Unified empirical relations for cavitation and liquid impingement erosion processes

Several attempts have been made in the past to predict erosion due to cavitation and liquid impingement. Most of the models and formulations suffer certain deficiencies so that they do not adequately predict the magnitude of erosion, particularly during the acceleration period and for long-term exposure. This report presents a power-law relationship between average erosion rate and cumulative erosion during the acceleration and deceleration zones of erosion for copper, brass and stainless steel specimens examined in a rotating disk device. Data analyses from other types of erosion devices, including venturi, magnetostriction and liquid jet impingement, conform to the present unified relation. This agreement is indicative of the similar nature of erosion in the acceleration and deceleration zones. Attempts are made to understand the relationship between the coefficients in the power-law relation and the material properties.     

Cavitation and high-velocity slurry erosion resistance of welded Stellite 6 alloy

The cavitation and slurry erosion resistances of Stellite 6 coatings and 13-4 stainless steel were compared in laboratory. The Cavitation Resistance (CR) was measured according to ASTM G32 standard and the Slurry Erosion Resistance (SER) was tested in a high-velocity erosion tester under several impact angles. The results showed that the coatings improved the CR 15 times when compared to bare stainless steel. The SER of the coatings was also higher for all the impingement angles tested, the highest erosion rate being observed at 45°. The main wear mechanisms were micro-cracking (cavitation tests), and micro-cutting and micro-ploughing (slurry erosion tests).     

Introduction to the microscopy of erosion

Erosion of materials by the impact of small solid particles, by the impact of liquid drops and by cavitation in a liquid is discussed. Erosion arising from these three sources is described, terminology is defined, and the methods available for erosion testing in the laboratory are reviewed. A brief discussion is presented of the microscopical techniques which have been used to study erosion, and some of their advantages and drawbacks are outlined.     

A unified relation for cavitation erosion

A power-law relationship between average erosion rate and cumulative erosion has been presented. Data analysis from Venturi, magnetostriction, and liquid impingement devices conform to this unified relation. A normalization technqiue is also suggested for prediction purposes.     

Cavitation erosion of aluminum considering bubble collapse,pulse height spectra and cavitation erosion efficiency

Water erosion data on 1100-0 aluminum specimens obtained using a cavitating venturi are compared with bubble collapse pulse height spectra measured using a microtransducer. The data are resolved into erosion power and acoustic power. The former is defined in terms of the power applied to the eroded material to cause the observed pitting and volume loss. The ratio between these power quantities is termed the cavitation erosion efficiency η incav and is found to be essentially constant for the range of tests, being approximately 1.4 × 10^?6. The acoustic power which is easily measured can then be used to estimate the eventual material volume erosion rates, i.e. the mean depth of penetration (MDPR), with much greater accuracy than is otherwise possible. The MDPR is measured directly from the weight loss and is calculated from individual pit counts on damaged surfaces. The effects of the degree of cavitation (the extent of the cavitation cloud or the cavitation number) and the throat velocity on the MDPR is examined. An overall velocity damage exponent of n = 4.75 is found.     

Effect of microstructure on the erosion of steel by solid particles

The effect of microstructure on the erosion of AISI-SAE 1078 and 10105 steels by 240 grit A1₂O₃ particles was investigated at particle velocities V of 40–100 m s^?1 and angles of impingement a of 10°–90° relative to the target surface. The microstructures investigated included spheroidite, pearlite, martensite and tempered martensite.Spheroidite and pearlite microstructures eroded by the ductile mode at all velocities, exhibiting a maximum erosion rate at an impingement angle of 40°. The effect of the angle of impingement on the erosion rate of martensite and tempered martensite varied with particle velocity, the erosion mode tending towards a brittle mode with increasing velocity. At all angles of impingement the erosion rate tended to increase with the volume fraction of Fe₃C. Examination of the eroded surfaces by scanning electron microscopy showed the occurrence of localized plastic flow of appreciable magnitude. No subsurface cracking or void formation was evident. The erosion rate E_r could be considered to vary with particle velocity according to the power law E_r = kVⁿ where n has a value of about 2 independent of the microstructure and the angle of impact.     

An application of bubble collapse pulse height spectra to venturi cavitation erosion of 1100-o aluminum

Venturi cavitation erosion tests were performed and correlated with bubble collapse pulse height spectra measured by a microtransducer. The effects of the throat velocity and the cavitation number σ (referred to the downstream pressure and throat velocity) on the erosion rate (MDPR) were studied. The velocity damage exponent was 4.11 for 0.62 ? σ ? 0.80, while the MDPR is almost independent of velocity for σ = 0.85. The MDPR decreases with increased σ for 0.62 ? σ ? 0.85. The data were reduced to “acoustic power” (from pulse height spectra) and “erosion power” (the ultimate resilience multiplied by the MDPR). A near-linear relationship was found between these. Their reciprocal ratio η_cav ≈ 7 × 10^?11. For σ = 0.62, the data deviated from the others, possibly because of the work hardening of the eroded surface.     

A Three-Dimensional Navier-Stokes–Based Numerical Model for Squeeze-Film Dampers. Part 1—Effects of Gaseous Cavitation on Pressure Distribution and Damping Coefficients without Consideration of Inertia

Even though most published results detailing damper behavior consider only the liquid phase, the cavitation process in the lubricant film, when it happens, is critical for the damper's performance. A number of modeling approaches, such as the half-Sommerfeld and Elrod models, were proposed in order to account for the effects of cavitation on the pressure generation, without directly simulating the cavitation process. Based on the experimental data, a few other homogeneous cavitation models have also been developed. All these models are based on the classical Reynolds equation. In this article, a three-dimensional numerical model is developed and validated in connection with the operation of a two-phase squeeze-film damper. The full Navier-Stokes equations (NSE), coupled with a homogeneous cavitation model, is solved to simulate the flow of the two-phase lubricant film and the associated pressures. The pressure variation on the journal surface and the gas concentration distribution in the lubricating fluid (cavitated region) will be presented. The damping coefficients predicted by the NSE model are compared to the ones that resulted from the application of the Reynolds equation.     

Cavitation–silt erosion in sand suspensions

Cavitation–silt erosion in sand suspensions has elicited research attention. However, erosion characteristics in various conditions of liquids remain unknown due to their complex mechanisms. Thus, the effects of sand size, concentration, and temperature of sand suspensions on cavitation–silt erosion and viscosity were experimentally investigated in the present work. The findings proved the existence of critical sand size. The silt–cavitation erosion decreased with the increase of sand concentration when the sand was smaller than the critical size, and it increased with the increment of the sand size and temperature. A good relationship between the viscosity and the sand size, concentration, and temperature was determined. Moreover, the cavitation–silt erosion mechanisms were obtained on the basis of the viscosity and impingement erosion analysis standpoint.     

Inelastic damages by stress wave on steel surface at the incubation stage of vibration cavitation erosion

In cavitation erosion, stress waves will be generated and propagated in the solid when a collapse impingement is acted on it. The cavitation damages on the solid surface are considered to be under the effect of the stress waves. An ultrasonic vibration cavitation erosion experiment was performed on a polished steel specimen, and not only the plastic deformations but also the brittle fractures appeared on the surface at the incubation stage of cavitation erosion. Some characteristics such as the hemispherical shape of the crater, intergranular fractures and subsurface comminution make the damages distinguishable from the common plastics deformations, and they are thought to be the results of shear waves. Thus, stress waves are proved to take part in the cavitation erosion, and they bring some special damage styles depending on the conditions of the impaction and mechanical properties of the specimen.     

Cavitation damage studies using plasticine

Two mechanisms, namely, the spherical pressure wave and the microjet, have been used to account for the erosion of materials resulting from the collapse of cavitation bubbles. In recent years, however, high speed photography of collapsing bubbles has added support to the microjet mechanism. Experiments have been undertaken by the authors to examine the mechanism of the erosion of materials subjected to a cavitation environment. Stationary specimens of plasticine held in close proximity to the end of an ultrasonic horn have been damaged by cavitation in distilled water. By virtue of the features of the pits formed, as shown in the photographs in the paper, it is concluded that the cavitation erosion damage results from the impingement of high velocity microjets on the material surface during bubble collapse.     

Which hardness (nano or macrohardness) should be evaluated in cavitation?

This paper is concerned with the analysis of data obtained from instrumented depth-sensing nanoindentation testing performed on materials whose hardness varies with depth from surface. The objective is to determine which hardness (nano or macrohardness) should be evaluated in functionally graded materials to correlate the material properties to its performance in cavitation. A linear relationship between H²/E and cavitation erosion resistance could be established. Significant improvements in the cavitation erosion resistance can be achieved when deep nitrided cases are present.     

Calculation of fuel spray impingement and fuel film formation in an HSDI diesel engine

Spray impingement and fuel film formation models with cavitation have been developed and incorporated into the computational fluid dynamics code, STAR-CD. The spray/wall interaction process was modeled by considering the effects of surface temperature conditions and fuel film formation. The behavior of fuel droplets after impingement was divided into rebound, spread and splash using the Weber number and parameter $K(\sqrt {We\sqrt {Re} } )$ . The spray impingement model accounts for mass conservation, energy conservation, and heat transfer to the impinging droplets. The fuel film formation model was developed by integrating the continuity, momentum, and energy equations along the direction of fuel film thickness. Zero dimensional cavitation model was adopted in order to consider the cavitation phenomena and to give reasonable initial conditions for spray injection. Numerical simulations of spray tip penetration, spray impingement patterns, and the mass of film-state fuel matched well with the experimental data. The spray impingement and fuel film formation models have been applied to study spray/wall impingement in high-speed direct injection diesel engines.     

Cavitation damage prediction

New results from cavitating venturi water tests were used to reinforce the concept of cavitation erosion efficiency previously developed from tests in a vibratory facility with both water and sodium. The concept emerges from a technique which allows a priori prediction of eventual cavitation erosion rates in flow machines. Bubble collapse pulse height spectra obtained from submerged microprobes are correlated with measured erosion rates in given laboratory and/or field devices to allow this prediction. Preliminary results from such correlations are presented together with other measurements of the effects of gas content, velocity and cavitation condition upon the mechanical cavitation intensity as measured by the pulse height spectra.New results from vibratory facility tests in tap water and synthetic seawater upon three materials of variable corrodability (304 stainless steel, 1018 carbon steel and 1100-0 aluminum) are presented. The ratio between maximum erosion rates for the saltwater and freshwater tests were found to increase toward unity as the mechanical cavitation intensity is increased, i.e. increased mean depth to penetration (MDPR), as expected on theoretical grounds.The relation between the incubation period and MDPR_max was examined from the vibratory test results, and was found to depend upon the material properties as well as the fluid flow conditions.     

Analysis of particulate erosion

A general analysis is developed for the erosion of materials whereby material is removed through a process of erosion pit nucleation and growth. This model is applicable to a variety of materials exposed to liquid drop impingement and impingement by rounded solid particles. A fundamental limitation of the model is that material removal has to occur as a preferential process.     

Scale effects on propeller cavitating hydrodynamic and hydroacoustic performances with non-uniform inflow

Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas(NCG) on cavitation inception are involved explicitly in the improved Sauer’s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency(BPF), whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.     

高压轴向柱塞泵配流空蚀特性的评价

分析高轴向柱塞泵的空蚀特性,提出了一种评价空蚀特性的方法,并将其用于泵的实际设计。针对实验中轴向柱塞泵出现的空蚀破坏,对轴向柱塞泵配流过程进行计算流体动力学(CFD,computational fluid dynam ics)解析,得到了配流盘不同位置的速度分布和压力、速度随缸体转角的变化曲线;得出轴向柱塞泵空蚀破坏的机理———空蚀破坏不仅取决于减压槽附近的速度和压力大小,还取决于速度的方向;并且指出如果减压槽处的射流角大小在30°~65°范围内高压轴向柱塞泵就不容易产生空蚀破坏的问题。应用该方法对配流盘进行改进后,从空蚀破坏方面讲,泵的寿命延长到了原来的4倍多。     

Corrosion fatigue of steel under cavitation erosion generated intermittently in 3% salt water (results of two-stage tests with and without cavitation erosion)

Two-stage fatigue tests with and without cavitation erosion were performed in 3% salt water. When corrosion fatigue with cavitation erosion (erosion fatigue) is changed to corrosion fatigue during a test, the fatigue life decreases remarkably and the total number of stress cycles to failure becomes smaller than that for tests involving erosion fatigue only. In the reverse case, when corrosion fatigue conditions are changed to erosion fatigue conditions, the fatigue life increases slightly compared with the life expected from the linear damage law (Miner's law). The variation in fatigue strength can be explained by the characteristics of crack propagation in each environment. From these results, it is presumed that the corrosion fatigue strength of the material exposed intermittently to cavitation erosion decreases remarkably.     

Model-based fault diagnosis in continuous dynamic systems

Traditional fault detection and isolation methods are based on quantitative models which are sometimes difficult and costly to obtain. In this paper, qualitative bond graph (QBG) reasoning is adopted as the modeling scheme to generate a set of qualitative equations. The QBG method provides a unified approach for modeling engineering systems, in particular, mechatronic systems. An input-output qualitative equation derived from QBG formalism performs continuous system monitoring. Fault diagnosis is activated when a discrepancy is observed between measured abnormal behavior and predicted system behavior. Genetic algorithms (GA's) are then used to search for possible faulty components among a system of qualitative equations. In order to demonstrate the performance of the proposed algorithm, we have tested it on a laboratory scale servo-tank liquid process rig. Results of the proposed model-based fault detection and diagnosis algorithm for the process rig are presented and discussed.     

Cavitation erosion size scale effects

Size scaling in cavitation erosion is a major problem confronting the design engineers of modern high speed machinery. An overview and erosion data analysis presented in this paper indicate that the size scale exponent n in the relation erosion rate ∞ (size or diameter)ⁿ can vary from 1.7 to 4.9 depending on the type of device used. There is, however, a general agreement as to the values of n if the correlations are made with constant cavitation number.