Vol. 25 No. 4 2023 3 EDITORIAL COUNCIL EDITORIAL BOARD EDITOR-IN-CHIEF: Anatoliy A. Bataev, D.Sc. (Engineering), Professor, Rector, Novosibirsk State Technical University, Novosibirsk, Russian Federation DEPUTIES EDITOR-IN-CHIEF: Vladimir V. Ivancivsky, D.Sc. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Vadim Y. Skeeba, Ph.D. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Editor of the English translation: Elena A. Lozhkina, Ph.D. (Engineering), Department of Material Science in Mechanical Engineering, Novosibirsk State Technical University, Novosibirsk, Russian Federation The journal is issued since 1999 Publication frequency – 4 numbers a year Data on the journal are published in «Ulrich's Periodical Directory» Journal “Obrabotka Metallov” (“Metal Working and Material Science”) has been Indexed in Clarivate Analytics Services. Novosibirsk State Technical University, Prospekt K. Marksa, 20, Novosibirsk, 630073, Russia Tel.: +7 (383) 346-17-75 http://journals.nstu.ru/obrabotka_metallov E-mail: metal_working@mail.ru; metal_working@corp.nstu.ru Journal “Obrabotka Metallov – Metal Working and Material Science” is indexed in the world's largest abstracting bibliographic and scientometric databases Web of Science and Scopus. Journal “Obrabotka Metallov” (“Metal Working & Material Science”) has entered into an electronic licensing relationship with EBSCO Publishing, the world's leading aggregator of full text journals, magazines and eBooks. The full text of JOURNAL can be found in the EBSCOhost™ databases.
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 4 EDITORIAL COUNCIL EDITORIAL COUNCIL CHAIRMAN: Nikolai V. Pustovoy, D.Sc. (Engineering), Professor, President, Novosibirsk State Technical University, Novosibirsk, Russian Federation MEMBERS: The Federative Republic of Brazil: Alberto Moreira Jorge Junior, Dr.-Ing., Full Professor; Federal University of São Carlos, São Carlos The Federal Republic of Germany: Moniko Greif, Dr.-Ing., Professor, Hochschule RheinMain University of Applied Sciences, Russelsheim Florian Nürnberger, Dr.-Ing., Chief Engineer and Head of the Department “Technology of Materials”, Leibniz Universität Hannover, Garbsen; Thomas Hassel, Dr.-Ing., Head of Underwater Technology Center Hanover, Leibniz Universität Hannover, Garbsen The Spain: Andrey L. Chuvilin, Ph.D. (Physics and Mathematics), Ikerbasque Research Professor, Head of Electron Microscopy Laboratory “CIC nanoGUNE”, San Sebastian The Republic of Belarus: Fyodor I. Panteleenko, D.Sc. (Engineering), Professor, First Vice-Rector, Corresponding Member of National Academy of Sciences of Belarus, Belarusian National Technical University, Minsk The Ukraine: Sergiy V. Kovalevskyy, D.Sc. (Engineering), Professor, Vice Rector for Research and Academic Aff airs, Donbass State Engineering Academy, Kramatorsk The Russian Federation: Vladimir G. Atapin, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Victor P. Balkov, Deputy general director, Research and Development Tooling Institute “VNIIINSTRUMENT”, Moscow; Vladimir A. Bataev, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Vladimir G. Burov, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Dmitry V. Lobanov, D.Sc. (Engineering), Associate Professor, I.N. Ulianov Chuvash State University, Cheboksary; Aleksey V. Makarov, D.Sc. (Engineering), Corresponding Member of RAS, Head of division, Head of laboratory (Laboratory of Mechanical Properties) M.N. Miheev Institute of Metal Physics, Russian Academy of Sciences (Ural Branch), Yekaterinburg; Aleksandr G. Ovcharenko, D.Sc. (Engineering), Professor, Biysk Technological Institute, Biysk; Yuriy N. Saraev, D.Sc. (Engineering), Professor, Institute of Strength Physics and Materials Science, Russian Academy of Sciences (Siberian Branch), Tomsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary
Vol. 25 No. 4 2023 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Akintseva A.V., Pereverzev P.P. Modeling the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains in fl at grinding........................................................................................................................................ 6 Sharma S.S., Joshi A., Rajpoot Y.S. A systematic review of processing techniques for cellular metallic foam production................. 22 Karlina Yu.I., Kononenko R.V., Ivantsivsky V.V., Popov M.A., Deryugin F.F., Byankin V.E. Review of modern requirements for welding of pipe high-strength low-alloy steels.......................................................................................................................................... 36 Startsev E.A., Bakhmatov P.V. The infl uence of automatic arc welding modes on the geometric parameters of the seam of butt joints made of low-carbon steel, made using experimental fl ux......................................................................................................................... 61 Martyushev N.V., Kozlov V.N., Qi M., Baginskiy A.G., Han Z., Bovkun A.S. Milling martensitic steel blanks obtained using additive technologies................................................................................................................................................................................ 74 Loginov Yu.N., Zamaraeva Yu.V. Evaluation of the bars’ multichannel angular pressing scheme and its potential application in practice................................................................................................................................................................................................... 90 EQUIPMENT. INSTRUMENTS Rajpoot Y.S., SharmaA.K., Mishra V.N., Saxena K., Deepak D., Sharma S.S. Eff ect of tool pin profi le on the tensile characteristics of friction stir welded joints of AA8011.................................................................................................................................................... 105 Chinchanikar S., Gadge M.G. Performance modeling and multi-objective optimization during turning AISI 304 stainless steel using coated and coated-microblasted tools........................................................................................................................................................ 117 Ghule G.S., Sanap S., Chinchanikar S. Ultrasonic vibration-assisted hard turning of AISI 52100 steel: comparative evaluation and modeling using dimensional analysis........................................................................................................................................................ 136 Pivkin P.M., Ershov A.A., Mironov N.E., Nadykto A.B. Infl uence of the shape of the toroidal fl ank surface on the cutting wedge angles and mechanical stresses along the drill cutting edge...................................................................................................................... 151 MATERIAL SCIENCE Sokolov R.A., Muratov K.R., Venediktov A.N., Mamadaliev R.A. Infl uence of internal stresses on the intensity of corrosion processes in structural steel....................................................................................................................................................................... 167 Klimenov V.A., Kolubaev E.A., Han Z., Chumaevskii A.V., Dvilis E.S., Strelkova I.L., Drobyaz E.A., Yaremenko O.B., Kuranov A.E. Elastic modulus and hardness of Ti alloy obtained by wire-feed electron-beam additive manufacturing................... 180 Vorontsov A.V., Filippov A.V., Shamarin N.N., Moskvichev E.N., Novitskaya O.S., Knyazhev E.O., Denisova Yu.A., Leonov A.A., Denisov V.V. In situ crystal lattice analysis of nitride single-component and multilayer ZrN/CrN coatings in the process of thermal cycling.......................................................................................................................................................................................... 202 Rubtsov V.E., Panfi lov A.O., Kniazhev E.O., Nikolaeva A.V., Cheremnov A.M., Gusarova A.V., Beloborodov V.A., Chumaevskii A.V., Grinenko A.V., Kolubaev E.A. Infl uence of high-energy impact during plasma cutting on the structure and properties of surface layers of aluminum and titanium alloys................................................................................................................... 216 Bobylyov E.E., Storojenko I.D., Matorin A.A., Marchenko V.D. Features of the formation of Ni-Cr coatings obtained by diff usion alloying from low-melting liquid metal solutions..................................................................................................................................... 232 Burkov А.А., Konevtsov L.А., Dvornik М.И., Nikolenko S.V., Kulik M.A. Formation and investigation of the properties of FeWCrMoBC metallic glass coatings on carbon steel.......................................................................................................................... 244 Sharma S.S., Khatri R., Joshi A. A synergistic approach to the development of lightweight aluminium-based porous metallic foam using stir casting method........................................................................................................................................................................... 255 Strokach E.A., Kozhevnikov G.D., Pozhidaev A.A., Dobrovolsky S.V. Numerical study of titanium alloy high-velocity solid particle erosion.......................................................................................................................................................................................... 268 EDITORIALMATERIALS 284 FOUNDERS MATERIALS 295 CONTENTS
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Numerical study of titanium alloy high-velocity solid particle erosion Evgeny Strokach a, *, Gleb Kozhevnikov b, Aleksey Pozhidaev c, Sergey Dobrovolsky d Moscow Aviation Institute (National Research University), 4 Volokolamskoe shosse, Moscow, 125993, Russian Federation a https://orcid.org/0000-0001-5376-1231, evgenij.strokatsch@mai.ru; b https://orcid.org/0009-0001-4622-7476, kozhevnikov.mai@yandex.ru; c https://orcid.org/0000-0002-7667-5392, pozhidaev.mai@xmail.ru; d https://orcid.org/0000-0002-1884-1882, dobrovolskiy_s@mail.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2023 vol. 25 no. 4 pp. 268–283 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2023-25.4-268-283 ART I CLE I NFO Article history: Received: 15 September 2023 Revised: 29 September 2023 Accepted: 28 October 2023 Available online: 15 December 2023 Keywords: Erosion wear Numerical simulation Solid particles Ansys FLUENT Shape factor Ti6Al4V CFD Solid particle erosion GEKO Turbulence model RANS erosion study Funding The research was funded by the ministry of Science and Higher Education of the Russian Federation, grant number FSFF-2023-0006. Acknowledgements Research was partially conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. Predicting solid particle erosion (SPE) in gaseous flow and managing its intensity is still a relevant problem in mechanical engineering. It requires the development of a general modeling methodology, which also depends upon many special cases studying various physical processes. Such studies should also include verification analysis, process parameters and model sensitivity studies. Mainly computational fluid dynamics and finite element analysis (and mesh-free methods such as smooth particle hydrodynamics or similar) are used to simulate the erosion process. Papers focused on CFD simulation of solid particle erosion of metal alloys are widely presented, but most of it is associated with relatively low or medium particle velocities (< 100–150 m/s) and is close to uniform diameter distribution. This paper presents a CFD study of Ti6Al4V titanium alloy SPE at relatively high particle velocities and sufficiently non-uniform unimodal particle diameter distribution. The paper also studies the turbulence model influence and particle shape effect which appears as a “shape factor” coefficient in the particle drag model. Methods. The heterogenous flow simulation was based on the Reynolds-averaged Navier-Stokes formulation, where the particles, according to EulerLagrange formulation, were simulated as mathematical points with corresponding properties. The influence of turbulence models, such as k-epsilon standard, RNG k-epsilon, and a relatively new Generalized equation k-omega (GEKO) model and its coefficients were also studied. Oka and DNV erosion models were also compared based on the general sample mass loss and more specific erosion intensity profile criterions. The simulation results were compared to the lab-scale experimental results. Results and discussion. It is shown that neither erosion intensity profile or sample mass loss do not depend upon the turbulence model choice or GEKO parameters variation. As expected, erosion is dependent on the erosion model and its coefficients. A notable influence of the shape factor is shown. As the drag coefficient increased due to the particle shape, the erosion intensity decreased and the erosive profile on the surface also changed due to the changing velocity and diameter distribution of the heterogenous flow. It is expected that such results would be useful not only for erosion prediction in all areas of mechanical engineering, but also for wear management in mechanical assemblies and shot peening / shot peen forming management and simulation. For citation: Strokach E.A., Kozhevnikov G.D., Pozhidaev A.A., Dobrovolsky S.V. Numerical study of titanium alloy high-velocity solid particle erosion. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2023, vol. 25, no. 4, pp. 268–283. DOI: 10.17212/1994-6309-2023-25.4-268-283. (In Russian). ______ * Corresponding author Strokach Evgeny A., Ph.D. (Engineering), leading engineer Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, 125993, Moscow, Russian Federation Tel.: +7 (916) 338-63-66, e-mail: evgenij.strokatsch@mai.ru Introduction Solid particle erosion, particularly in the gas flow, is a prevalent issue across aerospace, energy, automotive, and various other sectors. Experimentation on different particle materials, surface and coating materials, flow conditions, particle characteristics, and more has generated a wealth of research on this
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 phenomenon. Many empirical-analytical methods were developed to estimate engineering erosion rates. These include the Finnie, Bitter, Oka, Tabakoff approaches, among others. These methods were applied and continuously improved over time. Recently, numerical modelling methods using both CFD (computational fluid dynamics) and FEA (finite element analysis) as well as SPH (smooth particle hydrodynamics) and its derivatives, which allow for the study of micro-level processes [1, 9–14], have made significant progress. Previously, the text provided a brief overview of erosion modeling methods, examining some works that applied CFD and FEA [8]. One of the most commonly used methods for modeling and verification is a system comprising one or more 90° bent channels that accelerates particles using a carrier phase, typically air, which in turn erodes the surface [2, 3, 15]. When modelling particle motion using CFD, the EulerLagrange approach is commonly used to depict particle groups as mathematical points with known mass, material and dimensions [16–18]. In publications, authors compare and suggest various turbulence models, with calculations typically based on the Reynolds-averaged Navier-Stokes equation system, alongside semiempirical erosion models, depending on the specific issue. Shinde et al. [1] conducted an excellent review of the use of CFD and empirical-analytical models. The authors establish that CFD has a high level of accuracy for various issues and note the need for new empirical-analytical relationships and estimating particle angle of incidence, which relies on carrier phase. The findings regarding erosion wear caused by particles in fluid flow that cannot be compressed, known as “slurry erosion”, are relevant to erosion in a gaseous medium as well. Therefore, the E/CRC group’s representatives, H. Arabnejad [19] and A. Mansouri [20], have created and confirmed empirical-analytical connections by separating the types of wear: deformation and abrasion, which was previously suggested by Bitter [6, 7]. These models involve numerous parameters, covering aspects such as particle shape, flow conditions, and surface material. Overall, these relationships hold great potential for modelling erosion in gaseous media. The contemporary examination of erosion by particles involves FEA and SPH modelling. This approach was scrutinized in multiple reviews, including those by R. Tarodiya and A. Levy, A. Krella, V. Bonu and H. Barshilia, A. Fardan [9–12]. Modern works are focused on refining material models that describe plastic behavior and fracture conditions, as well as the influence of sample temperature, coatings effectiveness, particle shape and size. Additionally, these works also take into account the conditions of particle flow, including velocities, mutual collision, angles of incidence, and particle rotation. This became possible due to the ability to model particle-surface collisions explicitly [21–28]. Despite significant effort to develop a methodology for modelling the erosion caused by solid particles on different materials and under various conditions, there is currently no universally applicable methodology to describe both micro- and macro-level processes. However, ongoing studies examine specific phenomena and the impact of mathematical models on material erosion in particular cases. This paper is focused on the modelling of surface erosion in a popular titanium alloy (Ti6Al4V) caused by SiO2 particles flowing in air. Accurate gas flow description is crucial in this modelling process, particularly when using the most common Reynolds-averaged Navier-Stokes equations (RANS) approach that requires the selection of a turbulence model. CFD erosion modelling involves estimating the surface material entrainment rate as a function of particle impact conditions. Typically, empirical-analytical methods are used, relying on empirically-based coefficients for a narrow range of conditions. These coefficients may require adjustment, and it is necessary to evaluate the model sensitivity to its variation. Many studies analyzed the impact of turbulence models in CFD modelling of the particle erosion process. However, most of these studies were conducted at low velocities of heterogeneous mixture flowing on the surface (less than 150–200 m/s) and did not incorporate the relatively new generalized equation k-omega (GEKO) model [29–31]. The model can be calibrated using multiple coefficients to mimic a particular issue while sustaining coherence and physicality. In this paper, the GEKO model is analyzed in comparison to the commonly used k-epsilon standard and RNG, with particular emphasis on its unique features. Additionally, current publications primarily examine erosion caused by particles of a singular or limited diameter range. However, considering the non-uniform distribution of particles can significantly affect the
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 formation of a heterogeneous jet, ultimately altering the wear profile of the surface. This study introduces particles have a range of 2–63 µm, with a preference towards smaller diameters. Thus, this paper aims to examine the approach to CFD modelling of a particular scenario in which a highvelocity, heterogeneous jet with a significantly non-uniform particle size distribution flows onto a Ti6Al4V sample. Due to the limited space of this paper, the goals include studying how the choice of turbulence models and its adjustment coefficients, the selection of erosion models and its adjustment coefficients, as well as the influence of particle shape, affect the modelled wear rate. In addition, the selected approach’s performance is evaluated by comparing integral values of the calculated and experimental erosion rates, as well as by comparing the calculated specific erosion rate profiles and the experimental material entrainment profile. Research methodology Experiment For the purposes of this study, we utilized a laboratory experimental bench to examine surface erosion under the influence of heterogeneous flow. The operational principle involved introducing quartz particles into the mixing chamber, from where a mixture of gas (in this instance – air) and particles then was feed into the accelerator. The accelerator, which is a Laval nozzle, enabled the heterogeneous flow to accelerate under the action of pressure difference and impinge on the stationary sample. The significant parameters that define the experimental point were the pressure at the accelerator inlet and the initial gas temperature. This configuration enables the examination of wear under various particle flow angles, temperatures, and velocities. The observed test outcomes were the shape of the crater and the loss of the sample material. These results aid in quantifying the wear rate. The flow rate of particles at each experimental point was 7.64e-6 kg/s for 5 minutes, with a temperature of 140 °C and accelerator pressure of 5.75 bar. The accelerator cut-off was positioned 20 mm away from the sample at a 90° angle to the accelerator position. Fig. 1 displays the size distribution of SiO2 particles. The spectrum was mainly dominated by minute fractions, with the highest equivalent particle diameter of 63 μm. Problem formulation and geometric model Owing to insufficient experimental data on the flow and particle velocity distribution in accelerator regions during the flow onto the sample, the entire accelerator had to be modelled. This was done in order to adequately take into account the variables when estimating the erosion rate. To achieve this, an integral Fig. 1. Particle size distribution
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 computational domain was instituted within the accelerator, as well as between the nozzle slice of the tube and the eroded surface. Fig. 2 displays a general view of the accelerator tube with the nozzle. A mixture of particles and air enters the Laval nozzle, accelerates, and exits through the tube onto a sample comprised of titanium alloy Ti6Al4V. Due to the axisymmetric nature of the problem, the two-phase flow area can be depicted in a twodimensional axisymmetric format, which boosts the accuracy of the calculation and reduces computational resources. The computational domain was entirely modelled using two mesh regions, namely the accelerator, and the flow area between the accelerator and the sample. A block mesh with a structured design and a high dimensionless distance y+ near the erodible surface was created in ICEM CFD software. This was due to the utilization of a scaled wall function for boundary layer modelling. The labelled schematic diagram with the designation of the types of boundary conditions (BCs) is shown in fig. 3. Fig. 2. Flow accelerator model: mixer (1), converging part (2), diverging part (3) Fig. 3. 2d axisymmetrical schematic diagram and boundary conditions: accelerator area (1); outflow from accelerator to sample (2); inlet boundary condition (air + particle initialization area) (3); wall boundary condition (4); sample wall BC (4.1); pressure outlet boundary condition (5) Physical Models/ Grid Convergence Study The model in question is based on using Reynolds-averaged Navier-Stokes equations to describe the movement of the carrier phase – air (ideal gas). To average the results, considering turbulent phenomena through a turbulence model is necessary, the choice of which can substantially affect the outcomes. A specific evaluation of both models and its coefficients’ sensitivity is required. Next, we will discuss the impact of models founded on equations for turbulent kinetic energy (k), its dissipation rate (e), and models founded on k and specific dissipation rate (ω): k-epsilon standard, k-epsilon RNG, and Generalised equation k-omega (GEKO) [29–31]. The k-epsilon standard model serves as the foundation for numerous turbulence models intended to explain phenomena within the flow core. RNG is deemed to provide increased precision for high velocity gradient, swirling flows [30]. GEKO is a new model, based on k and ω, which uniquely
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 maintains its integrity even when adjusting its tuning coefficients. However, its full documentation remains inaccessible. Put simply, the user can modify the model’s behavior across a broad range of solutions without concern for physical implications. The fundamental equations are provided below. GEKO model equations from [29–32]: ( ) ( ) ; j t k j j k j u k k k P C k t x x x ρ ∂ ρ µ ∂ ρ ∂ ∂ + = µ + + - ρ ω ∂ ∂ ∂ σ ∂ (1) 2 1 1 2 2 3 ( ) ( ) . j t k j j k j u P C F F C CDF t x x x k ω ω ∂ ρ ω µ ∂ ρω ∂ ∂ω ω + = µ + + - ρω + ρ ∂ ∂ ∂ σ ∂ (2) The functions F1, F2 and F3 [29–31] implement the Cnw, Csep and Cnw coefficients, respectively.According to the authors, the Cnw coefficient is designed to modify the model’s behavior within the boundary layer and near the wall, although its influence is expected to be minimal given the use of the near-wall function. The Cjet coefficient, although mentioned in the documentation, is not the primary parameter for enhancing model performance. However, it can be beneficial for circular concentric flows. Given the cylindrical nozzle of the accelerator, this coefficient may have an impact under certain conditions. Ultimately, Csep is deemed the most dominant coefficient, with the aim to enhance performance for significant adverse pressure gradients and to resolve regions with laminar-turbulent transition. Previously, in the case of reacting flow [32], it was found that Csep was the most crucial coefficient for pressure and heat flux criteria, and reducing Csep brought GEKO performance closer to the k-epsilon model. Additionally, in earlier tests for heterogeneous flow with relatively low velocities within the pipe, the GEKO model and its parameters’ variations had only a minor impact on the velocity and wear pattern in the pipe elbow [33]. The Euler-Lagrangian approach, which is well established for such problems [2, 3, 8, 15–19], was used to model the particulate matter. During the accelerator inlet BC calculations, the pressure and temperature were set to match the experimental values for the point being investigated. Solid particles were also introduced, flowing at a rate of 7.65e-6 kg/s, based on the experimental number distribution and a zero velocity assumption (due to a lack of information regarding particle velocity in the precritical section of the accelerator). The particle velocity was made equal to the flow velocity, and a drag law based on particle sphericity was established. For modelling particle wear in CFD, an erosion model must be applied to the erodible surface. Empirical-analytical models are often employed to relate the material removal rate to the flowing particle parameters, including size, velocities, and angle of incidence. When performing these calculations, several empirical coefficients are utilized, generally chosen based on the specific materials being used. Among the most widely employed commercial software is Ansys FLUENT, with the Oka [34] model being one of its most frequently applied components, serving as a cornerstone for investigating grid convergence and turbulence model impact. Grid convergence was investigated by performing calculations on five grids of different dimensionality using the Oka model, the k-epsilon Standard Shear-Stress Transport Turbulence Model, and a turbulent Prandtl number of 0.85. A design point of 5.75 bar at 140 °C was utilized. After evaluating the total specific erosion criterion, a mesh with 1.65 million hexahedral cells in the region between the accelerator and the sample was chosen. The velocity profile criterion was selected to assess the accelerator mesh in the expulsion region. The accelerator area’s final computed grid consisted of 190,000 cells. Results and discussion It is evident that the rate of surface erosion is reliant on the distribution of particle velocities and incidence angles, which is linked to the velocity profile at the outflow from the accelerator. Fig. 4 displays a representative image of the flow at the accelerator outflow and surface flow using the k-epsilon turbulence model. In the normal direction of high-speed flow near the wall, velocity sharply decreases. Nonetheless,
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 a local region of flow acceleration forms, flowing around the braking region. The heterogeneous flow accelerator creates a high-velocity jet, which promotes the downstreamairflow’s ejection and its acceleration. As a consequence, a zone of opposing currents is created, which has no impact on the erosion process anymore, given its significant distance from the eroded surface (refer to fig. 4, located at the base of the high-velocity jet, in the center). Fig. 4. High-velocity flow impacting sample surface To construct an erosion rate analysis and develop model comparisons, we utilised the specific erosion wear criterion which was determined by calculating the ratio of mass that was removed to the mass of particles present in each cell on the sample surface (specifically region 4.1 in fig. 3). The turbulence model’s impact along the length of the sample, on the radius of the wear spot is shown in fig. 5 (where the centre of the spot is identified as 0 mm). The limited effect of the turbulence model is evident, which is caused by the similar distribution of flow velocities and turbulent viscosity (which is determined by the turbulence model), as shown earlier for the reacting flow [32]. As previously mentioned, the GEKO model provides unique opportunities to adjust the model coefficients. Figs. 6–8 demonstrate the effect of the GEKO model tuning parameters – Csep, Cnw, Cjet. It is apparent that the primary adjustment coefficients of the GEKO model have minimal or no impact on erosion wear when varied within a broad range, even when compared to the overall influence of the turbulence model. The impacts of the erosion model were evaluated using two of the most widely used models, Oka [30, 34] and DNV [30, 35]. The Oka model was utilized through the following formulation: 2 3 90 ( ), k k ref ref V d E E f V d = γ (3)
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Fig. 5. The effect of turbulence models Fig 6. The effect of Csep GEKO coefficient Fig. 7. The effect of Cnw GEKO coefficient at Csep 1.75 Fig. 8. The effect of Cjet GEKO coefficient at Csep 1.75 and Cnw 0.5 where E90 is the reference erosion rate at a particle incidence angle of 90°; V is the particle velocity; Vref is the reference velocity; d is the particle diameter; Dref is the reference diameter; k2 and k3 are the model coefficients; f(γ) is a function of angle defined as: ( ) 2 1 ( ) (sin ) 1 (1 sin ) , n n f Hν γ = γ + - γ (4) where g – represents the angle of incidence of the particle (in radians); Hν denotes the Vickers hardness coefficient (in GPa); n1 and n2 are constants. DNV model is formulated as: ( ), n P p E m KU f = α (5) where P m is erodent mass flow rate; K, n are constants; 1 ( ) 1 180 i i i f A + απ α = - ∑ , and its coefficients are presented in table 1. The coefficients of empirical-analytical models are dependent on the material and experimental conditions. In order to examine the independent parameters of the Oka model, the coefficients were established
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 utilizing the Vickers microhardness of the erodible material and following the guidelines stated in [36], while E90 is a tuned coefficient. Table 2 and figs. 9, 10 present a study of E90 and k3 coefficients’ influence, The calculated erosion rate termed “ER sim” is compared with the experimental “ER exp” from two identical experiments. k3 is a coefficient by the normalized diameter, while it is obvious that k2, being a factor by normalized velocity, and angle function would be influential. Ta b l e 1 DNV model coefficients A1 A2 A3 A4 A5 A6 A7 A8 9.37 42.295 110.864 175.804 170.137 98.398 31.211 4.17 Ta b l e 2 The effect of Oka parameters No. Oka ER sim E90 HV (GPa) n1 n2 k2 k3 Dref Velref 1 6.154e-4 0.35 0.613 6.439 2.21 0.19 0.00326 104 6.322e-4 2 3.077e-4 0.35 0.613 6.439 2.21 0.19 0.00326 104 3.161e-4 3 9.231e-4 0.35 0.613 6.439 2.21 0.19 0.00326 104 1.057e-3 4 6.154e-4 0.35 0.613 6.439 2.21 0.16 0.00326 104 6.88e-4 5 6.154e-4 0.35 0.613 6.439 2.21 0.21 0.00326 104 5.977e-4 6 4e-3 0.35 0.613 6.439 2.21 0.19 0.00326 104 4.239e-3 7 8e-3 0.35 0.613 6.439 2.21 0.19 0.00326 104 8e-3 8 5e-3 0.35 0.613 6.439 2.21 0.19 0.00326 104 5.046e-3 ER exp 4.43e-03 3.16e-03 Fig. 9. The effect of E90 coefficient Fig. 10. The effect of k3 coefficient
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Ta b l e 3 The effect of DNV parameters No. DNV ER sim K n 1 2e-9 2.6 5.919e-4 2 1e-9 2.6 2.959e-4 3 3e-9 2.6 8.878e-4 4 2e-9 3.9 7.044e-4 ER exp 4.43e-03 3.16e-03 The coefficient’s k3 effect is small compared to E90 (Eref) and similar to that of the turbulence model. The Ti6Al4V (Ti6Al4V analogue) DNV model parameters are taken from [37]. The influence of the linear coefficient K and power n can be seen in table 3 and figs. 11, 12. Fig. 11. The effect of K coefficient along the sample Fig. 12. The effect of n coefficient along the sample As can be observed, the linear coefficient has a much higher effect in contrast to the exponent. Also, notable erosion rate values are reached at approximately 2.7 mm from the center of the erosion crater, decaying to zero at ≈ 3.7 mm. Similar erosion area (fig. 13) is observed on the samples, which qualitatively confirms the simulation results. On the contrary, a mismatch between simulated erosion maximum along the sample length and the crater profile can be seen. This issue is discussed further. Motion of a particle is defined by the resultant of the acting forces. Drag force has a high effect, which depends upon the medium properties, particle velocity, its size and shape. The model used here is able to consider particle non-sphericity by means of a shape factor coefficient (SF). As other meaningful parameters are specified preliminary, the particle shape influence and its description by an additional coefficient are still to be studied. The drag coefficient accounting for particle non-sphericity is defined as presented by Haider and Levenspiel [30, 38]: ( ) 2 3 1 4 Re 24 1 Re ; Re Re sph b D sph sph sph b C b b = + + + (6)
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 where 2 1 exp(2.3288 6.4581 2.4486 ) b = - j + j ; 2 0.0964 0,5565 b = + j; 2 3 3 exp(4.905 13.8944 18.4222 10.2599 ) b = - j + j - j ; 2 3 4 exp(1.4681 12.2584 20.7322 15.8855 ) b = + φ - j + j ; j is a non-spherical shape constant; j = s/S, where s is the surface area of a sphere having the same volume as a particle; S is the particle surface area. The spherical drag coefficient was determined according to Morsi and Alexander [30, 39]: 2 3 1 2 Re Re D a a C a = + + , 1 a , 2 a , 3 a – constants. An additional study using Oka erosion model was conducted to estimate the influence of shape factor, which is presented in fig. 14. Fig. 13. Typical wear surface after testing Fig. 14. The effect of the “shape factor” (for Oka coefficients 90 0.004 E = , 1 0.613 n = , 2 6.439 n = , 2 2.21 k = , 3 0.19 k = )
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Ta b l e 4 “Shape factor” and erosion rate (ER) Shape factor ER 0.25 0.00349 0.5 0.0055466 0.75 0.0061866 It can be mentioned that more stretched particles having lower SF (0.25–0.5) give a qualitatively different profile compared to particles having a shape closer to spherical (1–0.75). It is also quantitatively reflected on the relative dimensionless erosion rate presented in table 4. Evidently, the same behavior would be observed for other empirical erosion models. Obviously, such a behavior is due to the change of particle velocity profile and the redistribution of particles having different sizes along the crater radii. The distributions of particle velocities and sizes, cellaveraged, for SF 0.25; 0.5; 0.75 are shown in fig. 15 and fig. 16. It can be seen that while SF decreases, the absolute velocity along the crater radii decreases slowly for SF=0.5 and more rapidly for SF=0.25, which follows the decrease of dimensionless erosion rate. Notable is also the change in profile shape: a drastic velocity decrease can be seen for SF=0.25 along the first 0.25 mm of crater radii. To the opposite, a smooth velocity decay is observed for SF=0.75 (having even a local increase). Decreasing SF leads to increase of the cell averaged diameter in the crater center vicinity, also followed by the growth of the cell-averaged diameters difference between the central and peripheral crater area. This also leads to the influence of averaged diameter local maximums for SF 0.75 and 0.5. Fig. 17 shows the abrasive powder. The shape factor is obviously depending on the surface area of a particle and, therefore, some relation between the sides and/or perimeter of a particle. It can be supposed that for most particles, despite angularities and some coagulated large structures, such relation, if expressed as an aspect ratio, would be no higher than 0.4–0.5. An estimate made using free ImageJ software [40] for the relation of a circle with area equivalent to the summary area of particles to the summary perimeter of particles showed a value of ≈ 0.35. Also, a qualitative similarity can be observed between the calculated erosion rate profile and experimental crater profile for shape factor 0.5 and lower. Therefore, using dimensionless erosion rate (table 2) and erosion rate profiles (fig. 13) the best agreement with experimental data is reached for SF ≈ 0.25 and Oka erosion model with E90 = 0.004, n1 = 0.613; n2 = 6.439; k2 = 2.21; k3 = 0.19. Fig. 15. Particle velocity near the sample wall along its length
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 0,0E+0 5,0E-4 1,0E-3 1,5E-3 2,0E-3 2,5E-3 3,0E-3 3,5E-3 4,0E-3 0,0E+0 5,0E-6 1,0E-5 1,5E-5 2,0E-5 2,5E-5 3,0E-5 3,5E-5 4,0E-5 4,5E-5 SF 0.25 SF 0.5 SF 0.75 Length, m Diameter, m Fig. 16. Average particle diameter distribution near the sample wall along its length Fig. 17. A micrograph of erodent particles (quartz particles) As is shown, erosion rate is independent of the turbulence model and its parameter choice at least or the studied conditions, and, oppositely, high dependence on the particle shape. This shows a need of more attention to the parameters of particles in contrast to the carrier flow modeling parameters. In future additional research should be carried on the effects of particle rotation, other particles distributions, angularity of particles and particles interactions – collisions, fracture and coalescence. As shown before, CFD modeling of erosion process accounting for particle shapes can allow to predict and manage erosion rate on the treated surface. This might be useful for managing the erosive wear location and amplitude in machinery parts and also for working of metals during peening and peen forming processes.
OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Finally, future work should be reasonably conducted together with finite element analysis on local level to explicitly study particle-particle and particle-surface interactions and consider material properties in details. Such studies will be needed also for the estimation of erosion resistance of different types of coatings. Conclusions The numerical study made it possible to determine that: 1. The described approach allows to obtain a good agreement with the qualitative experimental data expressed in erosion crater profile and quantitatively, compared by integral non-dimensional erosion rate values for the studied conditions. 2. The calculated erosion rate under high-speed normal particles impact weakly depends on the turbulence model choice, including GEKO and its parameters; 3. On the contrary, the calculated wear rate significantly depends on the empirical erosion model choice and its calibrating coefficients. 4. The erosion rate profile and integral erosion rate are highly affected by the particle shape. The growth of drag due to change of the particle shapes leads to erosion rate decrease. For the studied conditions, shape factor values of ≈ 0.25 give the best agreement with the experimental data qualitatively and quantitatively. References 1. Shinde S.M., Kawadekar D.M., Patil P.A., Bhojwani V.K. Analysis of micro and nano particle erosion by analytical, numerical and experimental methods: A review. Journal of Mechanical Science and Technology, 2019, vol. 33 (5), pp. 2319–2329. DOI: 10.1007/s12206-019-0431-x. 2. Hadziahmetovic H.D., Hodzic N., Kahrimanovic D., Dzaferovic E. Computational fluid dynamics (CFD) based erosion prediction model in elbows. Tehnicki vjesnik = Technical Gazette, 2014, vol. 21 (2), pp. 275–282. 3. Sun K., Lu L., Jin H. Modeling and numerical analysis of the solid particle erosion in curved ducts. Abstract and Applied Analysis, 2013, vol. 2013, art. 245074. DOI: 10.1155/2013/245074. 4. Finnie I. Erosion of surfaces by solid particles. Wear, 1960, vol. 3 (2), pp. 87–103. DOI: 10.1016/00431648(60)90055-7. 5. Grant G., Ball R., Tabakoff W. An experimental study of the erosion rebound characteristics of high-speed particles impacting a stationary specimen. Report No. 73-36. Cincinnati University Ohio, Department of Aerospace Engineering, 1973. 6. Bitter J.G.A. A study of erosion phenomena: Part I. Wear, 1963, vol. 6 (1), pp. 5–21. DOI: 10.1016/00431648(63)90003-6. 7. Bitter J.G.A. A study of erosion phenomena: Part II. Wear, 1963, vol. 6 (3), pp. 169–190. DOI: 10.1016/00431648(63)90073-5. 8. Strokach E.A., Kozhevnikov G.D., Pozhidaev A.A. Chislennoe modelirovanie protsessa erodirovaniya tverdymi chastitsami v gazovom potoke (obzor) [Numerical simulation of solid particle erosion in a gaseous flow (review)]. Vestnik Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo universiteta. Aerokosmicheskaya tekhnika = PNRPU Aerospace Engineering Bulletin, 2021, no. 67, pp. 56–69. DOI: 10.15593.2224-9982.2021.67.06. 9. Tarodiya R., Levy A. Surface erosion due to particle-surface interactions – A review. Powder Technology, 2021, vol. 387, pp. 527–559. DOI: 10.1016/j.powtec.2021.04.055. 10. Krella A. Resistance of PVD coatings to erosive and wear processes: A review. Coatings, 2020, vol. 10, p. 921. DOI: 10.3390/coatings10100921. 11. Fardan A., Berndt C.C., Ahmed R. Numerical modelling of particle impact and residual stresses in cold sprayed coatings: A review. Surface and Coatings Technology, 2021, vol. 409. DOI: 10.1016/j.surfcoat.2021.126835. 12. Bonu V., Barshilia H.C. High-temperature solid particle erosion of aerospace components: its mitigation using advanced nanostructured coating technologies. Coatings, 2022, vol. 12, p. 1979. DOI: 10.3390/coatings12121979. 13. Taherkhani B., Anaraki A.P., Kadkhodapour J., Farahani N.K., Tu H. Erosion due to solid particle impact on the turbine blade: experiment and simulation. Journal of Failure Analysis and Prevention, 2019, vol. 19 (6), pp. 1739–1744. DOI: 10.1007/s11668-019-00775-y.
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