The present study explores onset of Rayleigh–Taylor instability (RTI) and Kelvin–Helmholtz Rayleigh–Taylor instability (KHRTI) with highly-resolved direct numerical simulations of two setups considering air at different temperatures (or densities) and/or velocities in two halves of three-dimensional (3D) cuboidal domains. The RTI and KHRTI are simulated with 4.2 billion and 480 million mesh points, respectively. Here, we do not impose any external perturbation similar to the unforced experiments of RTI and KHRTI. The compressible Navier–Stokes equations are solved using a novel parallel algorithm which does not involve overlapping points at sub-domain boundaries. This removes the errors at sub-domain boundaries and provides same level of accuracy as sequential computing. The pressure disturbance field is compared during onset of RTI and KHRTI and corresponding convection- and advection-dominated mechanisms are highlighted by instantaneous features, spectra, and proper orthogonal decomposition. Relative contributions of pressure energy, kinetic energy and rotational energy to overall energy budget are explored, revealing acoustics to play a central role in initial perturbation for both RTI and KHRTI. The nonlinear, spatio-temporal nature of the instability is further explored by application of a transport equation for enstrophy of compressible flows. This provides insights into the similarities and differences between onset mechanisms of RTI and KHRTI, serving as a benchmark data set for shear and buoyancy-driven instabilities across diverse applications in geophysics, nuclear energy and atmospheric fluid dynamics.
{"title":"Comparing the highly-resolved onset of Rayleigh–Taylor and Kelvin–Helmholtz Rayleigh–Taylor instabilities","authors":"Bhavna Joshi , Aditi Sengupta , Yassin Ajanif , Lucas Lestandi","doi":"10.1016/j.euromechflu.2025.204382","DOIUrl":"10.1016/j.euromechflu.2025.204382","url":null,"abstract":"<div><div>The present study explores onset of Rayleigh–Taylor instability (RTI) and Kelvin–Helmholtz Rayleigh–Taylor instability (KHRTI) with highly-resolved direct numerical simulations of two setups considering air at different temperatures (or densities) and/or velocities in two halves of three-dimensional (3D) cuboidal domains. The RTI and KHRTI are simulated with 4.2 billion and 480 million mesh points, respectively. Here, we do not impose any external perturbation similar to the unforced experiments of RTI and KHRTI. The compressible Navier–Stokes equations are solved using a novel parallel algorithm which does not involve overlapping points at sub-domain boundaries. This removes the errors at sub-domain boundaries and provides same level of accuracy as sequential computing. The pressure disturbance field is compared during onset of RTI and KHRTI and corresponding convection- and advection-dominated mechanisms are highlighted by instantaneous features, spectra, and proper orthogonal decomposition. Relative contributions of pressure energy, kinetic energy and rotational energy to overall energy budget are explored, revealing acoustics to play a central role in initial perturbation for both RTI and KHRTI. The nonlinear, spatio-temporal nature of the instability is further explored by application of a transport equation for enstrophy of compressible flows. This provides insights into the similarities and differences between onset mechanisms of RTI and KHRTI, serving as a benchmark data set for shear and buoyancy-driven instabilities across diverse applications in geophysics, nuclear energy and atmospheric fluid dynamics.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204382"},"PeriodicalIF":2.5,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217835","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 : 2025-09-26DOI: 10.1016/j.euromechflu.2025.204381
Benedict C.-W. Tan
The collapse of air cavity towards the liquid surface that occurred immediately after deep seal following vertical entry of steel spheres into a pool of oil, was experimentally investigated. The vertical displacement between the pinch-off depth and the cavity base during the time when the cavity was collapsing towards the surface, was regularly measured and analysed using images taken from a high-speed camera. Furthermore, some phenomena associated with the upward oil jet generated during cavity collapse were also described and briefly studied. The results suggested that the rate of cavity collapse towards the surface, and the time taken for the lower part of the oil jet to reach surface level, were dependent on both the inertial and gravitational forces of the spheres.
{"title":"Cavity collapse associated with oil entry of steel spheres","authors":"Benedict C.-W. Tan","doi":"10.1016/j.euromechflu.2025.204381","DOIUrl":"10.1016/j.euromechflu.2025.204381","url":null,"abstract":"<div><div>The collapse of air cavity towards the liquid surface that occurred immediately after deep seal following vertical entry of steel spheres into a pool of oil, was experimentally investigated. The vertical displacement between the pinch-off depth and the cavity base during the time when the cavity was collapsing towards the surface, was regularly measured and analysed using images taken from a high-speed camera. Furthermore, some phenomena associated with the upward oil jet generated during cavity collapse were also described and briefly studied. The results suggested that the rate of cavity collapse towards the surface, and the time taken for the lower part of the oil jet to reach surface level, were dependent on both the inertial and gravitational forces of the spheres.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204381"},"PeriodicalIF":2.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155615","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}
The enhancement of energy efficiency in reciprocating compressor valves has long been constrained by the non-analytical nature of multi-parameter coupling effects. Traditional single-parameter strategies are inadequate for revealing the complex nonlinear interactions within flow paths. To address this limitation, this study proposes a response surface method (RSM)-based strategy for the topological optimization of stereoscopic flow channels. By constructing spatial interactions among contact surface tilt angles, flow path angles, and port-slot ratios, the study for the first time quantifies the influence of multi-parameter coupling mechanisms on effective flow area and flow coefficient. The optimal parameter combination obtained via RSM (α=71.8°, β=14.2°, γ=2:1) exhibited superior performance, as confirmed by both experimental and industrial tests: compared with the passive plate valve, the discharge volume increased by 50.1 % and the specific energy consumption per unit discharge volume decreased by 7.6 %; relative to the single-parameter numerical optimization group, the discharge volume further increased by 3.3 % and the specific energy consumption decreased by 2.7 %. The discrepancy between simulation and experimental results was less than 5 %, validating the reliability and accuracy of the proposed method. This study establishes an integrated methodological framework of “parameter coupling analysis-flow field characteristic regulation—system energy efficiency verification,” providing a novel paradigm for the intelligent design and energy-efficient optimization of high-performance fluid machinery.
{"title":"Stereoscopic valve flow path topology design in reciprocating compressors: Structural optimization via the response surface method","authors":"Xiao Hong, Weilin Cui, Dexi Wang, Dajing Liu, Xinrui Fu, Xiwen Cao","doi":"10.1016/j.euromechflu.2025.204378","DOIUrl":"10.1016/j.euromechflu.2025.204378","url":null,"abstract":"<div><div>The enhancement of energy efficiency in reciprocating compressor valves has long been constrained by the non-analytical nature of multi-parameter coupling effects. Traditional single-parameter strategies are inadequate for revealing the complex nonlinear interactions within flow paths. To address this limitation, this study proposes a response surface method (RSM)-based strategy for the topological optimization of stereoscopic flow channels. By constructing spatial interactions among contact surface tilt angles, flow path angles, and port-slot ratios, the study for the first time quantifies the influence of multi-parameter coupling mechanisms on effective flow area and flow coefficient. The optimal parameter combination obtained via RSM (<em>α</em>=71.8°, <em>β</em>=14.2°, <em>γ</em>=2:1) exhibited superior performance, as confirmed by both experimental and industrial tests: compared with the passive plate valve, the discharge volume increased by 50.1 % and the specific energy consumption per unit discharge volume decreased by 7.6 %; relative to the single-parameter numerical optimization group, the discharge volume further increased by 3.3 % and the specific energy consumption decreased by 2.7 %. The discrepancy between simulation and experimental results was less than 5 %, validating the reliability and accuracy of the proposed method. This study establishes an integrated methodological framework of “parameter coupling analysis-flow field characteristic regulation—system energy efficiency verification,” providing a novel paradigm for the intelligent design and energy-efficient optimization of high-performance fluid machinery.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204378"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217832","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 : 2025-09-25DOI: 10.1016/j.euromechflu.2025.204375
Congren Zheng , Yong Chen , Zijing Ding
A linear stability analysis is performed on rotating pipe flow with a non-ideal fluid. The study focuses on supercritical CO near its vapor–liquid critical point, where thermodynamic properties deviate significantly from ideal gas. Different wall temperatures are considered, ensuring centerline temperatures span subcritical, transcritical, and supercritical conditions. The modal analysis reveals that at low rotation speeds, unstable mode only exists at rotational speed . Also multiple unstable modes emerge, introducing a more complex instability mechanism compared to non-rotating pipe flow. As rotation speed increases, viscous dissipation plays a key role in flow stabilization, while thermodynamic effects remain secondary. The non-modal analysis further demonstrates that optimal system response under fixed-frequency forcing shifts due to rotation, with stronger deviations from incompressible behavior at high compressibility. In rotating pipe flow, the dependence of transient energy growth on the azimuthal wavenumber () is inherently nonlinear, which stands in stark contrast to the approximately linear relationship typically observed in non-rotating pipe flow. This nonlinearity arises primarily due to the influence of azimuthal velocity components introduced by rotation. These findings highlight the intricate coupling between rotation, compressibility, and thermodynamics, providing new insights into instability mechanisms in non-ideal fluid systems.
{"title":"Linear stability of rotating pipe flow with non-ideal fluid","authors":"Congren Zheng , Yong Chen , Zijing Ding","doi":"10.1016/j.euromechflu.2025.204375","DOIUrl":"10.1016/j.euromechflu.2025.204375","url":null,"abstract":"<div><div>A linear stability analysis is performed on rotating pipe flow with a non-ideal fluid. The study focuses on supercritical CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> near its vapor–liquid critical point, where thermodynamic properties deviate significantly from ideal gas. Different wall temperatures are considered, ensuring centerline temperatures span subcritical, transcritical, and supercritical conditions. The modal analysis reveals that at low rotation speeds, unstable mode only exists at rotational speed <span><math><mrow><mi>Ω</mi><mo><</mo><mn>0</mn></mrow></math></span>. Also multiple unstable modes emerge, introducing a more complex instability mechanism compared to non-rotating pipe flow. As rotation speed increases, viscous dissipation plays a key role in flow stabilization, while thermodynamic effects remain secondary. The non-modal analysis further demonstrates that optimal system response under fixed-frequency forcing shifts due to rotation, with stronger deviations from incompressible behavior at high compressibility. In rotating pipe flow, the dependence of transient energy growth on the azimuthal wavenumber (<span><math><mi>n</mi></math></span>) is inherently nonlinear, which stands in stark contrast to the approximately linear relationship typically observed in non-rotating pipe flow. This nonlinearity arises primarily due to the influence of azimuthal velocity components introduced by rotation. These findings highlight the intricate coupling between rotation, compressibility, and thermodynamics, providing new insights into instability mechanisms in non-ideal fluid systems.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204375"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155616","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 : 2025-09-25DOI: 10.1016/j.euromechflu.2025.204380
Xinwei Ye , Xiaojing Niu
This study aims to elucidate the motion and the evolution of shedding vortices in the wake of a wobbling bubble based on experimental observation. Experimental observations of bubble wakes were conducted using Particle Image Velocimetry (PIV) for the ambient continuous phase and the backlight shadow imaging technique for the bubble. Vortices are detected and tracked in a Lagrangian framework based on the flow field in the vertical section. To investigate the three-dimensional structure of the flow field and to supplement the experimentally measured bubble sizes, bubbles with a diameter of 3–5 mm are numerically simulated, incorporating adaptive dynamic mesh refinement based on the bubble wake location. The study establishes a correlation between the transport velocity and swirling strength of wake vortices generated by wobbling bubbles and the bubble's parameters, facilitating more convenient predictions of wake behavior. The results indicate that the vortices trail the bubble at a transport velocity that is approximately 30 % of the bubbles’ velocity. During the vortex shedding process, the swirling strength of these vortices intensifies within a distance of 1.58 times the bubble radius and then decays with increasing distance from the bubble, following the formula of .
{"title":"Lagrangian tracking of the wake vortices shedding from a wobbling bubble","authors":"Xinwei Ye , Xiaojing Niu","doi":"10.1016/j.euromechflu.2025.204380","DOIUrl":"10.1016/j.euromechflu.2025.204380","url":null,"abstract":"<div><div>This study aims to elucidate the motion and the evolution of shedding vortices in the wake of a wobbling bubble based on experimental observation. Experimental observations of bubble wakes were conducted using Particle Image Velocimetry (PIV) for the ambient continuous phase and the backlight shadow imaging technique for the bubble. Vortices are detected and tracked in a Lagrangian framework based on the flow field in the vertical section. To investigate the three-dimensional structure of the flow field and to supplement the experimentally measured bubble sizes, bubbles with a diameter of 3–5 mm are numerically simulated, incorporating adaptive dynamic mesh refinement based on the bubble wake location. The study establishes a correlation between the transport velocity and swirling strength of wake vortices generated by wobbling bubbles and the bubble's parameters, facilitating more convenient predictions of wake behavior. The results indicate that the vortices trail the bubble at a transport velocity that is approximately 30 % of the bubbles’ velocity. During the vortex shedding process, the swirling strength of these vortices intensifies within a distance of 1.58 times the bubble radius and then decays with increasing distance from the bubble, following the formula of <span><math><mrow><mn>1</mn><mo>−</mo><mi>exp</mi><mrow><mo>(</mo><mrow><mo>−</mo><mn>1.75</mn><mo>/</mo><mi>x</mi></mrow><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204380"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217837","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 : 2025-09-24DOI: 10.1016/j.euromechflu.2025.204377
Yihua Pan , Xiaomin An , Yuqi Lei , Xin Gao , Chen Ji
Identifying unsteady aerodynamic forces is a crucial and challenging task in aerodynamics. It is also a critical research foundation for other subjects such as aeroelasticity, aircraft design, and flight dynamics. The two mainstream methods used to identify unsteady aerodynamic forces are Computational Fluid Dynamics (CFD) and experiments. However, these methods have their limitations, such as lengthy computational expense and high resource consumption. This article proposes a new reduced-order model called Long Sequence to Sequence (Lseq2seq) based on deep sequence generation models to predict unsteady aerodynamic forces in an efficient way. The Lseq2seq model is then applied to determine the hysteresis loop for the NACA0012 airfoil and the unsteady aerodynamic force of the two-freedom oscillation of the NACA64A010 airfoil in transonic flow. The results are compared with other prevalent time-sequential networks, such as Sequence to Sequence (Seq2seq) and Gated Recurrent Unit (GRU). The proposed Lseq2seq model presents better precision and generalization ability for identification. Additionally, this article explores a combined predictor–corrector method called GRU-Lseq2seq to predict the flutter response of the NACA64A010 airfoil, and the results demonstrate that the combined model could achieve better prediction accuracy than the GRU model and could be used in flutter boundary prediction.
{"title":"Lseq2seq: A new reduced-order model for unsteady aerodynamic force identification","authors":"Yihua Pan , Xiaomin An , Yuqi Lei , Xin Gao , Chen Ji","doi":"10.1016/j.euromechflu.2025.204377","DOIUrl":"10.1016/j.euromechflu.2025.204377","url":null,"abstract":"<div><div>Identifying unsteady aerodynamic forces is a crucial and challenging task in aerodynamics. It is also a critical research foundation for other subjects such as aeroelasticity, aircraft design, and flight dynamics. The two mainstream methods used to identify unsteady aerodynamic forces are Computational Fluid Dynamics (CFD) and experiments. However, these methods have their limitations, such as lengthy computational expense and high resource consumption. This article proposes a new reduced-order model called Long Sequence to Sequence (Lseq2seq) based on deep sequence generation models to predict unsteady aerodynamic forces in an efficient way. The Lseq2seq model is then applied to determine the hysteresis loop for the NACA0012 airfoil and the unsteady aerodynamic force of the two-freedom oscillation of the NACA64A010 airfoil in transonic flow. The results are compared with other prevalent time-sequential networks, such as Sequence to Sequence (Seq2seq) and Gated Recurrent Unit (GRU). The proposed Lseq2seq model presents better precision and generalization ability for identification. Additionally, this article explores a combined predictor–corrector method called GRU-Lseq2seq to predict the flutter response of the NACA64A010 airfoil, and the results demonstrate that the combined model could achieve better prediction accuracy than the GRU model and could be used in flutter boundary prediction.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204377"},"PeriodicalIF":2.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155625","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}
Understanding and controlling transitions in wall-bounded flows through porous substrates are essential for designing and improving engineering systems. This study examines the linear stability of electrically conducting plane Couette flow within a Brinkman porous layer that is mechanically anisotropic and bounded by permeable walls with uniform cross-flow (injection at the lower wall, suction at the upper wall) under an applied magnetic field. A normal-mode linearisation leads to a modified Orr-Sommerfeld eigenvalue problem, which is solved using Chebyshev spectral collocation to identify neutral curves and growth-rate patterns as variables such as the Darcy number, Hartmann number, mechanical anisotropy, perturbation wavenumber, phase angle, cross-flow Reynolds number, and the orientation of the principal permeability axis are varied. Results show that increasing the Darcy number and Hartmann number stabilizes the flow, while a higher perturbation wavenumber reduces amplification, meaning disturbances grow most at longer wavelengths. Mechanical anisotropy consistently destabilizes the flow, increasing peak growth rates, whereas changes in the orientation angle have little effect. The phase angle has a slight influence on stability at low wavenumbers but tends to stabilize the flow at higher wavenumbers. Meanwhile, the cross-flow Reynolds number causes only minor shifts in the neutral curves. These findings suggest practical methods for flow control in anisotropic porous magnetohydrodynamic systems, highlighting the stabilizing effects of magnetic damping and porous-matrix diffusion, as well as the destabilizing impact of strong anisotropy.
{"title":"Stability of hydromagnetic Couette flow in an anisotropic porous medium with oblique principal axes and constant wall transpiration","authors":"Cédric Gervais Njingang Ketchate , Alain Dika , Pascalin Tiam Kapen , Didier Fokwa","doi":"10.1016/j.euromechflu.2025.204376","DOIUrl":"10.1016/j.euromechflu.2025.204376","url":null,"abstract":"<div><div>Understanding and controlling transitions in wall-bounded flows through porous substrates are essential for designing and improving engineering systems. This study examines the linear stability of electrically conducting plane Couette flow within a Brinkman porous layer that is mechanically anisotropic and bounded by permeable walls with uniform cross-flow (injection at the lower wall, suction at the upper wall) under an applied magnetic field. A normal-mode linearisation leads to a modified Orr-Sommerfeld eigenvalue problem, which is solved using Chebyshev spectral collocation to identify neutral curves and growth-rate patterns as variables such as the Darcy number, Hartmann number, mechanical anisotropy, perturbation wavenumber, phase angle, cross-flow Reynolds number, and the orientation of the principal permeability axis are varied. Results show that increasing the Darcy number and Hartmann number stabilizes the flow, while a higher perturbation wavenumber reduces amplification, meaning disturbances grow most at longer wavelengths. Mechanical anisotropy consistently destabilizes the flow, increasing peak growth rates, whereas changes in the orientation angle have little effect. The phase angle has a slight influence on stability at low wavenumbers but tends to stabilize the flow at higher wavenumbers. Meanwhile, the cross-flow Reynolds number causes only minor shifts in the neutral curves. These findings suggest practical methods for flow control in anisotropic porous magnetohydrodynamic systems, highlighting the stabilizing effects of magnetic damping and porous-matrix diffusion, as well as the destabilizing impact of strong anisotropy.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204376"},"PeriodicalIF":2.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217836","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 : 2025-09-22DOI: 10.1016/j.euromechflu.2025.204373
Sameer Kumar Sanu, Tanmoy Mondal
This study presents a numerical investigation of two plane parallel turbulent buoyant jets (TPBJ) to examine the combined effects of jet spacing and buoyancy on flow interaction and thermal transport. Steady-state simulations are conducted by solving the Reynolds-averaged Navier–Stokes equations using the standard turbulence model with the Boussinesq approximation. The analysis considers jet spacing ratios ( to 11), where is the centre-to-centre jet spacing and is the nozzle width, and Richardson numbers ( to 1/2) to represent varying buoyancy levels. Results indicate that narrower spacing enhances jet interaction, strengthens entrainment, and leads to earlier merging, while wider spacing delays interaction and weakens vertical momentum. Buoyancy significantly alters the flow structure by accelerating jet convergence, increasing centreline velocity, and confining both velocity and thermal plumes. Three characteristic axial locations, namely, the merging point (MP), combined point (CP), and maximum velocity point (MVP), are identified and correlated with and . In the far field, the lateral growth of velocity and thermal widths becomes approximately linear, though spreading rates decrease with increasing buoyancy. The centreline velocity and temperature exhibit decay consistent with power-law behaviour, influenced by buoyancy strength. Empirical correlations are proposed to predict the axial positions of MP, CP, and MVP with high accuracy. These correlations can be directly applied in engineering design and environmental applications, including the optimization of jet-based cooling configurations, ventilation layouts, and buoyant discharge systems, where a rapid yet reliable estimation of jet interaction characteristics is essential. Compared to isothermal jets (), buoyant jets show enhanced centreline velocities, stronger recirculation, and reduced lateral dispersion. These findings provide new insights into the coupled momentum and thermal dynamics of TPBJ systems and offer predictive tools for applications in thermal management and environmental jet discharge.
{"title":"Numerical investigation of two plane parallel turbulent buoyant jets: Effects of jet spacing and Richardson number on flow interaction and thermal transport","authors":"Sameer Kumar Sanu, Tanmoy Mondal","doi":"10.1016/j.euromechflu.2025.204373","DOIUrl":"10.1016/j.euromechflu.2025.204373","url":null,"abstract":"<div><div>This study presents a numerical investigation of two plane parallel turbulent buoyant jets (TPBJ) to examine the combined effects of jet spacing and buoyancy on flow interaction and thermal transport. Steady-state simulations are conducted by solving the Reynolds-averaged Navier–Stokes equations using the standard <span><math><mrow><mi>k</mi><mo>−</mo><mi>ϵ</mi></mrow></math></span> turbulence model with the Boussinesq approximation. The analysis considers jet spacing ratios (<span><math><mrow><mi>s</mi><mo>/</mo><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math></span> to 11), where <span><math><mi>s</mi></math></span> is the centre-to-centre jet spacing and <span><math><mi>d</mi></math></span> is the nozzle width, and Richardson numbers (<span><math><mrow><mi>R</mi><mi>i</mi><mo>=</mo><mn>0</mn></mrow></math></span> to 1/2) to represent varying buoyancy levels. Results indicate that narrower spacing enhances jet interaction, strengthens entrainment, and leads to earlier merging, while wider spacing delays interaction and weakens vertical momentum. Buoyancy significantly alters the flow structure by accelerating jet convergence, increasing centreline velocity, and confining both velocity and thermal plumes. Three characteristic axial locations, namely, the merging point (MP), combined point (CP), and maximum velocity point (MVP), are identified and correlated with <span><math><mrow><mi>s</mi><mo>/</mo><mi>d</mi></mrow></math></span> and <span><math><mrow><mi>R</mi><mi>i</mi></mrow></math></span>. In the far field, the lateral growth of velocity and thermal widths becomes approximately linear, though spreading rates decrease with increasing buoyancy. The centreline velocity and temperature exhibit decay consistent with power-law behaviour, influenced by buoyancy strength. Empirical correlations are proposed to predict the axial positions of MP, CP, and MVP with high accuracy. These correlations can be directly applied in engineering design and environmental applications, including the optimization of jet-based cooling configurations, ventilation layouts, and buoyant discharge systems, where a rapid yet reliable estimation of jet interaction characteristics is essential. Compared to isothermal jets (<span><math><mrow><mi>R</mi><mi>i</mi><mo>=</mo><mn>0</mn></mrow></math></span>), buoyant jets show enhanced centreline velocities, stronger recirculation, and reduced lateral dispersion. These findings provide new insights into the coupled momentum and thermal dynamics of TPBJ systems and offer predictive tools for applications in thermal management and environmental jet discharge.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204373"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217833","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 : 2025-09-17DOI: 10.1016/j.euromechflu.2025.204374
Oleg A. Logvinov , Isabel M. Irurzun
We considered the high-speed displacement of fluids from a Hele-Shaw cell where jumps on the interface in both viscosity and density drive the instability and the generation of viscous fingers. Mathematically, the density is a prior factor in the inertial nonlinear terms in the full–averaged Navier–Stokes–Darcy model. Therefore, we investigated the influence of inertial effects on the fingering process. We performed linear stability analysis and numerical simulations by finite–difference method considering dependences on two dimensionless parameters: density ratio and Reynolds number. Two main conclusions could be drawn. The first is that as the Reynolds number increases, the interface becomes more stable in the initial phase of displacement. The second is that the displacement of a denser fluid by a less dense one is more unstable than the opposite case, where a denser fluid displaces a less dense one. We also performed nonlinear simulations that also showed pronounced viscous bubble formation even when the viscosity ratio was relatively small.
{"title":"Density jump in high-speed Hele-Shaw flows","authors":"Oleg A. Logvinov , Isabel M. Irurzun","doi":"10.1016/j.euromechflu.2025.204374","DOIUrl":"10.1016/j.euromechflu.2025.204374","url":null,"abstract":"<div><div>We considered the high-speed displacement of fluids from a Hele-Shaw cell where jumps on the interface in both viscosity and density drive the instability and the generation of viscous fingers. Mathematically, the density is a prior factor in the inertial nonlinear terms in the full–averaged Navier–Stokes–Darcy model. Therefore, we investigated the influence of inertial effects on the fingering process. We performed linear stability analysis and numerical simulations by finite–difference method considering dependences on two dimensionless parameters: density ratio and Reynolds number. Two main conclusions could be drawn. The first is that as the Reynolds number increases, the interface becomes more stable in the initial phase of displacement. The second is that the displacement of a denser fluid by a less dense one is more unstable than the opposite case, where a denser fluid displaces a less dense one. We also performed nonlinear simulations that also showed pronounced viscous bubble formation even when the viscosity ratio was relatively small.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204374"},"PeriodicalIF":2.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106559","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}
Turbulence modeling poses significant challenges due to its nonlinear, multiscale nature. Classical methods like Reynolds-Averaged Navier–Stokes and Large Eddy Simulation often rely on empirical closures, which limit their accuracy in complex flows. This study aims to propose a hybrid model that integrates convolutional neural networks for capturing local spatial patterns with Transformer-based attention modules to model long-range dependencies. The architecture is informed by the Navier–Stokes equations and incorporates divergence-free constraints to preserve physical fidelity. The model is trained and evaluated on direct numerical simulation datasets representing 2D turbulence and turbulent channel flows. The model achieved up to 40 % reduction in prediction error compared to CNN and RNN baselines. It accurately reproduced key flow structures and energy spectra, showing strong agreement with DNS outputs. The hybrid architecture demonstrated stable long-term predictions and matched statistical flow properties over extended time horizons. For steady flows, it corrected RANS-predicted biases in mean velocity profiles with near-exact reconstruction. The results validate the effectiveness of combining physics-informed learning with deep neural architectures. The proposed framework offers a computationally efficient alternative to traditional turbulence models while retaining accuracy, marking a promising advancement in data-driven fluid mechanics.
湍流建模由于其非线性、多尺度的特性而面临着巨大的挑战。像reynolds - average Navier-Stokes和大涡模拟等经典方法通常依赖于经验闭包，这限制了它们在复杂流动中的准确性。本研究旨在提出一种混合模型，该模型将卷积神经网络与基于transformer的注意力模块集成在一起，用于捕获局部空间模式，以模拟远程依赖关系。建筑由Navier-Stokes方程提供信息，并结合无散度约束以保持物理保真度。该模型在二维湍流和湍流通道流的直接数值模拟数据集上进行了训练和评估。与CNN和RNN基线相比，该模型的预测误差降低了40% %。它准确地再现了关键流结构和能谱，与DNS输出结果具有很强的一致性。混合架构显示出稳定的长期预测，并在较长的时间范围内匹配统计流特性。对于稳定流，它通过近乎精确的重建纠正了ranss预测的平均速度剖面偏差。结果验证了将物理信息学习与深度神经结构相结合的有效性。该框架为传统湍流模型提供了一种计算效率高的替代方案，同时保持了准确性，标志着数据驱动流体力学的一个有希望的进步。
{"title":"A physics-embedded Transformer-CNN architecture for data-driven turbulence prediction and surrogate modeling of high-fidelity fluid dynamics","authors":"Sukanta Ghosh , Vinod Kumar Shukla , Amar Singh , Jayanta Chanda","doi":"10.1016/j.euromechflu.2025.204372","DOIUrl":"10.1016/j.euromechflu.2025.204372","url":null,"abstract":"<div><div>Turbulence modeling poses significant challenges due to its nonlinear, multiscale nature. Classical methods like Reynolds-Averaged Navier–Stokes and Large Eddy Simulation often rely on empirical closures, which limit their accuracy in complex flows. This study aims to propose a hybrid model that integrates convolutional neural networks for capturing local spatial patterns with Transformer-based attention modules to model long-range dependencies. The architecture is informed by the Navier–Stokes equations and incorporates divergence-free constraints to preserve physical fidelity. The model is trained and evaluated on direct numerical simulation datasets representing 2D turbulence and turbulent channel flows. The model achieved up to 40 % reduction in prediction error compared to CNN and RNN baselines. It accurately reproduced key flow structures and energy spectra, showing strong agreement with DNS outputs. The hybrid architecture demonstrated stable long-term predictions and matched statistical flow properties over extended time horizons. For steady flows, it corrected RANS-predicted biases in mean velocity profiles with near-exact reconstruction. The results validate the effectiveness of combining physics-informed learning with deep neural architectures. The proposed framework offers a computationally efficient alternative to traditional turbulence models while retaining accuracy, marking a promising advancement in data-driven fluid mechanics.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"115 ","pages":"Article 204372"},"PeriodicalIF":2.5,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106556","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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