Flow Erosion Research Articles

In Situ Testing and Finite Element Analysis of a Discontinuous Mortise and Tenon Stone Bridge Under Natural Excitation

To study the dynamic response of multi-span mortise and tenon stone bridges under natural excitation, a bluestone multi-span stone bridge with a main span of 2.56 m in southern China was taken as the research object. Based on the collected pulsating signals of bridge piers and slabs, the natural frequencies and damping ratios of the main span bridge slab and pier were analyzed using the half-power broadband method (HPBM) and random decrement technique (RDT). Modal analysis was conducted using ANSYS, and the results were compared with those obtained from on-site experiments for further performance analysis. The research results of this article indicate that the natural frequency range of the 2.56-m bridge slab identified by measured signals is 48–49 Hz, and the damping ratio range is 33.33–36.61%. The natural frequency of the central pier is 75–76 Hz, and the damping ratio range is 26.39–27.83%. Through finite element modal analysis, the natural frequency of the bridge slab is 54.401 Hz, with an error of 10.5%. The natural frequency of the overall stone bridge is about 82.2 Hz, with an error of about 8.2%. The validated finite element model was subjected to normal water flow impact and erosion simulation. The results indicate that under erosion with fewer particles and lower flow rates, the upstream pier bottom at the center receives the highest relative erosion mass and displacement per unit area. The bridge deck near the main span also experienced relative displacement. Therefore, in the subsequent protection work, special attention should be paid to these components.

Land-Use-Change-Driven Erosion and Sediment Transport in the Yaqui River Sub-Basin (Mexico): Insights from Satellite Imagery and Hydraulic Simulations

Soil erosion and sediment transport are significant concerns in the Yaqui River sub-basin in northwest Mexico, driven by land use changes and environmental degradation. This study aims to evaluate erosion processes between 2000 and 2020 using a combination of satellite imagery and numerical simulations with Iber software (Version 2.5.2). The primary objective is to assess the impacts of land use changes, particularly the conversion of forest to grassland, on erosion rates and sediment transport. Satellite images from 2000 and 2020 were analyzed to detect land cover changes, while Iber’s sediment transport module was used to simulate erosion patterns based on the Meyer–Peter and Müller equation for bedload transport. Hydrological and topographical data were incorporated to provide accurate simulations of flow velocity, depth, and erosion potential. The results reveal a 35.3% reduction in forest cover, leading to increased erosion and sediment transport in steep areas. Simulation predictions highlighted areas with high future erosion potential, which are at risk of further soil loss if current trends continue. Flow velocity increased, contributing to riverbank destabilization and higher sediment yield, posing a risk to infrastructure such as the Álvaro Obregón Dam. This study underscores the need for targeted erosion control measures and sustainable land management practices to mitigate future risks and protect vital infrastructure in the Yaqui River Basin.

Impact of the Draft Plate on the Wall Erosion and Flow Field Stability of a Cyclone Separator

Cyclone separators are commonly employed in the mining, metallurgy and chemical industries due to their simple structure, easy maintenance and high recovery efficiency. However, with the wide application of cyclone separators, many problems have become exposed in their practical operation, restricting their development. Among these, wall erosion is becoming a significant problem. In this study, to resolve the problem of severe erosion on the walls, the Eulerian–Lagrangian framework was employed to investigate a cyclone separator with a draft plate at the inlet and to evaluate the effect of a draft plate with angles of 0°, 45° and 90° on the degree of erosion and the stabilization of flow fields. Moreover, after verifying the reliability of the numerical model via data from experiments, the characteristics of gas–solid flow were analyzed and the effects of the new structure on the degree of wear were investigated. The results demonstrated that unfavorable phenomena such as secondary flow and wall erosion generated during the operation could be mitigated by the draft plate. When the plate angle was 90°, the wall erosion was the lightest and the range of influence of the secondary flow was the smallest. When the plate angle was 45°, the comprehensive performance was the best, and there was a better balance between the energy loss and the degree of wall erosion. Therefore, the presence of the draft plate has a significant impact on the interaction of gas–solid phases in a cyclone separator.

WGAN-Based Realization Process of Gravel Soil for Hydraulic Property Simulation

Gravel soil faces significant engineering challenges such as leakage erosion and soil flow due to its complex composition and susceptibility to groundwater effects. This study integrates the entire machine learning process, including pre- and post-processing of images, WGAN implementation, and validation of hydraulic and morphological properties. Obtaining intact gravel soil samples is difficult and costly due to their erodible nature in the Li River, China. A μ-CT scanning series is employed to capture detailed images with three microstructural characteristics of gravel soil, forming the basis for training datasets using WGANs. This approach allows the generation of similar 3D realizations that replicate the microstructural characteristics and hydraulic behaviors of a prototype of gravel soils. Through computational fluid dynamics (CFD) simulations, the effectiveness of the realizations in hydraulic behavior within reconstructed porous structures is verified. This process indirectly validates the consistency between the realization′s microstructure and the prototype. This integrated methodology not only enhances understanding but also aids in the optimization of engineering designs and applications in geotechnical and materials science disciplines.

Failure analysis of additively manufactured PLA with different morphological arrangements in erosive flow

This study investigated the impact of water-sand slurry on Polylactic Acid (PLA) in Fused Deposition Modeling (FDM), exploring different morphologies and variables using Taguchi design. Variables included three designs (D1: Flat, D2: Groove, D3: Square groove), slurry concentrations (1%, 3%, 5% by weight), and impact angles (60°, 75°, 90°). Surface damage observed on PLA included cracks, micro-cutting, flakes, and craters due to erosion. The Groove design (D2) showed superior erosion resistance compared to Flat (D1) and square groove (D3). Analysis identified slurry concentration (64.68%) as the primary influencer of erosion, followed by design (23.80%) and impact angle (10.56%). These findings highlight the importance of optimizing FDM parameters to enhance PLA durability against abrasive conditions.

Insights into the relationship between particulate flow characteristics and local erosion behaviour under waterjet: The role of particle-fluid-surface interaction

In this study, the erosion characteristics of eutectic high entropy alloy under the liquid–solid two-phase flow is investigated by a coupled numerical-experimental method, in order to reveal the intrinsic relationship between microscopic erosion mechanism (experimental test) and the related particle-fluid-surface interaction (CFD modelling). Furthermore, instead of the common relation between average erosion rate and mainstream flow velocity, the relationship between local erosion distribution and local particulate flow characteristics is clarified. The erosion rate and erosion pattern match well between the experiment and simulation. The results demonstrate that NiCoCrFeNb0.45 exhibits superior anti-erosion performance when compared to other widely used equipment metals. The erosion profile agrees well with the shape of surface velocity distribution, indicating a close relationship between surface erosion behaviour and flow characteristics. In particular, the erosion pattern at a normal angle appears as a symmetric ring due to the flow stagnation phenomenon, with slight erosion damage in the centre area and severe erosion in the surrounding, whereas the erosion profile at an oblique angle displays an elliptic shape, with severe erosion damage in centre. Notably, the primary erosion mechanism varies dramatically in different surface regions, induced by the various impact velocities and angles associated with the corresponding changes in the flow field. This study provides a deeper understanding of erosion behaviour in terms of the interrelationship among the material mechanical properties, particulate flow field and particle-surface impingement behaviour.

Study on gas–liquid–solid multiphase flow and erosion in ball valves

In industrial processes involving ball valves, gas–liquid–solid multiphase flows with continuous carrier and discrete particle phases are characterised by erosion challenges. These challenges reduce sealing performance and can lead to leakage and valve failure. To explore the characteristics of gas–liquid–solid multiphase flow and flow-induced erosion in ball valves, we conducted a combination of computational fluid dynamics numerical simulations and experimental testing. Results indicate that an increase in the gas content increases the flow coefficient, accelerates both liquid flow and particle movement and exacerbates erosion. In addition, particles are less concentrated in regions with higher gas concentrations. Erosion is primarily observed on the upstream surface and rear wall of the valve core as well as the upper side of the downstream pipeline. Severe erosion occurs more at smaller valve openings, and affected regions expand as the valve opening increases.

Numerical analysis of gas-solid flow erosion in different geometries as alternatives to a standard pipe elbow

This study was conducted with the aim of replacing different geometric fittings instead of the standard 90° elbow and trying to change the flow pattern to reduce erosion damage. Among fittings, the elbows are at a more serious risk. Numerical investigation of the present erosion with the novelty of research on non-spherical particles and changes in the impact angle of particles along with fluid flow using eight new proposed fittings, including two miter fittings, three blinded fittings, one reducer elbow fitting, and two spherical elbows fittings in comparison with the standard 90° elbow was controlled. The numerical simulation of the gas-solid two-phase flow of non-spherical particles was studied using the Euler-Lagrange approach. To carry out the study numerical, first, the gas flow was modeled by the Navier-Stokes equations and the turbulent Reynolds stress model, and then the solid particles were injected using Newton's equation. Finally, the erosion was calculated using Grant and Tabakoff model of the restitution of particles of after hitting the wall and the erosion model of Oka. The amount of erosion caused by changes in the flow pattern was investigated to evaluate the performance of the new proposed fittings. Numerical results for the most critical mode (Vin = 27 m/s and DP = 300 μm) showed that the new proposed fittings increase the erosion resistance by 22.5 % to 39.6 % compared to the standard 90° elbow. Also, in this research, the effect of different parameters including flow velocity, particle diameter size, particle input rate, and particle rotation on erosion were investigated.

The impact of Microbially Induced Calcite Precipitation (MICP) on sand internal erosion resistance: A microfluidic study

Fine particle internal erosion involves the detachment, transport, and deposition of fine particles within soil, significantly impacting agriculture, engineering, and environmental protection. Microbially induced calcite precipitation (MICP) has proven to be an effective method for controlling internal erosion. To optimize MICP protocols for effective erosion control, understanding the microscopic mechanisms by which MICP reduces fine particle erosion is essential but remains unclear. In this study, microfluidic chip experiments were conducted to observe the characteristics of calcium carbonate crystals and fine particles before and after MICP reinforcement and erosion. Through quantitative analysis of the calcium carbonate produced by MICP and eroded fine particles, the effects of bacterial density, concentration of cementation solution, and flow rate on the efficiency of MICP in resisting soil internal erosion were investigated. In addition, three primary mechanisms by which MICP reduces fine particle erosion were identified. Firstly, in situ sand stabilization occurs when calcium carbonate generated by MICP bonds and encapsulates fine particles, forming larger particles that remain stable under erosive flow conditions. Secondly, regional sand stabilization is achieved as MICP-produced calcium carbonate crystals narrow or block the flow channels, preventing extensive migration of fine particles. Lastly, adjacent particle stabilization is facilitated by calcium carbonate crystals, which remain stable during water flow erosion and alter the erosion flow lines, creating zones adjacent to the crystals where fine particle movement is minimized. These findings provide a deeper understanding of the role of MICP in erosion control and can inform the development of more effective erosion mitigation strategies.

Development Characteristics of Single Sand Body of Yan’An Formation in Western Ordos Basin

Abstract The precise characterization of the types and spatial distribution of strongly heterogeneous single sand bodies are a necessary prerequisite for the study of oil and gas reservoir formation. This article takes the Yan’an Formation in the western Ordos Basin as an example to systematically study the internal structure and profile distribution of strongly heterogeneous single sand bodies. The research results indicate that using mud interlayers, physical interlayers, and calcium interlayers as layered interfaces can effectively classify the single sand body types of each small layer in the Yan’an Formation. The drilling rate of a single sand body is between 50% and 85%, and the average number of sand layers is between 3 and 8. When two rivers intersect and are horizontally tangent, due to the mutual erosion of water flow, relatively thick sand bodies can be retained, ultimately resulting in a pattern of relatively thick on both sides and thin in the middle. The single sand body at the bottom is the most developed and has good continuity. In the transverse direction of the river, the continuity of a single sand body is relatively poor, and the extension range of a single sand body is 300m to 1200m. Along the river channel, single sand bodies are developed with good continuity, extending about 2km. The connectivity between the sand body and the well varies with the migration of the river in the transverse river profile of the research area. The lateral contact relationship of a single sand body determines the boundary of the river channel, and the profile characteristics of a single sand body also reflect its planar distribution. The intergranular pores of the Yan’an Formation sand body are relatively developed, and a large number of quartz particles offset the compressive stress of the rock. The corrosion of feldspar particles is relatively strong, retaining a large number of primary intergranular pores. There is a good quantitative relationship between the thickness of sand in a single level channel and the width of the channel. The control of the well network on the sand body is relatively small, and there is room for further densification of drilling. The vertical contact relationship of a single sand body in the Yan’an Formation of the research area can be divided into three modes: separation, stacking, and overlapping. Cut pile sand bodies with good connectivity have good production capacity. The different planar contact relationships reflect the degree of connectivity between channel sand bodies and wells, with lateral cutting type>docking type>isolation type. The side cut sand body has uniform longitudinal water absorption, small water absorption difference, and high-water drive degree. The isolation type has the greatest difference in water absorption rate and the lowest degree of water flooding.

Integration of CFD Analysis and Artificial Neural Networks for Estimation of Erosion Rate in Oil and Gas Pipelines

Transporting oil and gas via pipelines has been creating countless challenges; sand particles deposit and erode the pipelines wall. Generally, conventional erosion rate prediction models are conservative due to numerous generalizations and theories. Finite Element Analysis via computational fluid dynamics (CFD) approach has proven to be useful to solve sand deposition problems and to estimate the eroded pipe due to its capability to precisely determine erosion deficiencies and make predictions with great precision. In this study, a CFD model was developed to calculate sand erosion rates in a 2-inch, 90° elbow pipe. Effects of particle sizes, sand flowrates, fluids velocities and pipe diameters on erosion rates were studied. The model was validated against literature data, and it was then used to generate data via sensitivity analysis simulations. The data became the basis for developing artificial neural network (ANN) models, which were then deployed in the environment of a process simulation software called Symmetry. Based on this approach, a variety of pipelines can be modelled, and maximum erosion rates of pipelines are calculated using deployed ANN models. Hence, a comprehensive study on the fluid flow dynamics and erosion rates of the pipelines can be evaluated simultaneously.

DDPM investigation on centrifugal slurry pump with inlet and sideline configuration retrofit

The inlet and sideline configuration modifications are widely investigated to alter regional particle fluid flow conditions, considering pressure, turbulence and erosion, therefore to improve energy saving and compartment longevity of centrifugal slurry pump. This paper aims to analyse pump hydraulic and erosion characteristics with proposed pump sideline and inlet configuration retrofit by the DDPM method. Specifically, the inlet guide vane number () and angle (), and sidelining vane (SDV) curvature are investigated in quantitative manner. Accordingly, by adjusting inlet vane configuration and placement, a trade-off between wall erosion and hydraulic performance is observed. The sidelining vane (SDV) design is suggested to avoid resultant counter-current flow formulation, therefore, to mitigate turbulence induced erosion in impeller and volute. However, the SDV modification effect on pump hydraulic head and efficiency is found marginal. In general, this study offers realistic guideline for performance improvement and device upgrading of centrifugal slurry pumps.

Water erosion processes: Mechanisms, impact, and management strategies

This study rigorously explores water erosion, a critical environmental challenge diminishing land productivity and ecosystem stability worldwide. Addressing a notable gap in comprehensive, region-specific erosion assessments, this research underscores innovative strategies integrating traditional practices with modern technologies. It assesses the interplay between splash erosion, surface runoff, and subsurface flow, which collectively drive significant landscape changes and soil fertility loss. The influence of key factors such as rainfall intensity, soil type, topography, and vegetation is analyzed through case studies from the Loess Plateau, the Mississippi River Basin, and the Ethiopian Highlands, illustrating varying erosion dynamics. Importantly, this work evaluates the implementation of nanotechnology and biotechnological advances in soil stabilization, supported by robust policy frameworks, and demonstrates these technologies in context, ensuring relevancy to the observed erosion processes. By combining empirical research with cutting-edge science and active community participation, this paper champions adaptive and inclusive strategies to effectively manage water erosion, aiming to bolster environmental sustainability and resilience globally.

Effects of initial soil moisture on rill erodibility and critical shear stress factors in the WEPP model across diverse soil types

Rill erosion, a significant issue in agricultural regions, is intricately linked to initial soil moisture conditions, affecting the development of concentrated flow erosion processes. However, understanding its dynamics amidst varying soil moisture conditions remain challenging. This study aimed to assess the impact of different soil moisture levels on rill erodibility parameters in the Water Erosion Prediction Project (WEPP) model and to evaluate soil cohesion across a spectrum of soils. Through laboratory experiments employing a small V-shaped rill channel, we investigated rill erodibility (Kr) and critical hydraulic shear stress (τcr), under three soil moisture scenarios: initially dry, saturated, and drainage, with incremental surface inflow rates. Additionally, we examined the efficiency of soil cohesion obtained from an Automated Soil Cohesion Measurement Apparatus in predicting Kr and τcr across various soil textures. Our analysis encompassed twenty soils representing nine texture classes, revealing significant correlations between basic soil properties, cohesion parameters, and WEPP model rill erodibility. Notably, initial soil moisture conditions exerted substantial influence on erodibility potentials. Soils with higher silt contents demonstrated better fits in terms of Nash-Sutcliffe model efficiency, particularly under initially dry and saturated conditions. However, predictions for initially drained soils yielded poor fits, emphasizing the intricate interplay between soil properties and hydrological conditions. In conclusion, our findings emphasize the critical role of topsoil water dynamics in rill erodibility. We propose that soil cohesion serves as a valuable predictor, complementing friction forces within the soil and enhancing simulations of rill erodibility under shallow flow conditions in rills, particularly in next-generation process-based modeling approaches.

A meshless model for three-dimensional direct numerical simulation of local scour around cylinder bridge foundation

A meshless local scour model for cylinder bridge foundation based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper. Differing from the traditional Eulerian mesh model used for monopile local scour, it overcomes the high requirements of mesh quality and density for capturing large deformations at the fluid interface. Unlike the transient sediment erosion SPH model used for dam-break, sediment flushing, and water jet, the meshless approach is innovatively applied to the continuous simulation of bridge local scour under steady flow conditions. The present SPH model is established based on the SPH multi-phase fluid model, integrating a classical fluid model combined with numerical stabilization algorithms to govern water particle motion and a sediment model from Zhang et al. (2024) to govern sediment evolution, and tests a new scheme for boundary treatment in the model based on DualSPHysics. Furthermore, a novel scour visualization method that aims at extracting both visible and actual bed surfaces from discrete particles is proposed. The model is validated through comparison with rigid bed and live bed experiments, demonstrating favorable agreement in terms of flow and scour simulation. Importantly, the model results reveal a discrepancy between the elevation of the post-scour visible bed surface derived from the conventional Eulerian mesh model and experimental data, compared to the actual bed surface unaffected by water flow erosion. This indicates the necessity for incorporating a safety margin in foundation design when utilizing experimental results to determine the maximum scour depth.

Erosion and transport mechanisms of granular flow: insights from a flume experiment and block energy model

Erosion and transport mechanisms of granular flow: insights from a flume experiment and block energy model

Snow simulation for the rangeland hydrology and erosion model

In the western US, most rangelands receive snowfall. Yet, a commonly used tool to assess rangeland’s vulnerability to erosion, the USDA’s Rangeland Hydrology and Erosion Model (RHEM) is run using long-term simulated climate inputs that assumes that all precipitation occurs as rainfall. This can be problematic for areas that receive heavy snowfall or substantial rain-on-snow events. In this research, we have developed an efficient snow module for RHEM, called RHEM-Snow, which partitions precipitation between rainfall and snowfall, simulates snowpack accumulation and ablation, and passes net water input (consisting of rainfall, snowmelt, or both) to RHEM. In some areas, the inclusion of the snow module can reduce annual overland flow runoff and erosion estimates by more than 20 % of the total annual overland flow runoff and erosion produced without the snow module (or by as much as 10–50 mm/year for overland flow runoff or >100 kg/ha-yr for erosion). The reclassification of precipitation events from rainfall in RHEM to snowfall in RHEM-Snow tends to reduce overland flow runoff and erosion, but this reduction can be partially counterbalanced by increases from snowmelt and rain-on-snow. However, hydrologic responses to rain-on-snow events can either be enhanced or muted depending on the characteristics of the storm and the snowpack, as sometimes the snowpack can absorb the precipitation inputs, and sometimes snowmelt enhances the precipitation inputs. Because of this mixed impact, the average difference in erosion caused by rain on snow events is relatively small compared to corresponding events where only the liquid phase is considered. Further study is needed of the complex erosion processes under snowpack and frozen soil/variable saturation conditions. Overall, RHEM-Snow provides more realistic timing and magnitude of overland flow runoff and erosion in cold environments, better satisfying the conditions for RHEM applications.

Effect of CeO2 on the preparation of functional ceramsite and the adsorption effect of ammonia-nitrogen wastewater treatment

This study investigates the effect of rare earth oxide CeO2 on the physical properties of ceramsite and its efficiency in treating ammonia-nitrogen wastewater. Ceramsite was prepared from solid waste with 10 % coal gangue added as a pore-forming agent. Ceramsite sample I with CeO2 and sample II without CeO2 were prepared using pure reagents. The process parameters for both samples were optimized using an orthogonal test. Additionally, the effects of CeO2 on ceramsite performance and the treatment of ammonia-nitrogen wastewater were studied, and the adsorption mechanism of CeO2 on ammonia-nitrogen wastewater was clarified. The process parameters for preparing ceramsite sample Ⅰ were: preheating for 30 min at 600 °C, followed by roasting for 20 min at 1090 °C. The parameters for preparing ceramsite sample Ⅱ were: preheating for 30 min at 600 °C, followed by roasting time for 15 min at 1090 °C. The presence of CeO2 increased the porosity of the ceramsite by 0.89 % and the specific surface area by 0.66 m2/g. Under neutral environmental conditions of water samples, CeO2 increased the removal rate of ammonia nitrogen by 1.85 %. Ceramsite has a high porosity and specific surface area, indicating that it has abundant internal pores, a large contact area with ammonia-nitrogen, a strong ability to remove ammonia nitrogen, and resistance to erosion and water flow shear, which are conducive to the treatment of ammonia-nitrogen wastewater.

Experimental study on overtopping failure of concrete face rockfill dam

With the frequent occurrence of natural disasters, the problem of dam failure with low probability and high risk has gradually attracted people's attention. This paper uses flume model tests to systematically analyze the overtopping failure mechanisms of concrete face rockfill dam (CFRD) and identify its failure modes. The tests reveal that the longitudinal erosion of the CFRD breach progress through stages of soil erosion, panel failures, and water flow stabilization. Meanwhile, the cross-section breach process involves the evolution of breach size in rockfill materials, including traceable erosion, lateral broadening, and breach morphology stabilization. The fracture characteristics of the water-blocking panel are primarily evident in the flow-time curve. By analyzing the breach morphology evolution processes in longitudinal and cross sections, the flow-time curve can be subdivided into stages of burst flow formation, breach expansion with flow increase, rapid increase of breach flow discharge due to panel failures, and stabilization of breach flow and size. The primary damage process of the CFRD occurs in a cyclical stage of breach expansion, flow increase, panel failure, and rapid discharge. The rigid face plate and granular body structure contribute to partial dam failure, showing a tendency for gradual expansion of the breach. The longitudinal section illustrates dam failure resulting from panel fracture and rockfill erosion interaction, while downstream slopes exhibit failure due to lateral intrusion of rockfill and cyclic instability. These research results can serve as a reference for constructing a concrete CFRD failure prediction model and conducting disaster risk assessments.

Effect of the leakage flow through guide vanes on the erosion pattern and performance of Francis runner

Abstract The role of hydropower as a renewable energy source is well understood. However, due to the geological characteristics of certain regions, hydropower systems there are facing a unique challenge of excessive sedimentation in rivers. A significant number of research works were performed in the past, which focused on the effects of sediments on the turbine components, that includes reduction in efficiency of the turbine and increase in the erosion wear. Experimental studies of erosion in laboratory conditions are usually limited by several characteristics that affect erosion and complications of handling sediments. As a result, these investigations are normally carried out in a simplified apparatus. This study focuses on using a non-recirculating type of sediment erosion test rig, where a model of Francis turbine is used for experimental investigations. Previous studies have shown that in the case of Francis turbines, erosion occurs in the clearance gap of guide vanes, which increases the size of the gap. The flow from the pressure side of the guide vane is driven into the suction side due to the pressure difference between the two sides. This leakage flow ultimately develops into a vortex filament and hits the runner blades towards the hub and shroud. In this study, the erosion pattern of the runner blades towards these locations are studied by using color coatings. A clearance gap of 4 mm has been created in the guide vane and the consequent impact on the erosion and efficiency of the turbine are studied. The objective is to isolate the effects of leakage flow on erosion in the runner inlet, as well as the overall performance of the Francis turbine. The effect has been observed in terms of increased flow rate, decreased efficiency and erosion in the leading edge of the runner.