Pub Date : 2026-01-14DOI: 10.1016/j.euromechflu.2026.204470
Zafar Hayat Khan , Waqar Ahmed Khan , Alexander Trounev , Li-Bin Liu
This study presents a finite element investigation of laminar viscous flow around two Julia-set-based fractals: the San Marco and the Siegel disk. The analysis focuses on the influence of multi-scale boundary complexity on aerodynamic behavior. Simulations are conducted for Reynolds numbers () using the unsteady incompressible Navier–Stokes equations solved through the finite element method (FEM) implemented in Wolfram Mathematica. Flow visualization and quantitative analysis reveal significant differences in wake topology between the two fractal configurations. The symmetric San Marco fractal exhibits a stabilized wake and a moderate drag coefficient ( at ), slightly lower than that of a canonical circular cylinder (). In contrast, the asymmetric Siegel disk fractal generates a strong negative lift ( at ) and achieves further drag reduction () at higher Reynolds numbers, accompanied by intensified wake unsteadiness and an increased pressure loss ( at ). A distinct transitional regime occurs between and , followed by partial recovery of steady flow for the Siegel disk fractal at . These findings demonstrate that fractal-induced multi-scale boundaries modulate shear layers, suppress vortex shedding, and alter drag–lift characteristics, offering new design strategies for passive flow control in laminar and transitional regimes.
{"title":"Finite element analysis of viscous flow around Julia fractals based on comparative study of San Marco and Siegel disk geometries","authors":"Zafar Hayat Khan , Waqar Ahmed Khan , Alexander Trounev , Li-Bin Liu","doi":"10.1016/j.euromechflu.2026.204470","DOIUrl":"10.1016/j.euromechflu.2026.204470","url":null,"abstract":"<div><div>This study presents a finite element investigation of laminar viscous flow around two Julia-set-based fractals: the San Marco and the Siegel disk. The analysis focuses on the influence of multi-scale boundary complexity on aerodynamic behavior. Simulations are conducted for Reynolds numbers (<span><math><mrow><mi>Re</mi><mo>=</mo><mn>20</mn><mtext>-</mtext><mn>260</mn></mrow></math></span>) using the unsteady incompressible Navier–Stokes equations solved through the finite element method (FEM) implemented in <em>Wolfram Mathematica</em>. Flow visualization and quantitative analysis reveal significant differences in wake topology between the two fractal configurations. The symmetric San Marco fractal exhibits a stabilized wake and a moderate drag coefficient (<span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>≈</mo><mn>5.01</mn></mrow></math></span> at <span><math><mrow><mi>Re</mi><mo>=</mo><mn>20</mn></mrow></math></span>), slightly lower than that of a canonical circular cylinder (<span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>≈</mo><mn>5.57</mn><mtext>-</mtext><mn>5.59</mn></mrow></math></span>). In contrast, the asymmetric Siegel disk fractal generates a strong negative lift (<span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>≈</mo><mo>−</mo><mn>2.52</mn></mrow></math></span> at <span><math><mrow><mi>Re</mi><mo>=</mo><mn>240</mn></mrow></math></span>) and achieves further drag reduction (<span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>≈</mo><mn>2.58</mn></mrow></math></span>) at higher Reynolds numbers, accompanied by intensified wake unsteadiness and an increased pressure loss (<span><math><mrow><mi>Δ</mi><mi>p</mi><mo>≈</mo><mn>13.98</mn></mrow></math></span> at <span><math><mrow><mi>Re</mi><mo>=</mo><mn>260</mn></mrow></math></span>). A distinct transitional regime occurs between <span><math><mrow><mi>Re</mi><mo>=</mo><mn>60</mn><mspace></mspace></mrow></math></span> and <span><math><mrow><mi>Re</mi><mo>=</mo><mn>100</mn></mrow></math></span>, followed by partial recovery of steady flow for the Siegel disk fractal at <span><math><mrow><mi>Re</mi><mo>=</mo><mn>200</mn><mtext>-</mtext><mn>220</mn></mrow></math></span>. These findings demonstrate that fractal-induced multi-scale boundaries modulate shear layers, suppress vortex shedding, and alter drag–lift characteristics, offering new design strategies for passive flow control in laminar and transitional regimes.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204470"},"PeriodicalIF":2.5,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-13DOI: 10.1016/j.euromechflu.2026.204466
D. Matuz , F. Méndez , J. Arcos , O. Bautista , R. Baños
In this study, we examine the oscillatory squeeze flow of a viscoelastic fluid confined between two hydrophobic spheres of differing radii. The fluid flow is generated by the harmonic motion of an upper sphere, while the lower sphere remains stationary. We have considered that the gap between the spheres is much smaller than their radii and that the oscillation amplitude of the moving sphere is small compared to this gap. Under these conditions, the curved surfaces can be approximated by quadratic functions of the radial coordinate . A dynamic slip law is used to model slippage at the fluid–solid interface, which incorporates interfacial memory effects through the slip-relaxation time, together with the slip-yield Spikes–Granick condition, in which interfacial slippage arises when the fluid shear stress exceeds a critical value; otherwise, a non-slip region persists. Given the dominance of viscous over inertial effects, the convective terms in the momentum equation were neglected, and the analysis was carried out in a strictly periodic regimen. An analytical solution of the governing equations is derived, where the following parameters control the phenomenon: the Deborah number , the Womersley number , the Navier slip length , the slip relaxation number and the critical shear stress at the fluid–solid interface . Our findings indicate that, relative to flat surfaces, when curved surfaces are assumed, the zone of the non-slip region decreases. Additionally, incorporating viscoelastic fluids results in a diminished compression force, and lower mechanical power is consumed by implementing hydrophobic surfaces, high oscillation frequencies, and viscoelastic fluids.
{"title":"Influence of slip-yield stress model on the oscillatory squeeze flow of a viscoelastic fluid confined between two spheres","authors":"D. Matuz , F. Méndez , J. Arcos , O. Bautista , R. Baños","doi":"10.1016/j.euromechflu.2026.204466","DOIUrl":"10.1016/j.euromechflu.2026.204466","url":null,"abstract":"<div><div>In this study, we examine the oscillatory squeeze flow of a viscoelastic fluid confined between two hydrophobic spheres of differing radii. The fluid flow is generated by the harmonic motion of an upper sphere, while the lower sphere remains stationary. We have considered that the gap between the spheres is much smaller than their radii and that the oscillation amplitude of the moving sphere is small compared to this gap. Under these conditions, the curved surfaces can be approximated by quadratic functions of the radial coordinate <span><math><mi>r</mi></math></span>. A dynamic slip law is used to model slippage at the fluid–solid interface, which incorporates interfacial memory effects through the slip-relaxation time, together with the slip-yield Spikes–Granick condition, in which interfacial slippage arises when the fluid shear stress exceeds a critical value; otherwise, a non-slip region persists. Given the dominance of viscous over inertial effects, the convective terms in the momentum equation were neglected, and the analysis was carried out in a strictly periodic regimen. An analytical solution of the governing equations is derived, where the following parameters control the phenomenon: the Deborah number <span><math><mtext>De</mtext></math></span>, the Womersley number <span><math><mi>α</mi></math></span>, the Navier slip length <span><math><mover><mrow><mi>λ</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>, the slip relaxation number <span><math><msub><mrow><mtext>De</mtext></mrow><mrow><mi>s</mi></mrow></msub></math></span> and the critical shear stress at the fluid–solid interface <span><math><msub><mrow><mover><mrow><mi>τ</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub></math></span>. Our findings indicate that, relative to flat surfaces, when curved surfaces are assumed, the zone of the non-slip region decreases. Additionally, incorporating viscoelastic fluids results in a diminished compression force, and lower mechanical power is consumed by implementing hydrophobic surfaces, high oscillation frequencies, and viscoelastic fluids.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204466"},"PeriodicalIF":2.5,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.euromechflu.2026.204463
Xishuai Yu, Jianxi Zhou, Yong Li
This study investigates the effectiveness of leading-edge serrations as a passive noise control strategy for tandem airfoils across different angles of attack. Far-field noise measurements indicate that applying leading-edge serrations to the front airfoil significantly reduces wake turbulence interaction noise at 5° and 10° angles of attack; however, the reduction effect weakens as the angle of attack increases. At an angle of attack of 17°, the leading-edge serrations no longer reduce the peak wake turbulence interaction noise. Furthermore, neither the application of leading-edge serrations nor changes in the airfoil angle of attack affect the noise directivity. Flow field analyses based on Particle Image Velocimetry (PIV) reveal that the serrated leading edge markedly attenuates turbulence and vortex shedding in the wake of the front airfoil. Notably, as the angle of attack increases, the influence of vortex shedding and vortex–solid interference between the front and rear airfoils on the overall noise decreases. The intensity of the front airfoil wake turbulence and the extent of its interaction with the rear airfoil are identified as the dominant factors governing the interaction noise in tandem airfoils. Therefore, the application of leading-edge serrations in tandem airfoils is recommended only for low angles of attack. These findings may offer practical guidance for noise reduction in airfoil arrays of rotating machinery, such as guide vane rows, fan blade rows, and turbine blade rows.
{"title":"Influence of front airfoil leading-edge serrations on turbulence interaction noise characteristics of tandem airfoils at different angles of attack","authors":"Xishuai Yu, Jianxi Zhou, Yong Li","doi":"10.1016/j.euromechflu.2026.204463","DOIUrl":"10.1016/j.euromechflu.2026.204463","url":null,"abstract":"<div><div>This study investigates the effectiveness of leading-edge serrations as a passive noise control strategy for tandem airfoils across different angles of attack. Far-field noise measurements indicate that applying leading-edge serrations to the front airfoil significantly reduces wake turbulence interaction noise at 5° and 10° angles of attack; however, the reduction effect weakens as the angle of attack increases. At an angle of attack of 17°, the leading-edge serrations no longer reduce the peak wake turbulence interaction noise. Furthermore, neither the application of leading-edge serrations nor changes in the airfoil angle of attack affect the noise directivity. Flow field analyses based on Particle Image Velocimetry (PIV) reveal that the serrated leading edge markedly attenuates turbulence and vortex shedding in the wake of the front airfoil. Notably, as the angle of attack increases, the influence of vortex shedding and vortex–solid interference between the front and rear airfoils on the overall noise decreases. The intensity of the front airfoil wake turbulence and the extent of its interaction with the rear airfoil are identified as the dominant factors governing the interaction noise in tandem airfoils. Therefore, the application of leading-edge serrations in tandem airfoils is recommended only for low angles of attack. These findings may offer practical guidance for noise reduction in airfoil arrays of rotating machinery, such as guide vane rows, fan blade rows, and turbine blade rows.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204463"},"PeriodicalIF":2.5,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.euromechflu.2026.204462
Prathamesh Banda, Mayank Verma , D.V.G. Prasad, Ashoke De
This study investigates the aerodynamic performance of VAWT clusters under varying array geometries. Staggered V-shaped clusters of vertical-axis wind turbines (VAWTs) are examined to assess aerodynamic interactions in compact wind farm layouts. Configurations use six UNH-RVAT reference turbines, with variations in cluster angle, streamwise spacing, and turbine count. High-fidelity actuator-line large-eddy simulations (LES) are performed using a modified Xcompact3D solver. A six-turbine cluster is analyzed for cluster angles of 20°, 30°, and 45° and streamwise spacings of 2D and 3D (two or three rotor diameters). Results are compared to a reduced five-turbine cluster. Cluster angle strongly affects wake overlap and power capture. At a narrow angle (20°), wake shielding is severe and downstream output is lowered, whereas a wide angle (45°) improves wake recovery but reduces upstream synergy. The intermediate angle (30°) yields the highest overall array performance by balancing these effects. Increased streamwise spacing (3D vs 2D) markedly enhances wake recovery and significantly raises downstream turbine efficiency. Reducing the turbine count from six to five further alleviates wake losses, resulting in higher average power coefficients and more uniform inflow. Flow-field diagnostics (velocity, vorticity, kinetic energy deficit) confirm these trends. These results provide design guidelines: optimizing cluster angle, spacing, and turbine count can substantially improve the efficiency and robustness of high-density VAWT arrays.
本文研究了不同阵列几何形状下VAWT簇的气动性能。研究了垂直轴风力涡轮机（VAWTs）的交错v形集群，以评估紧凑风电场布局中的气动相互作用。配置使用六个UNH-RVAT参考涡轮机，在集群角度，流向间距和涡轮机计数的变化。采用改进的Xcompact3D求解器进行了高保真作动线大涡模拟（LES）。对六涡轮集群进行了分析，集群角度为20°，30°和45°，流向间距为2D和3D（两个或三个转子直径）。结果与减少的五涡轮集群进行了比较。簇角对尾迹重叠和功率捕获有很大影响。在窄角（20°）时，尾流屏蔽严重，下游输出降低，而广角（45°）可以改善尾流恢复，但会降低上游协同。中间角度（30°）通过平衡这些影响产生最高的整体阵列性能。增加的流向间距（3D vs 2D）显著提高了尾迹恢复，并显著提高了下游涡轮效率。将涡轮数量从6台减少到5台进一步减轻了尾迹损失，从而提高了平均功率系数和更均匀的流入。流场诊断（速度、涡度、动能亏损）证实了这些趋势。这些结果为设计提供了指导：优化簇角、间距和涡轮数量可以大大提高高密度VAWT阵列的效率和鲁棒性。
{"title":"High-fidelity actuator line large eddy simulations of multi-turbine VAWT clusters under varying geometric configurations","authors":"Prathamesh Banda, Mayank Verma , D.V.G. Prasad, Ashoke De","doi":"10.1016/j.euromechflu.2026.204462","DOIUrl":"10.1016/j.euromechflu.2026.204462","url":null,"abstract":"<div><div>This study investigates the aerodynamic performance of VAWT clusters under varying array geometries. Staggered V-shaped clusters of vertical-axis wind turbines (VAWTs) are examined to assess aerodynamic interactions in compact wind farm layouts. Configurations use six UNH-RVAT reference turbines, with variations in cluster angle, streamwise spacing, and turbine count. High-fidelity actuator-line large-eddy simulations (LES) are performed using a modified Xcompact3D solver. A six-turbine cluster is analyzed for cluster angles of 20°, 30°, and 45° and streamwise spacings of 2D and 3D (two or three rotor diameters). Results are compared to a reduced five-turbine cluster. Cluster angle strongly affects wake overlap and power capture. At a narrow angle (20°), wake shielding is severe and downstream output is lowered, whereas a wide angle (45°) improves wake recovery but reduces upstream synergy. The intermediate angle (30°) yields the highest overall array performance by balancing these effects. Increased streamwise spacing (3D vs 2D) markedly enhances wake recovery and significantly raises downstream turbine efficiency. Reducing the turbine count from six to five further alleviates wake losses, resulting in higher average power coefficients and more uniform inflow. Flow-field diagnostics (velocity, vorticity, kinetic energy deficit) confirm these trends. These results provide design guidelines: optimizing cluster angle, spacing, and turbine count can substantially improve the efficiency and robustness of high-density VAWT arrays.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204462"},"PeriodicalIF":2.5,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.euromechflu.2025.204452
Yutaro Motoori, Hideki Murahata, Susumu Goto
We visualise the hierarchy of coherent vortices generated by a freely swimming dolphin, obtained from direct numerical simulations at a high Reynolds number. The visualisations are based on isosurfaces of the second invariant of the velocity gradient tensor evaluated from scale-decomposed velocity fields. We describe in detail the scale-decomposition procedure and the polygon-based visualisation, which enables the rendering of the data despite their large size. We also emphasise that visualising the hierarchy of coherent vortices clarifies the physical mechanism of dolphin propulsion, and more generally, provides physical insight into turbulence around swimming and flying organisms.
{"title":"Visualising coherent vortices generated by a swimming dolphin","authors":"Yutaro Motoori, Hideki Murahata, Susumu Goto","doi":"10.1016/j.euromechflu.2025.204452","DOIUrl":"10.1016/j.euromechflu.2025.204452","url":null,"abstract":"<div><div>We visualise the hierarchy of coherent vortices generated by a freely swimming dolphin, obtained from direct numerical simulations at a high Reynolds number. The visualisations are based on isosurfaces of the second invariant of the velocity gradient tensor evaluated from scale-decomposed velocity fields. We describe in detail the scale-decomposition procedure and the polygon-based visualisation, which enables the rendering of the data despite their large size. We also emphasise that visualising the hierarchy of coherent vortices clarifies the physical mechanism of dolphin propulsion, and more generally, provides physical insight into turbulence around swimming and flying organisms.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204452"},"PeriodicalIF":2.5,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-02DOI: 10.1016/j.euromechflu.2025.204453
G. Antar , J. El Kuweiss , K. Schneider , C. Habchi , S. Benkadda
We experimentally investigate quasi-two-dimensional (Q2D) forced shallow flows in the presence of solid boundaries and analyze the deviation from the Kolmogorov–Kraichnan (KK) theory. Complex motion is generated using a thin electrolyte subject to electromagnetic forces, and we employ particle tracking velocimetry to resolve the flow properties down to the Kolmogorov scale. Although the velocity probability distribution function closely resembles a Gaussian, deviations from Gaussianity emerge for velocity increments as scales decrease. The second-order structure function supports the onset of local anisotropy at small scales. The sign of the third-order structure function indicates the dominance of the inverse cascade in energy transfer, and the cross-correlation between longitudinal and transverse directions proves to be significant at large scales. The breakdown of local isotropy is consistent with the effect of bottom friction, which primarily affects the longitudinal motion, while leaving the perpendicular direction unaffected. This local anisotropy propagates to larger scales via the inverse energy cascade, with nonlinear interactions eventually influencing the perpendicular direction.
{"title":"On the local anisotropy of quasi-two-dimensional forced shallow flow: An experimental study","authors":"G. Antar , J. El Kuweiss , K. Schneider , C. Habchi , S. Benkadda","doi":"10.1016/j.euromechflu.2025.204453","DOIUrl":"10.1016/j.euromechflu.2025.204453","url":null,"abstract":"<div><div>We experimentally investigate quasi-two-dimensional (Q2D) forced shallow flows in the presence of solid boundaries and analyze the deviation from the Kolmogorov–Kraichnan (KK) theory. Complex motion is generated using a thin electrolyte subject to electromagnetic forces, and we employ particle tracking velocimetry to resolve the flow properties down to the Kolmogorov scale. Although the velocity probability distribution function closely resembles a Gaussian, deviations from Gaussianity emerge for velocity increments as scales decrease. The second-order structure function supports the onset of local anisotropy at small scales. The sign of the third-order structure function indicates the dominance of the inverse cascade in energy transfer, and the cross-correlation between longitudinal and transverse directions proves to be significant at large scales. The breakdown of local isotropy is consistent with the effect of bottom friction, which primarily affects the longitudinal motion, while leaving the perpendicular direction unaffected. This local anisotropy propagates to larger scales <em>via</em> the inverse energy cascade, with nonlinear interactions eventually influencing the perpendicular direction.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204453"},"PeriodicalIF":2.5,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145904126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-30DOI: 10.1016/j.euromechflu.2025.204441
M.S. Faltas , E.A. Ashmawy , Samar A. Mahrous , M. Magdy El Sayed , Kareem E. Ragab
This study investigates the quasi-steady axisymmetric thermophoretic motion of a spherical particle partially submerged at the flat interface of a semi-infinite Brinkman medium. The analysis is conducted under the assumptions of small Reynolds and Péclet numbers, while the capillary number is considered sufficiently small to preserve the flatness of the interface. The specific case of a contact angle with the flat surface is examined. To avoid singularities at the contact line, the Knudsen number is assumed to lie within the slip-flow regime. Analytical expressions are derived for the thermophoretic velocity and force acting on the half-submerged particle. Graphical results illustrate the influence of parameters such as Fourier thermal conductivity ratio, Knudsen number, medium permeability, frictional slip, and thermal stress slip. Furthermore, the limiting behavior corresponding to thermophoresis in a classical viscous fluid is discussed. Since the present solution is exact, the case of a contact angle also serves as a benchmark for validating numerical solutions at other contact angles. The findings are relevant to applications involving particle manipulation at fluid–porous interfaces, such as targeted drug delivery across biological membranes, pollutant transport at soil–air boundaries, and the design of microfluidic systems for controlled colloidal assembly.
{"title":"Thermophoresis of a spherical particle straddling a flat interface in a Brinkman medium at a 90° contact angle","authors":"M.S. Faltas , E.A. Ashmawy , Samar A. Mahrous , M. Magdy El Sayed , Kareem E. Ragab","doi":"10.1016/j.euromechflu.2025.204441","DOIUrl":"10.1016/j.euromechflu.2025.204441","url":null,"abstract":"<div><div>This study investigates the quasi-steady axisymmetric thermophoretic motion of a spherical particle partially submerged at the flat interface of a semi-infinite Brinkman medium. The analysis is conducted under the assumptions of small Reynolds and Péclet numbers, while the capillary number is considered sufficiently small to preserve the flatness of the interface. The specific case of a <span><math><mrow><mn>90</mn><mo>°</mo></mrow></math></span> contact angle with the flat surface is examined. To avoid singularities at the contact line, the Knudsen number is assumed to lie within the slip-flow regime. Analytical expressions are derived for the thermophoretic velocity and force acting on the half-submerged particle. Graphical results illustrate the influence of parameters such as Fourier thermal conductivity ratio, Knudsen number, medium permeability, frictional slip, and thermal stress slip. Furthermore, the limiting behavior corresponding to thermophoresis in a classical viscous fluid is discussed. Since the present solution is exact, the case of a <span><math><mrow><mn>90</mn><mo>°</mo></mrow></math></span> contact angle also serves as a benchmark for validating numerical solutions at other contact angles. The findings are relevant to applications involving particle manipulation at fluid–porous interfaces, such as targeted drug delivery across biological membranes, pollutant transport at soil–air boundaries, and the design of microfluidic systems for controlled colloidal assembly.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"117 ","pages":"Article 204441"},"PeriodicalIF":2.5,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.euromechflu.2025.204430
N. Nouaime , B. Després , M.A. Puscas , C. Fiorini
This paper uses the intrusive polynomial chaos method (IPCM) to analyze sensitivity in heat transfer problems governed by the Navier–Stokes equations with heat transfer. The intrusive polynomial chaos method incorporates uncertain variables as combinations of orthogonal polynomials, known as polynomial chaos expansions (PCEs), directly into the governing equations. This transformation turns the original deterministic PDEs into coupled deterministic equations for the PCE coefficients. We apply first-order IPCM and propose a decoupling approach for state and sensitivity systems. We discretize the state equations and their sensitivity using the Finite Element-Volume (FEV) method. We establish a stability estimate for the continuous and discrete state and sensibility equations.
{"title":"Sensitivity analysis of Navier–Stokes equations with heat transfer using the first-order polynomial chaos method and FEV discretization","authors":"N. Nouaime , B. Després , M.A. Puscas , C. Fiorini","doi":"10.1016/j.euromechflu.2025.204430","DOIUrl":"10.1016/j.euromechflu.2025.204430","url":null,"abstract":"<div><div>This paper uses the intrusive polynomial chaos method (IPCM) to analyze sensitivity in heat transfer problems governed by the Navier–Stokes equations with heat transfer. The intrusive polynomial chaos method incorporates uncertain variables as combinations of orthogonal polynomials, known as polynomial chaos expansions (PCEs), directly into the governing equations. This transformation turns the original deterministic PDEs into coupled deterministic equations for the PCE coefficients. We apply first-order IPCM and propose a decoupling approach for state and sensitivity systems. We discretize the state equations and their sensitivity using the Finite Element-Volume (FEV) method. We establish a stability estimate for the continuous and discrete state and sensibility equations.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"118 ","pages":"Article 204430"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-27DOI: 10.1016/j.euromechflu.2025.204451
Sanjay Kumar Pandey, Kriti Yadav
This study presents an analytical model that extends previous formulations by incorporating axial dependence in all velocity components, thus offering a more realistic representation of dust devil dynamics. We address the limitations of the fundamental model of Vyas and Majdalani (2006), such as unbounded velocity and infinite vortex width, by modifying the stream function, which captures radial and axial variation of velocity. The velocity components are physically bounded and consistent with observed vortex structures. Additionally, the radial pressure distribution is derived, and the flow field is analysed using normalized radial, axial, and azimuthal velocities. The azimuthal velocity is computed from the radial and axial flows using the angular momentum equation. It increases from the centre, peaks near the periphery, and gradually decays to zero toward the axis. This model represents the compact features of dust devils by producing a smooth, confined structure with consistent vertical dependence, unlike alternative models that introduce abrupt transitions or unbounded behaviour. The profile maintains central stability in accordance with the Rayleigh criterion, while peripheral centrifugal instability reflects the transient and dissipative nature of dust devils. The model captures dust lifting and charge separation in dust devils, linking strong updrafts and confined flow to enhanced electrification and particle transport.
{"title":"An analytical model for whirlwinds of finite width rising with bounded velocity and decaying outflow: Application to dust devils","authors":"Sanjay Kumar Pandey, Kriti Yadav","doi":"10.1016/j.euromechflu.2025.204451","DOIUrl":"10.1016/j.euromechflu.2025.204451","url":null,"abstract":"<div><div>This study presents an analytical model that extends previous formulations by incorporating axial dependence in all velocity components, thus offering a more realistic representation of dust devil dynamics. We address the limitations of the fundamental model of Vyas and Majdalani (2006), such as unbounded velocity and infinite vortex width, by modifying the stream function, which captures radial and axial variation of velocity. The velocity components are physically bounded and consistent with observed vortex structures. Additionally, the radial pressure distribution is derived, and the flow field is analysed using normalized radial, axial, and azimuthal velocities. The azimuthal velocity is computed from the radial and axial flows using the angular momentum equation. It increases from the centre, peaks near the periphery, and gradually decays to zero toward the axis. This model represents the compact features of dust devils by producing a smooth, confined structure with consistent vertical dependence, unlike alternative models that introduce abrupt transitions or unbounded behaviour. The profile maintains central stability in accordance with the Rayleigh criterion, while peripheral centrifugal instability reflects the transient and dissipative nature of dust devils. The model captures dust lifting and charge separation in dust devils, linking strong updrafts and confined flow to enhanced electrification and particle transport.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"117 ","pages":"Article 204451"},"PeriodicalIF":2.5,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-26DOI: 10.1016/j.euromechflu.2025.204450
Manuel Rubio , Francisco Castro-Ruiz , José Sierra-Pallares , César Barrios-Collado , Joaquín Anatol
This study examines asymmetric pumping in Liebau pumps, a type of valveless pump that generates unidirectional flow through the periodic compression of a flexible (compliant) tube. This pumping has applications in biomedical devices, microfluidics, and organ support. We investigate how the properties of the compliant tube and the operating conditions affect the pump performance, using dimensionless parameters. Experiments were performed with different configurations, varying the tube material (latex and rubber) and the fluid (water and water–glycerine mixture). The results indicate that the flow rate and resonant period depend on the stiffness of the tube and the viscous effects. It was observed that for small values of the Womersley number (), viscous effects significantly reduce the flow rate. In contrast, for large Womersley values, the semiempirical models previously proposed adequately predict the experimental behaviour. Effects such as the compliant tube depression, which were not accounted for in previous models, were also found to influence performance. This work extends the analysis of this type of pump to unexplored conditions, with the aim of expanding knowledge and enabling the use of Liebau pumps in real-world applications.
{"title":"Analysis of compliant tube properties and operating conditions in a Liebau pump","authors":"Manuel Rubio , Francisco Castro-Ruiz , José Sierra-Pallares , César Barrios-Collado , Joaquín Anatol","doi":"10.1016/j.euromechflu.2025.204450","DOIUrl":"10.1016/j.euromechflu.2025.204450","url":null,"abstract":"<div><div>This study examines asymmetric pumping in Liebau pumps, a type of valveless pump that generates unidirectional flow through the periodic compression of a flexible (compliant) tube. This pumping has applications in biomedical devices, microfluidics, and organ support. We investigate how the properties of the compliant tube and the operating conditions affect the pump performance, using dimensionless parameters. Experiments were performed with different configurations, varying the tube material (latex and rubber) and the fluid (water and water–glycerine mixture). The results indicate that the flow rate and resonant period depend on the stiffness of the tube and the viscous effects. It was observed that for small values of the Womersley number (<span><math><msup><mrow><mi>W</mi><mi>o</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>), viscous effects significantly reduce the flow rate. In contrast, for large Womersley values, the semiempirical models previously proposed adequately predict the experimental behaviour. Effects such as the compliant tube depression, which were not accounted for in previous models, were also found to influence performance. This work extends the analysis of this type of pump to unexplored conditions, with the aim of expanding knowledge and enabling the use of Liebau pumps in real-world applications.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"117 ","pages":"Article 204450"},"PeriodicalIF":2.5,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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