vortex formation length Lf is found to be increased monotonically with the decrease of the gap ratio, which is ascribed to the extended lower recirculation due to the blockage effect. The maximum wake width W is observed at G/D = 0.5, corresponding to the large base pressure. The interaction of the Kelvin-Helmholtz vortices and von Kármán vortex street has been clearly captured through.

Fast Solution of 3-D Eddy-Current Problems in Multiply Connected Domains by a, v-φ and t-φ Formulations With Multigrid-Based Algorithm for Cohomology Generation

The fast solution of three-dimensional eddy current problems is still an open problem, especially when real-size finite element models with millions of degrees of freedom are considered. In order to lower the number of degrees of freedom a magnetic scalar potential can be used in the insulating parts of the model. This may become difficult when the model geometry presents some conductive parts which are multiply connected. In this work a multigrid-based algoritm is proposed that allows for a calculation in linear-time of cohomology, which is needed to introduce the scalar potential without cuts. This algorithm relies on an algebraic multigrid solver for curl-curl field problems, which ensures optimal computational complexity. Numerical results show that the novel algorithm outperforms state-of-the-art methods for cohomology generation based on homological algebra. In addition, based on this algoritm, novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a,v$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> formulations to analyze three-dimensional eddy current problems in multiply connected domains are proposed. Both formulations, after discretization by the cell method, lead to a complex symmetric system of linear equations amenable to fast iterative solution by Krylov-subspace solvers. These formulations are able to provide very accurate numerical results, with a minimum amount of degrees of freedoms to represent the eddy current model. In this way the computational performance is improved compared to the classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A,V$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> formulation typically implemented in finite element software for electromagnetic design.

Three dimensional flow over elliptic cylinders arrays in octagonal arrangement

A numerical study of flow characteristics around eight elliptic cross-section cylinders in an octagonal configuration is presented. The axis ratio of elliptic cylinder is taken as 1:2. Three spacings between the cylinders (0.07 m, 0.14 m and 0.2 m), two angles of attack (α=0° and α=15°) and two Reynolds numbers (Re=4060 and Re=45800) are considered to investigate the parametric influences. The flow is modelled using three-dimensional large eddy simulation. Simulations are performed by utilizing ANSYS Fluent software. The results comprise of flow patterns and force coefficients (drag and lift). It is seen that both the drag and lift forces acting on the cylinders vary with the spacings values, angle of attack and Reynolds numbers. The lift force peaks at α=15° and Reynolds number 45800. The drag force on the upstream cylinder reaches its peak at α=0° and Reynolds number 4060. It is observed that the drag on the upstream cylinders decreases as the value of the Reynolds number increases. Contours of velocity and subgrid turbulent viscosity are also presented. Moreover, it is concluded from the present study that the effect of change in the Reynolds number on flow characteristics is more significant as compared to the change in the spacing between the cylinders.

Research on Life Loss of Generator Retainer Caused by Negative Sequence Current

With a large number of wind and solar power sources connected to the power grid, higher requirements are put forward for the power generation equipment to respond to the power grid imbalance. The safety research of generator rotor retaining ring under the impact of negative sequence current is of great significance. For 300MW turbogenerator, the two-dimensional and three-dimensional eddy current, temperature rise, stress and life of generator rotor under the impact of negative sequence current are analyzed and studied. The two-dimensional calculation models of stator and rotor are established, and the distribution of negative sequence eddy current field in rotor section is analyzed; considering the contact resistance between rotor and retaining ring and the end effect of magnetic field, a three-dimensional analysis model is established, and the calculation results of three-dimensional eddy current field, temperature field and stress field are obtained. The analysis shows that after considering the contact resistance between rotor and retaining ring and end effect, the current density at the contact between retaining ring and rotor big tooth edge is 17.6 times of the two-dimensional calculation result of rotor section, and the maximum temperature of rotor retaining ring reaches 170.36°C.

Numerical study on vortex-induced vibration of circular cylinder with two-degree-of-freedom and geometrical nonlinear system

The vortex-induced vibration (VIV) of circular cylinder in uniform flow with two-degree-of-freedom (2DOF) and geometrical nonlinear system is investigated numerically using the combined sliding and layering dynamic meshes. The characteristics of vibration amplitude, fluid force coefficients, branching behaviour, vibration trajectory, energy transfer and flow pattern of circular cylinder in VIV are studied with two-dimensional shear stress transfer (SST) k-ω turbulence model and three-dimensional large eddy simulation (LES). It is found that in the simulation with LES model the predicted vibration amplitude and fluid force coefficients show good agreement with the experimental data, while in the simulation with SST k-ω model these parameters are significantly underestimated. The two triplets (2T) vortex shedding mode happens in the super upper branch of circular cylinder with 2DOF linear system and leads the large-magnitude positive energy transferring from fluid to cylinder, which causes the maximum vibration amplitude. For the circular cylinder with 2DOF nonlinear system, the vibration simulated by LES model shows a galloping-like phenomenon that the amplitude keeps increasing with the reduced velocity Ur. The crescent-shaped trajectory and the 2T vortex shedding mode happen upon the critical Ur, which is similar to that in the super upper branch of circular cylinder with 2DOF linear system. This phenomenon is caused by the amplitude-dependent stiffness of nonlinear system and the modified reduced velocity U∗ reveals the universality of vibration amplitude for the circular cylinders with linear and nonlinear systems.

Experiments and Simulations of Free-Surface Flow behind a Finite Height Rigid Vertical Cylinder

We present the results of a combined experimental and numerical study of the free-surface flow behind a finite height rigid vertical cylinder. The experiments measure the drag and the wake angle on cylinders of different diameters for a range of velocities corresponding to 30,000 &lt;Re&lt; 200,000 and 0.2&lt;Fr&lt;2 where the Reynolds and Froude numbers are based on the diameter. The three-dimensional large eddy simulations use a conservative level-set method for the air-water interface, thus predicting the pressure, the vorticity, the free-surface elevation and the onset of air entrainment. The deep flow looks like single phase turbulent flow past a cylinder, but close to the free-surface, the interaction between the wall, the free-surface and the flow is taking place, leading to a reduced cylinder drag and the appearance of V-shaped surface wave patterns. For large velocities, vortex shedding is suppressed in a layer region behind the cylinder below the free surface. The wave patterns mostly follow the capillary-gravity theory, which predicts the crest lines cusps. Interestingly, it also indicates the regions of strong elevation fluctuations and the location of air entrainment observed in the experiments. Overall, these new simulation results, drag, wake angle and onset of air entrainment, compare quantitatively with experiments.

The early-time dynamics of Rayleigh-Taylor mixing with a premixed layer

The early-time dynamics of Rayleigh-Taylor instability with a premixed density gradient layer was investigated by three-dimensional implicit large eddy simulation. Compared with the classic Rayleigh-Taylor instability, it was found that the mixing layer undergoes an inactive stage when the mixing width of the layer is nearly unchanged. The development of hydrodynamic instability with a premixed layer was studied. Energy transfer and vortex generation at the early time show that span-wise vortices predominate at this stage. Afterwards, initial conditions including the parameters of initial perturbations and the mixing width of premixed layer were investigated in detail. In our study, it was found that the amplitude of initial perturbations and the width of premixed layer are important for determining the characteristic time scale of the inactive stage while the wave number has less effect. The influence of initial conditions on the early-time dynamics of mixing layer was also analysed.

Pumping ventilation of corner and single sided rooms with two openings

Corner rooms with two or more open windows in perpendicular facades can be naturally ventilated in cross-ventilation or pumping ventilation. These two airflow regimes also occur in rooms with two openings in the same façade, in the form of single sided pumping or cross sided ventilation. This paper presents an experimental and numerical simulation study of the scale and occurrence of these two flow regimes for rooms in a rectangular building exposed to wind. Flow visualization and tracer gas measurement of effective airflow were performed in an atmospheric boundary layer wind tunnel using a rectangular model of a three-story building (1/20 scale) with a ventilated middle floor. Experimental results show that pumping ventilation occurs when the wind is perpendicular to the façade (single sided rooms) or aligned with the building corner (corner rooms). In addition to these two perfectly aligned wind directions, pumping also occurs for a range of incoming wind angles: ±19° for single sided; and ±9° for corner rooms. As a result, for isolated rectangular buildings that have, at least, one single sided and two corner rooms in each facade, pumping ventilation can potentially occur in two or more rooms for 62 % of incoming wind directions. To investigate the transition between steady cross-ventilation and unsteady pumping ventilation, three-dimensional computational fluid dynamics large eddy simulations were performed to obtain wind generated pressures in the ventilation openings. Results show that the transition from cross-ventilation to pumping occurs when the steady pressure becomes smaller than the unsteady component. These results are used to develop a pressure based simplified model for corner ventilation that can predict effective airflow from external wind generated pressures with an average error below 10.2 %.

Three-dimensional mesoscale eddy identification and tracking algorithm based on pressure anomalies

Three-dimensional mesoscale eddy identification and tracking algorithm based on pressure anomalies

Detailed numerical simulations of low-temperature oxidation of NOx by ozone

Limiting gaseous nitrogen oxide (NOx) emissions is a major global concern due to their harmful effect on human health and the environment. During the past decade, low-temperature oxidation by ozone (O3) has emerged as a promising solution for NOx removal in the transportation and energy generation sectors. In the present study, three-dimensional (3D) large eddy simulations (LES) of the turbulent reacting flow inside a NOx-O3 reactor are performed. It is the first publication using LES and detailed finite rate chemistry for such a reactor. Additionally, plug-flow reactor (PFR) simulations are employed to identify the best performing chemical kinetic mechanisms among those available in the literature over the range of conditions studied. Furthermore, results from different experimental works are reviewed to analyze the variability in the literature. Additionally, this will aid in devising a strategy for validation. Time-averaged results obtained from PFR and combined LES-PFR simulations are observed to agree well with experimental results. The species correlation, distribution, and overall flow uniformity in the pure LES simulations are also assessed and the results highlight the benefits of a high mixing efficiency reactor geometry. Moreover, relevant features of the unsteady flow throughout the present reactor are studied. In particular, the analysis of coherent structures and the existence of regions with non-reacted gases and their relation to mixing and NOx oxidation efficiency are evaluated. The present simulations enable a novel understanding of the interplay between mixing and chemistry and highlight, for the first time, details of the oxidation of NOx by O3.

Numerical investigation of flow structures and aerodynamic interference around stationary parallel box girders

Many parallel bridges have been recently designed and built around the world to accommodate the ever-increasing volumes of vehicle and rail traffic. Accordingly, the aerodynamic interference around the parallel girders becomes important to investigate for a more accurate estimation of wind-induced effects on bridges. In this study, a wide range of gap-width ratios (0–15) for parallel box girders are selected to investigate the aerodynamic interference using three-dimensional large eddy simulation at zero wind attack angle. Specific aerodynamic characteristics, including the flow structures, pressure distributions, mean values and standard deviations of the force coefficients, Strouhal number as well as spanwise correlations of the aerodynamic coefficients are examined with various gap-width ratios. The detailed comparison work demonstrates a good agreement with the experimental work. The simulation results reveal that all the aerodynamic characteristics are significantly influenced by the gap-width ratio. The three regions are bounded by critical gap-width ratios of G/B = 0.25 and G/B = 5. There are large changes in behavior at G/B = 0.25, whereas, for G/B > 5, interference effects are not evident. The interference effects on both mean and fluctuating aerodynamic coefficients of parallel box girders are also quantified and summarized.

Vortex Dynamics and Instability Mechanisms in a Radially Lobed Nozzle

AbstractThe application of radially lobed nozzles has seen renewed challenges in the recent past with their roles in combustion chambers and passive flow control. The free jet flow from such nozzles has been studied for different flow conditions and compared to jets from round nozzles, verifying their improved mixing abilities. The precise mixing mechanisms of these nozzles are, however, not entirely understood and yet to be analyzed for typical jet parameters and excitation modes. This study carries out three-dimensional large eddy simulations (LESs) of the flow from a tubular radially lobed nozzle to identify instability mechanisms and vortex dynamics that lead to enhanced mixing. The flow is studied at two Reynolds numbers of around 6000 and 75,000, based on the effective jet diameter. The low Reynolds number jet is compared to that from a round nozzle and experimental data to demonstrate changes in mixing mechanisms. The present simulations confirmed the presence of Kelvin–Helmholtz (K–H)-like modes and their evolution. The analysis also confirms the evolution of three distinct types of structures—the large-scale streamwise modes at the lobe crests, corresponding K–H structures at the troughs, and an additional set of structures generated from the lobe walls. The higher Reynolds number simulations indicate changes in the mechanics with a subdued role of the lobe walls.

Towards multiscale modeling of ocean surface turbulent mixing using coupled MPAS-Ocean v6.3 and PALM v5.0

Abstract. A multiscale modeling approach for studying the ocean surface turbulent mixing is explored by coupling an ocean general circulation model (GCM) MPAS-Ocean with the Parallelized Large Eddy Simulation Model (PALM). The coupling approach is similar to the superparameterization approach that has been used to represent the effects of deep convection in atmospheric GCMs. However, the focus of this multiscale modeling approach is on the small-scale turbulent mixing and their interactions with the larger-scale processes in the ocean, so that a more flexible coupling strategy is used. To reduce the computational cost, a customized version of PALM is ported on the general-purpose graphics processing unit (GPU) with OpenACC, achieving 10–16 times overall speedup as compared to running on a single CPU. Even with the GPU-acceleration technique, a superparameterization-like approach to represent the ocean surface turbulent mixing in GCMs using embedded high fidelity and three-dimensional large eddy simulations (LESs) over the global ocean is still computationally intensive and infeasible for long simulations. However, running PALM regionally on selected MPAS-Ocean grid cells is shown to be a promising approach moving forward. The flexible coupling between MPAS-Ocean and PALM allows further exploration of the interactions between the ocean surface turbulent mixing and larger-scale processes, as well as future development and improvement of ocean surface turbulent mixing parameterizations for GCMs.

Numerical study and buoyancy–drag modeling of bubble and spike distances in three-dimensional spherical implosions

High-resolution three-dimensional implicit large eddy simulations of implosion in spherical geometries are presented. The growth of perturbations is due to Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and also to geometric convergence and compression effects. RM and RT instabilities have been studied extensively in planar configurations, but there are comparatively few studies on spherical geometries. Planar geometries lack the effect of convergence that changes the morphology and growth of perturbations in spherical geometries. This paper presents a study of turbulent mixing in spherical geometries considering different narrowband (NB) and broadband multimode initial perturbations and examines several quantities including the evolution of the integral mixing layer width and integral bubble and spike heights using novel integral definitions. The growth of the bubble and spike is modeled using a Buoyancy–Drag (BD) approach that is based on simple ordinary differential equations to model the growth of the turbulent mixing layer. In a recent study, Youngs and Thornber [“Buoyancy-drag modelling of bubble and spike distances for single-shock Richtmyer-Meshkov mixing,” Physica D 410, 132517 (2020)] constructed modifications to the BD equations to take into account the early stages of the mixing process that are dependent on the initial conditions. Those modifications are shown to be important to obtain correct results. The current study adopted the same modifications and adapted the BD equations to the spherical implosion case. The results of the BD model are compared with those of different initial NB cases that include different initial amplitudes and wavelengths of the perturbations, for validation purposes. The predictions from the new BD model are in very good agreement with the numerical results; however, there exist some limitations in the accuracy of the model, in particular the use of the interface position and fluid velocity from one-dimensional data.

Numerical study on reducing aerodynamic drag and noise of circular cylinders with non-uniform porous coatings

This paper presents a numerical study on the flow and noise control of circular cylinders with non-uniform porous coating over the circumference in the subcritical flow regime (Re=4.7×104). A numerical method is employed that combines three-dimensional large eddy simulation (LES) with Ffowcs Williams-Hawkings (FW-H) acoustic analogy, and is validated by comparing with available experimental and numerical data of flow over circular cylinders. The numerical results show that applying high-porosity material in the separation zone is most effective on reducing aerodynamic drag and noise. This partial high-porosity coating enhances the slip velocity at the porous-fluid interface, stabilizes shear layers detached from the cylinder, and hence suppresses vortex shedding, as well as raising the base pressure on the leeward side and reducing drag. A high-porosity coating with a 60∘ circumferential coverage of the separation zone is found to be a cost-effective configuration in controlling both drag and noise. Varying the porosity on the leeward side of a cylinder, however, shows slight differences on flow and acoustic characteristics. This study is expected to provide some useful information for porous coated cylinders aimed at flow and noise control towards practical applications with constrains on coating area.

Large eddy simulations of solitons colliding with intrusions

The dynamics of lock-release Intrusive Gravity Currents (IGCs) generating Internal Solitary Waves (ISWs) are investigated by three-dimensional large eddy simulations. We set the numerical, laboratory-scale domain in order to release a uniform fluid in multi-layer, stratified ambient, exciting pycnocline displacements. By adopting different initial settings, we analyzed the influence of the ambient stratification on both IGCs and ISWs features. We present the main flow dynamics and the time evolution of IGC and ISW front and trough positions, respectively. During the simulations, the ISW is allowed to reach the vertical wall at the end of the domain, and it undergoes reflection. We then analyzed the interaction between the IGC and the reflected ISW: the wave is observed to accelerate as it is pushed upwards by the intrusion, which, in turns, flows below the ISW, decelerating. By analyzing instantaneous velocity fields and flow rates, we found that during this interaction, the ISW increases its celerity in response of the reduced area available for its propagation, partially occupied by the intrusion, and because the velocity field in the IGC interface surroundings acts to facilitate the ISW passage.

Mechanism of low frequency high amplitude pressure fluctuation in a pump-turbine during the load rejection process

ABSTRACT Owing to the complexity of the load rejection process, the accompanied complex low frequency pressure fluctuations and their sources have not been determined. Herein, the load rejection transient process of a pump-turbine was simulated with a three-dimensional (3-D) large eddy simulation method and a dynamic mesh technology. The simulation results were validated against the experimental data. Through the joint time-frequency analysis of simulated pressure, the complex low frequency pressure fluctuation components were captured, which are generally lower than the rated rotational frequency of the runner. A comprehensive formation mechanism of these complex low frequency pressure fluctuation components was attributed to three transient hydraulic phenomena and their interactions: the water hammer in the pump-turbine, local reverse flow near the runner inlet, and 3-D blocking water ring in the vaneless space. These findings facilitate the elucidation and elimination of complex low frequency high amplitude pressure fluctuations during the load rejection transient process.