Theoretical and Computational Fluid Dynamics最新文献

{"title":"Development of amplification factor transport equation for hypersonic boundary layer reflecting wall temperature variation","authors":"Sunoh Kang,&nbsp;Junyoung Byeon,&nbsp;Donghun Park","doi":"10.1007/s00162-026-00783-3","DOIUrl":"10.1007/s00162-026-00783-3","url":null,"abstract":"<div><p>To predict the amplification factor of the Mack second mode instability in a hypersonic boundary layer, an amplification factor transport equation was developed within a RANS framework. Its production term is based on the approximate <i>N</i>-envelope method and modeled using compressible boundary layer profiles and linear stability theory (LST) analysis data. The transport equation is designed to use only local variables and does not require wall temperature as an explicit parameter. Furthermore, it accounts for the influence of wall temperature on the growth of the Mack second mode instability, which is a key contribution of this study. The amplification factor and the modified turbulence intermittency transport equations are coupled with a k-<span>(omega )</span> SST turbulence model as the transition model. The model was implemented in SU2, and grid experiments were performed. The predicted amplification factor was compared with the LST results with differences typically ranging from 0.4% to 17% across a range of flow and wall-temperature conditions, including non-uniform wall temperature distributions. Analysis of the transition model revealed that it is possible to predict the boundary layer transition with appropriate application of the critical amplification factors.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00783-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A carrier-wave factored one-way Navier–Stokes method for boundary-layer instability modelling","authors":"Elliot James Badcock,&nbsp;Shahid Mughal","doi":"10.1007/s00162-026-00790-4","DOIUrl":"10.1007/s00162-026-00790-4","url":null,"abstract":"<div><p>We present M-OWNS, a spatial marching method that combines the carrier-wave factoring of the parabolised stability equations (PSE) with a recursive one-way Navier–Stokes (OWNS-R) projection framework. A distinct numerical resolution and efficiency advantage is offered by the approach, in modelling disturbance and instability state evolution. A spectral resolution comparison analysis shows that to leading order, for any excited eigenfunction whose eigenvalue lies closer to the carrier wavenumber than to the origin, the wave-factored system resolves the mode at a coarser streamwise numerical step size relative to the unfactored system. A non-iterating variant, with the carrier wavenumber determined from the base flow, temporal frequency and spanwise wavenumber alone, achieves equivalent resolution accuracy at identical per-step cost to unfactored OWNS. For the fixed-carrier variant, M-OWNS reduces the total solve count by factors of two to eight relative to unfactored OWNS across the test cases considered, with larger reductions possible when the iterated closure condition of PSE is suitable. The method is validated across incompressible and subsonic flat-plate boundary-layers, three-dimensional crossflow disturbances, and a Mach 4.5 hypersonic boundary-layer with four forcing configurations: eigenfunction inlet forcing, wall suction/blowing, multi-mode freestream forcing and randomised inlet forcing. The wall suction/blowing case is validated against a fully elliptic linear harmonic Navier–Stokes solver. For deterministic forcing scenarios, M-OWNS captures disturbance amplitudes, acoustic radiation fields, and modal synchronisation sequences at coarser streamwise resolution than unfactored OWNS. Under broadband randomised forcing, M-OWNS resolves mixed-mode disturbance development at half the numerical cost relative to standard OWNS.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00790-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mean particle drift in gravity-modified acoustic waves over a compressible seabed","authors":"Jan Erik H. Weber,&nbsp;Kai H. Christensen","doi":"10.1007/s00162-026-00792-2","DOIUrl":"10.1007/s00162-026-00792-2","url":null,"abstract":"<div><p>Acoustic-gravity waves (AGWs) are sound waves in the ocean slightly modified by a gravity wave boundary condition at the surface. Typical frequencies are in the range <span>(0.1-1,textrm{Hz})</span>. In the study of such waves, the acoustic properties of the seabed are usually not discussed, and the sea floor is taken to be insulating to sound waves. In this paper, we allow the seabed to be acoustically conducting such that a small part of the acoustic wave energy may propagate though the sea floor. To model this process in a principal way, we apply a Robin boundary condition for the velocity potential. Because of the energy loss at the bottom, the AGW motion becomes slightly damped in the fluid. Nonlinearly, this leads to a nonzero forcing term for the mean Eulerian velocity (the acoustic streaming), when averaged over the wave period. We utilize the fact that the planetary rotation is very slow compared with the AGW period and derive the Coriolis-Stokes force for the mean Eulerian motion in the cross-wave direction. We use that the mean Lagrangian (particle) motion is the sum of the Eulerian mean motion and the Stokes drift. We then find, by averaging over the inertial period, that the Stokes drift in the wave propagation direction is balanced by a negative Eulerian mean current (an anti-Stokes flow) at all depths. The mean Lagrangian drift in the cross-wave direction is a result of a balance between the Coriolis force and the gradient of the mean Reynolds stresses, constituting the Eulerian acoustic forcing in this case. It appears that the associated Lagrangian mass flux could be of importance for the circulation in the deep ocean.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00792-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Instability and transition to turbulence of the stationary-disk boundary layer of a rotor-stator cavity","authors":"Lei Xie,&nbsp;Siyi Li,&nbsp;Yaguang Xie,&nbsp;Qiang Du,&nbsp;Junqiang Zhu,&nbsp;Ruonan Wang,&nbsp;Qingzong Xu,&nbsp;Zihao Zhu","doi":"10.1007/s00162-026-00791-3","DOIUrl":"10.1007/s00162-026-00791-3","url":null,"abstract":"<div><p>This investigation examines instability mechanisms and turbulent transition in the stationary disk boundary layer of a rotor-stator cavity through an integrated approach combining two-dimensional direct numerical simulations (2D DNS), global linear stability analysis, and three-dimensional direct numerical simulations (3D DNS). The base flow characteristics, the global linear stability properties, and the nonlinear evolution processes leading to turbulence are explored. The research examines an annular, enclosed rotor-stator cavity with curvature parameter <span>(Rm = (b^*+a^*)/(b^*-a^*)=1.8)</span>, and an aspect ratio <span>(L=(b^*-a^*)/(2h^*) = 5)</span>, where <span>(a^*)</span> and <span>(b^*)</span> are the minimum and maximum radius, respectively, and <span>(2h^*)</span> denotes the inter-disk spacing. The current study examines Reynolds numbers <span>(Re_varphi = Omega ^*_db^{*2}/nu ^*)</span> ranging from <span>(10^4)</span> to <span>(10^5)</span>, where <span>(Omega ^*_d)</span> is the angular velocity of the rotor, <span>(nu ^*)</span> is the fluid’s kinematic viscosity. The results reveal that for <span>(Re_varphi le 3.6 times 10^4)</span>, the base flow converges to a stable equilibrium state. However, when <span>(Re_varphi )</span> exceeds <span>(3.7 times 10^4)</span>, the base flow destabilizes, giving rise to persistent velocity oscillations within the stationary disk boundary layer. Global linear stability analysis confirms these observations. For axisymmetric disturbances (azimuthal wavenumber <span>(beta = 0)</span>), the critical Reynolds number for global linear instability is <span>(Re_varphi = 3.67 times 10^4)</span>, precisely demarcating the threshold for self-sustained oscillations in the base flow. For non-axisymmetric disturbances with <span>(beta = 15)</span>, a more complex dynamics is identified: the maximum linear temporal growth rate occurs at <span>(Re_varphi = 2.5 times 10^4)</span>, while the critical threshold for global linear instability emerges at a lower <span>(Re_varphi = 1.58 times 10^4)</span>, marking the onset conditions for a self-sustained spiral wave mode. The 3D DNS results reveal sophisticated nonlinear dynamics where spiral wave energy is transferred from higher to lower radial positions through complex mode interactions. When circular waves dominate in the flow field, their interaction with spiral waves across various radial positions generates a rich spectral composition with multiple distinct dominant frequencies within the boundary layer. At <span>(Re_varphi ge 7.0 times 10^4)</span>, the flow transitions to a chaotic state with turbulent characteristics. Remarkably, even in this strongly chaotic regime, coherent circular wave structures remain observable within the chaotic flow field, although distinct dominant frequencies are no longer present in the spectral analysis.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465946","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}

{"title":"A Graph-based rank-reduced interface preconditioner for the harmonic linearized navier-stokes equations","authors":"David A. Cook,&nbsp;Joshua G. Bugel,&nbsp;Joseph W. Nichols","doi":"10.1007/s00162-026-00787-z","DOIUrl":"10.1007/s00162-026-00787-z","url":null,"abstract":"<div><p>Many advanced prediction and analysis tools for hypersonic boundary layer transition—including resolvent and Input/Output (I/O) analysis—rely on solutions of the harmonic, linearized Navier-Stokes equations (H-LNSE), which produce ill-conditioned and highly non-normal discrete systems. To overcome these challenges, we present a graph-based, rank-reduced interface preconditioner (GRIP) for the iterative solution of the hypersonic H-LNSE, combining ideas from domain decomposition and graph propagation into a single framework. Along an application-driven Reynolds-number/frequency scaling path, in which the physically relevant disturbance frequency and mesh requirements increase with unit Reynolds number, GRIP exhibits favorable empirical cost growth, with near-linear CPU-time and memory growth relative to the resulting discrete problem size over the tested range. GRIP is inherently parallel, memory-efficient, physics-informed, and scalable. In testing, we expose a cause of F-GMRES breakdown for hypersonic linear systems and other non-normal operators. GRIP is applied to two- and three-dimensional Mach 6 boundary layer flows over a flat plate, shedding light on the importance of three-dimensional effects in canonical flows. Additionally, GRIP is applied to three-dimensional Mach 6 flow over a cone with a highly swept fin. Analysis of the response at 247 kHz shows amplification of vortical waves along the strong inboard vortex as well as milder amplification along the weaker, outboard vortex.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00787-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global instability onset in high-speed compression corner flows","authors":"Anton Scholten,&nbsp;Pedro Paredes,&nbsp;Meelan Choudhari,&nbsp;Fei Li","doi":"10.1007/s00162-026-00785-1","DOIUrl":"10.1007/s00162-026-00785-1","url":null,"abstract":"<div><p>Compression corner flows exhibit a shock-wave/boundary-layer interaction that induce flow separation and potential laminar-to-turbulent transition that may produce high surface heating in the reattachment region. Laminar separated flows can sustain the amplification of global instabilities that can be the origin for boundary-layer transition. A computational study of double wedge and cone-flare geometries at zero degrees angle of attack is performed to investigate the effects of geometrical parameters, wall temperature, and freestream conditions on the laminar separation and its global instability characteristics, with the objective of deriving a simple correlation between the separated flow properties and the global instability onset. Regardless of the nosetip/leading edge bluntness, the global instability is first dominated by a stationary mode with low azimuthal wavenumber that extends across the entire separated region. To examine the correlation between separation bubble strength and the onset of global instability, we created and analyzed a database spanning a wide range of parameters, including freestream Mach number, Reynolds number, surface temperature, nosetip/leading edge radius, an intermediate cylindrical section ahead of the flare, radius of curvature at the cone-flare corner, and flow turning angles. Multiple normalized quantities are investigated as potential metrics toward an empirical criterion for global instability onset. Generally, the separation bubble becomes globally unstable when the maximum reverse streamwise velocity exceeds 10% of the freestream speed. This work provides a computational overview of how each flow and geometrical parameter affects the laminar separation regions, guiding future experimental studies to distinguish whether observed flow trends result from global instability and potential laminar-to-turbulent transition prior to reattachment.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 4","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285475","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}

{"title":"Assessment of species-specific vibrational temperature modelling in hypersonic non-equilibrium flows","authors":"Arun Kumar Chinnappan,&nbsp;Minkwan Kim","doi":"10.1007/s00162-026-00786-0","DOIUrl":"10.1007/s00162-026-00786-0","url":null,"abstract":"<div><p>A species-specific multi-vibrational model for hypersonic non-equilibrium flows is presented in this work, along with a systematic analysis of its impact across multiple cases, ranging from zero-dimensional adiabatic relaxation to rapid expansion flows and axisymmetric blunt-body configurations. This model assumes a single temperature to characterise both translational and rotational energies, while a separate vibrational temperature is considered for each species. It explicitly accounts for vibrational-translational (V-T) relaxation of individual species and vibrational-vibrational (V-V) relaxation between unlike molecules. The V-V relaxation probabilities for <span>(hbox {N}_2)</span>-<span>(hbox {O}_2)</span> and <span>(hbox {N}_2)</span>-NO collisions are determined by fitting experimental and Schwartz-Slawsky-Herzfeld (SSH) data from the literature, whereas, the probability of <span>(hbox {O}_2)</span>-NO is assumed to follow the <span>(hbox {N}_2)</span>-NO system. The proposed model is implemented in an in-house hypersonic computational fluid dynamics (CFD) solver and validated against the numerical simulations for a non-reacting one-dimensional system, and compared with the high-fidelity state-to-state (STS) and direct simulation Monte Carlo (DSMC) approaches for a reacting flow. Further validation is performed against experimental measurements and DSMC for rapid expansion flow and flow over a cylinder. Comparisons with the single-vibrational temperature model reveal noticeable differences in vibrational temperature profiles, shock stand-off distance and vibrational freezing values. The additional computational cost associated with this formulation is also detailed, supporting its applicability as an intermediate-fidelity modelling approach for hypersonic CFD simulations.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00786-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Laminar boundary layers over small-scale textured surfaces","authors":"Samuel D. Tomlinson,&nbsp;Demetrios T. Papageorgiou","doi":"10.1007/s00162-026-00784-2","DOIUrl":"10.1007/s00162-026-00784-2","url":null,"abstract":"<div><p>We develop a model for steady, laminar boundary layers over small-scale textured surfaces. Although the texture is small relative to the boundary-layer thickness, it modifies the flow via a slip length. We use matched asymptotic expansions to simplify the problem, dividing the flow into outer, boundary-layer and inner regions. The far-field behaviour of the inner problem yields a slip boundary condition for the boundary layer. We derive an asymptotic solution valid when the slip length is small, and for arbitrary slip lengths, we develop a numerical method combining Chebyshev collocation and finite differences. We apply this framework to canonical small-scale textured surfaces, including superhydrophobic surfaces and riblets, and utilise existing analytical slip formulae. However, the framework is expected to extend to liquid-infused, porous, compliant or deformable surfaces with a variety of regular or random textures. We demonstrate how slip modifies the boundary layer’s velocity field, wall shear stress and displacement thickness across a range of surface configurations, and examine the linear stability of the resulting slip-modified boundary layers. Our approach enables computationally inexpensive modelling of a wide range of small-scale textured surfaces within laminar boundary-layer flows, providing predictive capability for drag, boundary-layer growth and transition across applications ranging from microfluidics to turbo-machinery and marine transport.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00784-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A three-dimensional analytical model for multiple jets based on reichardt’s hypothesis and velocity deflection interface concept","authors":"Fengsheng Qi,&nbsp;Liangyu Zhang,&nbsp;Deqiang Li,&nbsp;Xudong Tang,&nbsp;Zhongqiu Liu,&nbsp;Sheraman C. P. Cheung,&nbsp;Baokuan Li","doi":"10.1007/s00162-026-00782-4","DOIUrl":"10.1007/s00162-026-00782-4","url":null,"abstract":"<div><p>Analytical models are among the most direct and efficient methods for predicting jet behavior in engineering and practical applications. Based on Reichardt’s hypothesis, the momentum transformation equation for a single free jet was derived. Using a superposition approach, the momentum distribution for multiple jets was determined, enabling the development of a three-dimensional analytical model for multiple parallel jets. The effectiveness of this superposition technique in predicting the mean streamwise velocity components of multiple jets was validated through a combination of experimental and numerical simulations. For non-parallel jets, interactions between jets result in deflections as they enter the flow field, introducing the concept of a“velocity deflection interface”. Due to experimental limitations, accurately determining the position of the velocity deflection interface is challenging, making numerical simulations the preferred approach. The Shear-Stress transport (SST) k-<span>(upomega )</span> turbulence model was employed, and jet angles between 1<span>(^circ )</span> and 20<span>(^circ )</span> , commonly used in industrial applications, were analyzed. By fitting data along the flow direction, the position of the velocity deflection interface was identified, and its relationship with the jet angle was established. In the upstream region of the velocity deflection interface, the relationship between the velocity deflection interface and the initial jet exit characteristics was quantified. In the downstream region, the parallel jet theory based on Reichardt’s hypothesis was extended to derive analytical equations for three-dimensional non-parallel jets. Finally, a comparison of jet analysis results with experimental data and computational fluid dynamics (CFD) simulations confirmed the validity of the analytical model. It provides theoretical support for predicting the behavior of multiple jets in engineering applications.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738409","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}

{"title":"Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions","authors":"Ilya Barmak,&nbsp;Subham Pal,&nbsp;Alexander Gelfgat,&nbsp;Neima Brauner","doi":"10.1007/s00162-026-00780-6","DOIUrl":"10.1007/s00162-026-00780-6","url":null,"abstract":"<div><p>This study explores the effects of a non-conductive gas layer flowing concurrently with a conductive liquid on the two-phase flow characteristics in wide horizontal ducts under a constant vertical magnetic field. To this end, analytical solutions for the velocity profile and induced magnetic field are presented for laminar gas-liquid stratified magnetohydrodynamic (MHD) flow between two infinite plates of various conductivities. The contributions of the Lorentz force and wall shear stresses to the pressure gradient are examined. To the best of our knowledge, it is shown for the first time that, unlike the single-phase Hartmann flow, the velocity profiles in two-phase flow differ significantly depending on whether the bottom wall is conducting or insulating. In the case of an insulating bottom wall, the gas lubrication effect and potential pumping power savings are significantly greater (up to 50%), regardless of the magnetic Reynolds number. This conclusion also holds for gas-liquid MHD flows in rectangular ducts with finite width-to-height aspect ratios. To assess the applicability of the Two-Plate (TP) model to wide ducts, numerical solutions of the two-dimensional problem are used to investigate the influence of side walls on the two-phase flow characteristics, considering various combinations of bottom and side wall conductivities. In all cases, the results for high aspect ratios converge to the analytical solution obtained from the TP model with the same bottom wall conductivity. However, the influence of insulating side walls remains significant even at large aspect ratios when the bottom wall is conducting. Unexpectedly, in such cases, the change in the induced magnetic field due to the presence of side walls has a dramatic effect on the velocity profile, leading to a reduced pressure gradient compared to that predicted by the TP model. The results of this work are of practical significance for design of gas-liquid MHD flow systems with wide ducts of large, but finite, aspect ratio.</p></div>","PeriodicalId":795,"journal":{"name":"Theoretical and Computational Fluid Dynamics","volume":"40 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00162-026-00780-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}