Evaluation of cavitation-induced pressure loads applied to material surfaces by finite-element-assisted pit analysis and numerical investigation of the elasto-plastic deformation of metallic materials

doi:10.1016/j.wear.2014.12.048

Wear

Volumes 330–331, May–June 2015, Pages 618-628

https://doi.org/10.1016/j.wear.2014.12.048 Get rights and content

Highlights

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We reconstructed cavitation-induced pressure loads applied to material surfaces.
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The maximum pressure loads were calculated (FEM algorithm) to 2400–3500 MPa.
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The numerically calculated deformation under cavitation load is highly elastic.
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Small and deep cavitation pits show the highest damaging potential.
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CFD simulations are used for reconstructing possible bubble collapse configurations.

Abstract

Implosion of cavitation bubbles close to a material applies a high pressure load on the surface that leads to cyclic, elasto-plastic deformation followed by damage and loss of material. The load strongly depends on the flow conditions and its experimental determination is extremely difficult. This study presents a method for quantitative calculation of the pressure loads induced by collapsing bubbles. This method is based on the analysis of pits on the material surface formed within the incubation period. The pits are footprints of collapsing bubbles and are measured by atomic force microscopy (AFM). An inverse algorithm based on finite element method (FEM) simulations is then used to determine the pressure load that is necessary to form the measured pits. The pressure fields, which are assumed to be axially symmetric (bell-shape profile), were calculated for cavitation pits formed in pure copper. The pits were induced by short-term exposure to cavitation in an ultrasonic cavitation testing device. Additionally, the elasto-plastic deformation of copper was numerically (FEM) investigated for a given cavitation load. It was found that the deformation is mostly elastic and that the maximum stress is located in a subsurface region. The maximum pressure of the cavitation load, the resulting maximum plastic strain in the material, and the ratio of the elastic to total deformation work correlate well with the ratio of pit width to pit depth. In order to evaluate the simplified assumption of a static pressure profile (bell-shape), the calculated pressure loads were critically compared to those determined by a detailed single bubble simulation with a compressible CFD flow algorithm. The maximum pressure profiles of the highly-transient CFD results show partly significant deviations dependent on the non-dimensional bubble stand-off distance to the wall. An improved pressure load profile and transient effects will be considered next in the FEM algorithm.

Introduction

Cavitation in hydraulic fluid machinery such as pipes, valves, ship propellers, pumps, and turbines leads to wear of their components (cavitation erosion). Consequences of cavitation erosion include negative effects such as failure of components, reduction in efficiency, noise, or vibration [1]. Cavitation erosion is attributed to the collapse of individual cavitation bubbles in the vicinity of the material׳s surface [2]. Repeated collapses apply local cyclic pressure loads to the surface, which lead to damage and loss of material [3]. Quantitative knowledge of the induced pressure loads is crucial for understanding the material behavior and the underlying deformation processes. Thus, a precise understanding of cavitation erosion of materials implies a detailed knowledge of both the material behavior and the applied load.

Much research has been focused on the deformation processes of materials under cavitation load [4], [5], [6], [7], [8], [9], [10]. However, it is difficult to obtain detailed and quantitative knowledge of the load induced by cavitation due to the extremely small scales of duration and localization on the surface. One possible method of measuring the impact pressure is to use pressure sensors such as piezoelectric films [11]. However, these sensors do not generally provide an accurate measurement under the present conditions [12], [13]. Another method of estimating the pressure load is the analysis of pits formed on the material surface within the incubation period. The pits are the footprints of collapsing bubbles and are formed due to the high local pressure by plastic deformation. Tzanakis et al. investigated pits caused by collapsing bubbles in an ultrasonic test device and estimated the corresponding pressures with the analogy of spherical indentation [12]. They determined impact pressures in the range of approx. 400–1400 MPa. Carnelli et al. analyzed cavitation pits caused by a cavitation field in a hydrodynamic tunnel [13]. Using the analogy of spherical indentation and instrumented indentation testing, they determined peak loads of hydrodynamic pressures to be approx. 1000–1600 MPa. Lauer et al. used numerical simulations to calculate single bubble collapse events leading to pressure loads on the material surface of up to approx. 6000 MPa [14].

These different estimates show that the load strongly depends on the flow conditions. Thus, results cannot be transferred to different fluid machineries or test devices. For these reasons, the cavitation-induced loads on materials are not known for most fluid machineries or cavitation erosion test devices.

The resistance to cavitation erosion is often tested in ASTM G32 standardized vibratory apparatus (ultrasonic transducer) [15]. In spite of, being a standardized test, the local pressure loads caused by collapsing bubbles are not known. This paper presents a method for the quantitative calculation of the pressure loads induced by collapsing bubbles. The method is applied to cavitation pits formed in the standardized ultrasonic vibratory apparatus. In analogy to the approach of Tzanakis et al. and Carnelli et al., the method is based on the analysis of cavitation pits that form within the incubation period [12], [13]. However, a FEM-based inverse algorithm is used to calculate the pressure field that is necessary to form a given pit, taking into account the local strength of the material. In addition, FEM simulations give an insight into the deformation processes of the material and create a link between load and deformation.

In this study, single, non-overlapping cavitation pits are analyzed in order to calculate the corresponding pressure that is necessary to form the pits. However, it is also known that cavitation clouds occur and the resulting pressure loads might be higher and more complex compared to single collapsing bubbles [16]. In addition, attention must be paid to the influence of strain rate or temperature, which are not taken into account. The extremely rapid bubble collapse and high deformation speed as well as an increase in temperature may influence the deformation behavior [17], [18]. The pressure field in the FEM model is assumed to be axially symmetric with a pressure maximum located at the axis of symmetry and calculated for this ideal shape (see Section 2.5). Due to these assumptions the pressures determined by the inverse algorithm based on pit analysis are compared to the load profiles calculated from CFD simulations of near-wall vapor bubble collapses. The CFD simulations are also used to try a first reconstruction of possible bubble collapse scenarios that lead to the pressure calculated with the FEM-based algorithm.

This paper addresses following issues:

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Determination of the pressure applied locally to material surfaces by collapsing cavitation bubbles in the standardized ultrasonic vibratory apparatus. The pressure loads, which are assumed to follow an idealized axially symmetric shape, are reconstructed with a numerical (FEM) inverse algorithm based on the pit analysis. Due to the assumptions made within the inverse algorithm wall pressures are additionally calculated with single bubble CFD simulations.
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Numerical analysis (FEM) of the elasto-plastic deformation processes of pure copper under the calculated pressure loads with the FEM-based inverse algorithm.
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Relating the measured pit geometries, calculated pressures, and material deformation to each other.
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Comparing pressures calculated from the pit geometry to those determined by the detailed CFD single bubble simulation and reconstruction of possible bubble collapse scenarios.

Section snippets

Material and methods

The experimental and numerical procedures for calculating the cavitation-induced pressure loads based on measured pit geometries are summarized in Fig. 1. The key element is an inverse algorithm that compares a measured to a numerically calculated pit geometry. The numerical pit geometry is calculated with a finite-element-method (FEM) model with an assumed pressure distribution p(x) acting on the surface. The pressure field p(x) is subsequently adjusted until the numerically calculated pit

Results and discussion

Fig. 8(a) shows the mean load–displacement curves of the copper specimen measured with the Berkovich and cube corner indenters. Fig. 8(b) shows the hardness as a function of the indentation depth. The hardness (strength) of the material increases with decreasing indentation depth. This is caused by the mechanical sample preparation and is superimposed by the ISE. The measured load–displacement curves were used to determine the depth-dependent material parameters given in Fig. 5 using an inverse

Conclusions

This paper presents a method for calculating the cavitation-induced pressure loads on material surfaces based on the analysis of single cavitation pits and CFD simulations. The results create a link between the cavitation load and material deformation. In combination with FEM simulations, they provide an insight into the deformation behavior of copper under cavitation loading. We also propose a numerical approach based on CFD for reconstructing possible bubble wall collapse configurations ( $L_{0} / R_{0}$

Acknowledgments

The authors gratefully acknowledge financial support by the Kompetenzzentrum Hydraulische Strömungsmaschinen at the Ruhr-Universität Bochum (Germany).

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