Empirical Erosion Research Articles

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.

An empirical approach to predict droplet impact erosion in low-pressure stages of steam turbines

At the Institute of Thermal Turbomachinery and Machinery Laboratory (ITSM) Stuttgart, the droplet impact erosion phenomenon has been simulated with the help of an erosion test rig. The experiments confirm that the erosion resistance of steam turbine blade materials can be associated with different mechanical properties of materials. Different combinations of material properties, like hardness, yield strength, Young's modulus and resilience, are analysed and their role in the formation of material erosion resistance is investigated. These material properties are, later on, used to predict the erosion behaviour of blade materials in a given erosive environment. In the end, an empirical erosion prediction model is presented and described. With the help of this erosion model, the rig-specific erosion resistance of a candidate blade material can be predicted if its material properties are known.

Process-based soil erodibility estimation for empirical water erosion models

ABSTRACTFunctional relationships between soil erodibility equations of empirically-based revised universal soil loss equation and process-based water erosion prediction project models were investigated using new datasets from rainfall simulation experiments to overcome conceptual differences of models in estimating soil erodibility. Erodibility potentials of two different soils were quantified for three different initial soil moisture conditions, and relations between the process-based erodibility, partitioned as interrill erodibility, rill erodibility and critical shear stress, and empirically-based erodibility were examined. A process-based soil erodibility assessment within the universal soil loss equation was attempted. Statistically significant differences are found when considering the effects of surface hydrologic conditions on soil erodibility. Process-based soil erodibility estimates under dry conditions were found to be comparable with original water erosion prediction project datasets. The results showed that procedure could be useful for tapping into the large number of datasets available and building the next generation of process-based erosion models.

Erosion Wear Investigation of HVOF Sprayed WC-10Co4Cr Coating on Slurry Pipeline Materials

In the present work, erosion wear due to slurry mixture flow has been investigated using a slurry erosion pot tester. Erosion tests are conducted on three different slurry pipe materials, namely, mild steel, SS202, and SS304, to establish the influence of rotational speed, concentration, and time period. In order to increase erosion wear resistance, a high-velocity oxy-fuel (HVOF) coating technique is used to deposit a WC-10Co4Cr coating on the surface of all piping materials. Experimental results show that rotational speed is a highly-influencing parameter for the erosion wear rate as compared to solid concentration, time duration, and weighted mean diameter. WC-10Co4Cr HVOF coating improved the erosion resistance of piping materials up to 3.5 times. From experimental data, the exponents of solid concentration, velocity, and the size of particles are calculated for the empirical erosion wear equation. A functional equation of the erosion wear rate is developed. The predicted erosion wear is in agreement with the experimental data and found to be within a deviation of ±12%.

A mechanistic model for stochastic rebound of solid particles with application to erosion predictions

Erosive wear due to solid particle impacts is a significant challenge in process industries, especially for oil and gas industries where multiphase flow with the presence of solid particles conveyed by the fluid is very common. Solid particle erosion is a complex phenomenon with multiple factors contributing to its severity. Based on available studies in the literature, mechanistic and empirical erosion models are available that are being used by investigators to predict erosion in complex geometries. The erosion models require particle impact speed and angle to be determined for predicting solid particle erosion. Thus, in many applications, Computational Fluid Dynamics (CFD) codes are used to track the trajectories of solid particles to model erosion in complex geometries. However, the problem of predicting erosion in complex geometries where rebounded particles can have a significant effect on erosion pattern has been addressed only by a few investigators in the literature. The complexity results from the fact that trajectories of rebounded particles and their resulting velocities must be determined. The current investigation uses experimental data and modelling to determine the effects of particle rebounds on erosion patterns. The experimental setup is composed of two stainless steel and aluminum specimens at a right angle to each other, and the angle between the nozzle and first specimen is 45 degrees. The second specimen is painted to determine the erosion pattern caused by rebounding particles from the first. The effects of material composition and surface roughness on the rebounding particles are presented. Additionally, a mechanistic rebound model describing the erosion pattern, erosion intensity and location of maximum erosion is presented, and the predictions are compared with experimental data. It is found that the rebound model has a great influence on erosion prediction especially where subsequent particle impacts are expected. It is also shown that the existing empirical rebound correlations in the literature are not effective for erosion calculation purposes.

Flow erosion and flow induced vibration of gas well relief line with periodic fluctuation of boosting output

Gas well relief line plays the key role in timely discharging high-pressure particle-laden gas flow to ensure safe test and exploitation. However, the boosting output is usually fluctuation, intensifying the flow erosion and flow induced vibration of relief line. In this work, numerical investigation was carried out to examine the effects of fluctuation amplitude and fluctuation period of discharge capacity on the flow erosion and flow induced vibration. Unsteady Reynolds- Averaged-Navier-Stokes (URANS) equations are employed to describe the hydrodynamic characteristics of continuous phase (compressible gas), and discrete phase model (DPM) is utilized to describe the kinematics and trajectory of discrete solid particles (sand particles). The erosion rate and flow induced displacement of relief line are obtained by an empirical erosion model and a fluid-structure interaction (FSI) model, respectively. The results indicate that the flow properties, flow erosion and flow induced vibration are sensitive to the fluctuation of boosting output. Large displacement and severe erosion present in relief line with large fluctuation amplitude or small fluctuation period of discharge capacity.

Physics of soil erosion at the microscale

We focus here on the major and still relevant issue of soil erosion by fluid flows, and more specifically on the determination of both a critical threshold for erosion occurrence and a kinetics that specifies the rate of eroded matter entrainment. A state-of-the-art is first proposed with a critical view on the most commonly used methods and erosion models. It is then discussed an alternative strategy, promoting the use of model materials that allow systematic parametric investigations with the purpose of identifying more precisely the local mechanisms responsible for soil particle erosion and ultimately quantifying both critical onsets and kinetics, possibly through existing or novel empirical erosion laws. Finally, we present and discuss several examples following this methodology, implemented either by means of experiments or numerical simulations, and coupling erosion tests in several particular hydrodynamical configurations with wisely selected mechanical tests.

Erosion mitigation in the Waikato District, New Zealand: economic implications for agriculture

AbstractSoil erosion, in its various forms, is caused or aggravated by agricultural activities. Mitigation of surface erosion comprises the construction of shelterbelts, fencing, riparian buffering, and stock reduction. Mitigation of mass‐movement erosion, in turn, takes the form of spaced planting of trees to maintain a persistent, healthy, and complete ground cover. In this article, we assess the economic implications to agriculture of the adoption of mitigation alternatives for erosion control in the Waikato District, New Zealand. The Waikato District presents a spatial pattern of erosion that affects profitability of dairy, and sheep and beef enterprises. We use the Universal Soil Loss Equation and the New Zealand Empirical Erosion Model to estimate erosion figures that are then fed into an economic‐focused, nonlinear, partial equilibrium mathematical programming model of New Zealand land use. Different scenarios are constructed for surface and mass‐movement soil erosion targets ranging from 0% to 50% below baseline levels. We find that achieving surface erosion targets is more expensive than mass‐movement targets, and results in different responses in regional‐level costs, land use, enterprise net revenue, and adoption of mitigation alternatives.

Life cycle impacts of topsoil erosion on aquatic biota: case study on Eucalyptus globulus forest

This study illustrates the applicability of a framework to conduct a spatially distributed inventory of suspended solids (SS) delivery to freshwater streams combined with a method to derive site-specific characterisation factors for endpoint damage on aquatic ecosystem diversity. A case study on Eucalyptus globulus stands located in Portugal was selected as an example of a land-based system. The main goal was to assess the relevance of SS delivery to freshwater streams, providing a more comprehensive assessment of the SS impact from land use systems on aquatic environments. The WaTEM/SEDEM model, which was used to perform the SS inventory, is a raster-based empirical erosion and deposition model. This model allowed to predict the amount of SS from E. globulus stands under study and route this amount through the landscape towards the drainage network. Combining the spatially explicit SS inventory with the derived site-specific endpoint characterisation factors of SS delivered to two different river sections, the potential damages of SS on macroinvertebrates, algae and macrophytes were assessed. In addition, this damage was compared with the damage obtained with the commonly used ecosystem impact categories of the ReCiPe method. The relevance of the impact from SS delivery to freshwater streams is shown, providing a more comprehensive assessment of the SS impact from land use systems on aquatic environments. The SS impacts ranged from 15.5 to 1234.9 PDF m3.yr.ha−1.revolution−1 for macroinvertebrates, and from 5.2 to 411.9 PDF.m3.yr.ha−1.revolution−1 for algae and macrophytes. For some stands, SS potential impacts on macroinvertebrates have the same order of magnitude than freshwater eutrophication, freshwater ecotoxicity, terrestrial ecotoxicity and terrestrial acidification impacts. For algae and macrophytes, most of the stands present SS impacts of the same order of magnitude as terrestrial ecotoxicity, one order of magnitude higher than freshwater eutrophication and two orders of magnitude lower than freshwater ecotoxicity and terrestrial acidification. The SS impact results allow concluding that the increase of SS in the water column can cause biodiversity damage and that the calculated impacts can have a similar or even higher contribution to the total environmental impact than the commonly used ecosystem impact categories of the ReCiPe method. A wide application of the framework and method developed at a local scale will enable the establishment of a regionalised SS inventory database and a deep characterisation of the potential environmental impacts of SS on local aquatic environments.

Construction of erosion mechanism maps for pipeline steels

Oil and gas industry spends millions of dollars every year dealing with problems caused by erosion. Erosion is a complex phenomenon and in order to recommend ways to mitigate its effect, it is essential to have a full understanding of the tribo-mechanisms involved. In the present study, erosion tests were conducted on AISI 1018, AISI 1080, API X42, API X70 and API X100 steels using aluminum oxide as erodent. Particle velocities and attack angles employed were as follows: 36, 47, 63 and 81ms−1 at 30°, 45°, 60° and 90°, respectively. Erosion rate decreases with increasing impact angle and increases with increasing particle velocity. Several mechanisms are found to be responsible for the behavior of these steels under the experimental conditions employed in this work. Heavy plastic deformation and fracture, ploughing, delamination and different forms of metal cutting are identified as operative mechanisms during erosion. Empirical erosion mechanism maps are constructed showing the variation in erosion regimes, as a function of impact angle and normalized velocity.

Gully catchments as a sediment sink, not just a source: Results from a long‐term (~12 500 year) sediment budget

AbstractSediment delivery from hillslopes to trunk streams represents a significant pathway of mass transfer in the landscape, with a large fraction facilitated by gully systems.The internal gully geomorphic dynamics represent a considerable gap in many landscape and empirical erosion models, therefore a better understanding of these processes over longer timescales (10–104 years) is needed. This study analyses the sediment mass balance and storage dynamics within a headwater gully catchment in central Europe over the last ~12 500 years. Human induced erosion resulted in hillslope erosion rates ~2.3 times higher than under naturally de‐vegetated conditions (during the Younger Dryas), however the total sediment inputs to the gully system (and therefore gully aggradation), were similar. Net gully storage has consistently increased to become the second largest term in the sediment budget after hillslope erosion (storage is ~45% and ~73% of inputs during two separate erosion and aggradation cycles). In terms of the depletion of gully sediment storage, the sediment mass balance shows that export beyond the gully fan was not significant until the last ~500 years, due to reduced gully fan accommodation space. The significance of storage effects on the gully sediment mass balance, particularly the export terms, means that it would be difficult to determine the influences of human impact and/or climatic changes from floodplain or lake sedimentary archives alone and that the sediment budgets of the headwater catchments from which they drain are more likely to provide these mechanistic links. Copyright © 2015 John Wiley & Sons, Ltd.

Formulating Fine to Medium Sand Erosion for Suspended Sediment Transport Models

The capacity of an advection/diffusion model to predict sand transport under varying wave and current conditions is evaluated. The horizontal sand transport rate is computed by vertical integration of the suspended sediment flux. A correction procedure for the near-bed concentration is proposed so that model results are independent of the vertical resolution. The method can thus be implemented in regional models with operational applications. Simulating equilibrium sand transport rates, when erosion and deposition are balanced, requires a new empirical erosion law that involves the non-dimensional excess shear stress and a parameter that depends on the size of the sand grain. Comparison with several datasets and sediment transport formulae demonstrated the model’s capacity to simulate sand transport rates for a large range of current and wave conditions and sand diameters in the range 100–500 μm. Measured transport rates were predicted within a factor two in 67% of cases with current only and in 35% of cases with both waves and current. In comparison with the results obtained by Camenen and Larroudé (2003), who provided the same indicators for several practical transport rate formulations (whose means are respectively 72% and 37%), the proposed approach gives reasonable results. Before fitting a new erosion law to our model, classical erosion rate formulations were tested but led to poor comparisons with expected sediment transport rates. We suggest that classical erosion laws should be used with care in advection/diffusion models similar to ours, and that at least a full validation procedure for transport rates involving a range of sand diameters and hydrodynamic conditions should be carried out.

Numerical investigation of flow erosion and flow induced displacement of gas well relief line

High-pressure particle-laden gas flow should be discharged through relief line of gas well timely to ensure safe test and exploitation. Erosion and vibration usually take place on the bend in relief lines, bringing a potential safety hazard to field operation. The majority of this paper investigates the factors affecting the erosion of bend and displacement of relief line in the downstream of bend using the computational fluid dynamics (CFD) methodology. A three-dimensional elbow pipe is selected as computational domain in this investigation. The kinematics and trajectory of discrete solid particles and liquid droplets are described by discrete phase model (DPM) while the hydrodynamic characteristics of continuous phase are obtained based on Reynolds-Averaged-Navier-Stokes (RANS) equations. An empirical erosion model is employed to predict the erosion rate of bend, and a fluid–structure interaction (FSI) model is adopted to calculate the displacement of relief line. The effects of types of multiphase flow (such as gas–solid two-phase flow and gas–liquid–solid three-phase flow), inlet flow rate and pipe diameter on erosion and displacement are discussed. The results show that large displacement and severe erosion present with large inlet flow rate in minor diameter pipe. The increase in liquid droplet content has less effect on flow erosion than that by the same increase in sand particle content.

Numerical investigation of mass loading effects on elbow erosion

Wear due to particles is often the key factor for pipeline failure. In this work, the effects of different sand particle concentrations on the erosion of an elbow pipe are investigated numerically. In order to assess the quality of the numerical predictions of the erosion rate, experimental data were first used to validate the erosion and restitution models at low concentration. The input parameters for the empirical erosion correlation were obtained from accurate CFD models for the gas–solid flow within the bend. One, two and four-way couplings were evaluated at different mass loadings. In general, it was found that even at low to moderate mass loadings, the effects of inter-particle collisions on the penetration ratio cannot be neglected. Another important finding is that the maximum penetration ratio gradually diminishes as the mass loading increases. As counterintuitive as it may appear, this phenomenon has actually been observed in experiments and is named cushioning effect. Based on the analysis of the simulation results, it can be concluded that a layer of particles builds up adjacent to the elbow wall, protecting it from direct particle collisions. Conversely, the inter-particle collisions damp the particle impact to the surface, therefore reducing the penetration peak.

Riverbed and basin components of erosion and suspended sediments runoff within river basins: a new method of assessment

Sheet, rivulet, and gully erosion form the basin runoff. A new hydrological method of basin and riverbed components of erosion assessment is proposed. The method is based on functional dependence: r i = А эр IQ µ , where r i and Q – monthly averages water suspended sediments (SS) runoff, А эр – empirical complex erosion coefficient, I – slope of riverbed, µ – power coefficient. This dependence was obtained for drought periods in different years with different low water runoff and was extrapolated on other phases of hydrological regime. This extrapolation allows calculating riverbed and basin components of SS runoff in its bulk multiyear average. Data of more than ten years observation on 124 small and average rivers of East European Plain, the Urals, East Carpathian, Cis-Caucasus, mountains of Middle Asia were used. The average share of riverbed erosion and SS runoff was shown to be 8.8±1.6% with minimum of 6.3±2.3% in the low mountain rivers and maximum of 11.8±3.9% in the plain river basins.

A combined CFD/experimental methodology for erosion prediction

The prediction of erosion damage caused by solid particles within flow lines is crucial for many industries. In most erosion modeling approaches, empirical erosion equations are commonly used to relate particle impact information to erosion magnitude. These equations are usually generated from jet impingement testing in air, since the particle impact speed and angle are assumed not to deviate from conditions in the jet. However, in slurry flows, a wide range of particle impact angles and speeds are produced on the target surface. In this work combining CFD simulation results with experimental data obtained from a normal slurry jet test, an erosion equation has been developed. In this methodology, a computational fluid dynamics (CFD) simulation is used to characterize the particle impact speed, angle and frequency at specific locations on the specimen. Then, the particle impact data are related to the measured erosion depth to achieve an erosion equation from submerged testing. The erosion equation has been validated for oblique impingement configurations and it has been shown that, the equation is well suited for various test conditions and it can successfully predict the local erosion depth.Furthermore, a series of dry impinging jet tests for normal and oblique configurations has been performed. Utilizing a particle image velocimetry (PIV) technique, the slip velocity between the gas and sand particles has been determined. In order to gain a better understanding of the erosion pattern, local erosion depth has been measured using a 3D surface profilometer. The effect of gas velocity and impingement angle on erosion profile has also been investigated.

FULLY PROBABILISTIC DUNE SAFETY ASSESSMENT USING AN ADVANCED PROBABILISTIC METHOD

In this paper, an advanced probabilistic method - Adaptive Directional Importance Sampling (ADIS) - is used in concert with a process-based dune erosion model - XBeach - to perform a dune safety assessment. The efficiency of the probabilistic method removes the restriction of only using simple empirical dune erosion models for probabilistic calculations. The proposed combination of ADIS and XBeach is able to handle complex cross-shore profiles that empirical dune erosion models cannot, as shown in several case studies.

Three-Dimensional Model for Erosion of a Hall-Effect Thruster Discharge Channel Wall

The erosion of the channel wall in Hall-effect thrusters limits the maximum thruster operating lifetime. Hall-effect thruster channel wall materials are often binary composites of BN and . The heterogeneity of the material drives the development of complex surface features and roughness during the erosion process. A three-dimensional model of the atomic sputtering of a heterogeneous material is developed. The model investigates, through a ray-tracing technique and empirical erosion rate models of each phase, the interaction between the plasma and the material microstructure. Simulated surface profiles are compared with experimental data collected from the eroded channel wall of the U.S. Air Force Research Laboratory/University of Michigan P5 Hall-effect thruster. The channel wall is composed of M26, a composite material. Simulated surface features and roughnesses for an ion incidence angle of 30 deg resemble those observed through scanning electron microscopy and optical profilometry of the P5 channel wall. Predicted root mean square roughnesses, for 30 deg ion incidence, of are within 33% of the root mean square measured experimentally. The composition of the channel wall surface is investigated via x-ray photoelectron spectroscopy and is comparable to prior work, but the reduction in the presence of BN with erosion is not adequately captured by this model.

Combined experimental and numerical approach for wear prediction in feed pipes

Within this work, a combined experimental and numerical approach to fundamentally understand erosive wear in feed pipes was initiated. By experimental lab-scale testing, it was shown that erosion rates strongly depend on the material's properties and testing conditions. Steel wear was more pronounced at higher impact angle, whereas low impact angle was more critical for rubber. Lab-tests results distinguish from empirical erosion models because material dependent critical impact energies and fatigue phenomena cannot be considered there. A CFD–DEM approach was conducted for simulation of particulate flow in pipes. In addition, long term wear measurements were done to gain data of the wear progress. Although further validation and testing are necessary, very promising results on erosion prediction could be achieved.

Numerical Modeling of Turbulent Kinetic Energy of 2D Horizontal Flow for Scouring Simulation in Cohesive and Granular Bed around Circular Piers

In order to simulate the bed scouring around piers, many researchers have developed sophisticated numerical algorithms. In this work, the numerical modeling of souring around cylindrical piers are performed by solution of the shallow water equations flow and depth averaged turbulent model equations coupled with the empirical relations for cohesive and granular beds. The shallow water flow equations include to the depth average continuity and motion and depth average turbulent model equations in horizontal Cartesian coordinate systems. For computation of bed erosion at each time step, the numerical results of turbulent flow model are combined with SRICOS empirical bed erosion empirical relations, which are derived from laboratory experiments. The governing partial differential equations of depth average turbulent flow are converted to discrete form using a vertex base finite volume method suitable for triangular unstructured meshes. Therefore, scouring due to flow around piers with arbitrary shape can be modeled. Several test cases of scouring on the cohesive and sandy beds around circular piers are modeled using the developed numerical model and the computed results are compared with the laboratory measurements reported for scouring in cohesive and granular bed around circular piers by the previous experimental workers. Despite of the simplicity and light computational work load of the introduced algorithm, the computed results show promising agreements with the anticipated trends.