Impact erosion prediction using the finite volume particle method with improved constitutive models

Erosion damage in hydraulic turbines is a common problem caused by the high- velocity impact of small particles entrained in the fluid. In this investigation, the Finite Volume Particle Method is used to simulate the three-dimensional impact of rigid spherical particles on a metallic surface. Three different constitutive models are compared: the linear strain- hardening (L-H), Cowper-Symonds (C-S) and Johnson-Cook (J-C) models. They are assessed in terms of the predicted erosion rate and its dependence on impact angle and velocity, as compared to experimental data. It has been shown that a model accounting for strain rate is necessary, since the response of the material is significantly tougher at the very high strain rate regime caused by impacts. High sensitivity to the friction coefficient, which models the cutting wear mechanism, has been noticed. The J-C damage model also shows a high sensitivity to the parameter related to triaxiality, whose calibration appears to be scale-dependent, not exclusively material-determined. After calibration, the J-C model is capable of capturing the material’s erosion response to both impact velocity and angle, whereas both C-S and L-H fail

GPU-Accelerated Finite Volume Particle Simulation of Free Jet Deviation by Multi-jet Rotating Pelton Runner

Numerical simulation of Pelton turbine hydrodynamics is helpful to identify the energy loss mechanisms in the runner and minimize their effect. However, it is a challenging task that involves handling the unsteady free surface flow and moving boundaries requiring dynamic mesh approach, as well as run-time local grid refinements at the interphase. Unlike the mesh-based methods, the Lagrangian particle-based methods are robust in handling free surface problems with moving boundaries such as Pelton turbine flow. Within the framework of the present research, the 3-D Finite Volume Particle Method (FVPM) has been developed and accelerated on Graphics Processing Unit (GPU). FVPM is locally conservative and consistent, employing an Arbitrary Lagrangian-Eulerian (ALE) approach for particle motion to achieve a reasonably uniform particle distribution. The method is based on spherical-support top-hat kernels in which the particle interaction vectors are computed and used to weigh the conservative flux exchange. To capture the turbulence, the standard and realizable k-¿ as well as k-¿ Shear Stress Transport (SST) turbulence models have been implemented and integrated into ALE based FVPM. The wall function approach has been used for near-wall turbulence computations. The solver is called GPU-SPHEROS and has been implemented from scratch in the CUDA C++ parallel computing platform. All the parallel algorithms and data structures have been designed speci¿cally for the GPU many-core architecture. The roofline analysis method has been utilized to assess the performance of the CUDA kernels and define the appropriate optimization strategies. In particular, the neighbor search algorithm, accounting for almost a third of the overall computation time, features an e¿cient Space-Filling Curve (SFC) as well as an optimized octree construction and traverse procedure. The memory-bound interaction vector computation, accounting for almost two-thirds of the overall computation time, features ¿xed-size memory pre-allocation, and an e¿cient data ordering to reduce memory transactions and avoid the cost of dynamic memory operations. A speedup by a factor of almost six times has been achieved for a single NVIDIA® TeslaTM P100 16GB GPU with GP100 Pascal architecture vs. a dual-setup Broadwell Intel® Xeon® E5-2690 v4 CPU node with 28 total physical cores. Once GPU-SPHEROS validated, it is used for jet interference investigation in a six-jet Pelton turbine as an industrial-size practical application. The numerical simulations have been performed at eight operating points ranging from N / N_BEP = 89% to N / N_BEP = 131%, where N is the runner rotational speed, and BEP is the Best Efficiency Point. It is shown by the numerical results that a significant torque and efficiency drop occurs at high speed factors due to jet interference, whereas large load fluctuations caused by jet disturbance can occur at about any N not equal to N_BEP. Compared to the available experimental data provided by Hitachi-Mitsubishi Hydro Corporation, the torque and efficiency trends, as well as the range of the specific speed in which the jets interfere, are well-predicted, which provides confidence in the use of the GPU-SPHEROS for the design optimization of Pelton turbines. All the multi-jet Pelton turbine computations have been performed on Piz Daint, a GPU-powered supercomputer with 5¿704 GPU nodes, developed and operated by Swiss National Supercomputing Centre - CSCS

Multiscale simulation of erosive wear in a prototype-scale Pelton runner

The technical capacity to predict the erosion process is instrumental for the optimization of the runner designs and operation strategies of hydroelectric plants. A multiscale model of erosion recently formulated by the authors and validated on a laboratory-scale jet impingement case is used to study the erosion of a prototype-scale Pelton runner. The model is shown to provide physically-sound descriptions of the sediment impact condition distributions on the bucket surface; furthermore, the erosion distribution obtained is explained in terms of these underlying impact condition distributions. The model predictions for the erosion depth distribution on the bucket surface are validated with the corresponding experimental data, resulting in an average error of 35% for eight point-wise comparisons, 14% for line-averaged values along four transversal sections, and 4% for the surface-averaged erosion depth, directly linked to the total eroded mass. A careful error propagation analysis of the comparison between simulation and field data yields an uncertainty of ±22%. Based on these considerations, the modeling error is estimated to be 26±22%. The results obtained, namely quantitative predictions of the erosion of industrial-scale hydraulic machines, have no precedent in the literature; they demonstrate the accuracy and transferability of the multiscale model of erosion and suggest an improvement over the state-of-the-art computational fluid dynamics models based on empirical erosion correlations

A multiscale model for sediment impact erosion simulation using the finite volume particle method

The erosion of a surface by a sediment-laden flow is an inherently multiscale phenomenon which includes physical interactions covering many orders of magnitude in both length and time scales. Conforming to the nature of the problem, we propose a novel multiscale model for simulating this complex process. On the one hand, a macroscale model encompassing the whole domain of interest solves the turbulent sediment transport problem. On the other hand, a microscale model simulates the sediment impacts against the surface. A sequential multiscale strategy is used to link the sub models, such that the microscale model provides closure to the macroscale model in terms of the calculated steady state erosion rate and restitution coefficients, therefore reproducing the original coupled problem. The proposed methodology is validated against experimental data for the slurry jet erosion of a copper plate at three impingement angles. Both the global erosion rate and the erosion depth profile are predicted with mean relative errors of 18% compared to the corresponding experimental values, achieving a significant improvement over correlation-based approaches

Simulation of the hydroabrasive erosion of a bucket: A multiscale model with projective integration to circumvent the spatio-temporal scale separation

The hydroabrasive erosion of hydraulic machine components, especially Pelton buckets and needles, is a widespread problem that entails significant costs. The multiscale nature of the process renders its simulation very computationally demanding unless specific strategies are used to approach it. A previously validated multiscale model of erosion that tackles the problem of spatial scale separation is presented. It involves two coupled submodels that describe the microscopic sediment impacts and the macroscopic turbulent sediment transport, respectively, without introducing the uncertainty inherent to empirical erosion correlations. As a further step and in order to circumvent the temporal scale separation, a novel projective integration scheme is introduced. It allows simulating the erosion process for long time periods, including the eroded surface evolution and its effect on the flow field. The proposed model is tested on a 2D case involving a bucket being eroded by a slurry jet. The results are compared qualitatively with experimental data on Pelton buckets. The main features of the erosion distribution, the surface transformation and its effect on the flow are captured correctly

Multiscale Simulation of the Hydroabrasive Erosion of a Pelton Bucket: Bridging Scales to Improve the Accuracy

Erosive wear of hydraulic machines is a common issue, which results in efficiency degradation, the enhancement of cavitation, and the need for expensive maintenance. Although numerical simulations of the erosion process could be very useful, both for understanding and predicting the process, its multiscale nature renders it very difficult to simulate. A previously validated multiscale model of erosion is presented. It consists of two coupled sub-models: On the microscale, the sediment impacts are simulated by means of comprehensive physical models; on the macroscale, the turbulent sediment transport and erosion accumulation are calculated. A multiscale simulation of the erosion of a prototype-scale Pelton bucket impacted by a sediment-laden water jet is presented. The simulation results, namely the erodent flux and the distributions of average impact angle and velocity on the bucket surface, bring insight into the erosion process. Furthermore, the results explain the obtained erosion distribution, which is in very good agreement with the experimental erosion measurements available in the literature for the same test case

FVPM numerical simulation of the effect of particle shape and elasticity on impact erosion

The erosion of hydraulic machines by solid particle impacts is a widespread problem that leads to outage for expensive repairs, efficiency reduction, and cavitation enhancement. Numerical simulations can be used to study the phenomenon, provided they feature accurate thermomechanical and contact modeling. Numerical investigations often assume that the impacting particles are spherical and rigid, with only some recent studies modeling them as elastic polyhedrons or spheres. However, in the specific case of the erosion of hydraulic machines, particles are far from spherical or polyhedral and are less rigid than the base material. The present investigation focuses on the effect of the particle shape and elasticity on the erosion of oxygen-free copper and martensitic stainless steel 13Cr-4Ni impacted by quartz sediments. First, a novel algorithm to generate realistically-shaped sediment discretizations is presented, bypassing the need to use simplified shapes such as polyhedrons. The algorithm is shown to produce particle discretizations of predefined characteristic size that closely follow the objective sphericity value selected, which can cover the full range of sphericity values found in real sediments. Then, the effect of the particle elasticity on the impact damage is investigated, revealing that an error of up to 38 % is introduced by assuming that the particles are rigid. The effect of the particle shape is then assessed. For the case of copper, sharp sediments generate an increase in damage per unit mass of up to 225 % with respect to spherical particles; a comparable effect is expected on the erosion rate. For the martensitic stainless steel, the shape effect is similar in character but significantly weaker in magnitude. The results are analyzed and explained in terms of the known erosion mechanisms and their dependence on the particle shape, the material ductility and hardness